Geodesic
Kronecker covers, V-construction, unit-distance graphs and isometric point-circle configurations
Ars Mathematica Contemporanea, Tome 7 (2014) no. 2, pp. 317-336.

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We call a convex 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 the 1-skeleton of P. 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 all of whose members are subconfigurations of the renowned
DOI : 10.26493/1855-3974.359.8eb
Keywords: V-construction, unit-distance graph, isometric point-circle configuration 
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Gábor Gévay; Tomaž Pisanski. Kronecker covers, V-construction, unit-distance graphs and isometric point-circle configurations. Ars Mathematica Contemporanea, Tome 7 (2014) no. 2, pp. 317-336. doi : 10.26493/1855-3974.359.8eb. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.359.8eb/

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