Kronecker covers, V-construction, unit-distance graphs and isometric point-circle configurations
Combinatorics
2012-07-31 v2
Abstract
We call a polytope P of dimension 3 admissible if it has the following two properties: (1) for each vertex of P the set of its first-neighbours is coplanar; (2) all planes determined by the first-neighbours are distinct. It is shown that the Levi graph of a point-plane configuration obtained by V-construction from an admissible polytope P is the Kronecker cover of its 1-skeleton. We investigate the combinatorial nature of the V-construction and use it on unit-distance graphs to construct novel isometric point-circle configurations. In particular, we present an infinite series whose all members are subconfigurations of the renowned Clifford configurations.
Cite
@article{arxiv.1206.5477,
title = {Kronecker covers, V-construction, unit-distance graphs and isometric point-circle configurations},
author = {Gábor Gévay and Tomaž Pisanski},
journal= {arXiv preprint arXiv:1206.5477},
year = {2012}
}