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There are <jats:inline-formula><jats:alternatives><jats:tex-math>$$344\\, 843 \\,867$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>344<\/mml:mn>\n                    <mml:mspace\/>\n                    <mml:mn>843<\/mml:mn>\n                    <mml:mspace\/>\n                    <mml:mn>867<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> such cones, organized into a database of <jats:inline-formula><jats:alternatives><jats:tex-math>$$14\\,373\\,645$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>14<\/mml:mn>\n                    <mml:mspace\/>\n                    <mml:mn>373<\/mml:mn>\n                    <mml:mspace\/>\n                    <mml:mn>645<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> symmetry classes. The Schl\u00e4fli 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.<\/jats:p>","DOI":"10.1007\/s00454-020-00215-x","type":"journal-article","created":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T15:03:47Z","timestamp":1592838227000},"page":"355-381","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Schl\u00e4fli Fan"],"prefix":"10.1007","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4974-9659","authenticated-orcid":false,"given":"Michael","family":"Joswig","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8631-6329","authenticated-orcid":false,"given":"Marta","family":"Panizzut","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6642-1479","authenticated-orcid":false,"given":"Bernd","family":"Sturmfels","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,22]]},"reference":[{"key":"215_CR1","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/0097-3165(73)90074-5","volume":"15","author":"A Altshuler","year":"1973","unstructured":"Altshuler, A., Steinberg, L.: Neighborly $$4$$-polytopes with $$9$$ vertices. 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