Automorphism groups of 3-orbit polyhedra

Hubard, Isabel; Mochán, Elías

doi:10.1007/s10801-022-01127-0

Cited by 3 publications

(1 citation statement)

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“…This means that the poset P can be reconstructed from the graph Γ P , and vice versa. The possibility of jumping freely from the poset to the graph, and back, offers some obvious advantages, as it A c c e p t e d m a n u s c r i p t allows us to use graph theoretical tools to tackle problems pertaining to abstract polytopes (see for instance [7] or [5] for a nice example of this).…”

Section: Introductionmentioning

confidence: 99%

Faithful and thin non-polytopal maniplexes

Leemans,

Toledo

2024

Ars Math. Contemp.

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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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Section: Introductionmentioning

confidence: 99%