6x6x6 simulator and solver

Info

Pieces

Type	Count	Stickers	Positions	Orientation (physical)	Orientation (visual)
5	24	1	24	1	1
6	24	1	24	1	1
6	24	1	24	1	1
7	24	2	24	1	1
7	24	1	24	1	1
8	24	2	24	1	1
9	8	3	8	3	3

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

Stickers

216

Axes

315 cut planes across them

Solver

Available

Distinct-piece states

≈ 1.31 × 10¹⁴⁸314,400,584,525,598,793,267,442,224,243,065,087,614,921,141,588,495,489,391,257,470,548,807,254,229,625,219,119,563,974,615,817,890,733,502,415,818,587,095,317,872,640,000,000,000,000,000,000,000,000 arrangements of the stickers the moves reach (Schreier–Sims)÷ 24 turns of the whole puzzle= 13,100,024,355,233,283,052,810,092,676,794,378,650,621,714,232,853,978,724,635,727,939,533,635,592,901,050,796,648,498,942,325,745,447,229,267,325,774,462,304,911,360,000,000,000,000,000,000,000,000Tracks 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

1,333,735,776,850,284,124,449,081,472,843,7764! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! × 4! = 1,333,735,776,850,284,124,449,081,472,843,77624 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 = 1,333,735,776,850,284,124,449,081,472,843,776 × 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 48 reaches the original sticker identities8!·3⁸ · 24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ · 24!·1²⁴ = 15,091,228,057,228,742,076,837,226,763,667,124,205,516,214,796,247,783,490,780,358,586,342,748,203,022,010,517,739,070,781,559,258,755,208,115,959,292,180,575,257,886,720,000,000,000,000,000,000,000,000 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 314,400,584,525,598,793,267,442,224,243,065,087,614,921,141,588,495,489,391,257,470,548,807,254,229,625,219,119,563,974,615,817,890,733,502,415,818,587,095,317,872,640,000,000,000,000,000,000,000,000 arrangements the moves reach = 48This uses distinct piece identities; the chance of reaching a visually solved state may be higher.

Moves

Face turns

Well known algorithms and patterns

Patterns

Checkerboard — four sides

(2L2 4L2 R2) (2B2 4B2 F2) (2L2 4L2 R2) (2D2 4D2 U2)

Generalized alternating-layer checkerboard, verified against every sticker on each face. Even cubes have four checkered faces and two solid faces.

Outer-layer Superflip

U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2

Outer-layer adaptation of the published 3×3 Superflip: all edge rows flip in place, corners stay solved, center colors stay on their faces.

Outer-layer cube in a cube

F L F U' R U F2 L2 U' L' B D' B' L2 U

Outer-layer adaptation of the published 3×3 cube-in-a-cube pattern.

Six spots

U D' R L' F B' U D'

Outer-layer adaptation of the published 3×3 Six spots. The larger interior squares form the spots.