Play a virtual Master Face-Turning Rhombic Dodecahedron in your browser. Master Face-Turning Rhombic Dodecahedron is a jumbling puzzle.
Info
Pieces
Type
Count
Stickers
Positions
Orientation (physical)
Orientation (visual)
0
1
0
1
24
1
1
12
0
12
2
1
2
24
0
24
1
1
3
8
0
8
3
1
3
24
0
24
1
1
4
24
0
24
1
1
4
24
0
24
1
1
4
6
0
6
4
1
5
24
0
24
1
1
5
24
0
24
1
1
5
24
0
24
1
1
5
24
0
24
1
1
6
8
3
8
3
3
6
24
1
24
1
1
6
24
1
24
1
1
6
24
0
24
1
1
6
12
1
12
2
1
7
24
2
24
1
1
7
24
1
24
1
1
8
6
4
6
4
4
One row per orbit. Orientation counts are per position; multiple values mean positions differ. Jumbling: counts cover placements discovered so far, not all possible placements.
Stickers
180
Axes
624 cut planes across them
Turns
Jumbling
Solver
Not availableSolving is not available while jumbling moves are enabled.
Distinct-piece states
Not computedIt is worked out from the same model of the puzzle the solver uses.
Indistinguishable arrangements
68,719,476,7362! × 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! = 68,719,476,73636 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 = 68,719,476,736 × 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.