{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T17:19:43Z","timestamp":1774027183622,"version":"3.50.1"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T00:00:00Z","timestamp":1706054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Czech Academy of Sciences","award":["RVO 67985840"],"award-info":[{"award-number":["RVO 67985840"]}]},{"name":"Czech Academy of Sciences","award":["24-10586S"],"award-info":[{"award-number":["24-10586S"]}]},{"name":"GA\u010cR","award":["RVO 67985840"],"award-info":[{"award-number":["RVO 67985840"]}]},{"name":"GA\u010cR","award":["24-10586S"],"award-info":[{"award-number":["24-10586S"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We first briefly summarize several well-known properties of regular tessellations of the three two-dimensional maximally symmetric manifolds, E2, S2, and H2, by bounded regular tiles. For instance, there exist infinitely many regular tessellations of the hyperbolic plane H2 by curved hyperbolic equilateral triangles whose vertex angles are 2\u03c0\/d for d=7,8,9,\u2026 On the other hand, we prove that there is no curved hyperbolic regular tetrahedron which tessellates the three-dimensional hyperbolic space H3. We also show that a regular tessellation of H3 can only consist of the hyperbolic cubes, hyperbolic regular icosahedra, or two types of hyperbolic regular dodecahedra. There exist only two regular hyperbolic space-fillers of H4. If n&gt;4, then there exists no regular tessellation of Hn.<\/jats:p>","DOI":"10.3390\/sym16020141","type":"journal-article","created":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T09:57:42Z","timestamp":1706090262000},"page":"141","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Regular Tessellations of Maximally Symmetric Hyperbolic Manifolds"],"prefix":"10.3390","volume":"16","author":[{"given":"Jan","family":"Brandts","sequence":"first","affiliation":[{"name":"Faculty of Science, KDV, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5271-5038","authenticated-orcid":false,"given":"Michal","family":"K\u0159\u00ed\u017eek","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Czech Academy of Sciences, \u017ditn\u00e1 25, 115 67 Prague, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1976-3169","authenticated-orcid":false,"given":"Lawrence","family":"Somer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Catholic University of America, Washington, DC 20064, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,24]]},"reference":[{"key":"ref_1","unstructured":"Weinberg, S. (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley."},{"key":"ref_2","unstructured":"Penrose, R. (2005). The Road to Reality, Vintage Books."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Brandts, J., Korotov, S., and K\u0159\u00ed\u017eek, M. (2020). Simplicial Partitions with Applications to the Finite Element Method, Springer International Publishing.","DOI":"10.1007\/978-3-030-55677-8"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Beardon, A.F. (1983). The Geometry of Discrete Groups, Springer.","DOI":"10.1007\/978-1-4612-1146-4"},{"key":"ref_5","first-page":"17","article-title":"The story of the 120-cell","volume":"48","author":"Stillwell","year":"2001","journal-title":"Not. Am. Math. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Conway, J.H., and Sloane, N.J.A. (1988). 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Lie Groups and Algebraic Groups, Springer.","DOI":"10.1007\/978-3-642-74334-4"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/2\/141\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:48:44Z","timestamp":1760104124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/2\/141"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,24]]},"references-count":16,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["sym16020141"],"URL":"https:\/\/doi.org\/10.3390\/sym16020141","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,24]]}}}