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 71º for the tetrahedron and about 109º 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