Notation

SSE 5x5 Gigaminx

The SSE 5x5 Gigaminx (Superset ENG) is a notation for dodecahedrons with 4 layers, such as the Gigaminx. 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', ... T3R, T4R

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'
○○●●● +72° T3R T3F T3L T3UL T3UR T3U
○○●●● -72° T3R' T3F' T3L' T3UL' T3UR' T3U'
○○●●● +144° T3R2 T3F2 T3L2 T3UL2 T3UR2 T3U2
○○●●● -144° T3R2' T3F2' T3L2' T3UL2' T3UR2' T3U2'
○●●●● +72° T4R T4F T4L T4UL T4UR T4U
○●●●● -72° T4R' T4F' T4L' T4UL' T4UR' T4U'
○●●●● +144° T4R2 T4F2 T4L2 T4UL2 T4UR2 T3U2
○●●●● -144° T4R2' T4F2' T4L2' T4UL2' T4UR2' T4U2'
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'
○○●●● +72° T3DR T3DL T3BL T3B T3BR T3D
○○●●● -72° T3DR' T3DL' T3BL' T3B' T3BR' T3D'
○○●●● +144° T3DR2 T3DL2 T3BL2 T3B2 T3BR2 T3D2
○○●●● -144° T3DR2' T3DL2' T3BL2' T3B2' T3BR2' T3D2'
○●●●● +72° T4DR T4DL T4BL T4B T4BR T4D
○●●●● -72° T4DR' T4DL' T4BL' T4B' T4BR' T4D'
○●●●● +144° T4DR2 T4DL2 T4BL2 T4B2 T4BR2 T4D2
○●●●● -144° T4DR2' T4DL2' T4BL2' T4B2' T4BR2' T4D2'

Twists which go two layers deep (tier twists) are described by prepending the letter T to a face twist: TR, TU', TF2.

The depth of the tier can be specified by inserting a number after the letter T. For example, T3R twists three layers deep in clockwise direction as seen from the right face.

If the dept is not explicitly specified, the value 2 is assumed: TL, TD', TB2.

To keep scripts short, T1R is never used, because it is equivalent to R. T2R is never used, because it is equivalent to TR.

Numbered layer twists: NR, NR', NR2, NR2'

Move Right Front Left Up
Left
Up
Right
Up
○○○●○ +72° NR NF NL NUL NUR NU
○○○●○ -72° NR' NF' NL' NUL' NUR' NU'
○○○●○ +144° NR2 NF2 NL2 NUL2 NUR2 NU2
○○○●○ -144° NR2' NF2' NL2' NUL2' NUR2' NU2'
Move Down
Right
Down
Left
Back
Left
Back Back
Right
Down
○○○●○ +72° NDR NDL NBL NB NBR ND
○○○●○ -72° NDR' NDL' NBL' NB' NBR' ND'
○○○●○ +144° NDR2 NDL2 NBL2 NB2 NBR2 ND2
○○○●○ -144° NDR2' NDL2' NBL2' NB2' NBR2' ND2'

Twists of an individual layer of the dodecahedron (twist of the n-th layer) are described by prepending the letter N to a face twist. The number of the layer can be specified by inserting the number of the layer after the letter N, for example N4R, N3U', N4F2.

Layers are numbered starting from the face described by the face twist towards the opposite face. The layer at the face of the cube has number 1, the next layer has number 2, and so on.

If the layer is not explicitly specified, the value 2 is assumed, for example NL, ND', NB2.

To keep scripts short, N1R is never used, because it is equivalent to R. N2R is never used, because it is equivalent to NR.

Numbered range twists: N2-3R, N2-3R', N2-3R2, ...

Twists of a range of layers are described by prepending the letter N to a face twist, followed by the number of the first layer, a - character, and the number of the last layer.

N2-3R twists the layers 2 through 3 in clockwise direction as seen from the right face.

To keep scripts short, ranges which start with 1 or end with the last layer of the cube are written as tier twists, instead of N1-2F2 we write TF2, instead of N3-4F we write TB'. Ranges of only one layer are written as N layer twists, instead of N2-2D' we write N2D'.

Verge twists: VR, VR', VR2, VR2'

Move Right Front Left Up
Left
Up
Right
Up
○○●●○ +72° VR VF VL VUL VUR VU
○○●●○ -72° VR' VF' VL' VUL' VUR' VU'
○○●●○ +144° VR2 VF2 VL2 VUL2 VUR2 VU2
○○●●○ -144° VR2' VF2' VL2' VUL2' VUR2' VU2'
Move Down
Right
Down
Left
Back
Left
Back Back
Right
Down
○○●●○ +72° VDR VDL VBL VB VBR VD
○○●●○ -72° VDR' VDL' VBL' VB' VBR' VD'
○○●●○ +144° VDR2 VDL2 VBL2 VB2 VBR2 VD2
○○●●○ -144° VDR2' VDL2' VBL2' VB2' VBR2' VD2'

Tier twists without the cube face (verge twists) can be described by prepending the letter V to a face twist: VR, VU', VF2.

The depth of verge layers can be specified by inserting a number after the letter V. For example, V3R twists the layers 2 through 4 in clockwise direction as seen from the right face.

If the depth is not explicitly specified, the value 2 is assumed: VL, VD', VB2.

To keep scripts short, V1R is never used, because it is equivalent to NR. V2R is never used, because it is equivalent to VR.

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.

The number of layers twisted can be specified by inserting a number after the letter M. For example, M3R rotates three layers in the middle in clockwise direction as seen from the right face.

If the depth is not explicitly specified, the value 1 is assumed, for example ML, MD', MB2.

To keep scripts short, M1R is never used, because it is equivalent to MR.

Wide-layer twists: WR, WR', WR2, WR2'

Move Right Front Left Up
Left
Up
Right
Up
○●●●○ +72° WR WF WL WUL WUR WU
○●●●○ -72° WR' WF' WL' WUL' WUR' WU'
○●●●○ +144° WR2 WF2 WL2 WUL2 WUR2 WU2
○●●●○ -144° WR2' WF2' WL2' WUL2' WUR2' WU2'
Move Down
Right
Down
Left
Back
Left
Back Back
Right
Down
○●●●○ +72° WDR WDL WBL WB WBR WD
○●●●○ -72° WDR' WDL' WBL' WB' WBR' WD'
○●●●○ +144° WDR2 WDL2 WBL2 WB2 WBR2 WD2
○●●●○ -144° WDR2' WDL2' WBL2' WB2' WBR2' WD2'

Twists of all layers except the outer faces (wide-layer twists) can be described by prepending the letter W to a face twist: WR, WU', WF2.

WR is equal to M3R and twists three layers in the middle 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.

Slice range twists: S2-3R, S2-3R', S2-3R2, S2-3R2', ...

Slice twists around an arbitrary range of layers are described by prepending the letter S to a face twist, followed by the number of the first layer, a - character, and the number of the last layer.

S2-3R performs a slice twists around the layers 2 through 3 in clockwise direction as seen from the right face.

To keep scripts short, slice range twists are only used, if there is no equivalent slice twist. For example, instead of S2-4F2 we write SF2.

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.