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Polytope of Type {10,4,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,2,9}*1440
if this polytope has a name.
Group : SmallGroup(1440,1593)
Rank : 5
Schlafli Type : {10,4,2,9}
Number of vertices, edges, etc : 10, 20, 4, 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 : {10,2,2,9}*720
   3-fold quotients : {10,4,2,3}*480
   4-fold quotients : {5,2,2,9}*360
   5-fold quotients : {2,4,2,9}*288
   6-fold quotients : {10,2,2,3}*240
   10-fold quotients : {2,2,2,9}*144
   12-fold quotients : {5,2,2,3}*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 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,17)(10,15)(12,13)(14,18)(16,19);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,15)(12,16)(17,19)(18,20);;
s3 := (22,23)(24,25)(26,27)(28,29);;
s4 := (21,22)(23,24)(25,26)(27,28);;
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*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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(29)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20);
s1 := Sym(29)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,17)(10,15)(12,13)(14,18)(16,19);
s2 := Sym(29)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,15)(12,16)(17,19)
(18,20);
s3 := Sym(29)!(22,23)(24,25)(26,27)(28,29);
s4 := Sym(29)!(21,22)(23,24)(25,26)(27,28);
poly := sub<Sym(29)|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*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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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