Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240798)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 80, 480, 120
Order of s₀s₁s₂ : 10
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 : {8,6}*960a, {4,12}*960b
   4-fold quotients : {8,6}*480a, {8,6}*480b, {4,12}*480a, {4,12}*480b, {4,6}*480
   8-fold quotients : {4,6}*240a, {4,6}*240b, {4,6}*240c
   16-fold quotients : {4,6}*120
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 4)( 5,25)( 6,26)( 7,17)( 8,18)( 9,22)(10,21)(11,13)(12,14)
(15,29)(16,30)(19,36)(20,35)(23,34)(24,33)(27,39)(28,40)(31,32)(41,44)(42,43)
(45,47)(46,48)(49,70)(50,69)(51,62)(52,61)(53,65)(54,66)(55,58)(56,57)(59,74)
(60,73)(63,79)(64,80)(67,77)(68,78)(71,84)(72,83)(81,82)(85,87)(86,88);;
s1 := ( 3, 4)( 7,32)( 8,31)( 9,36)(10,35)(13,39)(14,40)(15,34)(16,33)(17,37)
(18,38)(19,29)(20,30)(21,23)(22,24)(25,43)(26,44)(27,28)(41,42)(47,48)(51,76)
(52,75)(53,80)(54,79)(57,83)(58,84)(59,78)(60,77)(61,81)(62,82)(63,73)(64,74)
(65,67)(66,68)(69,87)(70,88)(71,72)(85,86);;
s2 := ( 1,47)( 2,48)( 3,45)( 4,46)( 5,55)( 6,56)( 7,66)( 8,65)( 9,62)(10,61)
(11,49)(12,50)(13,70)(14,69)(15,59)(16,60)(17,54)(18,53)(19,85)(20,86)(21,52)
(22,51)(23,83)(24,84)(25,58)(26,57)(27,77)(28,78)(29,74)(30,73)(31,81)(32,82)
(33,71)(34,72)(35,88)(36,87)(37,75)(38,76)(39,67)(40,68)(41,63)(42,64)(43,80)
(44,79);;
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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0, 
s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(88)!( 1, 3)( 2, 4)( 5,25)( 6,26)( 7,17)( 8,18)( 9,22)(10,21)(11,13)
(12,14)(15,29)(16,30)(19,36)(20,35)(23,34)(24,33)(27,39)(28,40)(31,32)(41,44)
(42,43)(45,47)(46,48)(49,70)(50,69)(51,62)(52,61)(53,65)(54,66)(55,58)(56,57)
(59,74)(60,73)(63,79)(64,80)(67,77)(68,78)(71,84)(72,83)(81,82)(85,87)(86,88);
s1 := Sym(88)!( 3, 4)( 7,32)( 8,31)( 9,36)(10,35)(13,39)(14,40)(15,34)(16,33)
(17,37)(18,38)(19,29)(20,30)(21,23)(22,24)(25,43)(26,44)(27,28)(41,42)(47,48)
(51,76)(52,75)(53,80)(54,79)(57,83)(58,84)(59,78)(60,77)(61,81)(62,82)(63,73)
(64,74)(65,67)(66,68)(69,87)(70,88)(71,72)(85,86);
s2 := Sym(88)!( 1,47)( 2,48)( 3,45)( 4,46)( 5,55)( 6,56)( 7,66)( 8,65)( 9,62)
(10,61)(11,49)(12,50)(13,70)(14,69)(15,59)(16,60)(17,54)(18,53)(19,85)(20,86)
(21,52)(22,51)(23,83)(24,84)(25,58)(26,57)(27,77)(28,78)(29,74)(30,73)(31,81)
(32,82)(33,71)(34,72)(35,88)(36,87)(37,75)(38,76)(39,67)(40,68)(41,63)(42,64)
(43,80)(44,79);
poly := sub<Sym(88)|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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0, 
s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2 >;

References : None.
to this polytope