Order-5 hexagonal tiling honeycomb

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Order-5 hexagonal tiling honeycomb
Rank4
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymPhexah
Coxeter diagramx6o3o5o ()
Schläfli symbol{6,3,5}
Elements
Cells10N hexagonal tilings
Faces5NM hexagons
Edges6NM
VerticesNM
Vertex figureIcosahedron, edge length 3
Measures (edge length 1)
Circumradius
Related polytopes
ArmyPhexah
RegimentPhexah
DualOrder-6 dodecahedral honeycomb
Abstract & topological properties
OrientableYes
Properties
Symmetry[6,3,5]
ConvexYes

The order-5 hexagonal tiling honeycomb is a paracompact regular tiling of 3D hyperbolic space. Each cell is a hexagonal tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. 5 hexagonal tilings meet at each edge, and 20 meet at each vertex.

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