3D symmetry group
Polyhedron great rhombi 6-8 dual max.png
The octahedral group Oh with fundamental domain
applied on the 90° rotation 22′
Subgroup of Oh; S4 blue red; cycle graph.svg
grupo de simetría tridimensional
Rotational subgroups
Full octahedral group; subgroups Hasse diagram; rotational.svg
gives the 90° rotoreflection 17.
Cube permutation 4 4.svg
left
applied on the 120° rotation 4
Subgroup of Oh; S4 green orange; cycle graph.svg
Full octahedral group; subgroups Hasse diagram; reflective.svg
Full octahedral group; subgroups Hasse diagram; inversion.svg
gives the 60° rotoreflection 8′.
Cube permutation 5 1.svg
Cycle graphs of subgroups of order 24
Cube permutation 0 4.svg
Subgroups containing inversion
Subgroup of Oh; A4xC2; cycle graph.svg
Octahedral group
OctahedralGroup
transformasi yang menggabungkan refleksi dan rotasi
Sphere symmetry group oh.png
The reflection 7′
Each face of the disdyakis dodecahedron is a fundamental domain.
Cube permutation 4 0.svg
Polyhedron pair 6-8.png
Cube permutation 1 1.svg
Reflective subgroups
Simetría octaédrica
정팔면체 대칭
Oktaedergruppe
Simetri oktahedral
Okedra simetrio
Octahedral symmetry