Enumerating All Convex Polyhedra Glued from Squares in Polynomial Time
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We present an algorithm that enumerates and classifies all edge-to-edge gluings of unit squares that correspond to convex polyhedra. We show that the number of such gluings of n squares is polynomial in n, and the algorithm runs in time polynomial in n (pseudopolynomial if n is considered the only input). Our technique can be applied in several similar settings, including gluings of regular hexagons and triangles.
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