Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240838)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 80, 480, 120
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 12
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 : {4,12}*960a, {8,6}*960b
   4-fold quotients : {4,6}*480
   8-fold quotients : {4,6}*240a, {4,6}*240b, {4,6}*240c
   16-fold quotients : {4,6}*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 := ( 1,71)( 2,78)( 3,77)( 4,52)( 5,16)( 6,21)( 7,70)( 8,38)( 9,37)(10,61)
(11,60)(12,69)(13,72)(14,28)(15,27)(17,39)(18,34)(19,44)(20,40)(22,76)(23,64)
(24,59)(25,56)(26,55)(29,65)(30,79)(31,54)(32,51)(33,50)(35,47)(36,48)(41,53)
(42,62)(43,63)(45,73)(46,80)(49,75)(57,67)(58,68)(66,74)(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, 
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*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)!( 1,71)( 2,78)( 3,77)( 4,52)( 5,16)( 6,21)( 7,70)( 8,38)( 9,37)
(10,61)(11,60)(12,69)(13,72)(14,28)(15,27)(17,39)(18,34)(19,44)(20,40)(22,76)
(23,64)(24,59)(25,56)(26,55)(29,65)(30,79)(31,54)(32,51)(33,50)(35,47)(36,48)
(41,53)(42,62)(43,63)(45,73)(46,80)(49,75)(57,67)(58,68)(66,74)(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, 
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*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope