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Two three-fold deeper-than-origin turns.
The inventor presented this puzzle together with the Binary Dodecahedron. He figured it would be interesting if he could design that two-fold shallower-than-origin turn into a three-fold axis instead.
Unlike the predecessor the Binary Gem no longer has the shape of a platonic solid.
This puzzle seems superficially related to the Trapentrix at first, as both have two three-fold axes with pentagonal parts in them, but the underlying geometry is not the same.
Edge length (pentagonal sides): 24 mm
The puzzle has 7433565325148475060387840000000000 = 7.43*10^33 permutations if all pieces are considered distinguishable. Due to the limited number of moves it has a huge number of restrictions:
-The largest triangles allow only even permutations.
-The pentagons allow only even permutations.
-The orientation of the last pentagon is determined by the first three.
-The long triangles (adjacent to the largest ones) allow only even permutations.
-The large corners allow only even permutations.
-The orientation of the large corners is determined by their position.
-The sharp triangles inside of the pentagons allow only even permutations.
-The paired triangles inside the pentagons allow only even permutations.
The orientation of the unmoveable corner is coupled to both (1.) the permutation of the largest triangles and (2.) the permutation of the pentagons.
Stickered as shown here the puzzle has 34414654283094791946240000000 = 34.4*10^27 permutations.
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Binary Gem
