10217

# Cubic Symmetry Types

This Demonstration illustrates cubic symmetry types.

### 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

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Curriculum Standards

US Common Core State Standards, Mathematics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.