20.500.12556/RUP-22689 Playing with the Pappus configuration Igranje s Pappusovo konfiguracijo Faced with the enormity of Hexagrammum Mysticum, trying to understand it and wishing to discover in it something genuinely new, I decided to first try my hand at something smaller and easier to handle, to get some practice. To this end I have chosen the Pappus layout of two lines with three points on each, a degenerate variation of the Pascal’s sextet of coconic points which is the construction base of Hexagramum Mysticum. I permuted the points on one of the lines, and generated the six Pappus three-point lines corresponding to the permuted hexagons. Six three-point lines was too little material even for a Hexagrammum Brevis, so I adopted into the configuration the nine lines connecting pairs of points on the opposite lines of a Pappus layout, and for good measure added the two points of concurrence of two tercets of Pappus lines. The resulting Frankenstein Creature configuration, sewed together from three so different parts, surprisingly turned out to be the highly symmetric Adler configuration, of type (20, 15). And this was only the warm-up. After some slightly weird configuration mining I dug up thirty-three configurations of type (21), the inward Pappus configurations (as I named them), that are partitioned into four classes of isomorphic combinatorial configurations. Besides that I found also a cross-eyed cousin to the Desargues configuration, of type (10), and then, using a special geometric realization of this configuration, composed a configuration of type (28, 21). Ko sem se soočil z ogromnostjo Hexagrammum Mysticum, ga skušal razumeti in si želel v njem odkriti kaj resnično novega, sem se odločil, da se najprej preizkusim na nečem manjšem in lažje obvladljivem, da pridobim nekaj prakse. V ta namen sem izbral Pappusovo postavitev dveh premic s po tremi točkami, degenerirano razlicico Pascalovega šestčlenika točk na isti koniki, ki je konstrukcijska osnova Hexagrammum Mysticum. Tocke na eni izmed premic sem permutiral in ustvaril šest Pappusovih tritočkovnih premic, ki ustrezajo permutiranim šestkotnikom. Šest tritockovnih premic je bilo premalo gradiva celo za Hexagrammum Brevis, zato sem konfiguraciji dodal devet premic, ki povezujejo pare tock na nasprotnih premicah Pappusove postavitve, ter za vsak primer še dve točki, kjer se sekata po dva terceta Pappusovih premic. Nastala Frankensteinova konfiguracija, sešita iz treh tako razlicnih delov, se je presenetljivo izkazala za visoko simetrično Adlerjevo konfiguracijo tipa (20, 15). In to je bil šele ogrevalni del. Po nekoliko nenavadnem izkopavanju konfiguracij sem iz zemlje privlekel triintrideset konfiguracij tipa (21), notranje Pappusove konfiguracije (kot sem jih poimenoval), ki so razdeljene v štiri razrede izomorfnih kombinatoricnih konfiguracij. Poleg tega sem našel še postrani gledajočega sorodnika Desarguesove konfiguracije tipa (10), nato pa z uporabo posebne geometrijske realizacije te konfiguracije sestavil konfiguracijo tipa (28, 21). Pappus line Pappus layout configuration incidence collinearity concurrence Pappusova premica Pappusova postavitev konfiguracija incidenca kolinearnost konkurentnost true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2026-03-03 11:41:38 2026-03-03 11:41:38 2026-03-04 03:09:10 0000-00-00 00:00:00 2026 0 0 32 str. no. 2, [article no.] P2.01 Vol. 26 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-06 51 1855-3974 10.26493/1855-3974.3429.96e AMC_Dacar_2026.pdf AMC_Dacar_2026.pdf 1 36E8AB2185E094C33B435E681B7C168D d9f9ab708e7b111ee6b2f78520f31bc1b1b2fbaf1aa56775a75c8ac80b5c7ade d9ca49e0-16ed-11f1-b092-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33038 Založba Univerze na Primorskem 0 0 0