The Twist Operator on Maniplexes

Ian Douglas, Isabel Hubard, Daniel Pellicer, Stephen E Wilson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Maniplexes are combinatorial objects that generalize, simultaneously, maps on surfaces and abstract polytopes. We are interested on studying highly symmetric maniplexes, particularly those having maximal ‘rotational’ symmetry. This paper introduces an operation on polytopes and maniplexes which, in its simplest form, can be interpreted as twisting the connection between facets. This is first described in detail in dimension 4 and then generalized to higher dimensions. Since the twist on a maniplex preserves all the orientation preserving symmetries of the original maniplex, we apply the operation to reflexible maniplexes, to attack the problem of finding chiral polytopes in higher dimensions.

Original languageEnglish (US)
Title of host publicationDiscrete Geometry and Symmetry - Dedicated to Karoly Bezdek and Egon Schulte on the Occasion of Their 60th Birthdays
PublisherSpringer New York LLC
Pages127-145
Number of pages19
Volume234
ISBN (Print)9783319784335
DOIs
StatePublished - Jan 1 2018
EventInternational Conference on Geometry and Symmetry, GeoSym 2015 - Veszprem, Hungary
Duration: Jun 29 2015Jul 3 2015

Other

OtherInternational Conference on Geometry and Symmetry, GeoSym 2015
CountryHungary
CityVeszprem
Period6/29/157/3/15

Keywords

  • Automorphism group
  • Chiral
  • Flag
  • Graph
  • Maniplex
  • Map
  • Polytope
  • Reflexible
  • Rotary
  • Symmetry
  • Transitivity

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Douglas, I., Hubard, I., Pellicer, D., & Wilson, S. E. (2018). The Twist Operator on Maniplexes. In Discrete Geometry and Symmetry - Dedicated to Karoly Bezdek and Egon Schulte on the Occasion of Their 60th Birthdays (Vol. 234, pp. 127-145). Springer New York LLC. https://doi.org/10.1007/978-3-319-78434-2_7