2556 KB56 KB200820252014Gévay, Gáborštevilka:1letnik:7str. 175-199COBISSID:16796761ISSN:1855-3966URN:URN:NBN:SI:doc-MSVK3TB9enDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneagrafiincidence statementkombinatorikaPlatonic solidproduct of configurationsregular 4-polytopespatial configurationConstructions for large spatial point-line (n sub k) configurations|Highly symmetric figures, such as regular polytopes, can serve as a scaffolding on which spatial ?$(n_k)$? 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 ?$(n_k)$? 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 ?$(100_4)$? configuration in 3-space derived from the product of two complete pentalaterals; it is posed as a conjectureTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije