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Polytope of Type {40,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,2,9}*1440
if this polytope has a name.
Group : SmallGroup(1440,339)
Rank : 4
Schlafli Type : {40,2,9}
Number of vertices, edges, etc : 40, 40, 9, 9
Order of s0s1s2s3 : 360
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) :
   2-fold quotients : {20,2,9}*720
   3-fold quotients : {40,2,3}*480
   4-fold quotients : {10,2,9}*360
   5-fold quotients : {8,2,9}*288
   6-fold quotients : {20,2,3}*240
   8-fold quotients : {5,2,9}*180
   10-fold quotients : {4,2,9}*144
   12-fold quotients : {10,2,3}*120
   15-fold quotients : {8,2,3}*96
   20-fold quotients : {2,2,9}*72
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {4,2,3}*48
   60-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)
(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)(14,20)
(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);;
s2 := (42,43)(44,45)(46,47)(48,49);;
s3 := (41,42)(43,44)(45,46)(47,48);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(49)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)
(17,23)(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);
s1 := Sym(49)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)
(14,20)(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);
s2 := Sym(49)!(42,43)(44,45)(46,47)(48,49);
s3 := Sym(49)!(41,42)(43,44)(45,46)(47,48);
poly := sub<Sym(49)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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