{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:34:12Z","timestamp":1760240052702,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,18]],"date-time":"2019-03-18T00:00:00Z","timestamp":1552867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11461035 and 11761039"],"award-info":[{"award-number":["11461035 and 11761039"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Plan Project of Jiangxi Provincial Education Department","award":["GJJ160749, GJJ160758 and GJJ180565"],"award-info":[{"award-number":["GJJ160749, GJJ160758 and GJJ180565"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Regular polytopes (RPs) are an extension of 2D (two-dimensional) regular polygons and 3D regular polyhedra in n-dimensional (    n \u2265 4    ) space. The high abstraction and perfect symmetry are their most prominent features. The traditional projections only show vertex and edge information. Although such projections can preserve the highest degree of symmetry of the RPs, they can not transmit their metric or topological information. Based on the generalized stereographic projection, this paper establishes visualization methods for 5D RPs, which can preserve symmetries and convey general metric and topological data. It is a general strategy that can be extended to visualize n-dimensional RPs (    n &gt; 5    ).<\/jats:p>","DOI":"10.3390\/sym11030391","type":"journal-article","created":{"date-parts":[[2019,3,18]],"date-time":"2019-03-18T12:18:53Z","timestamp":1552911533000},"page":"391","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stereographic Visualization of 5-Dimensional Regular Polytopes"],"prefix":"10.3390","volume":"11","author":[{"given":"Xingchang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Jinggangshan University, Ji\u2019an 343009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7444-8789","authenticated-orcid":false,"given":"Tao","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Jinggangshan University, Ji\u2019an 343009, China"}]},{"given":"Kwokwai","family":"Chung","sequence":"additional","affiliation":[{"name":"Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9434-9307","authenticated-orcid":false,"given":"Krzysztof","family":"Gdawiec","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Silesia, 40-007 Katowice, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0447-3190","authenticated-orcid":false,"given":"Peichang","family":"Ouyang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Jinggangshan University, Ji\u2019an 343009, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,18]]},"reference":[{"key":"ref_1","unstructured":"Coxeter, H.S.M. 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