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180 Cube
Above:Solved
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This 3x3x3 allows only halfturns for one axes. Another puzzle deemed impossible before.

This puzzle was designed ba Tom van der Zanden but requested by Andreas Nortmann to complete another series of 3x3x3-variants.

The standard 3x3x3 allows 90°-moves for all three axis.
The HalfTurnCube (first made by Hidetoshi Takeji; later remade by Oskar van Deventer) allows only 180° on all three axes.
The Slim Cube and the Tie Cube (see the museum for both) both allow 90° on one axis and only 180° on the other two.
This new creation is the missing one which allows 90° on two axis and only 180° on the third axis.
These four subgroups of the 3x3x3 represent the four phases of Thistlethwaite's algorithm. Search the internet for more detail.

The other two versions can be made by bandaging a 5x5x5 or a 7x7x7 but this new one is impossible with bandaging alone because of geometric reasons. For similar reasons it was impossible to make the restriction visible in the puzzles outer appearance. The creator had to introduce additional internal parts to implement these restrictions. In theory this technique could be used (but has not yet) to block jumbling moves.

The number of permutations is 1/2048 of the number of the unrestricted 3x3x3. This is explained by the fact that edges can't be flipped without the third axes. Interestingly the 180°-moves are not needed at all. If the restricted axes were totally blocked the number of permutations would be equal to the number of this variant.
Edge length: 58 mm
Weight: 60 grams


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Contributors

Thank you to the following people for their assistance in helping collect the information on this page: Andreas Nortmann.

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