Order-3 icosahedral honeycomb
- Order-3 icosahedral honeycomb
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}, cells.
See also
* Seifert-Weber space
* List of regular polytopes
* 11-cell - An abstract regular polychoron which shares the {3,5,3} Schläfli symbol.
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)
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