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This puzzle pretends to be based on a 4D polytope but it is not. Instead it is a cube with its antipodes connected.
Imagine a cube made of edges and their antipodes are also connected. This is in fact, the complete bipartite graph K4,4.
The goal of this puzzle is swap the positions of the blue and black rods (which form a blue and black square) with the positions of the red and yellow rods (half of which connect the squares and the other half are antipodes). Although it is not related to any polytope (higher than 3D) it has valency equal to four, so it can easily be labelled as a puzzle based on 4D symmetry. It is one of the most difficult puzzles, but for tanglement, not mathematical reasons.
It looks similar to Houlis Cube but is not identical.
The movement is done by elongating and contracting the telescopic rods such that corners pass through the faces.
Thank you to the following people for their assistance in helping collect the information on this page: Andreas Nortmann.
This puzzle can be found in collections of these members:
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