# Notation

## SSE 5x5 Pyraminx

The SSE 5x5 Pyraminx (Superset ENG) is a notation for pyramids with 5 layers, such as the Professor Pyraminx. 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 or tip axes. Permutation and orientation changes of individual pyramid 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 (tip).

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', ... T4R

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'`
○●●●● +120° `T4R` `T4U` `T4L` `T4B`
○●●●● -120° `T4R'` `T4U'` `T4L'` `T4B'`

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, T4R twists four layers deep in clockwise direction as seen from the right corner (tip).

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', ... N4R

Move Right Up Left Back
○○○●○ +120° `NR` `NU` `NL` `NB`
○○○●○ -120° `NR'` `NU'` `NL'` `NB'`
○○●○○ +120° `N3R` `N3U` `N3L` `N3B`
○○●○○ -120° `N3R'` `N3U'` `N3L'` `N3B'`
○●○○○ +120° `N4R` `N4U` `N4L` `N4B`
○●○○○ -120° `N4R'` `N4U'` `N4L'` `N4B'`

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 N4R, N4U'.

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.

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

Move Right Up Left Back
○○●●○ +120° `N2-3R` `N2-3U` `N2-3L` `N2-3B`
○○●●○ -120° `N2-3R'` `N2-3U'` `N2-3L'` `N2-3B'`
○●●○○ +120° `N3-4R` `N3-4U` `N3-4L` `N3-4B`
○●●○○ -120° `N3-4R'` `N3-4U'` `N3-4L'` `N3-4B'`

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 corner (tip).

To keep scripts short, ranges which start with 1 or end with the last layer of the pyramid are written as tier twists, instead of N1-2F we write TF, instead of N1-3F we write T3F. Ranges of only one layer are written as N layer twists, instead of N2-2U' we write N2U'.

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

Move Right Up Left Back
○●●●○ +120° `WR` `WU` `WL` `WB`
○●●●○ -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 (tip).

### 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.