Triakis truncated tetrahedron

Not to be confused with truncated triakis tetrahedron.

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.

Triakis truncated tetrahedron
Type	Plesiohedron
Faces	4 hexagons 12 isosceles triangles
Edges	30
Vertices	16
Conway notation	k3tT
Dual polyhedron	16|Order-3 truncated triakis tetrahedron
Properties	convex

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. As the Voronoi cell of a symmetric space pattern, it is a plesiohedron.

Construction

Triakis truncated tetrahedral honeycomb

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
• Triakis tetrahedron