![]() Involutional symmetry Cs, (*) [ ] = ![]() |
![]() Cyclic symmetry Cnv, (*nn) [n] = ![]() ![]() ![]() |
![]() Dihedral symmetry Dnh, (*n22) [n,2] = ![]() ![]() ![]() ![]() ![]() | |
Polyhedral group, [n,3], (*n32) | |||
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![]() Tetrahedral symmetry Td, (*332) [3,3] = ![]() ![]() ![]() ![]() ![]() |
![]() Octahedral symmetry Oh, (*432) [4,3] = ![]() ![]() ![]() ![]() ![]() |
![]() Icosahedral symmetry Ih, (*532) [5,3] = ![]() ![]() ![]() ![]() ![]() |
In three dimensional geometry, there are four infinite series of point groups in three dimensions (n≥1) with n-fold rotational or reflectional symmetry about one axis (by an angle of 360°/n) that does not change the object.
They are the finite symmetry groups on a cone. For n = ∞ they correspond to four frieze groups. Schönflies notation is used. The terms horizontal (h) and vertical (v) imply the existence and direction of reflections with respect to a vertical axis of symmetry. Also shown are Coxeter notation in brackets, and, in parentheses, orbifold notation.