Dihedron

From Wikipedia, the free encyclopedia

A dihedron is degenerate type of regular polyhedron, where two(!) n-sided hemispherical regular polygons tile a sphere, each polygon covering an entire hemisphere. An n-gonal dihedron resembles an n-sided bipyramid with each pyramid replaced by a single, hemispherical n-sided polygon. Its Schläfli symbol is {n, 2}.

The dual of the n-gonal dihedron {n, 2} is the n-gonal hosohedron, {2, n}, where n two-sided polygons (digons) tile a sphere. The polyhedron {2,2} is self-dual, and is both a hosohedron and a dihedron.

In a related sense, a dihedron is a degenerate prism consisting of two (planar) n-sided polygons connected "back-to-back", so that the resulting object has no depth.

[edit] See also

• Polyhedron
• Polytope

[edit] References

• Coxeter, H.S.M; Regular Polytopes (third edition). Dover Publications Inc. ISBN 0-486-61480-8
• Wolfram Research (http://mathworld.wolfram.com/Dihedron.html) Retrieved Aug 3, 2006.