Popular Searches
Definitions
Order-3_icosahedral_honeycomb

Order-3_icosahedral_honeycomb

Order-3 icosahedral honeycomb
Order-3 icosahedral honeycomb

Poincaré disk model
Type regular hyperbolic honeycomb
Schläfli symbol {3,5,3}
Coxeter-Dynkin diagram - Cells icosahedron {3,5}
Faces triangle {3}
Edge figure triangle {3}
Vertex figure dodecahedron {5,3}
Cells/edge {3,5}3
Cells/vertex {3,5}12
Euler characteristic 0
Dual Self-dual
Coxeter group [3,5,3]
Properties Regular
The order-3 icosahedral honeycomb is one of four regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.

Three icosahedra surround each edge, and 12 icosahedra surround each vertex, in a dodecahedral pattern.

The dihedral angle of a Euclidean icosahedron is 138.2°, so it is impossible to fit three icosahedra around an edge in Euclidean 3-space. However in hyperbolic space, properly scaled icosahedra can have dihedral angles exactly 120 degrees, so three of these fit nicely around an edge.

The bitruncated form, t1,2{3,5,3}, , of this honeycomb has all truncated dodecahedron cells.

See also

References

  • Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp. 294-296)
  • Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)

Wikipedia, the free encyclopedia © 2001-2006 Wikipedia contributors (Disclaimer)
This article is licensed under the GNU Free Documentation License.
Last updated on Saturday March 01, 2008 at 15:46:09 PST (GMT -0800)
View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

Search another word or see Order-3_icosahedral_honeycombon Dictionary | Thesaurus |Spanish
  • Please Login or Sign Up to use the Recent Searches feature
FAVORITES
RECENT