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A truncated Kleetopes, in this case a Truncated Triakis Tetrahedron.
The Alphaminx uses a 14-armed core, similar to the mechanism of the Concept 11 and DaYan Gem III puzzles but the Alphaminx was designed from scratch. It turns in three different ways as shown in the images and changes shape if 90�-turns are performed. The first and second demonstrated type of turn allow 120�-turns and reproduce the turns of the hexagons of Concept-11. The edge turns allow 90�-turns and reproduce the turns of the squares of the Concept-11.
It is the beginning of a series based on the geometries of Truncated Kleetopes. Its name was derived from the fact that it was meant to be the first of series. The following puzzles would have been named Betaminx, Gammaminx, etc.
Edge length: 26 mm
The puzzle can only be analyzed with GAP if it is strictly doctrinaire: Hexagons turns in steps of 120° and Edges in steps of 180°.
The puzzle has 10340341345600777455860582852811816960000000000 = 10.3*10^45 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 small triangles (adjacent the hexagons) are split into two sets.
-The edges are split into two sets.
-The permutation of one set of small triangles (those with three stickers) is always even.
-The permutations of both sets of edges always have the same parity.
-One subset of small triangles (those with one sticker), the edges and the large triangles (in the middle of the pentagons) always have the same parity. (Factor 4)
Stickered as shown here the puzzle has 15957316891359224468920652550635520000000000 = 16.0*10^42 permutations.
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Thank you to the following people for their assistance in helping collect the information on this page: Chandler Griscom.
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