Notation

Superset ENG 4x4

Superset ENG 4x4 is a notation for Rubik's Cubes with 4 layers, such as the Revenge Cube. The notation is based on the English language. It supports 90° and 180° twists of the layers of the cube. A whole cube can be rotated along its face axes. Permutation and orientation changes of individual cube parts can be specified using permutation cycles.

Face twists: R, R', R2

Move Right Up Front Left Down Back
○○○● +90° R U F L D B
○○○● -90° R' U' F' L' D' B'
○○○● +180° R2 U2 F2 L2 D2 B2

Clockwise 90° twists of the six faces of the cube are described by the capital letters: R, U, F, L, D and B, (right, up, front, left, down, back). 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.

180° twists and rotations are described by appending the number 2 to a move: R2, U2, F2, ...

Tier twists: TR, TR', TR2, ... T3R

Move Right Up Front Left Down Back
○○●● +90° TR TU TF TL TD TB
○○●● -90° TR' TU' TF' TL' TD' TB'
○○●● +180° TR2 TU2 TF2 TL2 TD2 TB2
○●●● +90° T3R T3U T3F T3L T3D T3B
○●●● -90° T3R' T3U' T3F' T3L' T3D' T3B'
○●●● +180° T3R2 T3U2 T3F2 T3L2 T3D2 T3B2

Twists which go multiple 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.

Mid-layer twists: MR, MR', MR2

Move Right Up Front Left Down Back
○○●○ +90° MR MU MF ML MD MB
○○●○ -90° MR' MU' MF' ML' MD' MB'
○○●○ +180° MR2 MU2 MF2 ML2 MD2 MB2

Twists of the layer in the middle (mid-layer twists) are described by prepending the letter M to a face twist: MR, MU', MF2.

On cubes with an even amount of layers, the mid-layers are the ones closer to the face of the cube.

The number of layers twisted can be specified by inserting a number after the letter M. For example, M2R twists two 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

Move Right Up Front Left Down Back
○●●○ +90° WR WU WF WL WD WB
○●●○ -90° WR' WU' WF' WL' WD' WB'
○●●○ +180° WR2 WU2 WF2 WL2 WD2 WB2

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 M2R and twists two layers in the middle in clockwise direction as seen from the right face.

Slice twists: SR, SR', SR2

Move Right Up Front Left Down Back
●○○● +90° SR SU SF SL SD SB
●○○● -90° SR' SU' SF' SL' SD' SB'
●○○● +180° SR2 SU2 SF2 SL2 SD2 SB2

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 left face in clockwise direction as seen from the right face.

Slice range twists: S2-2R, S2-2R', S2-2R2, ...

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 S2-3F2 we write SF2.

Cube rotations: CR, CR', CR2

Move Right Up Front Left Down Back
●●●● +90° CR CU CF CL CD CB
●●●● -90° CR' CU' CF' CL' CD' CB'
●●●● +180° CR2 CU2 CF2 CL2 CD2 CB2

Rotations of the whole cube (cube rotations) are described by prepending the letter C to a face twist. For example, CR rotates the whole cube 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.

Further informations

See also the complete description of the Superset ENG 4x4 notation.

© Walter Randelshofer. All rights reserved.