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?

one would think that the answer is seven, that is the five sides of the pyramid plus the four of the tetrahedron minus the two faces that are glued.

however, two of the triangles of the tetrahedron become coplanar with two triangles of the pyramid, creating two quadrangle faces.

this gives our new solid FIVE faces.

Posted by rixar on 2004-10-06 07:50:23