Polytope of Type {2,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,5890)
Rank : 4
Schlafli Type : {2,20,4}
Number of vertices, edges, etc : 2, 90, 180, 18
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   5-fold quotients : {2,4,4}*288
   10-fold quotients : {2,4,4}*144
   18-fold quotients : {2,10,2}*80
   36-fold quotients : {2,5,2}*40
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 >;

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