Cyclotruncated tetrahedraloctahedral honeycomb
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Cyclotruncated tetrahedraloctahedral honeycomb  

Rank  4 
Type  Uniform 
Space  Euclidean 
Notation  
Bowers style acronym  Cytatoh (old: Batatoh) 
Coxeter diagram  x3x3o3o3*a () 
Elements  
Cells  N tetrahedra, N truncated tetrahedra 
Faces  4N triangles, 2N hexagons 
Edges  6N 
Vertices  2N 
Vertex figure  Triangular antiprism, edge lengths 1 (base) and √3 (sides) 
Measures (edge length 1)  
Vertex density  
Related polytopes  
Army  Cytatoh 
Regiment  Cytatoh 
Dual  Triangular antitegmatic honeycomb 
Conjugate  None 
Abstract & topological properties  
Orientable  Yes 
Properties  
Symmetry  P_{4}×2 
Convex  Yes 
Nature  Tame 
The cyclotruncated tetrahedraloctahedral honeycomb, also known as the quarter cubic honeycomb, is a convex uniform honeycomb. 2 tetrahedra and 6 truncated tetrahedra join at each vertex of this honeycomb. It can be formed by applying two successive alternated faceting to the cubic honeycomb. It is related to the mutetrahedron, whose faces are exactly its hexagonal faces.
Representations[edit  edit source]
A cyclotruncated tetrahedraloctahedral honeycomb has the following Coxeter diagrams:
 x3x3o3o3*a () (full symmetry)
 s4o3x o3*b () (as single alternated faceting)
 β4o3o4s () (as double alternated faceting)
Gallery[edit  edit source]

Wireframe

Slab

External links[edit  edit source]
 Klitzing, Richard. "cytatoh".
 Wikipedia contributors. "Quarter cubic honeycomb".
 Binnendyk, Eric. "Category 7: Triangular Podiumverts" (#140).