Danzer’s configuration revisited-Reference-Cited by-同舟云学术

Danzer’s configuration revisited

Published:2015-10-01 Issue:4 Volume:15 Page:393-408
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Boben Marko¹,Gévay Gábor²,Pisanski Tomaž³

Affiliation:

1. Faculty of Computer Science, University of Ljubljana, 1000 Ljubljana, Slovenia, University of Primorska, IAM, Muzejski trg 2, 6000 Koper, Slovenia

2. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., 6720 Szeged, Hungary

3. Faculty of Mathematics and Physics, University of Ljubljana, 1111 Ljubljana, Slovenia, University of Primorska, FAMNIT, Glagoljaška 8, 6000 Koper, Slovenia

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2015-0019/pdf

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