Symmetries: Identity | Rotations | Reflections | Rotoreflections

## Reflectional Symmetries 9

Symmetry group: `m`

and _{f}`m`

Order: _{e}`2`

Reflectional symmetries involve transforming a cube algorithm by mirroring it across a specific symmetry plane.

A cube has nine symmetry planes and respectively nine reflectional symmetries.

There are two kinds of reflectional symmetries in a cube:

### Reflectional Symmetries across midplanes 3

Symmetry group: `m`

Order: _{f}`2`

Reflectional Symmetries across midplanes involve mirroring the cube algorithm across three coordinate planes that intersects the cube center and are parallel to cube faces. There are three such symmetries.

#####
`25.`

M Reflection

Symmetry group: `m`

Order: _{f}`2`

In a `M`

Reflection symmetry, the cube algorithm is mirrored across the YZ coordinate plane that bisects
the cube in half vertically through its center, and is parallel to its Right and Left faces.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

#####
`26.`

E Reflection

Symmetry group: `m`

Order: _{f}`2`

In a `E`

Reflection symmetry, the cube algorithm is mirrored across the XZ coordinate plane that bisects
the cube in half horizontally through its center, and is parallel to its Upper and Down faces.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

#####
`27.`

S Reflection

Symmetry group: `m`

Order: _{f}`2`

In a `S`

Reflection symmetry, the cube algorithm is mirrored across the XY coordinate plane that bisects
the cube in half vertically through its center, and is parallel to its Front and Back faces.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

### Reflectional Symmetries across diagonal planes 6

Symmetry group: `m`

Order: _{e}`2`

Reflectional Symmetries across diagonal planes involve mirroring the cube algorithm across its six diagonal planes that intersect two opposite edges. There are six such symmetries in total.

#####
`28.`

RF Reflection

Symmetry group: `m`

Order: _{e}`2`

In an `RF`

Reflection symmetry, the cube algorithm is mirrored across the diagonal plane that connects the
Front-Right edge to the Back-Left edge.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

#####
`29.`

LF Reflection

Symmetry group: `m`

Order: _{e}`2`

In an `LF`

Reflection symmetry, the cube algorithm is mirrored across the diagonal plane that connects the Front-Left edge to the Back-Right edge.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

#####
`30.`

RU Reflection

Symmetry group: `m`

Order: _{e}`2`

In a `RU`

Reflection symmetry, the cube algorithm is mirrored across the diagonal plane that connects the
Right-Upper edge to the Left-Down edge.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

#####
`31.`

LU Reflection

Symmetry group: `m`

Order: _{e}`2`

In a `LU`

Reflection symmetry, the cube algorithm is mirrored across the diagonal plane that connects the
Left-Upper edge to the Right-Down edge.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

#####
`32.`

FU Reflection

Symmetry group: `m`

Order: _{e}`2`

In an `FU`

Reflection symmetry, the cube algorithm is mirrored across the diagonal plane that connects the
Front-Upper edge to the Back-Down edge.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

#####
`33.`

BU Reflection

Symmetry group: `m`

Order: _{e}`2`

In an `BU`

Reflection symmetry, the cube algorithm is mirrored across the diagonal plane that connects the
Back-Upper edge to the Front-Down edge.

To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:

To revert this symmetry, apply it again.

Symmetries: Identity | Rotations | Reflections | Rotoreflections