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Hoberman's Brain Twist
Above:Solved
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A vertex turning tetrahedron that can turn insideout

http://hoberman.com/fold/Braintwist/braintwist.htm

It has two solved states. Because of the dual flip and rotation moves, it is a lot of fun to play. Solvingwise it is equivalent to the Dino Cube, Rainbow Cube and many others, although it uses a completely different implementation.

Beautiful to look at and fun to play with!

The puzzle consists of a black central section shaped into three rings- one along each x,y,z axis- that form the outline of a sphere. Each arc is the base of a petal (making for 12 petals) and they are geared together at the crossing points.

This lets the puzzle flip into a closed tetrahedron position. Open it up, keep opening, and it flips closed into the "inverted" tetrahedron position.

When it is in a closed positon, you can rotate each of the four vertices. Opening, closing, and turning let you move the petals around into a 'matched' solution.

There are two ways to match it. One is to make all faces the same color. The other is to make all corners the same color (the pictures taken here show matched corners) Since there are two solutions, you can always 'match' it without 'mixing' it first- simply go from one solved solution to the other.

Solving it is a relatively straightforward process, with only one problem- keeping track of your place! When you are matching it, consider the open 'star' position your 'home' position- it's the only way to match both "sides" at once.

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