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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)

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 Surely not the intended solution ! | Comment 1 of 19

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

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