Cubic Symmetry Types

This Demonstration illustrates cubic symmetry types.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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

Files require Wolfram CDF Player or Mathematica.

Related Curriculum Standards

US Common Core State Standards, Mathematics

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+