Sprawling Clusters of Truncated Tetrahedra

Truncated tetrahedra make interesting building blocks. In the images below, the truncated tetrahedron “atoms” are grouped into four-part “molecules,” each with a triangular face pointed toward the molecular center, which is found in a small tetrahedral hole between the four truncated tetrahedra. These four-part “molecules” are then attached to other,  always with three coplanar triangular faces from one “molecule” meeting three from the other. If you start from a central “molecule,” and let such a cluster grow for a small number of iterations, you get this:

Cluster Truncateed Tetra

What does the cluster above look like if even more truncated tetrahedra are added, but without allowing overlap to occur? Like this:


Like the truncated tetrahedron itself, these sprawling clusters have tetrahedral symmetry. To keep such symmetry while building these clusters, of course, one must be careful about the exact placement of the pieces — and doing this becomes more difficult as the cluster grows ever larger. I was able to take this one more step:


All of these images were created using Stella 4d: Polyhedron Navigator. This program is available at http://www.software3d.com/Stella.php.