 # Duals by Rotating the Edges of Polyhedra

Initializing live version Requires a Wolfram Notebook System

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

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 .

[more]

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.

[less]

Contributed by: George Beck (March 2008)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Permanent Citation

George Beck

 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