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The Twist Operator on Maniplexes

  • Ian Douglas
  • Isabel Hubard
  • Daniel Pellicer
  • Steve Wilson
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 234)

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.

Keywords

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

Notes

Acknowledgements

We gratefully acknowledge financial support of the PAPIIT-DGAPA, under grant IN107015, and of CONACyT, under grant 166951. The completion of this work was done while the second author was on sabbatical at the Laboratoire d’Informatique de l’École Polytechnique. She thanks LIX and Vincent Pilaud for their hospitality, as well as the program PASPA-DGAPA and the UNAM for the support for this sabbatical stay.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ian Douglas
    • 1
  • Isabel Hubard
    • 2
  • Daniel Pellicer
    • 3
  • Steve Wilson
    • 4
  1. 1.TucsonUSA
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México Circuito ExteriorMexico D.F.Mexico
  3. 3.Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de MéxicoMoreliaMexico
  4. 4.Department of Mathematics and StatisticsNorthern Arizona UniversityFlagstaffUSA

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