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Polytope of Type {2,2,12,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,5}*1920
if this polytope has a name.
Group : SmallGroup(1920,240988)
Rank : 5
Schlafli Type : {2,2,12,5}
Number of vertices, edges, etc : 2, 2, 48, 120, 20
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
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 : {2,2,6,5}*960b
   4-fold quotients : {2,2,3,5}*480, {2,2,6,5}*480b, {2,2,6,5}*480c
   8-fold quotients : {2,2,3,5}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,14)( 7,16)( 8,21)( 9,23)(11,42)(15,32)(17,48)(18,47)(19,38)(24,27)
(25,40)(26,41)(28,30)(33,37)(34,35)(36,39)(43,51)(44,50)(45,49)(46,52);;
s3 := ( 5,17)( 6,44)( 7, 8)( 9,34)(10,39)(11,29)(12,27)(13,45)(14,25)(15,23)
(16,36)(18,20)(19,21)(22,33)(24,50)(26,30)(28,46)(31,43)(32,47)(35,37)(38,48)
(40,42)(41,51)(49,52);;
s4 := ( 5,12)( 6, 8)( 7,37)( 9,28)(10,29)(11,25)(13,20)(14,21)(15,36)(16,33)
(17,35)(18,38)(19,47)(22,31)(23,30)(24,50)(26,43)(27,44)(32,39)(34,48)(40,42)
(41,51)(45,46)(49,52);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s2*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(52)!(1,2);
s1 := Sym(52)!(3,4);
s2 := Sym(52)!( 6,14)( 7,16)( 8,21)( 9,23)(11,42)(15,32)(17,48)(18,47)(19,38)
(24,27)(25,40)(26,41)(28,30)(33,37)(34,35)(36,39)(43,51)(44,50)(45,49)(46,52);
s3 := Sym(52)!( 5,17)( 6,44)( 7, 8)( 9,34)(10,39)(11,29)(12,27)(13,45)(14,25)
(15,23)(16,36)(18,20)(19,21)(22,33)(24,50)(26,30)(28,46)(31,43)(32,47)(35,37)
(38,48)(40,42)(41,51)(49,52);
s4 := Sym(52)!( 5,12)( 6, 8)( 7,37)( 9,28)(10,29)(11,25)(13,20)(14,21)(15,36)
(16,33)(17,35)(18,38)(19,47)(22,31)(23,30)(24,50)(26,43)(27,44)(32,39)(34,48)
(40,42)(41,51)(45,46)(49,52);
poly := sub<Sym(52)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s2*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3 >; 
 

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