SSE 5x5 Gigaminx
The SSE 5x5 Gigaminx (Superset ENG) is a notation for dodecahedrons with 5 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'.
Void 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 (void twists) can be described by prepending the letter V to a face twist: VR, VU', VF2.
The depth of void 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', ... S2R
| 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' |
| ●●○●● +72° | S2R |
S2F |
S2L |
S2UL |
S2UR |
S2U |
| ●●○●● -72° | S2R' |
S2F' |
S2L' |
S2UL' |
S2UR' |
S2U' |
| ●●○●● +144° | S2R2 |
S2F2 |
S2L2 |
S2UL2 |
S2UR2 |
S2U2 |
| ●●○●● -144° | S2R2' |
S2F2' |
S2L2' |
S2UL2' |
S2UR2' |
S2U2' |
| 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' |
| ●●○●● +72° | S2DR |
S2DL |
S2BL |
S2B |
S2BR |
S2D |
| ●●○●● -72° | S2DR' |
S2DL' |
S2BL' |
S2B' |
S2BR' |
S2D' |
| ●●○●● +144° | S2DR2 |
S2DL2 |
S2BL2 |
S2B2 |
S2BR2 |
S2D2 |
| ●●○●● -144° | S2DR2' |
S2DL2' |
S2BL2' |
S2B2' |
S2BR2' |
S2D2' |
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.
The depth of the slices can be specified by inserting a number after the letter S, for example S2R.
If the depth is not explicitly specified, the value 1 is assumed, for example SL, SD', SB2.
To keep scripts short, S1R is never used, because it is equivalent to SR.
Slice range twists: S2-3R, S2-3R', S2-3R2, S2-3R2', ...
| Move | Right | Front | Left | Up Left |
Up Right |
Up |
|---|---|---|---|---|---|---|
| ●●○○● +72° | S2-3R |
S2-3F |
S2-3L |
S2-3UL |
S2-3UR |
S2-3U |
| ●●○○● -72° | S2-3R' |
S2-3F' |
S2-3L' |
S2-3UL' |
S2-3UR' |
S2-3U' |
| ●●○○● +144° | S2-3R2 |
S2-3F2 |
S2-3L2 |
S2-3UL2 |
S2-3UR2 |
S2-3U2 |
| ●●○○● -144° | S2-3R2' |
S2-3F2' |
S2-3L2' |
S2-3UL2' |
S2-3UR2' |
S2-3U2' |
| ●●●○● +72° | S2-2R |
S2-2F |
S2-2L |
S2-2UL |
S2-2UR |
S2-2U |
| ●●●○● -72° | S2-2R' |
S2-2F' |
S2-2L' |
S2-2UL' |
S2-2UR' |
S2-2U' |
| ●●●○● +144° | S2-2R2 |
S2-2F2 |
S2-2L2 |
S2-2UL2 |
S2-2UR2 |
S2-2U2 |
| ●●●○● -144° | S2-2R2' |
S2-2F2' |
S2-2L2' |
S2-2UL2' |
S2-2UR2' |
S2-2U2' |
| ●○○●● +72° | S3-4R |
S3-4F |
S3-4L |
S3-4UL |
S3-4UR |
S3-4U |
| ●○○●● -72° | S3-4R' |
S3-4F' |
S3-4L' |
S3-4UL' |
S3-4UR' |
S3-4U' |
| ●○○●● +144° | S3-4R2 |
S3-4F2 |
S3-4L2 |
S3-4UL2 |
S3-4UR2 |
S3-4U2 |
| ●○○●● -144° | S2-3R2' |
S2-3F2' |
S2-3L2' |
S2-3UL2' |
S2-3UR2' |
S2-3U2' |
| ●○●●● +72° | S4-4R |
S4-4F |
S4-4L |
S4-4UL |
S4-4UR |
S4-4U |
| ●○●●● -72° | S4-4R' |
S4-4F' |
S4-4L' |
S4-4UL' |
S4-4UR' |
S4-4U' |
| ●○●●● +144° | S4-4R2 |
S4-4F2 |
S4-4L2 |
S4-4UL2 |
S4-4UR2 |
S4-4U2 |
| ●○●●● -144° | S4-4R2' |
S4-4F2' |
S4-4L2' |
S4-4UL2' |
S4-4UR2' |
S4-4U2' |
| Move | Down Right |
Down Left |
Back Left |
Back | Back Right |
Down |
|---|---|---|---|---|---|---|
| ●●○○● +72° | S2-3DR |
S2-3DL |
S2-3BL |
S2-3B |
S2-3BR |
S2-3D |
| ●●○○● -72° | S2-3DR' |
S2-3DL' |
S2-3BL' |
S2-3B' |
S2-3BR' |
S2-3D' |
| ●●○○● +144° | S2-3DR2 |
S2-3DL2 |
S2-3BL2 |
S2-3B2 |
S2-3BR2 |
S2-3D2 |
| ●●○○● -144° | S2-3DR2' |
S2-3DL2' |
S2-3BL2' |
S2-3B2' |
S2-3BR2' |
S2-3D2' |
| ●●●○● +72° | S2-2DR |
S2-2DL |
S2-2BL |
S2-2B |
S2-2BR |
S2-2D |
| ●●●○● -72° | S2-2DR' |
S2-2DL' |
S2-2BL' |
S2-2B' |
S2-2BR' |
S2-2D' |
| ●●●○● +144° | S2-2DR2 |
S2-2DL2 |
S2-2BL2 |
S2-2B2 |
S2-2BR2 |
S2-2D2 |
| ●●●○● -144° | S2-2DR2' |
S2-2DL2' |
S2-2BL2' |
S2-2B2' |
S2-2BR2' |
S2-2D2' |
| ●○○●● +72° | S3-4DR |
S3-4DL |
S3-4BL |
S3-4B |
S3-4BR |
S3-4D |
| ●○○●● -72° | S3-4DR' |
S3-4DL' |
S3-4BL' |
S3-4B' |
S3-4BR' |
S3-4D' |
| ●○○●● +144° | S3-4DR2 |
S3-4DL2 |
S3-4BL2 |
S3-4B2 |
S3-4BR2 |
S3-4D2 |
| ●○○●● -144° | S3-4DR2' |
S3-4DL2' |
S3-4BL2' |
S3-4B2' |
S3-4BR2' |
S3-4D2' |
| ●○●●● +72° | S4-4DR |
S4-4DL |
S4-4BL |
S4-4B |
S4-4BR |
S4-4D |
| ●○●●● -72° | S4-4DR' |
S4-4DL' |
S4-4BL' |
S4-4B' |
S4-4BR' |
S4-4D' |
| ●○●●● +144° | S4-4DR2 |
S4-4DL2 |
S4-4BL2 |
S4-4B2 |
S4-4BR2 |
S4-4D2 |
| ●○●●● -144° | S4-4DR2' |
S4-4DL2' |
S4-4BL2' |
S4-4B2' |
S4-4BR2' |
S4-4D2' |
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.