Simplicial honeycomb

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(n − 1)-simplex honeycomb
Rankn 
TypeUniform
SpaceEuclidean
Notation
Coxeter diagramx3o3o3o...o3o3o3*a
Elements
CellsM tetrahedra, M octahedra
FacesM triangles
EdgesM
VerticesM
Vertex figureExpanded n -simplex, edge length 1
Measures (edge length 1)
Vertex density
Related polytopes
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryPn 
ConvexYеs
NatureTame

The simplicial honeycombs form an infinite series of uniform tessellations. Their vertex figures are expanded simplexes.

Examples[edit | edit source]

Simplicial honeycombs by dimension
Rank Name Picture
2 Apeirogon
3 Triangular tiling
4 Tetrahedral-octahedral honeycomb
5 Cyclopentachoric tetracomb
6 Cyclohexateric pentacomb
7 Cycloheptapetic hexacomb
8 Cyclooctaexic heptacomb

External links[edit | edit source]