HEXAGONAL PRISM NOTES

DOT PATTERNS
(U2 D2' F B' Uv)10 - 6 spot (center 120° rotation of period 3, first spot process)
(F2 U D' L2 Uv)4 U2' D2 - Improved 6 spot, order 3
(F2 U D' L2 Uv2)4 - Another improvement on 6 spot, order 3
(U2 D2' F2 B2 Uv)4 - 6 spot, center 120° rotation of period 3
U2 D2' L2 BR2 U2 D2' F2 B2 U2 D2' R2 BL2 U2 D2' BR2 L2 - 6 spot, face turns only (no rotations)

H PATTERNS
L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 D' - 6 H, order 3
(U2 D' F2 B2)6 - 6 H, order 2

CROSS PATTERNS
D' L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 U2 D2' - 6 cross, order 3
L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 U2 D3 - 6 cross, order 3 improved
(F B' Uv)45 - 6 cross, 2 spike
L2 D2 L2 D2 L2 D2 L2 D' L2 D2 L2 D2 L2 D2 L2 U3 L2 U2' L2 U2' L2 U2' L2 U' L2 U2' L2 U2' L2 U2' L2 U2 D3 (Uv' B2 F2 D2 U2')4 - 6X, order 3
(F2 B2 L2 BR2 R2 BL2 Uv)4 - 6 I pattern

EDGE CYCLES
(R' D' R D2)18 - Edge 5-cycle
R D3 R2 D' R' D R2 D3 R' D2' R' D3 R2 D R' D' R2 D3 R D2 - Edge 5-cycle extended
(R' D' R D' R' D R D' R' D2 R D)6 - Edge double swap in D
(L U L' U L U' L' U L U2' L' U')6 - Central reflection of above
python3 solve-prism-edge2.py -g L,U,F "(L-U, F-U)" - L2 U2 F2 U' F2 L2 F2 L2 F2 L2 U F2 U2' L2 - Edge double swap in U
(U L U L' U L U2' L' U L U L' U L U2' L')3 - Improvement, 3-cycle of edges in U

Superflip / Multiple Edge Flips
(U F U L U' F' U' F L' F2 L2 F L' F' L' F) - 2 flip (U face)
(L' F2 L F L F' L2 F2 L F' U F U L' U' F' U' F L) - 2 flip adapted for F face
(L F L' U)7 - 8 flip
(BR' B' BR D')7 - 8 flip
(F2 R2 Uv2)15 - 2 spike
GAP 2-flip solution: L' U L U' L' U' F U2 L U' F' U' F L' F2 L F U2 L U2' F U F2 L F U' L' F' L F U F U L U' L' F' L2 F U' F' U L' F' L' F L' U L' U' L2 U L U' L' U' F U F' U' L' F' L F U L' U' F' L' F L U L' - 80 moves

OBSERVATIONS / INSIGHTS

6 spot pattern requires all face turns; repeating sequences appear mainly when Uv rotations are used

Centers are fixed under face turns; full prism rotations move them

Commutator solutions exist for small patterns; 6 spot solutions are generally long and non-repeating

GAP solves the hexagonal prism efficiently but outputs very long sequences; conversion to SGN may need special handling for two-letter face names (BR, BL)

Superflip and supertwist patterns are part of the center of the hexagonal prism group (6 elements): Identity (solved), Superflip (all edges flipped), Supertwist+ (all corners twisted clockwise), Supertwist- (all corners twisted counterclockwise), Superflip + Supertwist+, Superflip + Supertwist-