Aequationes mathematicae

, Volume 90, Issue 5, pp 1045–1067 | Cite as

Highly symmetric hypertopes

  • Maria Elisa Fernandes
  • Dimitri LeemansEmail author
  • Asia Ivić Weiss


We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytope theory, we introduce the concept of chirality, a property of orderly asymmetry occurring frequently in nature as a natural phenomenon. The main result in this paper is that automorphism groups of regular and chiral thin residually connected geometries need to be C-groups in the regular case and \({C^+}\)-groups in the chiral case.


Regularity chirality thin geometries hypermaps abstract polytopes 

Mathematics Subject Classification

51E24 52B11 20F05 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Maria Elisa Fernandes
    • 1
  • Dimitri Leemans
    • 2
    Email author
  • Asia Ivić Weiss
    • 3
  1. 1.Department of Mathematics, Center for Research and Development in Mathematics and ApplicationsUniversity of AveiroAveiroPortugal
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand
  3. 3.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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