Polytope of Type {8,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240838)
Rank : 3
Schlafli Type : {8,20}
Number of vertices, edges, etc : 48, 480, 120
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
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 : {8,10}*960d, {4,20}*960c
   4-fold quotients : {4,10}*480c
   8-fold quotients : {4,5}*240, {4,10}*240a, {4,10}*240b
   16-fold quotients : {4,5}*120
   120-fold quotients : {2,4}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,66)( 2,22)( 4,68)( 6,44)( 7,11)( 8,80)( 9,35)(13,45)(14,42)(15,24)
(17,75)(18,36)(19,21)(23,56)(25,64)(26,32)(27,59)(28,62)(29,63)(31,67)(33,41)
(34,48)(37,47)(38,46)(39,49)(43,65)(50,53)(51,55)(52,58)(54,57)(60,70)(71,74)
(72,73)(76,78);;
s1 := ( 1,71)( 2,62)( 3,55)( 4,54)( 5,25)( 6,39)( 7,80)( 8,20)( 9,38)(10,32)
(11,36)(12,33)(13,72)(14,27)(15,19)(16,18)(17,34)(21,65)(22,64)(23,73)(24,79)
(26,78)(28,40)(29,56)(30,53)(31,52)(35,68)(37,44)(41,76)(42,74)(43,77)(45,59)
(46,58)(47,61)(48,57)(49,69)(50,60)(51,70)(63,66)(67,75)(82,84);;
s2 := ( 1,28)( 2, 7)( 3,16)( 4,18)( 5,10)( 6,76)( 8,31)( 9,48)(11,22)(12,40)
(13,25)(14,59)(15,71)(17,46)(19,60)(20,30)(21,70)(23,29)(24,74)(26,51)(27,42)
(32,55)(33,53)(34,35)(36,68)(37,52)(38,75)(39,54)(41,50)(43,73)(44,78)(45,64)
(47,58)(49,57)(56,63)(61,77)(62,66)(65,72)(67,80)(69,79)(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, 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(84)!( 1,66)( 2,22)( 4,68)( 6,44)( 7,11)( 8,80)( 9,35)(13,45)(14,42)
(15,24)(17,75)(18,36)(19,21)(23,56)(25,64)(26,32)(27,59)(28,62)(29,63)(31,67)
(33,41)(34,48)(37,47)(38,46)(39,49)(43,65)(50,53)(51,55)(52,58)(54,57)(60,70)
(71,74)(72,73)(76,78);
s1 := Sym(84)!( 1,71)( 2,62)( 3,55)( 4,54)( 5,25)( 6,39)( 7,80)( 8,20)( 9,38)
(10,32)(11,36)(12,33)(13,72)(14,27)(15,19)(16,18)(17,34)(21,65)(22,64)(23,73)
(24,79)(26,78)(28,40)(29,56)(30,53)(31,52)(35,68)(37,44)(41,76)(42,74)(43,77)
(45,59)(46,58)(47,61)(48,57)(49,69)(50,60)(51,70)(63,66)(67,75)(82,84);
s2 := Sym(84)!( 1,28)( 2, 7)( 3,16)( 4,18)( 5,10)( 6,76)( 8,31)( 9,48)(11,22)
(12,40)(13,25)(14,59)(15,71)(17,46)(19,60)(20,30)(21,70)(23,29)(24,74)(26,51)
(27,42)(32,55)(33,53)(34,35)(36,68)(37,52)(38,75)(39,54)(41,50)(43,73)(44,78)
(45,64)(47,58)(49,57)(56,63)(61,77)(62,66)(65,72)(67,80)(69,79)(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, 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1 >;

References : None.
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