Triakis truncated tetrahedral honeycomb

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]

Triakis truncated tetrahedral honeycomb
Cell type	Triakis truncated tetrahedron
Face types	hexagon isosceles triangle
Coxeter group	Ã3×2, [[3[4]]] (double)
Space group	Fd3m (227)
Properties	Cell-transitive

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 tetrahedral cells are subdivided by the center point into 4 shorter tetrahedra, and each adjoined to the adjacent truncated tetrahedral cells.

See also

• Disphenoid tetrahedral honeycomb