Punctured Polyhedra

A tetrahedron.
Examples of unacceptable faces.
A portion of an infinite lattice of interpenetrating tetrahedra.

A tetrahedron has four triangular faces, four vertices, and six edges.

Consider what happens when a vertex of one tetrahedron pierces the face of a second tetrahedron to form a new, more complicated polyhedron. In the resulting geometric form, one triangular face has a triangular “hole” where the face was pierced.