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Polytope of Type {8,2,9,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,9,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,154366)
Rank : 5
Schlafli Type : {8,2,9,4}
Number of vertices, edges, etc : 8, 8, 9, 18, 4
Order of s0s1s2s3s4 : 72
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {4,2,9,4}*576
   3-fold quotients : {8,2,3,4}*384
   4-fold quotients : {2,2,9,4}*288
   6-fold quotients : {4,2,3,4}*192
   12-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := ( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)(26,32)
(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);;
s3 := ( 9,13)(10,11)(12,20)(14,16)(15,17)(18,29)(19,30)(21,23)(22,25)(24,26)
(27,37)(28,38)(31,33)(32,34)(35,39)(36,43)(40,41)(42,44);;
s4 := ( 9,23)(10,15)(11,17)(14,24)(18,28)(20,30)(25,34)(27,36)(29,38)(31,40)
(33,41)(39,44);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(44)!(2,3)(4,5)(6,7);
s1 := Sym(44)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(44)!( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)
(26,32)(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);
s3 := Sym(44)!( 9,13)(10,11)(12,20)(14,16)(15,17)(18,29)(19,30)(21,23)(22,25)
(24,26)(27,37)(28,38)(31,33)(32,34)(35,39)(36,43)(40,41)(42,44);
s4 := Sym(44)!( 9,23)(10,15)(11,17)(14,24)(18,28)(20,30)(25,34)(27,36)(29,38)
(31,40)(33,41)(39,44);
poly := sub<Sym(44)|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, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, 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 >; 
 

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