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Polytope of Type {12,6,2}

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

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