20.500.12556/RUP-21769 Faithful and thin non-polytopal maniplexes Zvesti in tanki nepolitopski manipleksi 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. Manipleksi so barvni grafi, ki predstavljajo posplošitev tako zemljevidov na ploskvah kot tudi abstraktnih politopov. Vsak manipleks enolično določa delno urejeno množico, ki vsebuje informacijo o njegovi strukturi. Kadar je ta delno urejena množica abstrakten politop, pravimo, da je ustrezen manipleks politopski. Manipleksi, ki imajo dve lastnosti, imenovani zvestost in tankost, so povsem določeni z njim pridruženo delno urejeno množico, ki je pogosto abstrakten politop. Dokažemo, da so vsi zvesti tanki manipleksi ranga tri politopski. Doslej je bil znan samo en primer, in sicer ranga štiri, tankega manipleksa, ki ni politopski. Konstruiramo prvo neskončno družino manipleksov, ki so zvesti in tanki, niso pa politopski, in sicer za vse range večje kot tri. maniplex polytope faithful thin regular cover manipleks politop zvest tanek regularni krov true false false Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-09-17 11:24:38 2025-09-18 10:38:47 2026-02-02 12:15:16 0000-00-00 00:00:00 2025 0 0 17 str. no. 1, [article no.] P1.04 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-02-12 51 1855-3974 10.26493/1855-3974.3128.b29 AMC_Leemans,Toledo_2025.pdf AMC_Leemans,Toledo_2025.pdf 1 4C112558B0672F2988150C27F11FA6DE 22113a69708440ad6ea300f521c60d41932d1553a12df5a8e6b5ae262f3bd8fa 6cdfbecf-93a8-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31638 https://amc-journal.eu/index.php/amc/article/view/3128 1 3d07fc05-93a8-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31637 Založba Univerze na Primorskem 0 0 0