Octahedral Symmetry

Octahedral Symmetry

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation. A cube has the same set of symmetries, since it is the dual of 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 pairs of opposite sides of the octahedron.

Read more about Octahedral Symmetry:  Details, Chiral Octahedral Symmetry, Achiral Octahedral Symmetry, The Isometries of The Cube, Octahedral Symmetry of The Bolza Surface, Chiral Solids With Octahedral Rotational Symmetry

Famous quotes containing the word symmetry:

    What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.
    George Gordon Noel Byron (1788–1824)