Danzer's configuration revisited

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 $O_n$ 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 $D_7$, the dihedral group of order 14.