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The Dino CubeDino Cube (6 colours)
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Dino Cube (paper version)
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is a
cubic Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system w ...
twisty puzzle Twist may refer to: In arts and entertainment Film, television, and stage * ''Twist'' (2003 film), a 2003 independent film loosely based on Charles Dickens's novel ''Oliver Twist'' * ''Twist'' (2021 film), a 2021 modern rendition of ''Olive ...
in the style of the Rubik's Cube. It was invented in 1985 by Robert Webb, though it was not mass-produced until ten years later. It has a total of 12 external movable pieces to rearrange, compared to 20 movable pieces on the Rubik's Cube.


History

Robert Webb designed and made the first prototype of what would become the Dino Cube in 1985; his original prototype was made entirely out of
paper Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, Textile, rags, poaceae, grasses, Feces#Other uses, herbivore dung, or other vegetable sources in water. Once the water is dra ...
. Since then the puzzle was reinvented twice, but full mass production of the puzzle did not start until 1995. The first mass-produced version had pictures of
dinosaur Dinosaurs are a diverse group of reptiles of the clade Dinosauria. They first appeared during the Triassic Geological period, period, between 243 and 233.23 million years ago (mya), although the exact origin and timing of the #Evolutio ...
s depicted on each piece, which led to the adoption of the puzzle's current name of ''Dino Cube''.Dino Cube (with dinosaurs)
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It is not known what the puzzle had been called before this dinosaur version was introduced. The later versions, however, adopted the practice of using standard single-colour stickers, in common with most other twisty puzzles.


Overview

The Dino Cube is a twisty puzzle in the shape of a cube. It consists of 12 movable pieces, all of which are located on the edges of the cube. The puzzle can be thought of as twisting around its corners: each ''move'' changes the position of three edge pieces adjacent to the same corner, by rotating them around that corner. There are in fact eight more "hidden" pieces inside the puzzle, which are located at the corners and are fixed to the puzzle's core; these pieces only become visible in the middle of a move. The vast majority of mass-produced Dino Cubes have the standard six-colour scheme, with one colour on each face of the cube in the solved state. This is in common with most other cubic twisty puzzles, including the Rubik's Cube. However, a few versions with other colour schemes also exist, including one with four colours (where each colour is centred around one corner of the cube in the solved state), and one with just two colours (where each colour present on half of the puzzle).Dino Cube (2 colours)
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The purpose of the puzzle is to scramble the colours and then restore them to their original configuration, usually of one colour per face.


Solving

The Dino Cube is considered to be one of the easiest twisty puzzles to solve. One of the things that make it so easy is the fact that each move only affects three edge pieces at once, which means it is easy to solve one part of the puzzle without disturbing what is already solved. In addition, each edge piece only has one possible orientation, meaning that if a given piece is in the correct position, it will always be orientated the correct way as well. Therefore, the solver never has to worry about changing the orientation of any pieces. Although not obvious at the first glance, the six-colour Dino Cube actually has two distinct configurations that represent a solved puzzle. The two solutions are mirror images of each other and the only visual difference between them is their colour schemes; for example, one solution has the colours ''Blue - Yellow - Red'' going
clockwise Two-dimensional rotation can occur in two possible directions or senses of rotation. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands relative to the observer: from the top to the right, then down and then to ...
around one vertex, while in the other these colours go anticlockwise. Mathematically, the puzzle is identical to Hoberman's BrainTwist, which is a
tetrahedral In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet ...
puzzle that can "flip" inside out and reveal another set of four faces. Like the Dino Cube, The BrainTwist has twelve movable pieces, and each move rotates three pieces around one corner. It also likewise has two distinct solutions: one with the same colour on each of the faces and one with the same colour at each of the corners.


Number of combinations

The Dino Cube has twelve edge pieces. This means naturally there are twelve possible positions for the first given edge, however due to the lack of visible fixed "reference" pieces, all of these positions are rotationally symmetrical to each other. Therefore, the position of the first given edge is not taken into account. The remaining eleven edge pieces can be permutated in 11 ! different ways, relative to the first edge piece. Only even permutations of these pieces are possible (i.e. it is impossible to swap one pair of pieces while leaving the rest of the puzzle solved), which divides the limit by 2. The edge pieces cannot be flipped or misorientated (See ''Solving''), therefore this is also not taken into account. The total number of possible combinations on the six-colour Dino Cube is therefore equal to: :\frac = 19 958 400 This number is low compared to the number of combinations of the Rubik's Cube (which has over 4.3×1019 combinations) but still larger than many other puzzles in the Rubik's Cube family, notably the
Pocket Cube The Pocket Cube (also known as the Mini Cube and Twizzle) is a 2×2×2 combination puzzle invented in 1970 by American puzzle designer Larry D. Nichols. The cube consists of 8 pieces, which are all corners. History In February 1970, Larry D. ...
(over 3.6 million combinations) and the
Pyraminx The Pyraminx () is a regular tetrahedron puzzle in the style of Rubik's Cube. It was made and patented by Uwe Mèffert after the original 3 layered Rubik's Cube by Ernő Rubik, and introduced by Tomy Toys of Japan (then the 3rd largest toy c ...
(just over 930 thousand combinations, excluding rotations of the trivial tips).


Optimal solutions

The number of possible of configurations, 19 958 400, is sufficiently small to allow a computer search for optimal solutions. The table below summarises the result of such a search, stating the number ''p'' of positions that require ''n'' moves to solve the six-colour Dino Cube (''p2'' for either solution, ''p1'' for one specific solution): This table shows that the
God's Number God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It refers to any algorithm which produces a solution having the f ...
of the six-colour Dino Cube is 10 (when solving into either solution) or 11 (when solving into one specific solution).


Variations

Several shape modifications of the Dino Cube exist. These include the aforementioned '' BrainTwist'', in the shape of a tetrahedron that can flip inside out, the ''Platypus'', whose shape is also based on a tetrahedron, the ''Redi Cube'', a cubic version with shallower cuts, and the ''Rainbow Cube'', in the shape of a
cuboctahedron A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertex (geometry), vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edge (geometry), edges, each separating a tr ...
. The latter three puzzles, unlike the Dino Cube, also have their "core" pieces visible.


See also

*
Skewb The Skewb () is a combination puzzle and a mechanical puzzle similar to the Rubik's Cube. It was invented by Tony Durham and marketed by Uwe Mèffert. Although it is cubical, it differs from the typical cubes' construction; its axes of rotatio ...
* BrainTwist *
Pyraminx Duo The Pyraminx Duo (originally known as ''Rob's Pyraminx'') is a tetrahedral twisty puzzle in the style of the Rubik's Cube. It was suggested by Rob Stegmann, invented by Oskar van Deventer, and has now been mass-produced by Meffert's.
*
Pocket Cube The Pocket Cube (also known as the Mini Cube and Twizzle) is a 2×2×2 combination puzzle invented in 1970 by American puzzle designer Larry D. Nichols. The cube consists of 8 pieces, which are all corners. History In February 1970, Larry D. ...
*
Skewb Diamond The Skewb Diamond is an octahedron-shaped combination puzzle In mathematics, a combination is a selection of items from a set (mathematics), set that has distinct members, such that the order of selection does not matter (unlike permutation ...


References

{{Rubik's Cube Mechanical puzzle cubes