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Polytope of Type {3,2,40,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,40,2,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235349)
Rank : 6
Schlafli Type : {3,2,40,2,2}
Number of vertices, edges, etc : 3, 3, 40, 40, 2, 2
Order of s0s1s2s3s4s5 : 120
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {3,2,20,2,2}*960
   4-fold quotients : {3,2,10,2,2}*480
   5-fold quotients : {3,2,8,2,2}*384
   8-fold quotients : {3,2,5,2,2}*240
   10-fold quotients : {3,2,4,2,2}*192
   20-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,12)(10,14)(11,13)(15,16)(17,22)(18,24)(19,23)(20,26)
(21,25)(28,33)(29,32)(30,35)(31,34)(36,37)(38,41)(39,40)(42,43);;
s3 := ( 4,10)( 5, 7)( 6,18)( 8,20)( 9,13)(11,15)(12,28)(14,30)(16,21)(17,23)
(19,25)(22,36)(24,38)(26,31)(27,32)(29,34)(33,42)(35,39)(37,40)(41,43);;
s4 := (44,45);;
s5 := (46,47);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, 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(47)!(2,3);
s1 := Sym(47)!(1,2);
s2 := Sym(47)!( 5, 6)( 7, 8)( 9,12)(10,14)(11,13)(15,16)(17,22)(18,24)(19,23)
(20,26)(21,25)(28,33)(29,32)(30,35)(31,34)(36,37)(38,41)(39,40)(42,43);
s3 := Sym(47)!( 4,10)( 5, 7)( 6,18)( 8,20)( 9,13)(11,15)(12,28)(14,30)(16,21)
(17,23)(19,25)(22,36)(24,38)(26,31)(27,32)(29,34)(33,42)(35,39)(37,40)(41,43);
s4 := Sym(47)!(44,45);
s5 := Sym(47)!(46,47);
poly := sub<Sym(47)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, 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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