High Quality Content by WIKIPEDIA articles! A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a total of 24 symmetries including transformations that combine a reflection and a rotation. The group of all symmetries is isomorphic to the group S4 of 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.

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