Polytope of Type {20,4,2}

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

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

Permutation Representation (Magma) :

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

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