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.

中文翻译：

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枚举多项式时间内从正方形胶合的所有凸多面体

我们提出了一种算法，该算法枚举并分类了与凸多面体相对应的单位正方形的所有边到边粘合。我们显示，这种$ n $平方粘合的数量是$ n $的多项式，并且该算法以$ n $的时间多项式运行（如果将$ n $视为唯一输入，则为伪多项式）。我们的技术可以在几种类似的设置中应用，包括正六边形和三角形的粘合。