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Problem of the Week 1173

A Polyhedral Puzzle

Given a convex polyhedron P, get a new polyhedron Q by cutting off a small tip from each vertex of P.

Suppose Q has V vertices, E edges, and F faces, and one of V, E, F equals 1001.

What are the values of V, E, and F?

Source: G. Galperin, via the Berlekamp-Buhler puzzle section of Emissary, the MSRI newsletter.

© Copyright 2014 Stan Wagon. Reproduced with permission.

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19 December 2013