Truncated icosahedral honeycomb

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Truncated icosahedral honeycomb
Rank4
TypeUniform, compact
SpaceHyperbolic
Notation
Bowers style acronymTih
Coxeter diagramx3x5o3o ()
Elements
CellsN dodecahedra, N truncated icosahedra
Faces12N pentagons, 10N hexagons
Edges10N+30N
Vertices20N
Vertex figureTriangular pyramid, edge lengths (1+5)/2 (base) and 3 (side)
Measures (edge length 1)
Circumradius
Related polytopes
ArmyTih
RegimentTih
Abstract & topological properties
OrientableYes
Properties
Symmetry[3,5,3]
ConvexYes

The truncated icosahedral honeycomb, or tih, is a compact uniform tiling of 3D hyperbolic space. 1 dodecahedron and 3 truncated icosahedra meet at each vertex. As the name suggests, it can be derived by truncation of the icosahedral honeycomb.

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