Notation

Superset ENG 4x4 Pyraminx

Superset ENG 4x4 is a notation for Pyramids with 4 layers. The notation is based on the English language. It supports 120° twists of the layers of the pyramid. A whole pyramid can be rotated along its corner axes. Permutation and orientation changes of individual cube parts can be specified using permutation cycles.

Corner twists: R, R'

Move Right Up Left Back
○○○● +120° R U L B
○○○● -120° R' U' L' B'

Clockwise 120° twists of the four corners (tips) of the pyramid are described by the capital letters: R, U, L and B, (right, up, left, back). For example, R rotates the right corner in clockwise direction as seen from the right corner.

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

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

240° twists and rotations are described by appending the number 2 to a move: R2, U2, L2, ...

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

Move Right Up Left Back
○○●● +120° TR TU TL TB
○○●● -120° TR' TU' TL' TB'
○●●● +120° T3R T3U T3L T3B
○●●● -120° T3R' T3U' T3L' T3B'

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

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 corner.

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

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', ... N3R

Move Right Up Left Back
○○●○ +120° NR NU NL NB
○●○○ +120° N3R N3U N3L N3B

Twists of an individual layer of the pyramid (twist of the n-th layer) are described by prepending the letter N to a corner twist. The number of the layer can be specified by inserting the number of the layer after the letter N, for example N3R, N3U'.

Layers are numbered starting from the corner described by the corner twist towards the opposite layer. The layer at the corner of the pyramid 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, NU'.

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

Wide-layer twists: WR, WR'

Move Right Up Left Back
○●●○ +120° WR WU WL WB

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

Pyramid rotations: CR, CR'

Move Right Up Left Back
●●●● +120° CR CU CL CB
●●●● -120° CR' CU' CL' CB'

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

Grouping

Sequences of moves can be grouped using brackets: (TR TU TL).

Repetition

Moves and groups can be repeated multiple times by appending the number of repetitions to the closing bracket: (TR TU TL)3.

© Walter Randelshofer. All rights reserved.