Polytope of Type {10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240798)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 80, 480, 96
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 : {10,6}*960a, {10,12}*960a, {10,12}*960b
   4-fold quotients : {5,6}*480, {10,6}*480a, {10,12}*480a, {10,12}*480b, {10,6}*480b
   8-fold quotients : {5,6}*240a, {10,6}*240a, {10,6}*240b
   16-fold quotients : {5,6}*120a
   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 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,55)( 6,56)( 7,81)( 8,82)( 9,67)(10,68)
(11,50)(12,49)(13,87)(14,88)(15,63)(16,64)(17,75)(18,76)(19,60)(20,59)(21,79)
(22,80)(23,54)(24,53)(25,84)(26,83)(27,86)(28,85)(29,77)(30,78)(31,62)(32,61)
(33,74)(34,73)(35,66)(36,65)(37,52)(38,51)(39,69)(40,70)(41,71)(42,72)(43,58)
(44,57);;
s1 := ( 3, 4)( 5,15)( 6,16)( 7,24)( 8,23)(11,29)(12,30)(13,19)(14,20)(17,36)
(18,35)(25,33)(26,34)(27,38)(28,37)(31,42)(32,41)(39,40)(43,44)(47,48)(49,59)
(50,60)(51,68)(52,67)(55,73)(56,74)(57,63)(58,64)(61,80)(62,79)(69,77)(70,78)
(71,82)(72,81)(75,86)(76,85)(83,84)(87,88);;
s2 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7,25)( 8,26)( 9,22)(10,21)(13,17)(14,18)
(15,33)(16,34)(19,29)(20,30)(23,35)(24,36)(31,44)(32,43)(37,39)(38,40)(41,42)
(45,47)(46,48)(49,56)(50,55)(51,70)(52,69)(53,65)(54,66)(57,62)(58,61)(59,78)
(60,77)(63,74)(64,73)(67,80)(68,79)(71,72)(75,87)(76,88)(81,84)(82,83);;
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*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*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope