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Polytope of Type {12,20}

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