Enumerating All Convex Polyhedra Glued from Squares in Polynomial Time

Stefan Langerman; Nicolas Potvin; Boris Zolotov

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arXiv · 2104.06787

Enumerating All Convex Polyhedra Glued from Squares in Polynomial Time

Stefan Langerman·Nicolas Potvin·Boris Zolotov

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Abstract

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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BibTeX RIS

Stefan Langerman, Nicolas Potvin, Boris Zolotov. 2021-11-26. Enumerating All Convex Polyhedra Glued from Squares in Polynomial Time. https://arxiv.org/abs/2104.06787

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