## SSE 5x5

The SSE 5x5 (Superset ENG) is a notation for cubes with 5 layers, such as the Professor 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, T4R

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` |

○●●●● +90° | `T4R` |
`T4U` |
`T4F` |
`T4L` |
`T4D` |
`T4B` |

○●●●● -90° | `T4R'` |
`T4U'` |
`T4F'` |
`T4L'` |
`T4D'` |
`T4B'` |

○●●●● +180° | `T4R2` |
`T4U2` |
`T4F2` |
`T4L2` |
`T4D2` |
`T4B2` |

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**.

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

Move | Right | Up | Front | Left | Down | Back |
---|---|---|---|---|---|---|

○○○●○ +90° | `NR` |
`NU` |
`NF` |
`NL` |
`ND` |
`NB` |

○○○●○ -90° | `NR'` |
`NU'` |
`NF'` |
`NL'` |
`ND'` |
`NB'` |

○○○●○ +180° | `NR2` |
`NU2` |
`NF2` |
`NL2` |
`ND2` |
`NB2` |

Twists of an individual layer of the cube (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

Move | Right | Up | Front | Left | Down | Back |
---|---|---|---|---|---|---|

○○●●○ +90° | `VR` |
`VU` |
`VF` |
`VL` |
`VD` |
`VB` |

○○●●○ -90° | `VR'` |
`VU'` |
`VF'` |
`VL'` |
`VD'` |
`VB'` |

○○●●○ +180° | `VR2` |
`VU2` |
`VF2` |
`VL2` |
`VD2` |
`VB2` |

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

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**.

The number of layers twisted can be specified by inserting a number after the letter **M**. For example, **M3R**
twists 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

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 **M3R** and twists three layers in the middle in clockwise direction as seen from the right face.

### Slice twists: SR, SR', SR2, ... S2R

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` |

●●○●● +90° | `S2R` |
`S2U` |
`S2F` |
`S2L` |
`S2D` |
`S2B` |

●●○●● -90° | `S2R'` |
`S2U'` |
`S2F'` |
`S2L'` |
`S2D'` |
`S2B'` |

●●○●● +180° | `S2R2` |
`S2U2` |
`S2F2` |
`S2L2` |
`S2D2` |
`S2B2` |

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.

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, ...

Move | Right | Up | Front | Left | Down | Back |
---|---|---|---|---|---|---|

●●○○● +90° | `S2-3R` |
`S2-3U` |
`S2-3F` |
`S2-3L` |
`S2-3D` |
`S2-3B` |

●●○○● -90° | `S2-3R'` |
`S2-3U'` |
`S2-3F'` |
`S2-3L'` |
`S2-3D'` |
`S2-3B'` |

●●○○● +180° | `S2-3R2` |
`S2-3U2` |
`S2-3F2` |
`S2-3L2` |
`S2-3D2` |
`S2-3B2` |

●●●○● +90° | `S2-2R` |
`S2-2U` |
`S2-2F` |
`S2-2L` |
`S2-2D` |
`S2-2B` |

●●●○● -90° | `S2-2R'` |
`S2-2U'` |
`S2-2F'` |
`S2-2L'` |
`S2-2D'` |
`S2-2B'` |

●●●○● +180° | `S2-2R2` |
`S2-2U2` |
`S2-2F2` |
`S2-2L2` |
`S2-2D2` |
`S2-2B2` |

●○○●● +90° | `S3-4R` |
`S3-4U` |
`S3-4F` |
`S3-4L` |
`S3-4D` |
`S3-4B` |

●○○●● -90° | `S3-4R'` |
`S3-4U'` |
`S3-4F'` |
`S3-4L'` |
`S3-4D'` |
`S3-4B'` |

●○○●● +180° | `S3-4R2` |
`S3-4U2` |
`S3-4F2` |
`S3-4L2` |
`S3-4D2` |
`S3-4B2` |

●○●●● +90° | `S4-4R` |
`S4-4U` |
`S4-4F` |
`S4-4L` |
`S4-4D` |
`S4-4B` |

●○●●● -90° | `S4-4R'` |
`S4-4U'` |
`S4-4F'` |
`S4-4L'` |
`S4-4D'` |
`S4-4B'` |

●○●●● +180° | `S4-4R2` |
`S4-4U2` |
`S4-4F2` |
`S4-4L2` |
`S4-4D2` |
`S4-4B2` |

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**.

### 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 5x5 notation.