Polytope of Type {12,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,20}*1920h
if this polytope has a name.
Group : SmallGroup(1920,240800)
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
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,20}*960b, {12,10}*960b
   4-fold quotients : {12,10}*480a, {12,10}*480b, {6,10}*480b
   8-fold quotients : {6,5}*240a, {6,10}*240a, {6,10}*240b
   16-fold quotients : {6,5}*120a
   120-fold quotients : {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope