Cubic Symmetry Types

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send