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Polytope of Type {2,3,2,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,2,10,5}*1200
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 6
Schlafli Type : {2,3,2,10,5}
Number of vertices, edges, etc : 2, 3, 3, 10, 25, 5
Order of s0s1s2s3s4s5 : 30
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) :
   5-fold quotients : {2,3,2,2,5}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := ( 9,10)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30);;
s4 := ( 6, 9)( 7,15)( 8,12)(10,17)(11,23)(13,25)(14,19)(16,21)(20,29)(22,26)
(24,27)(28,30);;
s5 := ( 6, 7)( 8,11)( 9,13)(10,12)(15,20)(16,19)(17,22)(18,21)(23,24)(25,28)
(26,27)(29,30);;
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s1*s2*s1*s2*s1*s2, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(30)!(1,2);
s1 := Sym(30)!(4,5);
s2 := Sym(30)!(3,4);
s3 := Sym(30)!( 9,10)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30);
s4 := Sym(30)!( 6, 9)( 7,15)( 8,12)(10,17)(11,23)(13,25)(14,19)(16,21)(20,29)
(22,26)(24,27)(28,30);
s5 := Sym(30)!( 6, 7)( 8,11)( 9,13)(10,12)(15,20)(16,19)(17,22)(18,21)(23,24)
(25,28)(26,27)(29,30);
poly := sub<Sym(30)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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