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Polytope of Type {20,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,12}*1920i
if this polytope has a name.
Group : SmallGroup(1920,240838)
Rank : 3
Schlafli Type : {20,12}
Number of vertices, edges, etc : 80, 480, 48
Order of s0s1s2 : 8
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {10,12}*960a, {20,6}*960a
   4-fold quotients : {10,6}*480b
   8-fold quotients : {5,6}*240a, {10,6}*240a, {10,6}*240b
   16-fold quotients : {5,6}*120a
   120-fold quotients : {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 4)( 2,51)( 3,46)( 5,27)( 6,34)( 7,41)( 8,28)( 9,16)(10,23)(11,26)
(12,42)(13,31)(14,19)(15,39)(17,20)(18,25)(21,56)(22,50)(24,68)(29,40)(30,48)
(32,77)(33,79)(35,78)(36,73)(37,65)(38,44)(43,67)(45,49)(47,66)(52,71)(53,61)
(54,72)(55,69)(57,62)(58,64)(59,70)(60,63)(74,80)(75,76)(81,82)(83,84);;
s1 := ( 1,34)( 2,20)( 3,76)( 4,56)( 5, 7)( 6,79)( 8,64)( 9,71)(10,70)(11,40)
(12,60)(13,38)(14,31)(15,49)(16,22)(17,72)(18,62)(19,61)(21,69)(23,67)(24,37)
(25,36)(26,55)(27,54)(28,80)(29,52)(30,78)(32,50)(33,51)(35,73)(39,43)(41,53)
(42,68)(44,77)(45,48)(46,66)(47,65)(57,63)(58,59)(74,75)(82,84);;
s2 := ( 2,45)( 3,30)( 5,14)( 6, 9)( 7,67)( 8,65)(10,12)(11,68)(15,18)(16,34)
(17,44)(19,27)(20,38)(21,29)(22,66)(23,42)(24,26)(25,39)(28,37)(32,80)(33,36)
(40,56)(41,43)(46,48)(47,50)(49,51)(52,54)(53,64)(55,62)(57,69)(58,61)(71,72)
(73,79)(74,77);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(84)!( 1, 4)( 2,51)( 3,46)( 5,27)( 6,34)( 7,41)( 8,28)( 9,16)(10,23)
(11,26)(12,42)(13,31)(14,19)(15,39)(17,20)(18,25)(21,56)(22,50)(24,68)(29,40)
(30,48)(32,77)(33,79)(35,78)(36,73)(37,65)(38,44)(43,67)(45,49)(47,66)(52,71)
(53,61)(54,72)(55,69)(57,62)(58,64)(59,70)(60,63)(74,80)(75,76)(81,82)(83,84);
s1 := Sym(84)!( 1,34)( 2,20)( 3,76)( 4,56)( 5, 7)( 6,79)( 8,64)( 9,71)(10,70)
(11,40)(12,60)(13,38)(14,31)(15,49)(16,22)(17,72)(18,62)(19,61)(21,69)(23,67)
(24,37)(25,36)(26,55)(27,54)(28,80)(29,52)(30,78)(32,50)(33,51)(35,73)(39,43)
(41,53)(42,68)(44,77)(45,48)(46,66)(47,65)(57,63)(58,59)(74,75)(82,84);
s2 := Sym(84)!( 2,45)( 3,30)( 5,14)( 6, 9)( 7,67)( 8,65)(10,12)(11,68)(15,18)
(16,34)(17,44)(19,27)(20,38)(21,29)(22,66)(23,42)(24,26)(25,39)(28,37)(32,80)
(33,36)(40,56)(41,43)(46,48)(47,50)(49,51)(52,54)(53,64)(55,62)(57,69)(58,61)
(71,72)(73,79)(74,77);
poly := sub<Sym(84)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1 >; 
 
References : None.
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