Triakis truncated tetrahedron

Not to be confused with truncated triakis tetrahedron.

Triakis truncated tetrahedron
Triakis truncated tetrahedron (Click here for rotating model)
Type	Conway polyhedron
Conway notation	k3tT
Faces	4 hexagons 12 isosceles triangles
Edges	30
Vertices	16
Properties	convex, space-filling

In geometry, the triakis truncated tetrahedron is a convex polyhedron made from 4 hexagons and 12 isosceles triangles. It can be used to tessellate three-dimensional space, making the triakis truncated tetrahedral honeycomb.

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.

Construction

For space-filling, the triakis truncated tetrahedron can be constructed as follows:

1. Truncate a regular tetrahedron such that the big faces are regular hexagons.
2. Add an extra vertex at the center of each of the four smaller tetrahedra that were removed.

See also

• Quarter cubic honeycomb
• Truncated tetrahedron