Central-Cut Shallow Face-Turning Rhombic Dodecahedron without jumbling simulator and solver

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Info

Pieces

Type	Count	Stickers	Positions	Orientation (physical)	Orientation (visual)
7	24	1	24	1	1
8	24	1	24	1	1
8	24	1	24	1	1
9	24	1	24	1	1
9	24	1	24	1	1
9	24	1	24	1	1
10	24	1	24	1	1

One row per orbit. Orientation counts are per position; multiple values mean positions differ.

Stickers

168

Axes

618 cut planes across them

Solver

Available

Distinct-piece states

≈ 2.30 × 10¹⁶³553,044,040,942,079,343,709,175,601,064,838,198,829,741,501,148,195,221,882,569,115,141,415,851,782,534,978,063,124,973,456,900,809,662,814,858,287,252,845,756,000,077,364,215,152,640,000,000,000,000,000,000,000,000,000 arrangements of the stickers the moves reach (Schreier–Sims)÷ 24 turns of the whole puzzle= 23,043,501,705,919,972,654,548,983,377,701,591,617,905,895,881,174,800,911,773,713,130,892,327,157,605,624,085,963,540,560,704,200,402,617,285,761,968,868,573,166,669,890,175,631,360,000,000,000,000,000,000,000,000,000Tracks individual sticker identities, even on identical-looking pieces; whole-puzzle rotations are identified. Invisible rotations of a piece and internal pieces are not counted.

Indistinguishable arrangements

19,342,813,113,834,066,795,298,8162! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! × 2! = 19,342,813,113,834,066,795,298,81684 groups of visually interchangeable pieces within their movement orbits, using the original stickers.Counts all permutations within these groups, without checking which combinations are reachable. Internal pieces are excluded because the state count tracks stickers only.

Visually distinct states

Not computedVisually distinct states = distinct-piece states ÷ reachable indistinguishable arrangements.Reachable indistinguishable arrangements = 19,342,813,113,834,066,795,298,816 × reachable fraction.The reachable fraction accounts for restrictions such as permutation parity. Computing the correct fraction and the final visual state count is not yet implemented.

Put together at random

1 in 64 reaches the original sticker identities24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ = 35,394,818,620,293,077,997,387,238,468,149,644,725,103,456,073,484,494,200,484,423,369,050,614,514,082,238,596,039,998,301,241,651,818,420,150,930,384,182,128,384,004,951,309,769,768,960,000,000,000,000,000,000,000,000,000 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 553,044,040,942,079,343,709,175,601,064,838,198,829,741,501,148,195,221,882,569,115,141,415,851,782,534,978,063,124,973,456,900,809,662,814,858,287,252,845,756,000,077,364,215,152,640,000,000,000,000,000,000,000,000,000 arrangements the moves reach = 64This uses distinct piece identities; the chance of reaching a visually solved state may be higher.

Moves