Nick Baxter asks for references to the Colllege Board question: << Problem: Given an equilateral pyramid (square base), glue two regular tetrahedrons (same edge length) to two non-adjacent triangular faces. How many faces does the resulting polyhedron have?

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I may be wrong, but as I recall it, the problem was to glue a regular tetrahedron to a regular octahedron along one common face. --Dan