Truncated cubic honeycomb
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Truncated cubic honeycomb  

Rank  4 
Type  uniform 
Space  Euclidean 
Notation  
Bowers style acronym  Tich 
Coxeter diagram  x4x3o4o () 
Elements  
Cells  N octahedra, N truncated cubes 
Faces  8N triangles, 3N octagons 
Edges  3N+12N 
Vertices  6N 
Vertex figure  Square pyramid, edge lengths 1 (base) and √2+√2 (sides) 
Measures (edge length 1)  
Vertex density  
Dual cell volume  
Related polytopes  
Army  Tich 
Regiment  Tich 
Dual  Square pyramidal honeycomb 
Conjugate  Quasitruncated cubic honeycomb 
Abstract & topological properties  
Orientable  Yes 
Properties  
Symmetry  R_{4} 
Convex  Yes 
Nature  Tame 
The truncated cubic honeycomb, or tich, is a convex uniform honeycomb. 1 octahedron and 4 truncated cubes join at each vertex of this honeycomb. As the name suggests, it is the truncation of the cubic honeycomb.
Vertex coordinates[edit  edit source]
The vertices of a truncated cubic honeycomb of edge length 1 are given by all permutations of:
 ,
Where i, j, and k range over the integers.
Representations[edit  edit source]
A truncated cubic honeycomb has the following Coxeter diagrams:
 x4x3o4o () (regular)
 x4x3o2o3*b () (S_{4} symmetry)
 wx4xo3ox4xw&#zx
Gallery[edit  edit source]

Wireframe


Orthogonal projection into Euclidean plane with V_{3} symmetry
External links[edit  edit source]
 Klitzing, Richard. "tich".
 Wikipedia contributors. "Truncated cubic honeycomb".
 Binnendyk, Eric. "Category 2: Truncates" (#14).