This section is devoted to puzzles having similar pieces which must be re-arranged, or permuted, often as groups, in order to progress from a randomized (mixed or scrambled) state to a solved state. This group forms a sub-class of the Sequential Movement puzzles.

The "Twisty Polyhedra" comprise a large and growing sub-class. Many of these puzzles are mass-produced (or hand-crafted modifications to a mass-produced puzzle), colorful, and made of plastic. Every puzzler knows about Rubik's Cube, the quintessential representative of this group. These puzzles are in the form of a Platonic or an Archimedean solid, "sliced" along various planes to permit certain axes of rotation of pieces or groups of pieces. They contain clever internal mechanisms which keep the moving pieces coherent. (You can see many patents showing the mechanisms at Joshua Bell's site.) A lot of group-theory mathematics applies to this category. Useful sequences of moves are known as "operators" or "algorithms."

The illustration below shows many (not all!) of the twisty polyhedra (and some non-polyhedral) puzzles that are now or have in the past been mass-produced and commercially available. Starting in 2010, a new wave of twisty puzzles hit the market, and many custom designs made it into mass production. More continue to arrive and it is impossible to keep up. Some puzzles are members of a series exploring variations on a theme - e.g. the "Planets" series of Crazy cubes and dodecahedrons, various bandaged cubes, and the "Bermuda" cubes - I have not attempted to show all the series members. Also, there are many different brands and types of the conventional face-turning cubes of orders 1-4, including speed cubes, which often turn better than the Rubik's brand version. Usually the mechanical differences are not apparent in photos. I have also not attempted to show the many shape extensions of the FT cubes, including the "Crystal" shapes, nor all the 2x2x2 heads and objects.

Newcomers to twisty collecting have asked for a short list of essential puzzles, and many TP forum members have provided guidance.

In the illustration below, I have identified 10 fundamental puzzles most collectors feel every twisty collection should contain.

Based on collating various folks' recommendations, I have also identified a further 32 puzzles to extend a good collection. Of course, you eventually have to have them all, right?

Tetrahedra --   -- Cuboids --   -- Other Cubes --   -- Crazy/Circle/Super Cubes --   -- Shape & Sticker Mods --   -- Heads --   -- Octahedra --   -- Dodecahedra --   -- Other Polyhedra --   -- Dihedral & Other --   -- Spheres --   -- Edgematching -- 

This section contains several definitions. You can click the "_" symbol to hide it, if you'd like.

Definitions:

The basic form of a "twisty polyhedron puzzle" is a polyhedron (MathWorld, Wikipedia), although rounded shapes are traditionally included in the class, for example spheres, and cylinders or pucks (or "UFO"s). Polyhedra have been studied extensively since antiquity and formally classified, based on their features, and whether they are convex or concave (non-convex). For a comprehesive list, see George Hart's Encyclopedia of Polyhedra, or the Wikipedia page for Polyhedron. Only a few shapes have been used again and again as the basis for twisty polyhedra puzzles. Some have only appeared in custom puzzles. Polyhedra that are too spiky, too rounded, or too irregular might be of interest to a collector but probably won't make popular puzzles as they are difficult to handle and/or too difficult to visualize when solving. The five Platonic Solids (regular convex polyhedra) - tetrahedron, cube, octahedron, dodecahedron, and icosahedron - have proven to be the most popular shapes, though the icosahedron is infrequently used. There are four Kepler-Poinsot (regular non-convex) polyhedra - These shapes are also the result of stellation of some Platonic Solids. The tetrahderon and cube have no stellations. The octahedron has one stellation, called a stella octangula - that shape has appeared in the Starburst and the Dino Star. The dodecahedron has three stellations: the small stellated dodecahedron, the great dodecahedron, and the great stellated dodecahedron. Only the great dodecahedron has been used in a commercial puzzle - the Alexander's Star. There are 59 stellations of the icosahedron, one of which is the great icosahedron. Some of the Prisms and Anti-Prisms have been made. The larger category here is Prismatoid polyhedra, which also includes pyramids, cupolas, frustums, and wedges. There are also several varieties of Bi- or Di-pyramids. Of the 13 Archimedean (semi-regular convex) polyhedra, the truncated tetrahedron, cuboctahedron, truncated cube, truncated octahedron, rhombicuboctahedron, and truncated icosahedron (soccer ball) have appeared. The 13 Archimedean Duals, or Catalan Solids have not been much used, except for the rhombic dodecahedron and rhombic triacontahedron. There are three stellations of the rhombic dodecahedron, the first, second, and third. These shapes have been used more for interlocking puzzles than twisty puzzles. The 92 Johnson Solids have not been used much at all. A polyhedron becomes a twisty puzzle when it is cut into distinct pieces, and an internal mechanism preserves the coherence of all pieces while allowing groups of one or more pieces to be moved (a twist). After a move or twist, pieces have exchanged positions with other pieces and potentially changed their orientation. The objective of the puzzle is to mix up the pieces, then restore them to a specific target configuration. There are a variety of cutting schemes and internal mechanisms ("cores") that have been developed. You can see many of the relevant patents at Joshua Bell's website. Most mods are based on commercially available puzzle cores, though with the broader availability of improved design tools such as CAD and 3D printing, new and more complex mechanisms are easier to realize (such as those used in the Pentultimate and the 24 Cube). It may be better to classify puzzles by their use of internal mechanism, but I'm not sure I like that method. I think it's more interesting to challenge designers by specifying a shape, slicing format, turning mechanics, and other features, then let them figure out the necessary internals. Of course, this does make it hard to chart the various mods made from non-standard mechanisms such as the Square-1, or adaptations of the mechanism for one shape to make a different shape, resulting in weird asymmetric cuttings (Tony Fisher's Hexaminx - a cubic Megaminx - comes to mind). Chris Lohe has a nice, though not exhaustive, chart at his website, organized by mechanism versus shape. Here are several mechanisms and/or cutting formats: Cuboids AxAxA - A=2,3,4,5,6,7 AxBxB - 1x2x2 (Morph), 1x3x3 (Okamoto's Floppy Cube), 2x3x3 Domino, 3x2x2 Slim Tower and Franken Tower, 3x4x4 Specter and Chaos, 4x2x2 (Fisher 2003), 4x3x3 Phantom Cube, 5x3x3 Grown Tower and TF 2004, 5x4x4 TF 2003 AxBxC - 1x2x3, 2x3x4 Step Up Tower and TF 2003, 2x4x5 Chaos These can be made in fully functional, extended, or "chaos" (multiple core + extended) forms. The EastSheen A4 cube core allows interesting overlapping effects Pyramorphix Pyraminx/Skewb Dino/Stella Octangula Helicopter/Bevel Hybrid Chop (e.g. the 24 Cube) Megaminx Dogic Key features of a polyhedron include faces, vertices, and edges. Most twisty polyhedra puzzles will have different types of pieces corresponding to each of these features. A given face may have one or more center pieces, edge pieces (shared between faces), and corner pieces (again, shared between faces). Almost always, an edge joins two and only two faces, and the corner pieces (if present) are at vertices of the polyhedron. Faces and edges meet at a vertex, and define a particular vertex figure.

Members of this puzzle category are distinguished from their Sliding Piece brethren in the Sequential Movement class in several ways. For twisty puzzles, pieces move in distinct groups. There is no frame and there are no levers or plungers. Also, the space of possible states is typically very large and it is unreasonable for a person to navigate directly from a mixed state toward a solved state (i.e. using "God's algorithm") - instead, a variety of operators or algorithms (i.e. specific sequences of particular twists) must be used in series, each of which accomplishes a subgoal leading towards better order by moving subsets of pieces in determined ways while leaving other subsets undisturbed. Expert solvers have memorized many useful operators, can quickly recognize patterns or states when a given operator will be useful, can keep track mentally of where they are in the midst of a sequence of moves, and can apply operators (sequences of twists) very rapidly with great manual dexterity. Sometimes operators learned for one puzzle can be useful on another type, but often a distinct set of operators must be learned for each different puzzle type. A Deep Cut puzzle's cuts divide it into halves. Otherwise, the puzzle is Shallow Cut, though there are gradations of shallowness, and some puzzles might have a few deep cuts mixed with shallow cuts. Alternatively, circumscribe a sphere around the puzzle, and project the cutting planes to intersect the sphere. If the projections make great circles on the sphere, the cut is deep. This disqualifies the Pyraminx ( Pyraminx setting on Jaap's Sphere) but includes the Skewb ( Skewb setting on Jaap's Sphere). Read a debate about the definition of "deep cut" in the TwistyPuzzles forums. If the cutting scheme results in sets of regular pieces, essentially interchangeable within their groups, then it is customary to distinguish them by coloring their individual faces. The overall pattern of colors will define the goal state of the puzzle. In other cases when the pieces are distinctly proportioned, the puzzle might be monochromatic and its goal state defined by shape alone. I've defined the order based on the number of parallel cuts (either deep or shallow) between opposite pairs of faces, vertices, or edges, or for tetrahedrons, opposing face-vertex pairs. Also note that the term slice is used ambiguously to mean either a cut itself, or a layer between two cuts or between a cut and the surface of the puzzle. My definition of order might be at odds with they way some people think about these puzzles - for example I define the 2x2x2 Pocket or Mini Cube as order 1 but some might define it as order 2 based on it having two "slices" in each dimension. Note that it is possible to construct puzzles with asymmetric slicing schemes - i.e. different numbers of parallel cuts between different pairs of opposite features. These would be characterized using compound orders. It is also possible to arrange the cuts so that they are either equally or unequally spaced between the features that bound them - the resulting slices are correspondingly either equal or unequal. Another irregularity results when not all opposite features have the same set of cuts between them, though those that do, have the same number of cuts between them - i.e. subsets of opposite features are treated differently. I call this a Partially Cut puzzle and distinguish it from a Fully Cut puzzle. This can be a consequence of creating a shape modification with a particular underlying core mechanism originally clothed in a different shape. An example is the dodecahedral Skewb Ultimate which has a Skewb core, originally clothed in a cube. The cube has eight vertices, and in the Skewb every pair of vertices has one (deep) cut between them, so four cuts suffice. The dodecahedron has 20 vertices or 10 pairs of opposing vertices. Since there are only four (deep) cuts, there is a cut between each of only four out of the ten pairs of opposing vertices. If all the pieces in a face move during a twist, the puzzle is Face-turning. If instead all the pieces around a vertex move, the puzzle is Vertex-turning. Similarly, if all the pieces along an edge move, the puzzle is Edge-turning. Hybrids are possible, but the internal mechanisms become complex, and the puzzle becomes very "squishy" since it is difficult to hold without inadvertently twisting something. In tetrahedra, the distinction between face and vertex turning is blurred, since a vertex is opposite a face. A sphere has no faces, vertices, or edges. A more useful distinction is how the cuts divide the surface, and how they intersect. The cuts can make great circles or small circles. By convention, two points at diametrically opposite locations on an arbitray great circle are chosen as poles. All great circles passing through the poles are longitudinal. One great circle can perpendicularly bisect all longitudes - this is the equator. Small circles parallel to the equator are latitudinal. Symmetrically arranged small circles are typically centered on regular polyhedra inscribed within the sphere. A cylinder or puck has two parallel circular faces with a curved surface between them. Cuts can be radial and divide the circular faces, or sectional and lie between the faces. So to classify the various species of twisty polyhedra puzzles by their physical characteristics, one could use the following criteria in some priority: Shape Order Turning type - Face, Vertex, (Face/Vertex for tetrahedra), Edge, Hybrid Cutting style - Deep vs. Shallow, Equal vs. Unequal, Full vs. Partial, Symmetric vs. Asymmetric; for spheres, layout of longitudinal, latitudinal, and small-circle cuts; for cylinders/pucks/ufos, layout of radial and sectional cuts Features - Corners/Edges/Centers present? Internal core mechanism Decoration/coloring scheme One could additionally or alternatively use the total number of unique possible permutations or states, or some (subjective) rating of difficulty, or of rarity.

Notes About Sticker and Feature Variations

A standard face-turning 3³ has 26 visible moving parts (usually referred to as "cubies")- 8 corners, 6 face centers, and 12 edges, plus an internal core - a six-armed "spider."

As faces are turned, the corners and the edges permute (i.e. exchange positions with each other) in separate groups. The six face centers of the basic 3³ are attached to the ends of the internal spider, so are fixed relative to each other and do not permute. Each cubie can also assume different orientations depending on type:

• Face centers can be twisted among four orientations - depending on the coloring, either all rotations are distinguishable, or 180 degree rotations are indistinguishable, while +/-90 degree rotations remain distinguishable
• Edges can be flipped between 2 orientations
• Corners can end up "twisted" among 3 orientations

We assume that neither corners nor edges can be re-oriented if they cannot first be permuted, since unlike the face centers they do not twist in place.

Each corner exposes three "facelets" - each face center one, and each edge two, for a grand total of 8x3+6x1+12x2= 54 facelets. A sticker pattern is applied to the facelets, and is used to either make apparent or hide the permutations and orientations of the cubies.

Each facelet is usually covered with one sticker. In the standard configuration there are nine stickers of each of six different colors, and each of the six faces of the cube is stickered with a solid color. The basic sticker pattern has varied with respect to the six colors used and how they are arranged relative to each other. In addition, one or more stickers might bear a logo of some sort.

As the cube is twisted, the color arrangement becomes scrambled. The objective of the puzzle is to unscramble a scrambled cube, restoring the canonical color pattern on all faces simultaneously.

Sticker variations can serve four basic purposes:
1) pure decoration
2) advertising promotion
3) modify the difficulty of the basic coloring, without changing the basic objective of restoring a canonical pattern
4) alter the goal of the puzzle (e.g. calendar cube, sudo-kube)

Personally, I am uninterested in sticker variations of the 1st or 2nd varieties, except insofar as they simultaneously accomplish the 3rd or 4th purpose.

So, for a 3x3x3 with a uniform pattern, we have the following possible fundamentally different sticker variations:

3x Faces: (permutations not possible) - NO orientations visible (N), ALL orientations visible (A), or 180s obscured (O)
3x Edges: neither permutations nor orientations visible (N), permutations only visible (P), or both permutations and orientations visible (P+O)
3x Corners: N, P, or P+O

This gives 27 possibilities:

F:N

• E:N
• C:N = an unstickered cube, eq. to a 1x1x1
• C:P = eq. to the PyraDiamond - a 2x2x2 with truncated corners
• C:P+O = eq. to the standard 2x2x2
• E:P
• C:N
• C:P
• C:P+O
• E:P+O
• C:N = the traditional or void "edges-only" cube
• C:P = eq. to the truncated Trajber's Octahedron
• C:P+O = the standard 3x3x3 pattern

F:A

• E:N
• C:N = the simple babyface
• C:P = an 8-color simple overlapping cube
• C:P+O = a 12-color simple overlapping cube
• E:P
• C:N
• C:P
• C:P+O = eq. to the 3x3x3 Rhombic Dodecahedron
• E:P+O
• C:N = eq. to the Magic Octahedron or Christoph's Jewel
• C:P = an 8-color cube; eq. to the Trajber's Octahedron
• C:P+O = a "Super Cube" - commercially produced as the Ultimate Cube

F:O

• E:N
• C:N
• C:P
• C:P+O
• E:P
• C:N
• C:P
• C:P+O
• E:P+O
• C:N
• C:P
• C:P+O

Andreas Nortmann explores the first 18 members of this series in the TP forums.

We might also imagine applying the pattern non-uniformly - for example, making only a subset of the edge and corner permutations matter (and none of the orientations matter), as in the tri-color cube, or making only a subset of the face orientations matter, as in the Fisher Cube or the Rubik's Cube Fourth Dimension.

Tri-color Cube

Fisher's Cube

Fourth Dimension

Note that sticker variations are different from feature variations. Feature variations arise when actual physical features are present or absent. Any features that are present can, in turn, be stickered according to the possible variations. Also, feature variations can be used in lieu of sticker variations to enforce the visibility of some specific permutations or orientations.

A physical design might be contrived to disguise or eliminate face centers, corners, edges, or combinations thereof. This may necessitate allowing pieces to overlap as they turn past one another as the trajectory of the cut on the surface of the puzzle no longer follows the path of a great circle equivalent. Lately it has also become possible to eliminate the central core, forming a "Void" or "Holey" cube.

If we apply a uniform variation to all like features of a cube, we have the following possibilities:

• FEC -  - all features present
• FEN -  faces and edges but no corners - can be implemented in different ways:
• - this is what is typically referred to as an "edges-only" cube even though technically that's inaccurate (4x4x4 also shown)
• - by simply shaving down and blacking out the corners
• FNC -  faces and corners but no edges - can be implemented in different ways:
• - as a "simple overlapping cube" (4x4x4 version also shown)
• - by simply shaving down and blacking out the edges - the "Corners Cube"
• - taking this to its extreme, we end up with Oskar van Deventer's "Gerardo's Cube"
• FNN -  faces only - can be implemented in different ways:
• - a "babyface" cube - each face can be turned (oriented) in place, colored to make an edgematching challenge (4x4x4 Babyface also shown)
• - Oskar van Deventer has created the PantaCube, which has only five of six faces but allows those five faces to be permuted.

• NEC -  edges and corners but no faces - can be implemented in different ways:
• Eliminate the core, as in the Void or Holey Cube
• Hide the faces using overlapping, as in the "Brilicube"
• Just sticker all six faces gray or leave them unstickered - i.e. ignore them - which isn't really a feature variation after all, more a sticker variation
• NEN -  true edges-only - can be implemented in different ways:
• Using a Void Cube, cutting down and hiding the corners, then extending the edges to overlap them - this has been mass-produced.
• Extending edge plates to overlap hidden face centers and corners, so the cuts make a big X on each side (4x4x4 version also shown)
• NNC -  - true corners-only - since any size cube has only eight corner pieces, this boils down to the basic 2x2x2
  Also consider the Nightmare Cube, in which overlapping corner pieces hide an internal 3x3x3 that has been bandaged.
• NNN - nothing moves - this is the trivial 1x1x1

Andreas Nortmann discusses these variants in the TP forums.

Edges and corners can also be truncated rather than entirely eliminated. Furthermore, we might elect to apply feature variations selectively to only a subset of cubies. Andreas Nortmann has created the series of all possible corner truncations of the 3x3x3 and shows it in the TP forums. (And earlier, here.)

Sticker and/or feature variations will differentiate one puzzle from another otherwise of the same order, and can dictate different solution methods. In the most complex case, you need algorithms to permute corners, orient corners, permute edges, orient edges, and orient faces. (The PantaCube, and the Cubedron family, require algorithms to permute faces.)

Lastly, all we've said here about sticker and feature variations regarding the face-turning 3x3x3 cube, could be applied sytematically to other orders, to other turning regimes, and to other shapes.

This section contains a series of charts I made to organize my thinking about the relationships among various puzzles of each shape. You can click the "_" symbol to hide it, if you'd like.

The illustration below is my attempt to provide a fun "map" of the Twisty Polyhedra puzzle landscape, including most of the commercially produced puzzles as well as several of the interesting hand-made custom modifications. I have exercised personal judgement as to what to include or exclude, and though I have tried to be comprehensive there is no way I could be complete. Photos are from several sources, including Sandy's TwistyPuzzles.com, Jaap's Puzzle Page, and Hendrik Haak's PuzzleMuseum.

The basis of the map is a central pentagon, having the five regular Platonic solids at its vertices (the yellow circles). At the center of each vertex circle is the key commercially produced puzzle having that shape. Those and other key commercially produced puzzles are outlined in red. Spherical puzzles radiate outward from the center of the pentagon. For the most part, derivatives of the key puzzles are shown near their relations, though some placements may be problematic. Some interesting cube sticker variations and bandaged cubes are shown in the upper left, and cube derivatives in the upper right. The families of derivatives of the Skewb and the Square-1 are shown in bubbles on the left. A group of rhombic octahedra appear on the right, and a group of dihedral puzzles in the lower right. Radiating "arms" show the different sizes of Rubik's Cube, and puzzles related to the Dino Cube.

This chart is a 3-D scatter plot showing fully functional cuboid puzzles that have been made either commercially or as custom creations. A cuboid has a cubic or brick shape, with dimensions k x m x n. "Fully functional" cuboids allow turns through every cut - "extended" and multi-core (e.g. chaos, evil-twin, fused, and siamese) cuboids are not included here.

The puzzles in the chart are positioned such that k <= m <= n. In the chart, the left-to-right (x) axis is k, the front-to-back (y) axis is m, and the bottom-to-top (z) axis is n. Each axis except m (y) runs from 1 to 7 - puzzles where a dimension exceeds 7 are few and are shown off the chart. I omitted m=1 to reduce clutter. This prevents the inclusion of the so-called 1x1x1 (no big loss IMHO), and forces the 1x1x2 to be located at 1x2x1, the only violation of the m<=n rule. 1.1.n for n!=2 are omitted. A red "post" beneath each item gives a hint as to z scale.

In the table below, mass-produced commercially available puzzles are highlighted like this. Cuboids I have are highlighted like this.

When available, links are given to YouTube videos (shown as [Y]), websites (shown as [W]), TwistyPuzzles forum threads (shown as [T]), and Shapeways (shown as [S]).

Table last updated April 28 2013.

The following sections catalogue additional puzzles in my collection. (I moved all the cuboids to the section above.)

A while back I snagged a Usenet post of a list compiled by Mark Longridge (March 22, 1996) in which rearrangement puzzles were ranked by number of combinations. That list gave me the idea for the organization scheme of the table below. Jaap's Puzzle Page was invaluable in teaching me what puzzles were out there, and for providing combinations data for several puzzles, allowing me to add them to the table at the apropos rank. I include a few puzzles I do not own, for reference - they will be noted as such.

The number of permutations, positions, or states a puzzle can achieve is not always a good indicator of difficulty. Many cubers rank the Square-1 as more difficult to solve than many puzzles with larger numbers of permutations. I have not attempted to rank the puzzles by difficulty.

My favorites include the Pyraminx (I worked out solution procedures myself), the Square 1 (I wrote a program to explore moves), the Impossiball (I've had it for a long time though I've never solved it, and I love its organic motion), and the Skewb (its motion is so precise). I also like the Orb[-it]. I got a Masterball in Japan and the Tonne in Germany.

Puzzle	Name and Notes	Positions	Mechanism
	Petaminx This had been a very expensive custom-made puzzle (in the $3000 price range), designed by Drew Cormier. However, it has been mass-produced (at the $200 price range) by Mf8. (Included for reference to show number of positions - I don't have this.)	3.16*10996	Drew Cormier
	Teraminx Originally designed by Drew Cormier. According to Drew, the Teraminx contains 555 pieces! Produced commercially by Cube4you and Mf8. I got a C4U because of a misrepresentation by a vendor. The MF8 version is superior, and I got one from Meffert.	1.16*10525	Drew Cormier
	Gigaminx Originally realized by Tyler Fox. Subsequently made by others. Commercially released by James Lee at Cube4you (also Cubefans).	3.65*10263	Tyler Fox
	Mf8 Master Kilominx (solid colors) Also known as the Hyperminx This is essentially a Gigaminx where the central stars have been hidden. The pieces overlap during turns.	?
	Dogic Original version (with box), Mefferts I (12 color), II (10 color), and VI (20 color). I don't have Mefferts III (5 color), IV (2 color), or V (2 color). Jaap's page	2.199*1082	Zoltan and Robert Vecsei
	Megaminx (Tomy version, Meffert's tiled version, Original Hungarian Supernova in package, Hungarian Supernova re-issue, tiled Chinese version, stickered black Hong Kong version, stickered white Hong Kong version, DaYan Megaminx version with solid colored plastic pieces and corner ridges.) Also the Holey Megaminx from Mefferts (in black and white), designed by Lee Tutt.	1.0*1068 (12 color version) 6.144*1063 (6 color version)	Kersten Meier Ben Halpern 12-armed spider
	Meffert's Pyraminx Crystal (black tiled version, and black and white stickered versions) First patented in 1987 by Uwe Meffert: DE8707783 (U1). Katsuhiko Okamoto had created a version he called the Mega Crystal. Aleh Hladzilin created a version he eventually named the Brilic - he made around a dozen, some of which sold for over $1000. At first he used a Dogic core, then later a Megaminx core. Noah Hevey has written a nice history of this puzzle - see topic 85537 in the TwistyPuzzles forums. Also see thread 7711 for a discussion of solution methods. While a twist on the Megaminx moves 5 corners and 5 edges, a twist on the Crystal moves 5 corners and 10 edges.	1.68*1066	A build-up of the Megaminx, without centers.
	Mozaika	6.27*1049	Rudolf Destics
	The Ball.B From Poland - website here. This shape - a spherical Megaminx (aka Ballminx) - was first explored by Jürgen Brandt.	The version with dots is like an edges-only Megaminx, since for this version the corner orientations don't matter. 7.12*1040 The version with flags is equal to the Megaminx but with face centers orientation visible - i.e. a "Super-Megaminx." That has 2.5*1076 positions.	?
	Alexander's Star (Equal to a Megaminx with no corners and no centers.)	7.2*1034	Adam Alexander
	Logi-VIP	2.7*1025	1982 Logitoy AG, Austria Hubert Petutsching Patent WO8101638
The Thomasball is essentially the same but with a different mechanism	Impossiball (Equal to a Megaminx with no edges and no centers.)	2.36*1025	William O. Gustafson Wolfgang Kuppers
	Flower Minx From Mefferts, designed by David Litwin. This is a corners-only Megaminx, aka "Kilominx." Equiv. to Impossiball.	2.36*1025	Megaminx core.
	Kytka (Flower) A derivative of the Globall. This is a corners-only Megaminx or Pyraminx Crystal, same as Litwin's Kilominx / Meffert's Flower Minx.	2.36*1025	Globall core.
	GloBall See GloBall variants here.	?	?
	Logic Star A derivative of the Globall.	?	Globall core.
	3x3x3 Dodecahedron mass-produced by QJ More difficult than the regular 3x3x3, since all six centers must be properly oriented. Equivalent to a Super-Cube or "Picture Cube," such as Dan Hoey's Tartan Cube sticker variation, also shown (which I do not have). On a supercube, the orientation of all 6 faces are visible and each has four possible orientations, so the supercube has 46/2 = 2048 times as many positions as a regular 3x3x3. The 1/2 factor is because the number of quarter-turns among the centers must match the parity of the corner permutation.	8.8576*1022	3x3x3 core
play with a virtual calendar cube here	Rubik's Perpetual Calendar (Kalender Kubus) The "O" character on one center has only 2 distinct orientations	4.4*1022	Marvin Silbermintz
	Face-Turning Octahedron (FTO) (compared to the Magic Octahedron)	3.14*1022	8-axis?
	Dioctipoid 1 and 2 www.dioctipoid.com These are face-turning octahedra in spherical form.
	Lanlan Master Skewb in black (also have one in white) This is a relative of the FTO, and the Rex Cube is in turn a relative of this. The MS corners have no equivalents on the FTO.	?
	Rex Cube Vertex-turning like a Dino, but with additional face centers and "wings." This is similar to a cornerless Master Skewb. First designed by Drew Cormier back in early 2009 [T] [Y], then produced commercially (without his knowledge) [T]. Now offered via Meffert, with a royalty going to Drew.	?	Andrew Cormier
	LanLan Hydrangea - Face-Turning Truncated Octahedron	?	8-axis?
	Super Square 1 (4-layer) Produced by cube4you. See this thread at the cube4you forums. Watch a video.	1.19*1022	?
	3x3x3 Octahedron mass-produced by QJ	?	3x3x3 core
	Rubik's Cube 4th Dimension Four centers must have distinct orientations	1.1*1022	Erno Rubik
	Mastermorphix Traditional version designed by Tony Fisher, produced in China, offered with official Fisher stickers by Meffert's. Meffert's "Master Pyramorphinx" (the "curvy" version). Also known as a "Rice Dumpling" (stickerless).	? This is a 3x3x3 mod, but center orientations matter.	6-arm spider
	Rubik's World	2.7*1021	Erno Rubik
	Masterball (Geomaster, aka Rainbow version), Duo B&W, Dragon, Circus, Soccer See other versions at Les Casse-Tete de Chantal Mullen & Robinson solution	4.1*1020	Dr. Geza Gyovai patent 4856786
	Morph Egg Produced by Meffert, designed by Adam Cowan	? (More complex than a 3x3x3.)	3x3x3 core
	Various 3x3x3 Shape variants, including: Heart, Apple, Star, Egg/Potato, Cake, Ingot	? (More complex than a 3x3x3.)	3x3x3 core
	Qubami Designed and produced by Kelvin Stott The objective is to get 3 different colors and 3 different symbols on every row and column of every face. Read about Qubami in the TwistyPuzzles forums.	? (More complex than a 3x3x3.)	3x3x3 core
	Rubik's Mirror Blocks (aka Bump Cube) designed by Hidetoshi Takeji. The Bump Cube was entered in the IPP 2006 Design Competition. The hand-crafted version had been for sale at $320. I got a mass-produced boxed copy signed by Hidetoshi-san.	(Same as 3x3x3 cube.)
	4x4x4 Master Trajber's Octahedron also version with colored pieces	?	?
	3x3x3 Trajber's Octahedron The Trajber's Octahedron is a vertex-turning puzzle and has a 3x3x3 cube core. The group shot shows various kinds of octahedral twisty puzzles - the vertex-turning Magic Octahedron, the Trajber's, Meffert's Skewb Diamond (face-turning), and a face-turning octahedron from Taiwan (the next higher order from the Skewb Diamond). Hand-made version purchased from David Calzone - cast pieces molded from 3D-printed masters. Also shown is a mass-produced Trajber's, from QJ. The Trajber's solves like a 3x3x3, except 3x3x3 corners which are the triangular face centers on the Trajber's don't need orientation but 3x3x3 face centers which are the corners on the Trajber's do, so you need the supercube face centers algorithms. These are the Supercube face algorithms - algorithms exist to rotate a single face center by 180, or a pair - one by 90 and another -90. U180: ( (U R L U2) R' L') x2 U90 & F-90: F B' L R' - U D' F' U' D - L' R F' B U U90 & D-90: R L' F2 B2 R L' U R L' F2 B2 R L' D'	1.35*1019	3x3x3 core
	Truncated 3x3x3 Trajber's Octahedron Made by Tanner Frisby. On the truncated Trajber's the 3x3x3 face centers which are the Trajber's corners don't need orientation so you won't need the supercube algorithms. As on the normal Trajber's the 3x3x3 corners which are the Trajber's triangular faces do not need orientation, so the truncated Trajber's is simpler than a 3x3x3.	6.59*1015	6-arm spider
	Dodeca Nona A faces-only dodecahedron. This type of 3D edgematching puzzle is included here because I consider them "faces-only" versions of twisty polyhedra - no corners and no edges. 12 magnetic pentagonal 2-sided tiles fit to the faces. Each face has the numbers 1 through 5 arranged around its corners - all 24 possible arrangements are included. Place the tiles so that at every vertex of the dodecahedron, the numbers add up to nine.	3.99*1018 1122 solutions.	?
	The Void Cube, designed by Katsuhiko Okamoto. Manufactured by Gentosha Toys. Purchased from Torito. The Void Cube won the Jury Grand Prize in the IPP 2007 Design Competition. When solving the Void Cube, you might run across a parity problem. To see the internals, see this thread on TwistyPuzzles. Also a Rubik's Void.	1/12 of a normal 33 3.60*1018	Katsuhiko Okamoto
	Tantrix The Rock A truncated octahedron. This type of 3D edgematching puzzle is included here because I consider them "faces-only" versions of twisty polyhedra - no corners and no edges. Tantrix Home Page Jaap's page	1*1018 "over a billion billion"	?
	Mobius This type of 3D edgematching puzzle is included here because I consider them "faces-only" versions of twisty polyhedra - no corners and no edges.	?	?
	Octagonal Prism Jaap's page	4.5*1017	?
	Magic Octahedron Also a more recent larger version by DaYan Also comparison shot showing (L to R, front to back): original Cristoph's Magic Jewel, recent Gem, original Magic Octahedron, recent DaYan, face-turning octahedron.	8.23*1018 (including the trivial tips)	?
	Christoph's Magic Jewel (a Magic Octahedron minus the tips) I finally found one at IPP 29 in SF. Also, the DaYan Gem from China.	2.0*1015	Christoph Bandelow 6-armed spider
	Square 2 First designed by Dave Litwin, "Jake," and "Noda" back in 2003 [T], then mass-produced [T].	?	?
	Square 1	4.36*1011 90 possible shapes	Dr. Vojtech Kopsky
	Rainbow Cube Comes in 7-color and 14-color versions. Very easy to solve intuitively. Jaap's page	2.4*108 239,500,800	Bethel Japan
	Skewb Ultimate Jaap's page The Skewb Ultimate is the "most difficult" of the Skewb family - every piece has a proper orientation, unlike, for example, the face centers on the Skewb. The hierarchy is: Positions Moves to Antipode Puzzle 100,776,960 14 Skewb Ultimate 3,732,480 12 Halpern-Meier Tetrahedron 3,149,280 11 Skewb 933,120 11 Pyraminx 138,240 10 Skewb Diamond 2,160 6 Meffert's (4 color) Beachball	1.0*108	Uwe Meffert
	Rhombic Dodecahedron Skewb Since the orientation of every piece matters, this is similar to the Skewb Ultimate.	1.0*108	?
	Meffert's Skewb Hex Designed by Tony Fisher In this Skewb mod, the orientations of the corners do not matter but the orientation of the faces do.	?	Skewb core
	Rubik's UFO Original in gray, newer version in green.	4*107	Erno Rubik
	Dino Star (blue)	?	Dino Cube core
Jaap says these are analogous: Mefferts Jackpot, NGP, and Hoberman Braintwist	Dino Cube #1 6-color each side different New releases by SmaZ - a version with SmaZ' hollow stickers, and a version with repro Dino stickers.	1.9*107	James R. Holloway 1995 U.S. patent 6056290
	Hong Kong puzzle designer and craftsman Smaz has mass-produced his Dino Cylinder design [T] [T]. His original "hollow" stickers make for a beautiful puzzle! It is even shipped in a nice black velour drawstring bag. This puzzle solves like a Dino or Rainbow and is fairly easy. However, unlike the Dino, this puzzle exposes corner pieces each of which can be independently oriented in one of 3 positions. Using the same notation I used for the Mosaic Cube, here is an algorithm to rotate the df corner clockwise by 120 degrees: ur' df' dr' -- df dr ur -- uf df uf' In the second photo, I have applied this to all eight corners.	?	Originally a mod of a Rainbow core
	Halpern's Tetrahedron aka the Halpern-Meier Tetrahedron (Also comparison with Skewb.) This was produced commercially - but I have a custom-built example made by Matt Davis from cast pieces and a Skewb keychain core. Meffert is now producing a Reuleaux version of the HMT, designed by Adam Cowan. They call it Jing's Pyraminx. It is fairly large. Also shown is the Jade Club Pyraminx, which is smaller than the custom HMT. Solve as a Pyraminx, then fix centers. My operator to flip two edges in place: L T' R T R' T L' T' When 3 edges around the top would be solved if only you could circulate them clockwise: (R T' R') T' (R T' R') Fix centers - swap F-L and R-D: (T' R' T R)*3	3.7*106 3,732,480	Ben Halpern Kersten Meier
	Meffert's Fisher's Golden Cube Perhaps the most famous of the Skewb mods, now produced commercially by Meffert.	?	Tony Fisher
	The Skewb The order-1 vertex-turning cube (Mefferts stickered and tiled versions) Holey Skewb twins from Meffert (designed by Tony Fisher) Meffert's Pillowed Holey Skewb, in black, from PuzzleMaster Also various Skewb balls, and a white Skewb Egg from Meffert, designed by Tony Fisher. Jaap's page Meffert's solution. L means twist around down-front-left corner R means twist around down-front-right corner B means twist around down-back-right corner 0) Pick a top face, get 4 corners around it irrespective of their rotation. 1) Swap top-front-left with top-back-right if necessary: LBL 2a) Rotate TFL CW: LR L'R' 2b) Rotate TFR CCW: R'L' RL 3) Rotate bottom corners - depends on position of bottom-color facelets: 3a) None done: hold so 2 bottom-color facelets face right: LR'LR' L'R L'R 3b) Two done: hold so one not done is at DFR: do alg above, then do 3a. 4) Fix faces: swap F w/ D and L w/ R (fiddle combos until done) if 3 faces in a row are done, hold them L-B-R if 3 faces around a corner are done, hold them L-T-B [LR' L'R]x3	3.1*106 3,149,280	Tony Durham
	Einstein Cube A faces-only cube (granted, the faces are rounded). This type of 3D edgematching puzzle is included here because I consider them "faces-only" versions of twisty polyhedra - no corners and no edges. 12 positions per face. A similar puzzle called "Turn Twelve" has 24 positions per face.	12^6 = 2,985,984 (Einstein w/ 12 pos./face) 3*106 24^6 = 191,102,976 (Turn 12) 1.9*108	?
	Diamond Cube Jaap's page	2.0*106 2,425,500	?
	Bandaged Cube also "New Spring" clear 2x2x2 with internal colored bandaged 3x3x3 (The New Spring version is not a "Nightmare" cube, since all 2x2x2 moves always work.) Also, a Cubetwist Bandaged Cube Kit, ordered from Lightake Jaap's page Andreas Nortmann has investigated bandaged cube variations - read his articles (thread 3217) and (thread 15993) in the TwistyPuzzles forum. He says there are 7356 different bandaged 3x3x3 cubes, of which 5705 are (subjectively) non-trivial.	1.0*106 1,108,800	?
	The Pyraminx An original issued by Tomy, loose and in package, a Meffert's 25th Anniversary version, and Meffert's New Pyraminx, in black. My operator to flip two edges in place: L T' R T R' T L' T' When 3 edges around the top would be solved if only you could circulate them clockwise: (R T' R') T' (R T' R')	9.3*105 933,120 (not including trivial tips) 7.6*107 75,582,720 (with tips)	Uwe Meffert 4-armed spider
	Tetraminx (A Snub Pyraminx - same as Pyraminx with trivial tips removed.) Mefferts version, and transparent version from Smaz.		Uwe Meffert
	Brainbow Jaap's page	623,760	?
	"Square Octahedron" This version of the Skewb Diamond (actually the Mozhi brand diamond) has build-ups on the triangular faces which make their orientation matter, so it has more states than the Skewb Diamond.	?	?
	Skewb Diamond (also a clone from Mozhi, in white) and various truncations - Rugby ball and Treasure Box. Jaap's page	138,240	Uwe Meffert
The Starburst is a custom mod, and has been mass-produced. The Babymorphix is a Reuleaux Pyramorphix, custom-made by Taylor Howell. A Pyramorphix clone (different internals than Meffert version, and easier to turn)	Pyramorphix aka Pyramorphinx Also the East German FigurenMatch Jaap's page I find I can solve the Pyramorphix using only four operators (beyond fiddling to get it into a tetrahedron shape and properly position the corners): Move the bottom face down: D2 R2 L2 R2 Exchange the left and right faces: R2 L D2 R L2 D' (this twists corners,too) Twist Up corner clockwise: (R L' R' L)x2 Twist Up corner counter-clockwise: (L' R L R')x2 This can also be solved in the same way as a 2x2x2.	136,080	Rubik, Barry Lockwood
There are four versions of the Dino Cube: 2 colors 312.55/1 4 colors 528.99/1;535.55/1 6 colors, no dinos 337/1 6 colors, with dinos 667.96/1	Dino Cube 4 color version I find this very easy to solve even without operators. The four original Dino versions shown for reference. I've only got the 4-color, but the others are just sticker variations.	42,000	James R. Holloway 1995 U.S. patent 6056290
	Intellect Ball 9 cm (handy) and 13 cm (large!) versions.	?	?
	4D8	?	?
	PyraDiamond, Meffert's version of the Okki/Gem	?	Pyramorphix
	Tonne	?	?
	Mefferts Beach Ball (4 color Skewb ball) Also a Beijing Olympics ball	2160	Skewb
	Rubik's Cheese (Sajt)	96	Hungarian patent, 9 November 1980, HU 2679

This section contains dihedral puzzles - puzzles whose halves can move relative to each other and permit the exchange of pieces between them. Their shapes aren't convex polyhedra, nor simple spheres, cylinders, or pucks.

Puzzle	Name and Notes	Combinations
	The Bulgarian Barrel	?
	Smart Alex Dumitru A. Pop, patent on 26 May 1992 Jaap's page	6*1020
	Octo Bracelet	3.7*1018 (?)
	Sando Ring (aka King Ring)	4.97*1014
	Tricky Disky Jaap's page	2.1*1013
	Hungarian UFO	2.1*1013
	Brainball Andreas Unsicker Jaap's page	2*1012
	Sphere XYZ Offered by Lori Powers and Adam Giemek, and LA1 Products	3.37*1011
	Netblock UFO Wai K. Chan	2.0*108 200,121,075
	Gerdig UFO Gerhard Huncaga Jaap's page	130,040
Group shot:	Roundy (4-leaf/4-color version) Purchased at IPP28 in Prague.	40320
	Roundy (3-leaf/6-color version) Fritz Gruber 12/7/93 patent 5267731	23040
	Saturn Jaap's page	5040
	Roundy (3-leaf/3-color version) Fritz Gruber 12/7/93 Jaap's page	2880
	Clever Disk	?
	Turbo Mind Twister	?
	Snow Mystery	?

This section contains variations of puzzles, some mass-produced, and custom-built puzzles.

Puzzle	Name and Notes
	Tony Fisher's Mental Block 3x3x1 aka Rubik's Layer Custom-made by Tony, from a full-sized Skewb
	The Mental Flop by Grégoire Pfennig. [T] [S] Visually, it's a cross between a 1x3x3 Floppy and Tony Fisher's Mental Block, hence the (great) name. Mechanically, it is isomorphic to a 2x2x3 (Slim Tower). Shown in good company - with my original Floppy Cube hand-made by Okamoto, and my original Mental Block hand-made by Tony Fisher, along with a U.S. quarter. Very stable and playable!
	A "Bump Floppy"
	QJ Heart-to-Heart
	I took advantage of a special offer at Shapeways for a dyed, assembled, and stickered Floppy 2x3x3 designed by Oskar van Deventer.
	Prolific puzzle designer Oskar van Deventer [S] attended IPP 31 in Berlin, and I purchased his More Madness, which he was kind enough to sign for me. No-one has yet devised a comprehensive solution strategy for this puzzle. More Madness was announced and discussed on the TwistyPuzzles forum. It is based on the geometry of the triangular di-pyramid. Initially, each of the triangular faces turns. This puzzle has "overhang bandaging" - occasionally a piece juts out such that it blocks a twist that would otherwise be OK. Every move jumbles.
	Latch Cube - Okamoto
	The Quarter Cube, designed by Katsuhiko Okamoto and Takafumi Haseda, produced by Chronos Co. Ltd.
	The Constrained Cube designed by Tom van der Zanden. Several versions available that have different side turning constraints. I ordered the "Ultimate" version.
	A Wormhole I Cube by WitEden
	Camouflage Cube Ordered from WitEden
	Double and Triple Cubes Available commercially from various sources, made from keychain 2x2x2 cubes. Two cores share a corner in "Siamese" configuration.
	King Pillow Cube A commercially produced shape variation.
	Confused Pillow cube from "Socube"
	Hexagonal Prism 3x3x3
	Rhombohedron 3x3x3
	A "Blue Diamond" (Truncated Hexagonal Dipyramid shape mod to a 3x3x3). These are being mass-produced in China. 3x3x3 core
	A cheap way to make a Hexagonal Dipyramid - combine the parts from two Guo Jia diamonds. Now Hexagonal Dipyramids are mass-produced by Dian Sheng. 3x3x3 core
	Super Dipyramid (hexagonal dipyramid from 4x4x4 core)
	Dian Sheng "Tank Diamond" 3x3x3 core
	Dian Sheng Pyramid (aka "aXe") designed by John Lin 3x3x3 core
	Ultimate Cube A commercially produced sticker variation. I have an original in its packaging.
	3x3x5 Extended Cube This simple extended cube-variant has an extra piece glued to each of the nine facelets of two opposite faces.
	3x3x4 Extended Cube This simple extended cube-variant has an extra piece glued to each of the nine facelets of one face.
	3x3x3 Extended to 4x4x4 This is a cheap and simple extended cube-variant from Hong Kong, not a 4x4x4 Evil Twin as the description led me to believe. Caveat Emptor!
	Mini Evil Twin Designed by Mike Grimsley.
If the standard 33 cube is rotated 45° about one face's axis (e.g. z axis) then built up and cut down to be re-formed into a cube, one obtains the Fisher's Cube; approx. 30° around z [T] gives the Windmill Cube; 45° around z and x (or 90° about an edge-to-edge axis) gives the Slice Cube; combining Fisher's and Windmill gives a "normal-sized" Greenhill's Cube (which is actually larger - Anthony says [T] it is "a 'Truncated Cube' (corners trimmed down to triangles), stood on one corner then built out to a Cube shape. This basically determined the edge length - 77mm."); 60° about a corner-to-corner axis gives the Axis Cube [T] [T]. An "axised" Cube with twists, reformed into a cube gives the Ghost Cube [T].
	Fisher's Cube - originally designed by Tony Fisher, now mass-produced An axis-rotated 3x3x3 (single axis x 45 degrees) Solve as a 3x3x3, but also has four of six face centers that can be rotated by 90, 180, or 270 degrees. These are the Supercube face algorithms - algorithms exist to rotate a single face center by 180, or a pair - one by 90 and another -90. U180: ( (U R L U2) R' L') x2 U90 & F-90: F B' L R' - U D' F' U' D - L' R F' B U U90 & D-90: R L' F2 B2 R L' U R L' F2 B2 R L' D'
	Fisher's Cube / Diagonal Cube 8-color sticker variant
	Windmill Cube
	At the 2012 New York Puzzle Party (NYPP) hosted by Tom Cutrofello, I bought this hand-made Slice Cube from fellow attendee and twisty puzzle enthusiast "Zhewei." He had posted about this puzzle on the Twisty Forums here.
	Axis Cube Designed by Adam Cowan, made by Frank Schwartz.
	I am very pleased to have finally obtained a custom-made Helicopter Cube from Adam! The Helicopter Cube was first discussed in the TwistyPuzzles forums in thread 6253 - a particularly rich thread in which several ideas, including the concept of jumbling as opposed to shape-shifting, were broached. (More discussion on jumbling: 13071, 11126 .) Katsuhiko Okamoto mentions that he had completed his equivalent Bevel Cube the previous month. Robert Webb extrapolates a rhombic dodecahedral puzzle and Matt Shepit hints of its realization - it will be Shepit's Rua. Various folks have discussed their attempts to make their own Helicopter Cubes: 13856, 13520, 12030, 12423, 11679. The Helicopter Cube has also been produced commercially. I bought a black one and a white one. Helicopter Cube solution
	A Partially Unbandaged Helicopter Cube designed by Eric Vergo - this is copy number 1, obtained from Eric at NYPP2011. When a jumbling move is made, a triangular face piece can swap places with a corner - this is not possible on the regular Helicopter Cube.
	Meffert's is offering the mass-produced Curvy Copter created by Tom van der Zanden. Tom's Curvy Copter has been very popular as a custom-produced 3D printed puzzle, and is now available at one tenth the price. I bought the black and white "twins" pair. The Curvy Copter functions like a Helicopter cube, but it exposes central edge pieces that must be correctly oriented, making it a more difficult challenge.
	Curvy Copter II by Tom van der Zanden [T] [Y]
	I bought one of the large versions of Jason Smith's first run of the Compy Cube. The Compy Cube (aka Shallow Dino, aka Sausage's Cube) is a full custom 3-D print. It is easy to solve intuitively, requiring no memorized algorithms. I dyed my Compy Cube purple, just to be different.
	An Icosaminx made by Matt Davis
	A Super-Square-1 Star mod - Brett made it in all white then I swapped in the black pieces. You can find on-line [dis]assembly instructions here.
	The Quartet from the Shapeways shop of "RubixFreakGreg" -- designed by "Lykwid" [T], the Quartet is a square version of the triangular Grimace made by Smaz.
	2-layer Grimace
	3-layer Grimace
	An Edges-Only cube from "Smaz."
	I received a pleasant surprise in the post, in the form of this great Simple Overlapping Cube twisty puzzle, cleverly made by TP forum member "Zzupler" (Kevin Phelan, of Ireland) [T], and originally designed by David Calvo [T]. This "corners-only" 3x3x3 is kind of the brother to the "edges-only" 3x3x3 above. It is nicely done and turns very smoothly. Thanks, Kevin!
	The Brilicube. Originally designed by Aleh Hladzilin. [T] It is a 3x3x3 cube with hidden face centers. This version purchased from the Shapeways shop of "grigr." [T] I have not stickered mine yet. This is the first Shapeways puzzle I got in black strong flexible material. It is very tight and difficult to move, even after much wearing of the pieces, and lubrication.
	Nightmare Cube from Tanner Frisby [T] [Y] [Y] Conceptually, it is a bandaged 3x3x3 hidden inside a 2x2x2 shell. Before the first move, all normal 2x2x2 twists are permitted. After a few turns, however, the bandaging comes into play so various moves become blocked, and then solving becomes a nightmare! Tanner told me the YBR corner has no bandaging. In October 2008, Adam Cowan issued free STL files for the Nightmare Cube, in the TP Forums, based on an idea mentioned by Noah Hevey in a post from March 2008. Tanner's version is made from a different core, though. TP Forum member "sublime" made one from wooden corner pieces and a modified keychain 3x3x3 core, and then posted about his copy of the printed version. Folks have noted that solving a Nightmare cube is more akin to navigating a hidden maze, than applying conventional operators. The solution methodology is discussed at Jaap's page.
	Pillowed Hexaminx from Traiphum Prungtaengkit, of Thailand (Shown with Helicopter Cube)
	Here is a Mini-Hexaminx, designed and made by Grégoire Pfennig, printed by Shapeways. [T] [S] Shown in comparison to a U.S. quarter, a Pillowed Hexaminx hand-made (cast) by Traiphum Prungtaengkit, and a Tomy Megaminx. This small wonder is very stable and usable. I am impressed that something so compact works so well. Nice work, Greg!
	A pillowed white Master Skewb made by TP forums member "Cublem" [T]
	From Traiphum Prungtaengkit, of Thailand, an Edge-turning Pyraminx! He calls it a Mastermorphynx. Also shown compared to a curvy Mastermorphix and a Pyraminx.
	I dyed, assembled, and stickered my Shim's Master Pyraminx. I really like this puzzle! It was designed by Timur Evbatyrov and is available on Shapeways. Two photos show relative size - a comparison with an original Tomy Pyraminx, and a group photo including various tetrahedral twisty puzzles. The group photo includes, left to right, row by row from the top: the Hoberman BrainTwist, Meffert's Jing's Pyraminx (designed by Adam Cowan), Meffert's NGP (Platypus), Tomy Pyraminx, a custom Halpern-Meier Tetrahedron (keychain Skewb core) made by Matt Davis, Meffert's Pyramorphinx (a curvy Mastermorphix), Traiphum Prungtaengkit's (Traiphumi's) Mastermorphynx (a custom-made edge-turning Pyraminx), a keychain Meffert's Pyramorphi[n]x, Shim's Master Pyraminx, and a reuleaux Babymorphix custom-made by Taylor Howell. 2.2*1014 positions ignoring trivial tips.
	The Master Pyraminx, issued by Mefferts Designed by Timur Evbatyrov and Adam Cowan Another great design mass produced beautifully by Meffert!
	The Professor Pyraminx, issued by Mefferts Designed by Timur Evbatyrov Yet another great design from Timur, mass produced beautifully by Meffert! I love this puzzle!
	Elite Tetrahedron - by Chris Hemerich [T] [S] [Y] The Elite Tetrahedron is also shown in comparison to Meffert's Professor Pyraminx and Vergo's Master Pentultimate.
	From Meffert's, the Vulcano (aka Trignis) designed by Timur Evbatyrov.
	Dinomorphix - designed by Traiphumi, produced by Calvin Fan
	An Extended Cube.
	A set of ShengShou Cubes, and the "Circle Ball Cube"
	A 2x2x2 Rhombic Dodecahedron, made by Karl-Heinz Diekmann.
	Rhombic Dodecahedron (3x3x3) in black (QJ), and white (LanLan) also truncated version
	Lanlan 4x4x4 Rhombic Dodecahedron also truncated version
	Truncated Rhombic Dodecahedron This vintage cube-variant is almost a rhombic dodecahedron, except the four-color centers are flat, not pyramidal. The three-color corners are pyramidal.
	I bought the Dino-Rhombic Dodecahedron (DRD) DIY from Drew Cormier. This puzzle is a vertex-turning rhombic dodecahedron where all 4-part and 3-part vertices turn. It turns well, but due to a design issue the 3-part corners turn only counter-clockwise.
	This is a Rex Rhombic Dodecahedron (RRD), designed by William Kretschmer. It was announced on the TwistyPuzzles forums, and is available from Will's Shapeways shop. As Will says, the turning is nearly flawless. It's about the same size as the LanLan 4x4x4 RD. This is a great puzzle!
	A Mini Mini Rhombiminx from Eric Johnson. It's a vertex-turning Rhombic Dodecahedron, but unlike the similar-looking DRD, the Rhombiminx is order-3 and only the 4-part vertices turn. It's hand-made using cast custom parts and an Eastsheen mini 2x2x2 core.
This puzzle is the same size as the Dino-Rhombic Dodecahedron (DRD) I got from Drew Cormier - here are some comparison photos: Here is a group shot with various Rhombic Dodecahedra twisty puzzles. The black Mini-Rhombiminx is in the center. The white Mini-mini Rhombiminx is below it; clockwise from there is a 2x2x2 Rhombic Dodecahedron made by Karl-Heinz Diekmann, a Kite Skewb, a truncated 4x4x4 RD, a Lanlan 4x4x4 RD, a QJ 3x3x3 RD, and the custom DRD.	I received a black Mini Rhombiminx. This is an order-3 vertex-turning rhombic dodecahedron, built around a 2x2x2 using custom parts. (The first Rhombiminx was built around a cut-down 4x4x4.) Every 4-part vertex turns, and there are 3 mutually perpendicular cuts through each square cross-section (i.e. the 2x2x2 cuts). It is larger than the white Mini-mini Rhombiminx I got a while ago, which is built around a mini-Eastsheen 2x2x2.
	The Crazy 2x3x3 designed by Daqing Bao. Genuine DaYan versions made by WitEden. Available at Cube4you.
	Witeden Super 3x3x4 black
	The Crazy 4x4 I from Mf8. This cube was discussed on the Twistypuzzles forums in threads 14856 and 7918. You can see how this cube moves on YouTube here. 3.23*1053 positions
	The Crazy 4x4 II from Mf8. 3.1*1061 positions
	The Crazy 4x4 III from Mf8, purchased via Mefferts 3.1*1061 positions Same as version II according to Jaap.
	DaYan/Mf8 Crazy Megaminx Plus Saturn The fit and turning on the copy I got are very good, and I like the stickerless design and brightly colored plastic. It is about the same size and weight as a Meffert's Pyraminx Crystal. Purchased at the HK Now Store.
	Mf8 DaYan Crazy Tetrahedron (Jupiter) also Standard version (all circles turn with opposite vertex)
	DaYan Pentahedron 3x3
	The set of eight types of DaYan Crazy 3x3 Plus Cubes - "Eight Planets" The circle pieces either do or don't turn with the face. The eight types are different ways of arranging dos and don'ts. I got mine from Mefferts but you can find them at several vendors.
	DaYan Bermuda Cube Neptune (black) One of a series of eight types.
	The DaYan Gem (an edge-turning truncated octahedron, related to GB 4.3.6)
	The DaYan Gem II is a truncated cube where faces of the cube and vertices of the cuboctahedron rotate.
	Here is a new Limited Edition Blue DaYan Gem III. [T] It is a shallow-truncated octahedron where the vertices and faces turn. Independently designed by Daqing Bao, also appeared as the custom "Concept 11." [T] Shown compared to the DaYan Gem, which is a truncated edge-turning octahedron.
	The DaYan Gem IV resembles the Gem III, but here the 4-fold faces (the trancated octahedron tips) do not turn. Instead, the puzzle is deep-cut. Every hexagonal face turns, but the layer below and parallel to each hexagonal face also turns.
	A Dino Dodecahedron (aka Dinominx) by Mf8 (they call it a Starminx I), purchased from hknowstore. This puzzle was first proposed by Lukeharry then made by Kevin Uhrik, now mass-produced by Mf8. [T] I solve this with no algorithms - it's a fun puzzle. Also quite large - larger than a Pyraminx Crystal.
	Mf8 Helicopter Dodecahedron, in black
	Bauhinia
	Lolo's Octahedron, custom-made by Kevin Uhrik.
	I completed my first real twisty mod! I made an Octaminx (a design originated by Tony Fisher) from a couple of old Tomy Pyraminx puzzles. This is an "old school" mod - done with a saw, and various other implements of destruction - not casting. I've got the sliced and abraded fingers to prove it. I hand-cut the stickers myself. As of Feb. 2011 my first Octaminx is in the collection of Laurie Brokenshire. I still have another black one I made.
In comparison with other octahedral twisty puzzles: From top to bottom, left to right: Meffert's Skewb Diamond (order-1 face-turning octa); DaYan Gem I (edge-turning trunc. octa); order-2 vertex-turning octa; order-2 vertex-turning trunc. octa; order-3 vertex-turning master Trajber's; Meffert's Hex Skewb (order-1 face-turning trunc. octa); order-2 face-turning octa; Eitan's ETO (order-2 edge-turning octa); vintage Magic Octahedron (order-2 vertex-turning octa); QJ Trajber's (order-2 vertex-turning); hand-cast custom Trajber's made by David Calzone; QJ 3x3x3 octa (sort of hybrid edge- and vertex-turning); Octaminx custom made by me; Meffert's Pyradiamond (order-1 vertex-turning octa); vintage Christoph's Magic Jewel (order-2 vertex-turning trunc. octa); Lolo's Octahedron custom-made by Kevin Uhrik (order-3 vertex-turning octa); Truncated Trajber's custom-made by Tanner Frisby.	Here is Eitan's Edge-Turning Octahedron (ETO) - announced on the TP forums. Equivalent to Gelatinbrain 4.3.1. Available from Eitan's Shapeways shop. First shown by David Calzone back in 2009. Congrats to Eitan for making this available! The design moves well, is stable, and is a nice size. The puzzle came very nicely stickered. I still would like to find: a 24 octahedron, a Dino octa, a Rainbow octa, a Master octa, a Master FTO, and a Professor Trajber's. Maybe a Square-1 and/or Square-2 octa, too.
	Child's Play by Eric Vergo [T] [S] [Y] This is Eric's first copy! Two 2x2x2 cubes with shapes on each face reminiscent of the shapes in a child's shape sorter puzzle/toy - hence the name. One cube has the shapes embossed into the facelets, the other has raised shapes. The objective is to solve both cubes such that every face on the cube with raised shapes can be fit into a corresponding face on the cube with embossed shapes. Difficult, especially if you don't know what the shape arrangements are supposed to be! The colored layers aren't necessary, but have been added to simplify the challenge somewhat.
	I bought the 1st copy of Eric Vergo's Pentagram puzzle - first announced at the TwistyPuzzles forums. It is an order-2 vertex-turning dodecahedron, designed by Eric and 3D printed by Shapeways. It is the same size as the Meffert's Pyraminx Crystal. You can buy a copy at Eric's Shapeways shop. There is an online video review of this puzzle on YouTube.
	For the last puzzle in 2010, I received Tom van der Zanden's excellent Pentultimate. You can buy one, and several other great twisty puzzles, at Tom's Shapeways shop. This is the order-1 face-turning dodecahedron. It has six cuts, all of which pass through the center of the puzzle, midway between pairs of opposing faces, and are great circles on the circumscribed sphere. Each divides the puzzle into two halves. It is an engineering design masterpiece and employs a sophisticated "shells" mechanism. The shells build upon a Megaminx, through a Pyraminx Crystal, Master Pentultimate, to the outer Pentultimate. In a shells mechanism, the pieces of an inner shell hold in the pieces of the next shell out. For example, the Pyraminx Crystal has two shells - an inner Megaminx and the outer Crystal. The faces of the inner Megaminx hold in inner edges, which in turn hold in the outer Crystal corners, which hold in the outer Crystal edges. The Pentultimate is 25mm (1") on an edge, and is the same size as a QJ 3x3x3 dodecahedron. The design explores the limits of economical miniaturization within the 3D printing process, yet the puzzle is not fragile and is quite comfortable to hold and manipulate. It was announced on the TP Forums here. You can see an image of the complicated internal mechanism in that thread. For information on the earlier impressive albeit fragile so-called "knucklehead" mechanism pioneered by Jason Smith, who designed and constructed the first working version of this puzzle, see an article at Jason's Puzzle Forge website.
	I received a Master Pentultimate designed and made by Eric Vergo. It turns very smoothly. This is a great design! Shown along with Tom van der Zanden's Pentultimate.
	A Multidodecahedron by Tom van der Zanden [T] This is a custom 3D printed puzzle, but the pieces of my copy have been through a "tumbling" process that makes them smooth. [T] The Multidodecahedron is an outer Master Pentultimate, where the face centers expose an inner Megaminx shell having its own stickers. A full solution entails solving both layers. [T]
The mass-produced Mosaic Cube issued by Meffert was designed by Oskar van Deventer and originally available from Oskar's Shapeways Shop as the Fadi Cube. It is a vertex-turning, order-4 cube, related to Okamoto's Lattice Cube. There has been some controversy about the stability of the Mosaic Cube [T] and Oskar designed a new spherical core. I bought a black spherical core from Shapeways and modified a Mosaic Cube to swap out the standard core. To access the screws and disassemble the puzzle, one must first remove the corner caps, which are glued on and have three small legs that fit into sockets in the underlying stem piece. An Exacto knife, used with care, is helpful to pry up the corners. One or more legs might break when a cap is removed, however this is not catastrophic - you can use "Stik Tak," "Fun Tak," or a similar product to re-attach the corners so they remain easily removable. After swapping in the spherical core and adjusting the screw/spring tensions, I find the puzzle very stable, playable, and enjoyable. The Mosaic Cube is not overly difficult to solve. It is similar to a Dino or Rainbow Cube, as one might expect. The steps I employ are: Orient the corners - they are fixed in place so this step is trivial. Once the corners are oriented, the correct face colors are evident. Solve the small square centers. These centers are attached in pairs - a single piece provides a square center to two adjacent faces. There are 12 such pieces and they can be solved in the same way as Dino or Rainbow Cube edge pieces - intuitively. Solve the large edge pieces. There are 24 of them. I have three algorithms that sometimes prove useful. To describe the algorithms and their effects, we have to agree on a notation for the Mosaic Cube - here is what I use. I hold the cube at an angle and look at it edge-on - the up and down faces are held parallel to the floor, and an edge is towards you. I label the 8 vertices using two letters describing their position: UF, DF, UR, DR, UL, DL, UB, DB - as shown in the image (DB isn't visible). Any of the 24 large edge pieces can be identified by giving the labels of the two corners it lies between, with the adjacent corner first. For example, the large edge piece on the bottom in front would be DFUF while the piece above it would be UFDF. A move is a twist of a vertex by 120 degrees either clockwise or counterclockwise from the point of view of looking directly at the vertex. A move can encompass just a corner and the 3 large edge pieces surrounding it, or those pieces plus the further "layer" including 3 more large edge pieces, and 3 center dual-pieces (accounting for six small square centers). I will symbolize the latter move, clockwise, using the relevant corner name - e.g. UF means twist the UF corner and the two layers surrounding it 120 degrees clockwise. UF' symbolizes the corresponding counterclockwise move. I will use the lowercase name of the corner to symbolize the "smaller" move of just twisting the corner and the 3 large edges surrounding it - e.g. uf and uf' for counterclockwise. To 3-cycle DFUF => URUF => URDR, use: UF' ur UF ur' To twist just the single UF corner piece 120 degrees clockwise, use: (UR uf UR' uf)*2 To 3-cycle the far edges about the UF corner clockwise - i.e. DFUF => ULUF => URUF, use: ur UF' ur' UF' ur UF' ur' I figured that one out myself :-) - I do a setup (ur UF' ur'), then use the previous 3-cycle UF' ur UF ur', then undo the setup (ur UF ur'), which strung together looks like: (ur UF' ur') UF' ur UF ur' (ur UF ur') The adjacent ur' ur near the end cancels out, and the resulting adjacent UF UF simplifies to UF' giving the concise 7-step algorithm.
	Tuttminx - designed and prototyped by Lee Tutt in 2005 [T] - produced by Leslie Le [T] [W] The Tuttminx is a 32-sided truncated icosahedron. Leslie Le has also produced the Tuttminx Classic. [T]   www.verypuzzle.com
	Marusenko Spheres
	Dino Skewb by TomZ
	Redi 3x3x3 - Eric Vergo This puzzle turns at its vertices like Oskar van Deventer's Redi Cube, plus like a 3x3x3. Announced on the TwistyPuzzles forums, and available at Eric's Shapeways shop. Very clever, Eric!
	In 2011, I had the pleasure of meeting Tom van der Zanden [S] at IPP 31 in Berlin. Tom made me a slightly larger version of his Starminx I [T]. The Starminx is shown in comparison to Tom's Mini-Pentultimate. Previous versions of the Starminx have been made by Drew Cormier [T] and Aleh [T].
	Mf8 Starminx II - in translucent purple This is a mass-produced version of what the twisty forum knows as the Starminx I, previously custom-made by Aleh [T] , Drew Cormier [T] , and Tom van der Zanden, in mini [T], and larger size [T] . (Mf8 called their Dino-Dodecahedron a Starminx I, hence the naming confusion.) I finally stickered my purple Mf8 Starminx. As people have noted, it does not turn as smoothly as Tom's (admittedly much more costly) 3D printed version.
	In Berlin, I got one of Tom van der Zanden's Super-X cubes [T] - the Super-X turns like a Dino plus a 2x2x2. Adam Cowan made the first Super-X announced on the forum [T]. Drew Cormier improved on Adam's Super-X by adding magnets to stabilize it [T]. Tom's version uses printed-in detents for stability, and having played with different versions, I would venture to say that Tom's is the best to date.
	Eric Vergo made this Elite Skewb for me [T]. It's instance #1! This is the order-3 vertex-turning cube - a Skewb combined with a Master Skewb.
	A Mini Mixup Cube by "PuzzleMaster6262" (Mike Armbrust) [T] [S] (also see a version by Oskar van Deventer [S] ) The idea of a 3x3x3 cube which is able to interchange edges and centers via 45 degree turns of its middle slices seems to have originated with Sergey Makarov back in 1984. [T]
	Meffert has produced Oskar van Deventer's Caution Cube [S] and calls it the Gear Cube. The Gear Cube Extreme has four edge pieces in one layer replaced with alternatives that have less gearing. The Gear Cube Ultimate has alternative stickers requiring proper permutation of the small central gear pieces on each face. Positions: Gear Cube: 41,472 Gear Cube with edge base (small U piece) stickers: 165,888 Gear Cube Extreme: 2.56*1014 Gear Cube Ultimate (Extreme with edge base stickers): 3.28*1016
	Oskar's Gear Shift - Meffert (black and white versions) Video solution on Bram's YouTube channel
	Gear Pyraminx - from Meffert's, design by Timur Evbatyrov (I have black and white versions.) Also a Series II in black.
	A Gear Mastermorphix
	Gear Ball - designed by Oskar van Deventer, produced by Meffert
	Gear Minx II - gear twisty mechanism designed by Oskar van Deventer, produced by Meffert.
	I received a black Treasure Chest cube from Mefferts. This hollow, opening cube was designed by Oskar van Deventer - he called it the Gift Cube. [T]
	The Time Machine - a beautiful twisty puzzle designed, made, and stickered by Smaz. [T] [T] [T] A 2x2x2 where each face has a "dial" of 12 movable segments. Similar to the Square-1 Cross Cube. [T]
	The Rainbow Nautilus, designed by Tim Selkirk [T] and mass-produced by Meffert.

Here are other unusual and interesting takes on the permutation puzzle...

The Planets puzzle consists of four spheres arranged in a tetrahedron within a frame. The spheres have various craters in them and are contrived to interlock so as to only permit certain rotations depending on where the craters are at any moment. Rotate the spheres so that each side of the tetrahedron is a uniform color.	Cmetrick is from eLogIQ. There are 6.9*109 possible positions. Jaap's page eLogIQ has also released the Cmetrick Mini.	I got an Enigma from Norman Sandfield at the 2005 NYPP. He said the reason they've been so hard to find is that the firm that makes them only sells them in bulk for advertising promos. However, recently I've seen a color version for sale at the Puzzle-Shop. [Jaap's Enigma page]
This is a variant of the Enigma, a French puzzle called "Combinescion."	This is the Spectra, by Eng's I.Q. Co. Ltd. 1987. 3072 positions. Jaap's page	Hoppa Gula
Rubik's Clock	Rubik's Rabbits	Rubik's Pen by Ideal from 1982.
This is a Boomdas puzzle from Asia. It is an interesting take on the 2-dimensional sliding puzzle, but using a linking mechanism similar to that of the Muto Cube, and with no frame. One side is numbered 1 to 9, the other has a stylized drawing of a figure.
The Virus	Kinato Hex Pro (Warning: website requires Chinese character set) and Kinato Hex 7	Orbik
Kabalabda Ball See U.S. Design Patent D283523 awarded to Margit C. Balint in Apr. 1986.	Magellan This turns out to be based on the Four-Color Map Theorem. The objective is to ensure that all adjacent areas contain different colors on their wheels, on both sides of the puzzle at once. I have a white version, and a black one in its package.	Labyrint
Gear Up - designed by Oskar van Deventer made by George Miller	Eggcentric - designed by Oskar van Deventer	Writer's Block - designed by Oskar van Deventer, purchased from Bits and Pieces. Produced by RecentToys. Use an included "key" to find a set of moves that extends all the pens, allowing the box to be opened and the pens to be reset. Reminds me of "Lights Out."
A set of Bishop Cubes	Dual Rings, designed by Oskar van Deventer and Bram Cohen, manufactured by Hanayama.	Double Disk from Hog Wild LLC of Portland OR
The Double Think Binary Ring Puzzle from Hog Wild LLC of Portland OR Three layers - in the top and bottom layers, the pairs of interlinked rings turn independently, allowing segments to be mixed between them. In addition, each ring has twelve segments that can be flipped to mix between the layers - such a move also exchanges inside and outside segments from the middle layer. The segments flip smoothly but it is somewhat difficult to rotate the rings.
This is the Jugo Flower, made from metal, from William Strijbos. The Jugo Flower (aka Yugo Flower or Game Jugo) is one of the most rare twisty puzzles - I have read that only seven prototypes were made. You can see examples of the original plastic versions at Hendrik Haak's website. Wil has had the puzzle reproduced in metal. The fifteen petals can each be flipped over around the long axis. There are four marks on the top of the aluminum hub, and only those four petals positioned at the marks are able to flip, simultaneously. All the petals can be rotated around the hub, provided they are properly aligned (the mechanism is somewhat "catchy"), and a new set of four petals can be positioned at the marks. The goal is to scramble the petals, then restore them to all face-up. This puzzle is similar in principle to "Lights Out."

There are many 3-dimensional sliding piece (or sliding block) puzzles. Some consist of a framework or container inside of which are movable colored cubes. In some, there are moving marbles or beads instead of blocks, and in some cases the frame itself can be re-configured. Usually there is a single "hole" which can be thought of as moving around. Sometimes, however, the moving frame accomplishes the permutations of the piece positions and no hole is needed. In yet another sub-category, there are flat plates which can overlay each other. Still another sub-category accomplishes permutation using pieces as segments of interlocking rotating disks.

• Movable Gap, Rigid Frame
• Movable Gap, Movable Frame
• No Gap, Rigid Frame (Interlocking Orbits)
• No Gap, Movable Frame
• Overlapping Plates

Movable Gap, Rigid Frame
Pepsi Can Start with an idea as simple as mapping a 15-like puzzle onto a cylinder. This puzzle has advertised several popular drinks.	Billiards 9-Ball created by Joshua Frankel 3,628,800 positions Jaap's page	Massage Ball Otto Wu patent on 14 Feb 1995 6.1*1019 positions Jaap's page
Vadasz Cube (2x2x2 and 3x3x3 versions) (Also 4^3, which I don't have.)	Minus Cube (Russian)	Varikon black
Peter's Black Hole 5.4*1027 positions Jaap's page Twistypuzzles.com has an article by Ad van der Schagt titled "The History of Sliding Block Puzzles Before Peter's Black Hole" (PDF).	Clark's Cube	I-Qube
This is called the "Switch" or the "Knox Transposition Puzzle." It was issued by Mag-Nif in 1970 and also appears in their "Game Chest" set. The pegs slide in channels in the base. The object of the game is to exchange the sets of colored pegs in 24 moves or less. This actually borders on a non-jumping (exchange-only) type of Peg Solitaire.		Crossteaser 2.7*1011 positions [Crossteaser home page]
Inversion	Mad Marbles	Magic Jack
Tumbler - van Deventer	Pionir Cube	Panex Panex Puzzle resources page at Baxterweb Play a level-4 version online at cheesygames.com.
A cross between the Pionir Cube and Munroe's Marbles, from China.	Orbo, by Popular Playthings; and an Asian clone - the Magic Rainbow Ball by Yong Jun	Rainbow Black Hole
? (Hungarian barrel)	Diamond Bob's Billiards Eight Ball, and Diamond Bob's Diamond 8	Rubik's Brain Racker
Bolaris Designed by Hannu Hjerppe of Finland - website at www.bolaris.fi. Purchased at IPP28 in Prague.	The Bloxbox is notable since the design by Piet Hein is one of the first examples of sliding cubes in a cube. (The first U.S. patent, 416344, for a puzzle like this was awarded to Charles Rice in 1889.)	Cubedron and Cybedron Pantazis Houlis at Mindstrat Puzzles has invented a series of what he calls "Gravity Puzzles." These are edge-matching puzzles encloszed in transparent spheres, where the pieces must be tilted into position so that patterns along the edges match, and a piece flips as it moves from one position to another.
Equal-7 - issued by Recent Toys Invented by Vladimir Krasnoukhov Tilt the cube to slide the dice - four successively harder objectives - make the total on all sides: 10, 11, 12, 7.		Pionir Pyramid, designed and exchanged at IPP32 by Roxanne Wong; made by Mf8
Movable Gap, Movable Frame
Mind Twister aka Wisdom Ball Yang Ju-Hsun 1 June 1993 1.7*1075 positions Jaap's page	Saturn - LD Belgium white and black versions	Tomy Great Gears 1.46*1020 positions Jaap's page
This is called Entrapment. There are also some newer "clones" available. The clear plastic on the old ones is yellowed with age.	Atomic Chaos Christoph Hausammann 2.1*1012 positions Jaap's page	Pakovalec aka Xylinder 1.3*1010 positions Jaap's page
Missing Link and the rarer Limited Edition Marvin Glass & Associates 8.2*1010 positions	Whip-it 5.7*108 positions (for the 3) Jaap's page	Bola RUVI (Whip-it Ball)
Ivory Tower and Babylon Tower both 6 rows x 6 cols 1.9*1040 positions Jaap's page	Varikon 4x4, 5x4 and 7x7 1.4*1014 positions Jaap's page	Backspin and a clone by Jaru Ferdinand Lammertink 6.4*1028 positions Jaap's page
Tomy and Milton Bradley Rack 'Em Up Mizunuma Masanori and Watanabe Hiroyuki 1984 6.3*107 positions	Tomy Row By Row Mizunuma Masanori and Watanabe Hiroyuki 13 Nov 1984 2.8*1031 positions Jaap's page	SpongeBob Puzzlepants 10,080 positions
Russian Flower (the single-petal version), and the Russian Festival Flower with all petals.	Touchdown	Calendar/Bank
Da Vinci's Mona Lisa Codebreaker Twisted Mind - another version, using numbers, and with a transparent case. Twist O Mania	Heartache - Kohner	Double Sliding - Dario Uri
	Here are three different 3-D sliding piece puzzles by Doug Engel: Blocked Barrel 15, Barrel Slide 121, and Barrel Shuttle 11.
The Mini and Braille Eni Puzzles	Capzule	Instant Insanity II - by Winning Moves. This reminds me of the Pakovalec (aka Xylinder).
No Gap, Rigid Frame (Interlocking Orbits)
Equator, and Hungarian Globe 1.1*1025 positions Jaap's page	Hungarian Rings Endre Pap Also pictured - vintage cardboard/wood version Race War Puzzle Between Gold & Silver (I don't have). See U.S. Patent 507215 - Churchill 1893. 7.5*1019 positions Jaap's page	Magic 8
Rubik's Rings 1.9*1014 positions Jaap's page a source	Circle Puzzle 369,600 [Jaap's page]	Rotascope Raoul Henrique Raba 1982 9.1*107 positions I obtained this Rotascope which is a souvenir of the sixth IPP at Jerry Slocum's house. The front contains invitation text and Jerry's home address and phone number, which I don't want to display here. This is a picture of the back - not very puzzling without a pattern to scramble.
Tsukuda Magic Puzzle (Turnstile) Douglas Engel 6.3*109 positions Jaap's page
Lotica	Turn Push	Whirligig
Mad Triad 3.1*1045 (symbols matter) Jaap's Page	Handy Mad Triad 8.3*1023 positions Jaap's page	Rubik's Shells 4.7*1014 positions Jaap's page
Cmetrick Too There are colored disks riding in "craters" in spheres embedded in the frame. The spheres rotate and can exchange disks.	Cmetrick Too Hard In this more difficult version, the centers of the disks are colored, too.	The Arusloky Puzzle
3-layer and 4-layer Leesho (Liso)		Hungarian Olympic Rings
This puzzle is called Moeraki, a name chosen since the shape of its pieces is reminiscent of a formation of spherical boulders found in New Zealand. It was designed by Kasimir Landowski and won an IENA gold medal at the 2008 Nuremberg Trade Fair. You can read about the history of the puzzles and order them online at the Casland Games website. Various virtual examples are available at the website and each physical puzzle includes a disk offering some virtual puzzles. Moeraki is a type of sliding piece puzzle, which I would categorize as of the No Gap, Rigid Frame (Interlocking Orbits) variety. Moeraki No. 3, the one I have, has a square tray and two interlocking oval tracks of pieces in five colors. Moeraki No. 4 has a triangular tray and three interlocking circular tracks of pieces in four colors. I received my No. 3 as a gift at IPP32, on the condition that I review it. Normally, I don't blog or review puzzles per se, but I accepted it since I had planned on buying one anyway. A policy of mine in general is to try not to say anything if I don't have something nice to say (in print, at least). I don't always succeed in keeping to my policy, but happily I will be in no danger here since I honestly like the Moeraki puzzle. The concept of a set of markers riding in interlocking circular or oval tracks, which can be mixed by alternate rotations of the groups of pieces in the different tracks, is certainly not new. An example called "Race War Puzzle Between Gold & Silver" designed by William Churchill was awarded U.S. patent 507215 in October of 1893. More recent examples include the Hungarian Rings puzzle by Endre Pap et al (EP0050755) , and the Magic 8. On the Casland website it is mentioned that Ivan Moskovich also received a patent for a similar idea in 1979 (see U.S. patent 4509756), and is now collaborating with Landowski. Original concept or not, the Moeraki puzzle stands out as a very nice implementation and is probably among the most user-friendly of this class of puzzles in my collection. You can find analysis and solutions of the puzzles at Jaap's Puzzle Page. Jaap gives the total number of possible arrangements for No. 3 as 3,969,069,923,590,200, which, surprisingly, is still larger than the U.S. national debt. Jaap notes that any two diametrically opposed beads will always remain diametrically opposed no matter what moves you make, which I find non-obvious on initial inspection, and fascinating. Dieter Gebhardt has also published some analysis about this type of puzzle. Dieter's article "Rotational Puzzles with Two Tracks and Two Intersections" can be found in the March 2002 issue #57 of the journal of Cubism For Fun (CFF). Dieter's article supplies a notation convention and a general theoretical basis for deducing useful move sequences, and would be of interest to one attempting to gain a more than superficial understanding of such puzzles, although it deals with types of only two intersections. These puzzles may appear to be intrinsically simpler than puzzles such as Rubik's Cube and its ilk, and in truth it is possible to attack them without extensive knowledge or analysis of solution procedures or "operators." And, as with twisty puzzles in general, the large number of possible states is not a reliable indicator of difficulty. However, it should be noted that some piece swaps may require upwards of 100 moves to solve, so patience and perseverance will definitely be assets to the recipient of these puzzles. At his website, Diniar Namdarian gives instructions for accomplishing a last swap of two pieces. When I played with mine, I found the very first challenge to be simply opening the package! The puzzle ships in a cardboard box, which contains a clear plastic case for the puzzle, secured by four clips. A clip can be removed by prying its rounded end away from the case, but the force required makes one leery of breaking something. The puzzle is 135mm square and about 15mm thick. Production values are high - the plastic is good quality and brightly colored. A thoughtful touch is a removable block on the perimeter of the base, which will allow you to extract the sliding pieces from the puzzle in order to effect a brute-force restoration of the solved state, should you deem that necessary. The case also holds a CD-ROM containing additional puzzle software. For me, assuming one enjoys this class of puzzle, two criteria determine whether a puzzle of this type succeeds or fails as a mechanical puzzle worth playing. First, do the pieces remain securely in their tracks? I have had copies of Hungarian-Rings style puzzles where the beads just fell out. I can report that the puzzle is well-engineered and well-built, and the Moeraki beads will not come out by accident. Second, is it easy to rotate the pieces along their tracks, preferably while holding the puzzle in two hands and using only one's thumbs to slide the pieces? Here I can also give the Moeraki a good grade. As with all interlocking-orbit type puzzles, the orbits must be properly aligned so that the pieces do not catch and impede movement. Out of the box, the movement of the Moeraki beads is somewhat stiff, but a benefit is that the tracks of beads do not tend to overshoot on a move, and a simple tilt of the puzzle will not cause unwanted movement. I gave it a shot of CRC Industrial Food-Grade Silicone spray and now the action is silky smooth! I think the Moeraki would make good Christmas presents for the puzzler in your life (or for yourself). See what other puzzlers have had to say about the Moeraki puzzles here, here, and here.
No Gap, Movable Frame
Topspin Ferdinand Lammertink 2.4*1018 positions Jaap's page	Trillion - red, black Gunpei Yokoi 1.0*109 positions Jaap's page	Nintendo Ten Billion Barrel and Club Nintendo Star Barrel Gunpei Yokoi 2.7*1014 positions Solution site here.
I have seen this design from several places. I believe it has been called "Sortospherical."	The Orb[-it] Christopher C. Wiggs and Christopher J. Taylor 7.4*1028 positions Jaap's page	Astrolabacus John D. Harris Pat. 8 Jul 1997 3.6*1016 positions Jaap's page
Port to Port Triple Cross Ferdinand Lammertink Pat. Aug 6 1996 5.9*109 positions Jaap's page	Gripple Murray J. Gould, patented 5 April 1988 2.0*1013 positions Jaap's page	Russian Gripple
Magic Sphere	Rotos Jaap's page	Magic Cross (Zauberkreuz)
Flip Side - Thinkfun	Swissmad 369,600 [Jaap's page]	Tsukuda's Square / "it"
Rubik's Fifteen	Binary Bisect 5 - Doug Engel	Palette 7 - Doug Engel
Elemental: Neon (aka Biohazard) #051, designed and made by David Litwin		Uriblock (A custom version purchased at IPP28 in Prague.)
Tri-Trick	Super Brain Spinner, from FoxMind DieN Logical Toys	One Circle Two Circles, designed, made, and exchanged at IPP32 by Diniar Namdarian
Overlapping Plates
Mind Lock	3-Level Puzzle Dollar Tree	Jushbox

• Hessport's Rubik's Shop
• Hendrik Haak's Puzzle-shop.de
• Uwe Meffert's Site
• Cubikon.de
• Blake O'Hare's Nerd Paradise
• Rubik's Cube Museum
• Christian Eggermont's Square 1 Analysis
• Christoph Lohe's site
• Four-Dimensional Rubik's Cube