| Title: | Faithful and thin non-polytopal maniplexes |
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| Authors: | ID Leemans, Dimitri (Author)
ID Toledo, Micael (Author) |
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| Files: |  AMC_Leemans,Toledo_2025.pdf (632,07 KB)
MD5: 4C112558B0672F2988150C27F11FA6DE
 https://amc-journal.eu/index.php/amc/article/view/3128
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | Maniplexes are coloured graphs that generalise maps on surfaces and abstract polytopes. Each maniplex uniquely defines a partially ordered set that encodes information about its structure. When this poset is an abstract polytope, we say that the associated maniplex is polytopal. Maniplexes that have two properties, called faithfulness and thinness, are completely determined by their associated poset, which is often an abstract polytope. We show that all faithful thin maniplexes of rank three are polytopal. So far only one example, of rank four, of a thin maniplex that is not polytopal was known. We construct the first infinite family of maniplexes that are faithful and thin but are non-polytopal for all ranks greater than three. |
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| Keywords: | maniplex, polytope, faithful, thin, regular cover |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 12.02.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 17 str. |
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| Numbering: | Vol. 25, no. 1, [article no.] P1.04 |
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| PID: | 20.500.12556/RUP-21769  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3128.b29 |
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| Publication date in RUP: | 18.09.2025 |
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| Views: | 454 |
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| Downloads: | 6 |
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