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  • Kronecker covers, V-construction, unit-distance graphs and isometric point-circle configurations
    Gévay, Gábor ; Pisanski, Tomaž
    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 Clifford configurations.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 7, no. 2, 2014, str. 317-336)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2014
    Jezik - angleški
    COBISS.SI-ID - 16868185

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 7, no. 2, 2014, str. 317-336)

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