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Polytope of Type {5,2,4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,9}*720
if this polytope has a name.
Group : SmallGroup(720,394)
Rank : 5
Schlafli Type : {5,2,4,9}
Number of vertices, edges, etc : 5, 5, 4, 18, 9
Order of s0s1s2s3s4 : 45
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,4,9,2} of size 1440
Vertex Figure Of :
   {2,5,2,4,9} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,2,4,3}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,4,9}*1440, {5,2,4,18}*1440b, {5,2,4,18}*1440c, {10,2,4,9}*1440
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7,12)( 8,14)( 9,16)(10,18)(13,23)(15,25)(19,29)(26,35)(28,37)(30,38)
(32,39)(34,40);;
s3 := ( 6, 7)( 8,11)( 9,10)(12,20)(13,19)(14,21)(15,17)(16,18)(22,28)(23,29)
(24,26)(25,27)(30,36)(31,37)(32,34)(33,35)(38,41)(39,40);;
s4 := ( 6,11)( 7, 9)( 8,19)(10,15)(12,16)(13,28)(14,29)(17,24)(18,25)(20,21)
(22,36)(23,37)(26,32)(27,33)(30,34)(31,41)(35,39)(38,40);;
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, 
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*s4*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(41)!(2,3)(4,5);
s1 := Sym(41)!(1,2)(3,4);
s2 := Sym(41)!( 7,12)( 8,14)( 9,16)(10,18)(13,23)(15,25)(19,29)(26,35)(28,37)
(30,38)(32,39)(34,40);
s3 := Sym(41)!( 6, 7)( 8,11)( 9,10)(12,20)(13,19)(14,21)(15,17)(16,18)(22,28)
(23,29)(24,26)(25,27)(30,36)(31,37)(32,34)(33,35)(38,41)(39,40);
s4 := Sym(41)!( 6,11)( 7, 9)( 8,19)(10,15)(12,16)(13,28)(14,29)(17,24)(18,25)
(20,21)(22,36)(23,37)(26,32)(27,33)(30,34)(31,41)(35,39)(38,40);
poly := sub<Sym(41)|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, 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*s4*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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