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)

Nice, clear, elegant proof, Tristan!   Much simpler than the earlier posts--filled with trig.

Posted by Ken Haley on 2004-10-06 00:20:29