Mock AIME 5 2005-2006 Problems/Problem 8

Problem

Let $P$ be a polyhedron with $37$ faces, all of which are equilateral triangles, squares, or regular pentagons with equal side length. Given there is at least one of each type of face and there are twice as many pentagons as triangles, what is the sum of all the possible number of vertices $P$ can have?

Solution

Solution

See also

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by
Problem 7
Followed by
Problem 9
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