Truncated dodecahedral honeycomb

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Truncated dodecahedral honeycomb
Rank4
TypeUniform, compact
SpaceHyperbolic
Notation
Bowers style acronymTidd
Coxeter diagramx5x3o4o ()
Elements
Cells5N octahedra, 2N truncated dodecahedra
Faces40N triangles, 12N decagons
Edges15N+60N
Vertices30N
Vertex figureSquare pyramid, edge lengths 1 (base) and (sides)
Measures (edge length 1)
Circumradius
Related polytopes
ArmyTiddoh
RegimentTiddoh
Abstract & topological properties
OrientableYes
Properties
Symmetry[5,3,4]
ConvexYes

The truncated dodecahedral honeycomb is a compact uniform tiling of 3D hyperbolic space. 1 octahedron and 4 truncated dodecahedra meet at each vertex. As the name suggests, it can be derived by truncation of the dodecahedral honeycomb.

Representations[edit | edit source]

A truncated dodecahedral honeycomb has the following Coxeter diagram:

  • x5x3o4o () (full symmetry)
  • x5x3o *b3o () (half symmetry)

External links[edit | edit source]