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?

That's a neat little question, Brian. Charlie mentioned computing dihedrals at the juctions of the equilateral triangles. Actually, he did a bit more than a mention. I quick folded some paper strips and measured about 71� for the tetrahedron and about 109� for the square pyramid. Pretty supplementary. Convinced me there were now just five faces. Anyone know a special name for this resulting pentahedron?

Posted by CeeAnne on 2004-10-05 19:15:47