A regular tetrahedron has four equilateral triangles as faces. A regular square pyramid has four equilateral triangles and a square as faces. The faces of the tetrahedron are congruent to the triangular faces of the square pyramid.

A new polyhedron is created by gluing the tetrahedron and the square pyramid together at a triangular face so that the vertices of the triangles coincide. How many faces does this polyhedron have?

(In reply to Perhaps simpler calculations by Tristan)

That's a beautiful proof Tristan.  By far the best I have ever seen for this problem.  Nice job!

Posted by David Shin on 2004-10-05 20:36:55