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Polytope of Type {8,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,2}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240977)
Rank : 4
Schlafli Type : {8,6,2}
Number of vertices, edges, etc : 80, 240, 60, 2
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6,2}*960
   4-fold quotients : {4,6,2}*480a, {4,6,2}*480b, {4,6,2}*480c
   8-fold quotients : {4,6,2}*240
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)(12,64)
(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)(28,39)
(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)(51,69)
(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);;
s1 := ( 1,10)( 2,61)( 3,70)( 4,13)( 5, 6)( 7,41)( 8,32)( 9,54)(11,39)(12,35)
(14,33)(15,42)(16,21)(17,37)(18,31)(19,38)(20,69)(22,50)(23,66)(24,72)(25,51)
(26,58)(27,45)(28,59)(29,48)(30,43)(34,47)(36,46)(40,62)(44,53)(49,55)(52,64)
(56,75)(57,77)(60,80)(63,73)(65,76)(67,79)(68,74)(71,78);;
s2 := ( 1,13)( 2,16)( 3,72)( 4,67)( 5,44)( 6,22)( 7,30)( 8,74)( 9,55)(10,80)
(11,41)(12,75)(14,26)(15,23)(17,73)(18,20)(19,36)(21,61)(24,49)(25,59)(27,43)
(28,60)(29,71)(31,64)(32,48)(33,58)(34,66)(35,68)(37,70)(38,62)(39,57)(40,50)
(42,47)(45,76)(46,53)(51,79)(52,69)(54,63)(56,78)(65,77);;
s3 := (81,82);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(82)!( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)
(12,64)(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)
(28,39)(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)
(51,69)(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);
s1 := Sym(82)!( 1,10)( 2,61)( 3,70)( 4,13)( 5, 6)( 7,41)( 8,32)( 9,54)(11,39)
(12,35)(14,33)(15,42)(16,21)(17,37)(18,31)(19,38)(20,69)(22,50)(23,66)(24,72)
(25,51)(26,58)(27,45)(28,59)(29,48)(30,43)(34,47)(36,46)(40,62)(44,53)(49,55)
(52,64)(56,75)(57,77)(60,80)(63,73)(65,76)(67,79)(68,74)(71,78);
s2 := Sym(82)!( 1,13)( 2,16)( 3,72)( 4,67)( 5,44)( 6,22)( 7,30)( 8,74)( 9,55)
(10,80)(11,41)(12,75)(14,26)(15,23)(17,73)(18,20)(19,36)(21,61)(24,49)(25,59)
(27,43)(28,60)(29,71)(31,64)(32,48)(33,58)(34,66)(35,68)(37,70)(38,62)(39,57)
(40,50)(42,47)(45,76)(46,53)(51,79)(52,69)(54,63)(56,78)(65,77);
s3 := Sym(82)!(81,82);
poly := sub<Sym(82)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 >; 
 

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