Abstract K3 polytopes appear in complements of tropical quartic surfaces. They are dual to regular unimodular central triangulations of reflexive polytopes in the fourth dilation of the standard tetrahedron. Exploring these combinatorial objects, we classify K3 polytopes with up to 30 vertices. Their number is 36 297 333. We study the singular loci of quartic surfaces that tropicalize to K3 polytopes. These surfaces are stable in the sense of Geometric Invariant Theory.

中文翻译：

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K3 多胞体及其四次曲面

摘要 K3 多胞体出现在热带四次曲面的补充中。它们是标准四面体第四次膨胀中自反多胞体的对偶到规则单模中心三角剖分。探索这些组合对象，我们对具有多达 30 个顶点的 K3 多胞体进行分类。它们的数量是 36 297 333。我们研究了热带化为 K3 多胞体的四次曲面的奇异位点。这些表面在几何不变理论的意义上是稳定的。