# Triakis truncated tetrahedral honeycomb

Triakis truncated tetrahedral honeycomb
Cell type Triakis truncated tetrahedron
Face types hexagon
isosceles triangle
Coxeter group ${\tilde{A}}_3$×2, [[3[4]]] (double)
Space group Fd3m (227)
Properties Cell-transitive

The triakis truncated tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of triakis truncated tetrahedra. It was discovered in 1914.[1][2]

## Voronoi tessellation

It is the Voronoi tessellation of the carbon atoms in diamond,[3][4] which lie in the diamond cubic crystal structure.

Being composed entirely of triakis truncated tetrahedra, it is cell-transitive.

## Relation to quarter cubic honeycomb

It can be seen as the uniform quarter cubic honeycomb where its tetrahedal cells are subdivided by the center point into 4 shorter tetrahedra, and each adjoined to the adjacent truncated tetrahedral cells.