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Polytope of Type {2,20,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,2,9}*1440
if this polytope has a name.
Group : SmallGroup(1440,1584)
Rank : 5
Schlafli Type : {2,20,2,9}
Number of vertices, edges, etc : 2, 20, 20, 9, 9
Order of s0s1s2s3s4 : 180
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 : {2,10,2,9}*720
   3-fold quotients : {2,20,2,3}*480
   4-fold quotients : {2,5,2,9}*360
   5-fold quotients : {2,4,2,9}*288
   6-fold quotients : {2,10,2,3}*240
   10-fold quotients : {2,2,2,9}*144
   12-fold quotients : {2,5,2,3}*120
   15-fold quotients : {2,4,2,3}*96
   30-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,21)(14,18)(16,19)(20,22);;
s3 := (24,25)(26,27)(28,29)(30,31);;
s4 := (23,24)(25,26)(27,28)(29,30);;
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, 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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(31)!(1,2);
s1 := Sym(31)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);
s2 := Sym(31)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,21)(14,18)(16,19)
(20,22);
s3 := Sym(31)!(24,25)(26,27)(28,29)(30,31);
s4 := Sym(31)!(23,24)(25,26)(27,28)(29,30);
poly := sub<Sym(31)|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, 
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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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