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Gem-45
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A face turning cube which allows 45�-turns and is doctrinaire.

This is a cubic puzzle which allows 45-degree face turns. Due to its fudged geometry, it behaves like a doctrinaire puzzle. Related puzzles include the Sphere 612 (the "bandaged" version of this puzzle), the Skyglobe (the tetrahedral geometry equivalent of this puzzle), and Evgeniy Grigoriev's recently presented Kaleidoscope Ball which is the tetrahedral equivalent of the Sphere 612. All three have their own entries in the museum.
The inventor originally planned a different colour scheme for this puzzle, but the pentagons had a tendency to spin in place due to their nearly circular shape which makes this impossible. Image 4 shows this alternative colour scheme.

The puzzle has 20722614570507960611564888515068077693747876747882271047255855563228457587478840108440383302932429130135732251068193384825419830477694357101471434148836331027386089161044576957241855710286634212680135686327029703671191912645694324736000000000000000000000000000000000000000000000000000000000000000
= 20,7*10^294 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 these restrictions:
-The orientation of the last rhombus is determined by the other thirtyfive.
-The orientation of the last pentagon is determined by the other twentythree.
-The triangles allow only even permutations.
-The permutations of the rhombi and pentagons and the orientations of the octogons always have the same parity.

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