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. Mathematicians describe such a punctured face as being "multiply connected."
Several years ago, mathematician John H. Conway of Princeton University wondered whether a polyhedron could have such a polygonal hole passing thr