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.
COBISS.SI-ID: 17492569
All regular Cayley maps on dihedral group D_n, n)1, of order 2n are classified. Besides 4 sporadic maps on 4,4,8 and 12 vertices respectively, two infinite families of non-t-balanced Cayley maps on D_n are obtained.
COBISS.SI-ID: 1538922180
A permutation of the point set of the affine space AG(n,q) is called an integral automorphism if it preserves the integral distance defined among the points. In this paper, we complete the classification of the integral automorphisms of AG(n,q) for n\ge 3.
COBISS.SI-ID: 1538527940