Tetrahedral Symmetry
A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.
The group of all symmetries is isomorphic to the group S4, symmetric group, as a permutations of four objects, since there is exactly one such symmetry for each permutation of the vertices of the tetrahedron. The set of orientation-preserving symmetries forms a group referred to as the alternating subgroup A4 of S4.
Read more about Tetrahedral Symmetry: Details, Chiral Tetrahedral Symmetry, Achiral Tetrahedral Symmetry, Pyritohedral Symmetry, Solids With Chiral Tetrahedral 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)