The action on the set of facesSome cycle indicesThe action on the set of verticesThe action on the set of edges

The action on the set of edges

When labelling the edges of the fullerene C60 as is indicated in table the generators of the induced permutation group on the set of edges of the fullerene are given by:

p1= (86,87,88,89,90)(81,82,83,84,85)(72,74,76,78,80)(71,73,75,77,79)(58,61,64,67,70) (57,60,63,66,69)(56,59,62,65,68)(43,46,49,52,55)(42,45,48,51,54)(41,44,47,50,53) (36,37,38,39,40)(27,29,31,33,35)(26,28,30,32,34)(13,16,19,22,25)(12,15,18,21,24) (11,14,17,20,23)(6,7,8,9,10)(1,2,3,4,5)

p2= (51,67,78,77,66)(50,52,68,84,65)(33,69,90,76,39)(32,40,79,89,64)(22,54,86,75,31) (21,53,85,83,49)(20,34,80,88,48)(19,23,70,87,63)(13,27,37,28,14)(10,55,81,62,18) (9,24,56,82,47)(7,12,43,44,15)(6,41,59,46,8)(5,36,72 ,61,17)(4,35,71,74,30) (3,25,57,73,38)(2,11,42,60,29)(1,26,58,45,16)

s= (88,89)(87,90)(86)(83)(82,84)(81,85)(75,76)(74,77)(73,78)(72,79)(71,80)(63,64) (62,65)(61,66)(60,67)(59,68)(58,69)(57,70)(56)(48)(47,49)(46,50)(45,51)(44,52)(43,53) (42,54)(41,55)(38,39)(37,40)(36)(30,31)(29,32)(28,33)(27,34)(26,35)(18)(17,19)(16,20) (15,21)(14,22)(13,23)(12,24)(11,25)(8,9)(7,10)(6)(3)(2,4)(1,5) The cycle indices for the corresponding actions on the set of edges are given as

Z(R,Edges)=(1)/(60)(24 x518 +20 x330 +15 x12 x244 +x190)
Z(S,Edges)=(1)/(120)( 24 x109 +20 x615 +24 x518 +20 x330 +x245 +15 x12 x244 +15 x18 x241 +x190).
harald.fripertinger@kfunigraz.ac.at,
last changed: January 23, 2001

The action on the set of facesSome cycle indicesThe action on the set of verticesThe action on the set of edges