Geodesic
Constructions for large spatial point-line (n_k) congurations
Ars Mathematica Contemporanea, Tome 7 (2014) no. 1, pp. 175-199.

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Highly symmetric figures, such as regular polytopes, can serve as a scaffolding on which spatial (nk) point-line configurations can be built. We give several constructions using this method in dimension 3 and 4. We also explore possible constructions of point-line configurations obtained as Cartesian products of smaller ones. Using suitable powers of well-chosen configurations, we obtain infinite series of (nk) configurations for which both n and k are arbitrarily large. We also combine the method of polytopal scaffolding and the method of powers to construct further examples. Finally, we formulate an incidence statement concerning a (1004) configuration in 3-space derived from the product of two complete pentalaterals; it is posed as a conjecture.
DOI : 10.26493/1855-3974.270.daa
Keywords: spatial conguration, Platonic solid, regular 4-polytope, product of congurations, incidence statement 
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Gábor Gévay. Constructions for large spatial point-line (n_k) congurations. Ars Mathematica Contemporanea, Tome 7 (2014) no. 1, pp. 175-199. doi : 10.26493/1855-3974.270.daa. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.270.daa/

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