BrainTwist

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. 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.

Design

Basic Elements

The BrainTwist consists of 12 colored triangular elements each with a notch to aid in turning the apices of the puzzle. There are eight colors in the puzzle - Red, Orange, Yellow, LightGreen, DarkGreen, 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.

Manipulating the Puzzle

Rotating

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 clocwise rotations returns the apex to its original orientation.

Flipping

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.

huffling

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-LightGreen-DarkGreen (YBLD) tetrahedron.

Solutions

mall Hint

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. The only way to make sure the puzzle is completely solved is to check that the adjacent colors make sense in the stellated configuration

Bigger Hint

The puzzle is chiral: this means if you try to build the faces one at a time you might end up putting colors clockwise that should have been placed counterclockwise. The puzzle is set up so that this will not work! It can only be solved if (facing the red face in stellated form) the Blue, LightGreen, and Yellow faces are proceed clockwise in that order (BLY)

Face to Corner

There is a beautiful algorithm to switch from the "faces" solution to the "corners" solution, or vice versa.
#Turn all corners 1 step clockwise
#Flip
#Turn all corners 1 step counterclockwise
#Flip
#Turn all corners 1 step clockwise
#Done

Related puzzles

*Alexander's Star
*Domino
*Enigma
*K-Ball
*Masterball
*Missing Link
*Octahedron
*Pyraminx
*Pyramorphix
*Rubik's Cube
*Rubik's Revenge
*Rubik's Magic
*Skewb Diamond
*Tetraminx
*Whip-It