Polytope of Type {9,2,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,40}*1440
if this polytope has a name.
Group : SmallGroup(1440,339)
Rank : 4
Schlafli Type : {9,2,40}
Number of vertices, edges, etc : 9, 9, 40, 40
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 : {9,2,20}*720
   3-fold quotients : {3,2,40}*480
   4-fold quotients : {9,2,10}*360
   5-fold quotients : {9,2,8}*288
   6-fold quotients : {3,2,20}*240
   8-fold quotients : {9,2,5}*180
   10-fold quotients : {9,2,4}*144
   12-fold quotients : {3,2,10}*120
   15-fold quotients : {3,2,8}*96
   20-fold quotients : {9,2,2}*72
   24-fold quotients : {3,2,5}*60
   30-fold quotients : {3,2,4}*48
   60-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,18)(16,20)(17,19)(21,22)(23,28)(24,30)(25,29)(26,32)
(27,31)(34,39)(35,38)(36,41)(37,40)(42,43)(44,47)(45,46)(48,49);;
s3 := (10,16)(11,13)(12,24)(14,26)(15,19)(17,21)(18,34)(20,36)(22,27)(23,29)
(25,31)(28,42)(30,44)(32,37)(33,38)(35,40)(39,48)(41,45)(43,46)(47,49);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(49)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(49)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(49)!(11,12)(13,14)(15,18)(16,20)(17,19)(21,22)(23,28)(24,30)(25,29)
(26,32)(27,31)(34,39)(35,38)(36,41)(37,40)(42,43)(44,47)(45,46)(48,49);
s3 := Sym(49)!(10,16)(11,13)(12,24)(14,26)(15,19)(17,21)(18,34)(20,36)(22,27)
(23,29)(25,31)(28,42)(30,44)(32,37)(33,38)(35,40)(39,48)(41,45)(43,46)(47,49);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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