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?
The tetrahedron has a total of 4 faces... and the square pyramid has a total of 5 faces.
When joined together both of them lose a face each so the new polyhedron now has (4+5-2) 7 faces !!!
I would say this is a simplistic view...
Looking at the difficulty level, this is probably not the solution.
What am i missing ?
Posted by Syzygy
on 2004-10-05 12:08:24