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.

Rights

URN

URN:NBN:SI:DOC-UP0977P7

COBISSID

226080515

DOI

10.26493/1855-3974.3128.b29

Added

20.02.2026

Metadata

Citation

APA:

Leemans, Dimitri, Toledo, Micael (2025). Faithful and thin non-polytopal maniplexes. Ars mathematica contemporanea, volume 25, issue 1, article p1.04, 17 str. URN:NBN:SI:DOC-UP0977P7 from http://www.dlib.si

MLA:

Leemans, Dimitri, Toledo, Micael. "Faithful and thin non-polytopal maniplexes." Ars mathematica contemporanea volume 25. issue 1. article p1.04 (2025) 17 str..
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-UP0977P7>

Ars mathematica contemporanea
2008-
(Assembly record)