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 re: Surely not the intended solution ! by Fletch)

With 5 faces, it's not a tetrahedron.

Posted by Charlie on 2004-10-05 13:05:24