20.500.12556/DKUM-51454 The connection between the order of simple groups and the maximum number of elementary particles Povezava med redom enostavnih grup in maksimalnim številom elementarnih delcev Namen tega članka je predstaviti sferične, evklidske in hiperbolične poliedre in najti nekaj povezav reda njihovih grup zrcaljenj in grup, kot so na primer PGL(2,7), PGL(2,8), PGL(2,7)▫$times C_2$▫, PSL(2,31)▫$times C_2$▫, s številom elementarnih delcev. V tem delu pokažemo, da je večje število 72 ali 84 elementarnih delcev konsistentno s teorijo super strun, ▫$M$▫-teorijo in teorijo heterotičnih strun. Filozofija dela temelji na El Naschiejevi ▫$E$▫-neskončni interpretaciji izreka Emmy Nötherjeve. The aim of this article is to present spherical, Euclidean and hyperbolic polyhedra and find some connections of the order of their reflection groups and groups such as PGL(2, 7), PGL(2, 8), PGL(2, 7)▫$times C_2$▫, PSL(2, 31)▫$times C_2$▫ to the number of elementary particles. In the present work we show that a larger number of 72 or 84 elementary particles is consistent with super string theory, ▫$M$▫-theory and heterotic string theory. The philosophy of the work is based on El Naschie's ▫$E$▫-infinity interpretation of Emmy Nöther's theorem. Eulerjeva formula Schläfijev simbol enostavna grupa grupa zrcaljenj Euler's formula Schläfi symbol simple group reflection group true false false Angleški jezik Neznan jezik Delo ni kategorizirano 2015-07-10 14:49:10 2015-07-10 14:49:10 2022-05-30 03:05:53 2019-07-11 07:19:27 2008 0 0 str. 641-644 iss. 4 Vol. 35 2008 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.54:530.145 170011 11718166 0960-0779 URN:SI:UM:DK:TDSGLKHL http://dx.doi.org/10.1016/j.chaos.2007.07.014 1 https://dk.um.si/Dokument.php?lang=slv&id=76014 Fakulteta za strojništvo 0 0 0