Octahedral honeycomb

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Octahedral honeycomb
Rank4
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymOcth
Coxeter diagramo4o4o3x ()
Schläfli symbol{3,4,4}
Elements
CellsNM octahedra
Faces4NM triangles
Edges3NM
Vertices6N
Vertex figureSquare tiling, edge length 1
Measures (edge length 1)
Circumradius0
Related polytopes
ArmyOcth
RegimentOcth
DualSquare tiling honeycomb
Abstract & topological properties
OrientableYes
Properties
Symmetry[4,4,3]
ConvexYes

The order-4 octahedral honeycomb, or just octahedral honeycomb, is a paracompact regular tiling of 3D hyperbolic space. 4 ideal octahedra meet at each edge. All vertices are ideal points at infinity, with infinitely many octahedra meeting at each vertex in a square tiling arrangement.

Representations[edit | edit source]

The octahedral honeycomb has the following Coxeter diagrams:

External links[edit | edit source]