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Geometric point-circle pentagonal geometries from Moore graphs
University of Skovde, Sweden.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9557-9566
2016 (English)In: Ars Mathematica Contemporanea, ISSN 1855-3966, Vol. 11, no 1, 215-229 p.Article in journal (Refereed) PublishedText
Abstract [en]

We construct isometric point-circle configurations on surfaces from uniform maps. This gives one geometric realisation in terms of points and circles of the Desargues configuration in the real projective plane, and three distinct geometric realisations of the pentagonal geometry with seven points on each line and seven lines through each point on three distinct dianalytic surfaces of genus 57. We also give a geometric realisation of the latter pentagonal geometry in terms of points and hyperspheres in 24 dimensional Euclidean space. From these, we also obtain geometric realisations in terms of points and circles (or hyperspheres) of pentagonal geometries with k circles (hyperspheres) through each point and k 1 points on each circle (hypersphere).

Place, publisher, year, edition, pages
DMFA SLOVENIJE , 2016. Vol. 11, no 1, 215-229 p.
Keyword [en]
Uniform map; equivelar map; dessin denfants; configuration of points and circles
National Category
Mathematical Analysis Geometry
Identifiers
URN: urn:nbn:se:liu:diva-127757ISI: 000373939900015OAI: oai:DiVA.org:liu-127757DiVA: diva2:927479
Note

Funding Agencies|Spanish MEC project ICWT [TIN2012-32757]; Spanish MEC project ARES (CONSOLIDER INGENIO) [CSD2007-00004]

Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-19

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Izquierdo, Milagros
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Mathematics and Applied MathematicsFaculty of Science & Engineering
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