Achiral Tetrahedral Symmetry
Td, *332, or, of order 24 - achiral or full tetrahedral symmetry, also known as the (2,3,3) triangle group. This group has the same rotation axes as T, but with six mirror planes, each through two 3-fold axes. The 2-fold axes are now S4 axes. Td and O are isomorphic as abstract groups: they both correspond to S4, the symmetric group on 4 objects. Td is the union of T and the set obtained by combining each element of O \ T with inversion. See also the isometries of the regular tetrahedron.
The conjugacy classes of Td are:
- identity
- 8 × rotation by 120°
- 3 × rotation by 180°
- 6 × reflection in a plane through two rotation axes
- 6 × rotoreflection by 90°
Read more about this topic: 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)