{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:20Z","timestamp":1760145740581,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T00:00:00Z","timestamp":1724025600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The grand antiprism A is an outlier among the uniform 4-polytopes, since it is not obtainable from Wythoff\u2019s construction. Its symmetry group G(A) has been incorrectly described as [[10,2+,10]] or even as an \u2018ionic diminished Coxeter group\u2019. In fact, G(A) is another group of order 400, namely the group \u00b1[D10\u00d7D10]\u00b72, in the notation of Conway and Smith. We explain all this and so correct a persistent error in the literature. This fresh look at the beautiful geometry of the polytope A is also a fine opportunity to introduce the reader to the elegance of Wythoff\u2019s construction and to the less familiar use of quaternions to classify the finite 4-dimensional isometry groups.<\/jats:p>","DOI":"10.3390\/sym16081071","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T10:11:28Z","timestamp":1724062288000},"page":"1071","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Symmetry Group of the Grand Antiprism"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9901-9681","authenticated-orcid":false,"given":"Barry","family":"Monson","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1007\/BF01181449","article-title":"Regular and semi-regular polytopes. 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