page_title: Skewb Ultimate
section_title: Number of combinations
hierarchical_section_title: Skewb Ultimate / Number of combinations
caption_attribution_description: English: Ultimate Skewb puzzle with Rhombus shaped faces
context_page_description: The Skewb Ultimate, originally marketed as Pyraminx Ball, is a twelve-sided puzzle derivation of the Skewb, produced by famous toy-maker Uwe Meffert. Most versions of this puzzle are sold with six different colors of stickers attached, with opposite sides of the puzzle having the same color; however, some early versions of the puzzle have a full set of 12 colors.
context_section_description: The Skewb Ultimate has 6 large "edge" pieces and 8 smaller corner pieces. Only even permutations of the larger pieces are possible, giving 6!/2 possible arrangements. Each of them has two possible orientations, although the orientation of the last piece is determined by the orientations of the other pieces, hence giving us a total of 2⁵ possible orientations.
  The positions of four of the smaller corner pieces depend on the positions of the other 4 corner pieces, and only even permutations of these positions are possible. Hence the number of arrangements of corner pieces is 4!/2. Each corner piece has 3 possible orientations, although the orientation of the last corner is determined by the orientations of the other corners, so the number of possible corner orientations is 3⁷. However, the orientations of 4 of the corners plus the position of one of the other corners determines the positions of the remaining 3, so the total number of possible combinations of corners is only .
  Therefore, the number of possible combinations is:
caption: Rhombic dodecahedron version of the puzzle with equivalent mechanism.
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