---
_id: '7567'
abstract:
- lang: eng
  text: Coxeter triangulations are triangulations of Euclidean space based on a single
    simplex. By this we mean that given an individual simplex we can recover the entire
    triangulation of Euclidean space by inductively reflecting in the faces of the
    simplex. In this paper we establish that the quality of the simplices in all Coxeter
    triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate
    the Delaunay property for these triangulations. Moreover, we consider an extension
    of the Delaunay property, namely protection, which is a measure of non-degeneracy
    of a Delaunay triangulation. In particular, one family of Coxeter triangulations
    achieves the protection O(1/d2). We conjecture that both bounds are optimal for
    triangulations in Euclidean space.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Aruni
  full_name: Choudhary, Aruni
  last_name: Choudhary
- first_name: Siargey
  full_name: Kachanovich, Siargey
  last_name: Kachanovich
- first_name: Mathijs
  full_name: Wintraecken, Mathijs
  id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
  last_name: Wintraecken
  orcid: 0000-0002-7472-2220
citation:
  ama: Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good
    quality. <i>Mathematics in Computer Science</i>. 2020;14:141-176. doi:<a href="https://doi.org/10.1007/s11786-020-00461-5">10.1007/s11786-020-00461-5</a>
  apa: Choudhary, A., Kachanovich, S., &#38; Wintraecken, M. (2020). Coxeter triangulations
    have good quality. <i>Mathematics in Computer Science</i>. Springer Nature. <a
    href="https://doi.org/10.1007/s11786-020-00461-5">https://doi.org/10.1007/s11786-020-00461-5</a>
  chicago: Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter
    Triangulations Have Good Quality.” <i>Mathematics in Computer Science</i>. Springer
    Nature, 2020. <a href="https://doi.org/10.1007/s11786-020-00461-5">https://doi.org/10.1007/s11786-020-00461-5</a>.
  ieee: A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations
    have good quality,” <i>Mathematics in Computer Science</i>, vol. 14. Springer
    Nature, pp. 141–176, 2020.
  ista: Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have
    good quality. Mathematics in Computer Science. 14, 141–176.
  mla: Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” <i>Mathematics
    in Computer Science</i>, vol. 14, Springer Nature, 2020, pp. 141–76, doi:<a href="https://doi.org/10.1007/s11786-020-00461-5">10.1007/s11786-020-00461-5</a>.
  short: A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science
    14 (2020) 141–176.
date_created: 2020-03-05T13:30:18Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2021-01-12T08:14:13Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s11786-020-00461-5
ec_funded: 1
file:
- access_level: open_access
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  creator: dernst
  date_created: 2020-11-20T10:18:02Z
  date_updated: 2020-11-20T10:18:02Z
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file_date_updated: 2020-11-20T10:18:02Z
has_accepted_license: '1'
intvolume: '        14'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '03'
oa: 1
oa_version: Published Version
page: 141-176
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Mathematics in Computer Science
publication_identifier:
  eissn:
  - 1661-8289
  issn:
  - 1661-8270
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coxeter triangulations have good quality
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2020'
...