Notation

SSE 3x3 Megaminx

The SSE 3x3 Megaminx (Superset ENG) is a notation for dodecahedrons with 3 layers, such as the Megaminx. The notation is based on the English language. It supports 72°, and 144° twists of the layers of the dodecahedron. A whole dodecahedron can be rotated along its face axes. Permutation and orientation changes of individual dodecahedron parts can be specified using permutation cycles.

Face names and opposite faces

The 6 faces in the upper half of the dodecahedron are right, front, left, up left, up right and up. The 6 faces in the lower half are down right, down left, back left, back, back right and down. Each face has one opposite face, there are 6 pairs in total:

U (up), D (down)
R (right), BL (back left)
F (front), B (back)
L (left), BR (back right)
UL (up left), DR (down right)
UR (up right), DL (down left)

Face twists: R, R', R2, R2'

Move Right Front Left Up
Left
Up
Right
Up
○○● +72° R F L UL UR U
○○● -72° R' F' L' UL' UR' U'
○○● +144° R2 F2 L2 UL2 UR2 U2
○○● -144° R2' F2' L2' UL2' UR2' U2'
Move Down
Right
Down
Left
Back
Left
Back Back
Right
Down
○○● +72° DR DL BL B BR D
○○● -72° DR' DL' BL' B' BR' D'
○○● +144° DR2 DL2 BL2 B2 BR2 D2
○○● -144° DR2' DL2' BL2' B2' BR2' D2'

Clockwise 72° twists of the 12 faces of the dodecahedron are described by the capital letters: R, F, L, UL, UR, U DR, DL, BL, B, BR, D (right, front, left, up left, up right, up, down right, down left, back left, back, back right, down). For example, R rotates the right face in clockwise direction as seen from the right face.

Counterclockwise twists and rotations are described by appending the inversion operator ' to a move: R', U', F', ...

In environments, where the ' character can not be used, the character - can be used as an alternative inversion operator.

144° twists and rotations are described by appending the number 2 to a move: R2, U2, F2, ...

216° twists: To keep scripts short, R3, U3, F3, ... are never used, because they are equivalent to R2', U2', F2', ...

288° twists: To keep scripts short, R4, U4, F4, ... are never used, because they are equivalent to R', U', F', ...

Tier twists: TR, TR', TR2, TR2'

Move Right Front Left Up
Left
Up
Right
Up
○●● +72° TR TF TL TUL TUR TU
○●● -72° TR' TF' TL' TUL' TUR' TU'
○●● +144° TR2 TF2 TL2 TUL2 TUR2 TU2
○●● -144° TR2' TF2' TL2' TUL2' TUR2' TU2'
Move Down
Right
Down
Left
Back
Left
Back Back
Right
Down
○●● +72° TDR TDL TBL TB TBR TD
○●● -72° TDR' TDL' TBL' TB' TBR' TD'
○●● +144° TDR2 TDL2 TBL2 TB2 TBR2 TD2
○●● -144° TDR2' TDL2' TBL2' TB2' TBR2' TD2'

Twists which go two layers deep (tier twists) are described by prepending the letter T to a face twist: TR, TU', TF2. For example, TR rotates the outer two layers in clockwise direction as seen from the right face.

Mid-layer twists: MR, MR', MR2, MR2'

Move Right Front Left Up
Left
Up
Right
Up
○●○ +72° MR MF ML MUL MUR MU
○●○ -72° MR' MF' ML' MUL' MUR' MU'
○●○ +144° MR2 MF2 ML2 MUL2 MUR2 MU2
○●○ -144° MR2' MF2' ML2' MUL2' MUR2' MU2'
Move Down
Right
Down
Left
Back
Left
Back Back
Right
Down
○●○ +72° MDR MDL MBL MB MBR MD
○●○ -72° MDR' MDL' MBL' MB' MBR' MD'
○●○ +144° MDR2 MDL2 MBL2 MB2 MBR2 MD2
○●○ -144° MDR2' MDL2' MBL2' MB2' MBR2' MD2'

Twists of the layer in the middle (mid-layer twists) are described by prepending the letter M to a face twist: MR, MU', MF2. For example, MR rotates the middle layer in clockwise direction as seen from the right face.

Slice twists: SR, SR', SR2, SR2'

Move Right Front Left Up
Left
Up
Right
Up
●○● +72° SR SF SL SUL SUR SU
●○● -72° SR' SF' SL' SUL' SUR' SU'
●○● +144° SR2 SF2 SL2 SUL2 SUR2 SU2
●○● -144° SR2' SF2' SL2' SUL2' SUR2' SU2'
Move Down
Right
Down
Left
Back
Left
Back Back
Right
Down
●○● +72° SDR SDL SBL SB SBR SD
●○● -72° SDR' SDL' SBL' SB' SBR' SD'
●○● +144° SDR2 SDL2 SBL2 SB2 SBR2 SD2
●○● -144° SDR2' SDL2' SBL2' SB2' SBR2' SD2'

Twists of opposing faces (slice twists) are described by prepending the letter S to a face twist. For example, SR turns the right face and the opposing back left face in clockwise direction as seen from the right face.

Dodecahedron rotations: CR, CR', CR2, CR2'

Move Right Front Left Up
Left
Up
Right
Up
●●● +72° CR CF CL CUL CUR CU
●●● -72° CR' CF' CL' CUL' CUR' CU'
●●● +144° CR2 CF2 CL2 CUL2 CUR2 CU2
●●● -144° CR2' CF2' CL2' CUL2' CUR2' CU2'
Move Down
Right
Down
Left
Back
Left
Back Back
Right
Down
●●● +72° CDR CDL CBL CB CBR CD
●●● -72° CDR' CDL' CBL' CB' CBR' CD'
●●● +144° CDR2 CDL2 CBL2 CB2 CBR2 CD2
●●● -144° CDR2' CDL2' CBL2' CB2' CBR2' CD2'

Rotations of the whole dodecahedron (dodecahedron rotations) are described by prepending the letter C to a face twist. For example, CR rotates the whole dodecahedron in clockwise direction as seen from the right face.

Grouping

Sequences of moves can be grouped using brackets: (R U F).

Repetition

Moves and groups can be repeated multiple times by appending the number of repetitions to the closing bracket: (R U F)3.

© Walter Randelshofer. All rights reserved.