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Math Trek

Punctured Polyhedra

1:06pm, December 11, 2002

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

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