Danzer's configuration revisited
Combinatorics
2015-01-07 v2 Metric Geometry
Abstract
We revisit the configuration of Danzer DCD(4), a great inspiration for our work. This configuration of type (35_4) falls into an infinite series of geometric point-line configurations DCD(n). Each DCD(n) is characterized combinatorially by having the Kronecker cover over the Odd graph 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 , the dihedral group of order 14.
Cite
@article{arxiv.1301.1067,
title = {Danzer's configuration revisited},
author = {Marko Boben and Gábor Gévay and Tomaž Pisanski},
journal= {arXiv preprint arXiv:1301.1067},
year = {2015}
}