Symmetries: Identity | Rotations | Reflections | Rotoreflections
Rotoreflection Symmetries 15
Symmetry group: mfr4 and mer4
Order: 2, 4 and 6
Rotoreflection (rotary reflection) symmetries involve transforming a cube algorithm by mirroring it across a specific symmetry plane and rotating it around its axis. There are two kinds of rotoreflection symmetry:
Rotoreflectional Symmetries across midplanes 7
Symmetry group: mfr4
Order: 2 and 4
Rotoreflection Symmetries across midplanes involve transforming a cube algorithm by mirroring it across one of its midplanes (the three coordinate planes that intersect the cube's center and are parallel to its faces) and simultaneously rotating it around a specific mid (tetrad) axis.
34.
Mx Rotoreflection
Symmetry group: mfr4
Order: 4
In a Mx Rotoreflection symmetry, the cube algorithm is mirrored across the midplane M (intersecting the
cube's center and parallel to its Right and Left faces) while simultaneously rotating it 90 degrees clockwise around
its x-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the Mx' symmetry.
35.
Mx2 Rotoreflection
Symmetry group: mfr4
Order: 2
In a Mx2 Rotoreflection symmetry, the cube algorithm is mirrored across the midplane M (that intersects
the cube's center and is parallel to its Right and Left faces) while simultaneously rotating it 180 degree around
its x-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply it again.
36.
Mx' Rotoreflection
Symmetry group: mfr4
Order: 4
In a Mx' Rotoreflection symmetry, the cube algorithm is mirrored across the midplane M (intersecting
the cube's center and parallel to its Right and Left faces) while simultaneously rotating it 90 degrees
counterclockwise around its x-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the Mx symmetry.
37.
Ey Rotoreflection
Symmetry group: mfr4
Order: 4
In an Ey Rotoreflection symmetry, the cube algorithm is mirrored across the midplane E (intersecting the
cube's center and parallel to its Upper and Down faces) while simultaneously rotating it 90 degrees clockwise around
its y-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the Ey' symmetry.
38.
Ey' Rotoreflection
Symmetry group: mfr4
Order: 4
In an Ey' Rotoreflection symmetry, the cube algorithm is mirrored across the midplane E (intersecting
the cube's center and parallel to its Upper and Down faces) while simultaneously rotating it 90 degrees
counterclockwise around its y-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the Ey symmetry.
39.
Sz Rotoreflection
Symmetry group: mfr4
Order: 4
In a Sz Rotoreflection symmetry, the cube algorithm is mirrored across the midplane S (intersecting the
cube's center and parallel to its Front and Back faces) while simultaneously rotating it 90 degrees clockwise around
its z-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the Sz' symmetry.
40.
Sz' Rotoreflection
Symmetry group: mfr4
Order: 4
In a Sz' Rotoreflection symmetry, the cube algorithm is mirrored across the midplane S (intersecting
the cube's center and parallel to its Front and Back faces) while simultaneously rotating it 90 degrees
counterclockwise around its z-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the Sz symmetry.
Rotoreflectional Symmetries across diagonal planes 8
Symmetry group: mer4
Order: 6
Rotoreflection Symmetries across midplanes involve transforming a cube algorithm by mirroring it across one of its vertical diagonal planes (that intersect two opposite vertical edges) and simultaneously rotating it around a specific mid (tetrad) axis.
41.
RFx Rotoreflection
Symmetry group: mer4
Order: 6
In a RFx Rotoreflection symmetry, the cube algorithm is mirrored across its diagonal plane RF
(intersecting its opposite Right-Front and Left-Back vertical edges) while simultaneously rotating it 90 degrees
clockwise around its x-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the RFz' symmetry.
42.
RFx' Rotoreflection
Symmetry group: mer4
Order: 6
In a RFx' Rotoreflection symmetry, the cube algorithm is mirrored across its diagonal plane RF
(intersecting its opposite Right-Front and Left-Back vertical edges) while simultaneously rotating it 90 degrees
counterclockwise around its x-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the RFz symmetry.
43.
RFz Rotoreflection
Symmetry group: mer4
Order: 6
In a RFz Rotoreflection symmetry, the cube algorithm is mirrored across its diagonal plane RF
(intersecting its opposite Right-Front and Left-Back vertical edges) while simultaneously rotating it 90 degrees
clockwise around its z-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the RFx' symmetry.
44.
RFz' Rotoreflection
Symmetry group: mer4
Order: 6
In a RFz' Rotoreflection symmetry, the cube algorithm is mirrored across its diagonal plane RF
(intersecting its opposite Right-Front and Left-Back vertical edges) while simultaneously rotating it 90 degrees
counterclockwise around its z-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the RFx symmetry.
45.
LFx Rotoreflection
Symmetry group: mer4
Order: 6
In a LFx Rotoreflection symmetry, the cube algorithm is mirrored across its diagonal plane LF
(intersecting its opposite Left-Front and Right-Back vertical edges) while simultaneously rotating it 90 degrees
clockwise around its x-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the LFz' symmetry.
46.
LFx' Rotoreflection
Symmetry group: mer4
Order: 6
In a LFx' Rotoreflection symmetry, the cube algorithm is mirrored across its diagonal plane LF
(intersecting its opposite Left-Front and Right-Back vertical edges) while simultaneously rotating it 90 degrees
counterclockwise around its x-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the LFz symmetry.
47.
LFz Rotoreflection
Symmetry group: mer4
Order: 6
In a LFz Rotoreflection symmetry, the cube algorithm is mirrored across its diagonal plane LF
(intersecting its opposite Left-Front and Right-Back vertical edges) while simultaneously rotating it 90 degrees
clockwise around its z-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the LFx' symmetry.
48.
LFz' Rotoreflection
Symmetry group: mer4
Order: 6
In a LFz' Rotoreflection symmetry, the cube algorithm is mirrored across its diagonal plane LF
(intersecting its opposite Left-Front and Right-Back vertical edges) while simultaneously rotating it 90 degrees
counterclockwise around its z-axis.
To apply this symmetry, tap the menu button within the CubePal app and navigate as follows:
To revert this symmetry, apply the LFx symmetry.
Symmetries: Identity | Rotations | Reflections | Rotoreflections
