Tetrahedral honeycomb

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Tetrahedral honeycomb
Rank4
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymThon
Coxeter diagramx3o3o6o ()
Schläfli symbol{3,3,6}
Elements
CellsNM tetrahedra
Faces2NM triangles
EdgesNM
Vertices2N
Vertex figureTriangular tiling, edge length 1
Measures (edge length 1)
Circumradius0
Related polytopes
ArmyThon
RegimentThon
DualHexagonal tiling honeycomb
Abstract & topological properties
Flag count24NM
OrientableYes
Properties
Symmetry[6,3,3]
ConvexYes

The tetrahedral honeycomb, or order-6 tetrahedral honeycomb, is a paracompact regular tiling of 3D hyperbolic space. 6 ideal tetrahedra meet at each edge. All vertices are ideal points at infinity, with infinitely many tetrahedra meeting at each vertex in a triangular tiling arrangement.

Representations[edit | edit source]

A tetrahedral honeycomb has the following Coxeter diagrams:

  • x3o3o6o () (full symmetry)
  • x3o3o3o3*b () (tetrahedra of two alternating types)

External links[edit | edit source]