{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:35Z","timestamp":1740109595290,"version":"3.37.3"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T00:00:00Z","timestamp":1695772800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T00:00:00Z","timestamp":1695772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2024,4]]},"abstract":"Abstract<\/jats:title>A (convex) polytope $$P\\subset \\mathbb {R}^d$$<\/jats:tex-math>\n \n P<\/mml:mi>\n \u2282<\/mml:mo>\n \n \n R<\/mml:mi>\n <\/mml:mrow>\n d<\/mml:mi>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and its edge-graph $$G_P$$<\/jats:tex-math>\n \n G<\/mml:mi>\n P<\/mml:mi>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> can have\u00a0very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be \u201crectified\u201d by coloring the vertices and edges of\u00a0$$G_P$$<\/jats:tex-math>\n \n G<\/mml:mi>\n P<\/mml:mi>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they \u201ccapture polytopal\u00a0symmetries\u201d involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory.<\/jats:p>","DOI":"10.1007\/s00454-023-00560-7","type":"journal-article","created":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T18:02:28Z","timestamp":1695837748000},"page":"1003-1020","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Capturing Polytopal Symmetries by Coloring the Edge-Graph"],"prefix":"10.1007","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3817-9494","authenticated-orcid":false,"given":"Martin","family":"Winter","sequence":"first","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,27]]},"reference":[{"issue":"2\u20133","key":"560_CR1","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/BF02760511","volume":"47","author":"J Bokowski","year":"1984","unstructured":"Bokowski, J., Ewald, G., Kleinschmidt, P.: On combinatorial and affine automorphisms of polytopes. 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