The Hoberman BrainTwist is a 3D mechanical puzzle designed and marketed by Chuck Hoberman's company Hoberman Designs. The puzzle is in the same family as the Rubik's Cube and other puzzles that involve manipulating and scrambling colored face elements with the goal of returning them to their original order from a randomized state, commonly called twisty puzzles. This puzzle is unique in that in addition to solving one set of tetrahedral faces the puzzle can be flipped inside-out through an intermediate stellated shape to reveal another (dual) tetrahedron with a set of 4 different colored faces. The puzzle also has an alternate solution in which the apices are each a uniform color.
The BrainTwist consists of 12 colored triangular elements each with a detent to aid in aligning the apices of the puzzle after rotating them. There are eight colors in the puzzle: red, orange, yellow, light and dark green, blue, violet and magenta. Each of the 12 basic units has a unique combination of two of the colors - one per side. In the tetrahedral configuration each apex consists of 3 such elements. Each face of the tetrahedron is also composed of 3 basic color elements.
Manipulation
Hoberman BrainTwist Purple face
When folded into the tetrahedral arrangement, each of the 4 apices (corners) can be rotated so that the elements are oriented toward one of 3 faces. The puzzle locks into position when an element is aligned with a face. 3 clockwise rotations or 3 counter clockwise rotations returns the apex to its original orientation.
By lifting the three elements of a face and bringing them towards each other, the entire puzzle opens up into the stellated form shown above. Continuing the "flip" move completely inverts the tetrahedron into its dual tetrahedron. The elements that were face elements now comprise the apices of the new tetrahedron and vice versa.
By performing arbitrary combinations of flips and rotations the pieces can be scrambled almost completely. The only restriction is that the mechanism prevents a 180 degree rotation of a piece so that the colors on the obverse and reverse of each piece never interchange. Consequently, the two tetrahedrons are restricted to show only 4 of the eight colors at a time. There is a red-orange-violet-magenta (ROVM) tetrahedron and a yellow-blue-light green-dark green (YBLD) tetrahedron.
Solutions
A clue to solving a shuffled BrainTwist puzzle is to examine the stellated configuration. It is possible to solve for the ROVM tetrahedron while leaving the YBLD tetrahedron shuffled and vice versa. The only way to make sure the puzzle is completely solved is to check that the adjacent colors make sense in the stellated configuration
The puzzle is chiral: if one tries to build the faces one at a time then one might end up putting colors clockwise that should have been placed counterclockwise. The puzzle can only be solved if, for example, facing the Red face in stellated form the Blue, LightGreen, and Yellow faces proceed clockwise in that order (BLY). Sometimes this may not work.
In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.
The Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. Rubik's Cube won the 1980 German Game of the Year special award for Best Puzzle. As of January 2009, 350 million cubes had been sold worldwide, making it the world's top-selling puzzle game. It is widely considered to be the world's best-selling toy.
In geometry, a tetrahedron, also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces.
The CMYK color model is a subtractive color model, based on the CMY color model, used in color printing, and is also used to describe the printing process itself. CMYK refers to the four ink plates used in some color printing: cyan, magenta, yellow, and key (black).
In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges. It can be constructed by truncating all 4 vertices of a regular tetrahedron at one third of the original edge length.
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 Erno Rubik, and introduced by Tomy Toys of Japan in 1981.
The Square-1, also known as Back to Square One and Cube 21, is a puzzle similar to the Rubik's Cube. Its distinguishing feature among the numerous Rubik's Cube variants is that it can change shape as it is twisted, due to the way it is cut, thus adding an extra level of challenge and difficulty. The Super Square One and Square Two puzzles have also been introduced. The Super Square One has two additional layers that can be scrambled and solved independently of the rest of the puzzle, and the Square Two has extra cuts made to the top and bottom layer, making the edge and corner wedges the same size.
The Rubik’s Cube group is a group that represents the structure of the Rubik's Cube mechanical puzzle. Each element of the set corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be represented, but also any position of the cube as well, by detailing the cube moves required to rotate the solved cube into that position. Indeed with the solved position as a starting point, there is a one-to-one correspondence between each of the legal positions of the Rubik's Cube and the elements of . The group operation is the composition of cube moves, corresponding to the result of performing one cube move after another.
A regular tetrahedron has 12 rotational symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.
In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra, with Schläfli symbol {3,5⁄2} and Coxeter-Dynkin diagram of . It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence.
The compound of five tetrahedra is one of the five regular polyhedral compounds. This compound polyhedron is also a stellation of the regular icosahedron. It was first described by Edmund Hess in 1876.
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In geometry, a quasiregular polyhedron is a uniform polyhedron which has exactly two kinds of regular faces, which alternate around each vertex. They are edge-transitive, and hence a step closer to regular polyhedra than the semiregular, which are merely vertex-transitive. Their dual figures are also sometimes considered quasiregular, except that they are edge-transitive, are face-transitive, and alternate between two regular vertex figures.
The Pyramorphix, also called Pyramorphinx, is a tetrahedral puzzle similar to the Rubik's Cube. It has a total of 8 movable pieces to rearrange, compared to the 20 of the Rubik's Cube. Though it looks like a simpler version of the Pyraminx, it is an edge-turning puzzle with the mechanism identical to that of the Pocket Cube.
In geometry, a Goursat tetrahedron is a tetrahedral fundamental domain of a Wythoff construction. Each tetrahedral face represents a reflection hyperplane on 3-dimensional surfaces: the 3-sphere, Euclidean 3-space, and hyperbolic 3-space. Coxeter named them after Édouard Goursat who first looked into these domains. It is an extension of the theory of Schwarz triangles for Wythoff constructions on the sphere.
The Helicopter Cube is a Rubik's Cube-like puzzle invented by Adam G. Cowan in 2005 and built in 2006. It is also in the shape of a cube. At first glance, the Helicopter Cube may seem like a combination of the 2x2x2 and the Skewb, but it actually cuts differently, and twists around cube edges rather than cube faces. The purpose of the puzzle is to scramble the colors, and then restore them back to their original state of a single color per face.
The Pyraminx Duo 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.
The Floppy Cube is a cuboidal twisty puzzle in the style of the Rubik's Cube. It was originally invented by Katsuhiko Okamoto and mass-produced by Gentosha Toys, although several other companies have since mass-produced it as well.
The Gear Cube is a 3-D combination puzzle designed and created by Dutch puzzle maker Oskar van Deventer. It was initially produced by Shapeways in 2009 and known as "Caution Cube" due to the likeliness of getting fingers stuck between the gears while speedcubing. Later, in 2010, it was mass-produced by Meffert's as the "Gear Cube".
The Dino Cube is a cubic twisty puzzle in the style of the Rubik's Cube. It was invented in 1985 by Robert Webb, however 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.
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