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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

Online
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1615-7168
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Volume 15, Issue 4

Issues

Danzer’s configuration revisited

Dedicated to the memory of Ludwig Danzer (1927–2011)

Marko Boben
  • Faculty of Computer Science, University of Ljubljana, 1000 Ljubljana, Slovenia, University of Primorska, IAM, Muzejski trg 2, 6000 Koper, Slovenia
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/ Gábor Gévay / Tomaž Pisanski
  • Faculty of Mathematics and Physics, University of Ljubljana, 1111 Ljubljana, Slovenia, University of Primorska, FAMNIT, Glagoljaška 8, 6000 Koper, Slovenia
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Published Online: 2015-10-06 | DOI: https://doi.org/10.1515/advgeom-2015-0019

Abstract

We revisit the configuration DCD(4) of Danzer, a great inspiration for our work. This configuration of type (354) falls into an in_nite series of geometric point-line configurations DCD(n). Each DCD(n) is characterized combinatorially by having the Kronecker cover over the Odd graph On as its Levi graph. Danzer’s configuration is deeply rooted in Pascal’s Hexagrammum Mysticum. Although the combinatorial configuration is highly symmetric, we conjecture that there are no geometric point-line realizations with 7- or 5-fold rotational symmetry; on the other hand, we found a point-circle realization having the symmetry group D7, the dihedral group of order 14.

Keywords: Danzer configuration; Danzer graph; Odd graph; Kronecker cover,V-construction,Hexagrammum Mysticum; point-circle configuration; Cayley-Salmon configuration; Steiner-Plücker configuration; Coxeter (283)-configuration

About the article

Received: 2013-01-07

Revised: 2014-10-24

Published Online: 2015-10-06

Published in Print: 2015-10-01


Citation Information: Advances in Geometry, Volume 15, Issue 4, Pages 393–408, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0019.

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[1]
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