Smooth tropical cubic surfaces are parametrized by maximal cones in the unimodular secondary fan of the triple tetrahedron. There are $$344\, 843 \,867$$ 344 843 867 such cones, organized into a database of $$14\,373\,645$$ 14 373 645 symmetry classes. The Schläfli fan gives a further refinement of these cones. It reveals all possible patterns of lines on tropical cubic surfaces, thus serving as a combinatorial base space for the universal Fano variety. This article develops the relevant theory and offers a blueprint for the analysis of big data in tropical geometry.

中文翻译：

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Schläfli 风扇

光滑的热带立方表面由三重四面体的单模二次扇中的最大锥体参数化。有 $$344\, 843 \,867$$ 344 843 867 个这样的锥体，组织到 $$14\,373\,645$$ 14 373 645 个对称类的数据库中。Schläfli 风扇进一步改进了这些锥体。它揭示了热带立方体表面上所有可能的线条图案，从而作为通用 Fano 品种的组合基础空间。本文发展了相关理论，并为热带几何中的大数据分析提供了蓝图。