立方体割轨迹的同构类
Isomorphism classes of cut loci for a cube
摘要：
我们证明了立方体的一个面可以最优地划分成193个连通集，在这些连通集上，割迹或脊树直到同构为标号图为止是常数。这些是60个连接的开放集，它们的边界曲线，以及曲线的交点。给出了曲线的多项式方程。十六对集合支持相同的割迹类。我们提出了177个不同的割迹类。
英文摘要：
We prove that a face of a cube can be optimally partitioned into connected 193 sets on which the cut locus, or ridge tree, is constant up to isomorphism as a labeled graph. These are 60 connected open sets, curves bounding them, and intersection points of curves. Polynomial equations for the curves are provided. Sixteen pairs of sets support the same cut locus class. We present the 177 distinct cut locus classes.
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