@inproceedings{79d1a0d3a9524d1eab07a1d7cbb0fbf3,
title = "The Twist Operator on Maniplexes",
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 {\textquoteleft}rotational{\textquoteright} 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 = "Automorphism group, Chiral, Flag, Graph, Maniplex, Map, Polytope, Reflexible, Rotary, Symmetry, Transitivity",
author = "Ian Douglas and Isabel Hubard and Daniel Pellicer and Steve Wilson",
note = "Funding Information: 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{\textquoteright}Informatique de l{\textquoteright}{\'E}cole 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. Funding Information: 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{\textquoteright}Informatique de l{\textquoteright}{\'E}cole 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. Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.; International Conference on Geometry and Symmetry, GeoSym 2015 ; Conference date: 29-06-2015 Through 03-07-2015",
year = "2018",
doi = "10.1007/978-3-319-78434-2_7",
language = "English (US)",
isbn = "9783319784335",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "127--145",
editor = "Antoine Deza and Weiss, {Asia Ivic} and Conder, {Marston D.}",
booktitle = "Discrete Geometry and Symmetry - Dedicated to Karoly Bezdek and Egon Schulte on the Occasion of Their 60th Birthdays",
}