Heptagonal tiling honeycomb

The (order-3) heptagonal tiling honeycomb is a hypercompact regular tiling of 3D hyperbolic space. Each cell is a heptagonal tiling whose vertices lie on a 2-hypercycle. 3 heptagonal tilings meet at each edge, and 4 meet at each vertex.

Heptagonal tiling honeycomb
Rank4
TypeRegular
SpaceHyperbolic, noncompact
Notation
Coxeter diagramx7o3o3o ()
Schläfli symbol{7,3,3}
Elements
CellsHeptagonal tilings
FacesHeptagons
Vertex figureTetrahedron
Related polytopes
Army*
Regiment*
DualOrder-7 tetrahedral honeycomb
Abstract & topological properties
OrientableYes
Properties
Symmetry[7,3,3]
ConvexYes

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