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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.
Contents
Voronoi tessellation
It is the Voronoi tessellation of the carbon atoms in diamond, 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.
References
Triakis truncated tetrahedral honeycomb Wikipedia(Text) CC BY-SA