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Polytope of Type {20,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,12}*1920k
if this polytope has a name.
Group : SmallGroup(1920,240875)
Rank : 3
Schlafli Type : {20,12}
Number of vertices, edges, etc : 80, 480, 48
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 : {10,12}*960c, {20,6}*960d
   4-fold quotients : {10,12}*480c, {10,12}*480d, {20,3}*480, {10,6}*480c
   8-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   16-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   32-fold quotients : {5,3}*60
   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 := ( 2,38)( 3,32)( 4,46)( 5,29)( 6,21)( 7,36)( 8,28)( 9,16)(10,30)(11,24)
(12,41)(15,20)(17,34)(22,42)(25,26)(27,39)(31,48)(35,40)(37,43)(44,45);;
s1 := ( 1, 4)( 2,40)( 3,46)( 5,36)( 6,42)( 7,31)( 8,30)( 9,41)(10,37)(11,29)
(12,32)(13,24)(14,20)(15,19)(16,26)(17,28)(18,34)(21,25)(22,38)(23,27)(33,39)
(35,47)(43,45)(44,48)(51,52);;
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)(49,52)(50,51);;
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*s0*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, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(52)!( 2,38)( 3,32)( 4,46)( 5,29)( 6,21)( 7,36)( 8,28)( 9,16)(10,30)
(11,24)(12,41)(15,20)(17,34)(22,42)(25,26)(27,39)(31,48)(35,40)(37,43)(44,45);
s1 := Sym(52)!( 1, 4)( 2,40)( 3,46)( 5,36)( 6,42)( 7,31)( 8,30)( 9,41)(10,37)
(11,29)(12,32)(13,24)(14,20)(15,19)(16,26)(17,28)(18,34)(21,25)(22,38)(23,27)
(33,39)(35,47)(43,45)(44,48)(51,52);
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)(49,52)(50,51);
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, s0*s1*s2*s1*s2*s1*s0*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, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 >; 
 
References : None.
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