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About: Octahedral symmetry     Goto   Sponge   NotDistinct   Permalink

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Type: yago:Abstraction100002137yago:Group100031264yago:WikicatFiniteGroups New Facet based on Instances of this Class

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has the same set of symmetries, since it is the polyhedron that is dual to an octahedron. The group of orientation-preserving symmetries is S4, the symmetric group or the group of permutations of four objects, since there is exactly one such symmetry for each permutation of the four diagonals of the cube.