Truncated tetrahedraloctahedral honeycomb
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Truncated tetrahedraloctahedral honeycomb  

Rank  4 
Type  uniform 
Space  Euclidean 
Notation  
Bowers style acronym  Tatoh 
Coxeter diagram  
Elements  
Cells  2N truncated tetrahedra, N cuboctahedra, N truncated octahedra 
Faces  8N triangles, 6N squares, 8N hexagons 
Edges  6N+24N 
Vertices  12N 
Vertex figure  Rectangular pyramid, base edge lengths 1 and √2, side edge lengths √3 
Measures (edge length 1)  
Vertex density  
Dual cell volume  
Related polytopes  
Army  Tatoh 
Regiment  Tatoh 
Dual  Rhombic pyramidal honeycomb 
Conjugate  None 
Abstract & topological properties  
Orientable  Yes 
Properties  
Symmetry  S_{4} 
Convex  Yes 
Nature  Tame 
The truncated tetrahedraloctahedral honeycomb, or tatoh, also known as the cantic cubic honeycomb, is a convex uniform honeycomb. 1 cuboctahedron, 2 truncated octahedra, and 2 truncated tetrahedra join at each vertex of this honeycomb. As one of its names suggests, it can be formed by truncation of the tetrahedraloctahedral honeycomb, or as an alternated faceting from the small rhombated cubic honeycomb.
Vertex coordinates[edit  edit source]
The vertices of a truncated tetrahedraloctahedral 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 tetrahedraloctahedral honeycomb has the following Coxeter diagrams:
 (full symmetry)
 (P4 symmetry, as truncated cyclotetrahedral honeycomb)
 (as cantic cubic honeycomb)
Gallery[edit  edit source]

Wireframe

External links[edit  edit source]
 Klitzing, Richard. "tatoh".
 Wikipedia contributors. "Cantic cubic honeycomb".
 Binnendyk, Eric. "Category 2: Truncates" (#16).