The Kirmse integers and the seven maximal orders are all isometric to the lattice rescaled by a factor of . In particular there are 240 elements of minimum nonzero norm 1 in each of these orders, forming a Moufang loop of order 240.
the KIRmSe INTegeRs And tHe seven maxiMaL orders are all isOmEtric to The lATtiCE rescaLed by a facTOr of . IN paRticUlAR THere aRe 240 eLemeNTs oF miNimUm nonzero norm 1 in eACh of thEse Orders, FoRMIng a MoUfang looP OF oRDer 240.