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?
A friend of mine at work has a desk toy consisting of little round balls (about .2 inch in diameter) and little colored magnetic cylindrical rods also about .2 inch in diameter and about 1.5 inch long. Today, he had them assembled them into two adjacent square pyramids sharing a common base with a rod connecting the peaks--a perfect model of this puzzle. (He knew nothing about the puzzle; I just read it myself the first time tonight.)
Edited on October 6, 2004, 12:29 am