Polytope of Type {12,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,20}*1920m
if this polytope has a name.
Group : SmallGroup(1920,240875)
Rank : 3
Schlafli Type : {12,20}
Number of vertices, edges, etc : 48, 480, 80
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 20
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 : {6,20}*960d, {12,10}*960d
   4-fold quotients : {3,20}*480, {12,5}*480, {6,10}*480c
   8-fold quotients : {3,10}*240, {6,5}*240b, {6,10}*240c, {6,10}*240d, {6,10}*240e, {6,10}*240f
   16-fold quotients : {3,5}*120, {3,10}*120a, {3,10}*120b, {6,5}*120b, {6,5}*120c
   32-fold quotients : {3,5}*60
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,23)( 2,41)( 3,42)( 4,37)( 5,30)( 6,34)( 7,28)( 8,36)( 9,24)(10,29)
(11,16)(12,38)(13,14)(15,44)(17,21)(18,19)(20,45)(22,32)(25,27)(26,39)(31,35)
(33,47)(40,48)(43,46)(51,52);;
s1 := ( 1,12)( 2,35)( 3, 4)( 5,44)( 6,40)( 7,43)( 8,45)( 9,46)(10,48)(11,31)
(13,36)(14,15)(16,42)(17,37)(18,30)(19,20)(21,41)(22,47)(23,39)(24,29)(25,38)
(26,32)(27,33)(28,34)(49,52)(50,51);;
s2 := ( 1,23)( 2,12)( 3,22)( 4,43)( 5,10)( 6,17)( 7, 8)( 9,11)(13,14)(15,45)
(16,24)(18,19)(20,44)(21,34)(25,39)(26,27)(28,36)(29,30)(31,40)(32,42)(33,47)
(35,48)(37,46)(38,41)(51,52);;
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, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!( 1,23)( 2,41)( 3,42)( 4,37)( 5,30)( 6,34)( 7,28)( 8,36)( 9,24)
(10,29)(11,16)(12,38)(13,14)(15,44)(17,21)(18,19)(20,45)(22,32)(25,27)(26,39)
(31,35)(33,47)(40,48)(43,46)(51,52);
s1 := Sym(52)!( 1,12)( 2,35)( 3, 4)( 5,44)( 6,40)( 7,43)( 8,45)( 9,46)(10,48)
(11,31)(13,36)(14,15)(16,42)(17,37)(18,30)(19,20)(21,41)(22,47)(23,39)(24,29)
(25,38)(26,32)(27,33)(28,34)(49,52)(50,51);
s2 := Sym(52)!( 1,23)( 2,12)( 3,22)( 4,43)( 5,10)( 6,17)( 7, 8)( 9,11)(13,14)
(15,45)(16,24)(18,19)(20,44)(21,34)(25,39)(26,27)(28,36)(29,30)(31,40)(32,42)
(33,47)(35,48)(37,46)(38,41)(51,52);
poly := sub<Sym(52)|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, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
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