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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,12,2,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240988)
Rank : 5
Schlafli Type : {5,12,2,2}
Number of vertices, edges, etc : 20, 120, 48, 2, 2
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 : {5,6,2,2}*960b
   4-fold quotients : {5,3,2,2}*480, {5,6,2,2}*480b, {5,6,2,2}*480c
   8-fold quotients : {5,3,2,2}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)(20,23)
(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);;
s1 := ( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)(13,25)
(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);;
s2 := ( 1, 8)( 2,17)( 3,29)( 4,10)( 5,26)( 6,25)( 7,36)( 9,16)(11,35)(12,33)
(13,30)(14,15)(18,27)(19,24)(20,40)(21,38)(22,47)(23,46)(28,32)(31,44)(34,43)
(37,39)(41,48)(42,45);;
s3 := (49,50);;
s4 := (51,52);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)
(20,23)(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);
s1 := Sym(52)!( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)
(13,25)(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);
s2 := Sym(52)!( 1, 8)( 2,17)( 3,29)( 4,10)( 5,26)( 6,25)( 7,36)( 9,16)(11,35)
(12,33)(13,30)(14,15)(18,27)(19,24)(20,40)(21,38)(22,47)(23,46)(28,32)(31,44)
(34,43)(37,39)(41,48)(42,45);
s3 := Sym(52)!(49,50);
s4 := Sym(52)!(51,52);
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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1 >;

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