10182

# Duals by Rotating the Edges of Polyhedra

There are several ways to construct the dual of a polyhedron . Roughly speaking, and switch faces and vertices and the edges flip around. The dual of is .
Here is a combinatorial definition. The vertices of are the centers of the faces of . An edge of joins and if their corresponding faces and were adjacent in . Each face of corresponds to a vertex of : if was a vertex of the faces , , … of , then is the polygon with vertices , , …. This definition leads to skew polygonal faces if is not concave or has holes.
The dual can be constructed by various geometric operations on : truncating either at vertices or edges, augmenting faces, or by stellation.
The number of edges of and of are the same. Could the edges of be transformed to form ? Yes: by rotating each edge about the axis from the center of to the midpoint of the edge.

### 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 Topics

 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.