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Vertex-turning irregular triangular dipyramid with 2 turning axes.

Biaxe was based on the Constellation Six (from the same inventor) with the aim to get regular pentagons instead of circles in the face centers. This was only possible by changing the angle between turning axes from 120 to 130.42. As a cost, the puzzle has lost its rotational symmetry and one working axis.

The puzzle has 73286239402465689600000000000 = 73.3*10^27 permutations if all pieces are considered distinguishable and their orientations visible.
Compared with the number available if the puzzle can be disassembled and reassembled there are some restrictions:
-The permutation of the last three pentagons is determined by the first three.
-The orientation of the last pentagon is determined by the other five.
-The triangles fall into two subsets.
-Both subsets of triangles allow only even permutations.
-The edges can't be flipped.
-If the orientation of the tips is odd the permutations of edges and pentagons have to be odd too.
Stickered as shown here the puzzle has 2544661090363392000000 = 2.54 *10^21 permutations.



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


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