Polytope of Type {2,2,6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,20}*1440
if this polytope has a name.
Group : SmallGroup(1440,5921)
Rank : 5
Schlafli Type : {2,2,6,20}
Number of vertices, edges, etc : 2, 2, 9, 90, 30
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   5-fold quotients : {2,2,6,4}*288
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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