The triakis truncated tetrahedron is the shape of the Voronoi cell of the carbon atoms in diamond, which lie on the diamond cubic crystal structure.[3][4] As the Voronoi cell of a symmetric space pattern, it is a plesiohedron.[5]
Construction
For space-filling, the triakis truncated tetrahedron can be constructed as follows:
Truncate a regular tetrahedron such that the big faces are regular hexagons.
Add an extra vertex at the center of each of the four smaller tetrahedra that were removed.