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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5,12}*1920
if this polytope has a name.
Group : SmallGroup(1920,240988)
Rank : 5
Schlafli Type : {2,2,5,12}
Number of vertices, edges, etc : 2, 2, 20, 120, 48
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 : {2,2,5,6}*960b
   4-fold quotients : {2,2,5,3}*480, {2,2,5,6}*480b, {2,2,5,6}*480c
   8-fold quotients : {2,2,5,3}*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 := ( 6, 7)( 8,21)( 9,23)(11,32)(12,39)(13,33)(14,19)(15,30)(16,43)(17,29)
(18,31)(24,42)(25,37)(26,48)(27,35)(28,34)(36,46)(38,45)(44,47)(49,51);;
s4 := ( 5,12)( 6,21)( 7,33)( 8,14)( 9,30)(10,29)(11,40)(13,20)(15,39)(16,37)
(17,34)(18,19)(22,31)(23,28)(24,44)(25,42)(26,51)(27,50)(32,36)(35,48)(38,47)
(41,43)(45,52)(46,49);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3, 
s2*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s4*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)!( 6, 7)( 8,21)( 9,23)(11,32)(12,39)(13,33)(14,19)(15,30)(16,43)
(17,29)(18,31)(24,42)(25,37)(26,48)(27,35)(28,34)(36,46)(38,45)(44,47)(49,51);
s4 := Sym(52)!( 5,12)( 6,21)( 7,33)( 8,14)( 9,30)(10,29)(11,40)(13,20)(15,39)
(16,37)(17,34)(18,19)(22,31)(23,28)(24,44)(25,42)(26,51)(27,50)(32,36)(35,48)
(38,47)(41,43)(45,52)(46,49);
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3, 
s2*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s4*s3 >;

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