# Cubic Symmetry Types

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This Demonstration illustrates cubic symmetry types.

Contributed by: Izidor Hafner (May 2008)

Based on work by: Peter R. Cromwell

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

A polyhedron with cubic symmetry has the same axes of rotational symmetry as a cube (or an octahedron, so the system is labeled ) or an axis of four-fold symmetry is reduced to a two-fold axis and the result is a tetrahedral system of rotational symmetry (labeled ). If the polyhedron is placed so that an axis of four-fold symmetry points vertically and there is a horizontal reflection plane, the system of symmetry has label . If all reflection symmetries are destroyed, the system of symmetry has label . If a polyhedron is decorated so that four-fold axes are changed to two-fold axes and there is a horizontal reflection plane, the system is labeled . If there is no horizontal reflection plane (and as a consequence, there are no vertical reflection planes), but there are reflection planes that contain axes of three-fold symmetry, the system of symmetry is labeled . If all reflection symmetries are destroyed, the system is labeled .

Reference

[1] P. R. Cromwell, *Polyhedra*, New York: Cambridge Univ. Press, 1997 pp. 308–311.

## Permanent Citation

"Cubic Symmetry Types"

http://demonstrations.wolfram.com/CubicSymmetryTypes/

Wolfram Demonstrations Project

Published: May 21 2008