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 A New Solid (Posted on 2004-10-05)
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?

 See The Solution Submitted by Brian Smith Rating: 4.1250 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Perhaps simpler calculations | Comment 11 of 19 |
(In reply to Perhaps simpler calculations by Tristan)

That's a beautiful proof Tristan.  By far the best I have ever seen for this problem.  Nice job!

 Posted by David Shin on 2004-10-05 20:36:55

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