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Polytope of Type {2,6,10,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,10,2,3}*1440
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 6
Schlafli Type : {2,6,10,2,3}
Number of vertices, edges, etc : 2, 6, 30, 10, 3, 3
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) :
   3-fold quotients : {2,2,10,2,3}*480
   5-fold quotients : {2,6,2,2,3}*288
   6-fold quotients : {2,2,5,2,3}*240
   10-fold quotients : {2,3,2,2,3}*144
   15-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 9,10)(13,15)(14,16)(19,21)(20,22)(25,27)(26,28)(29,31)(30,32);;
s2 := ( 3, 5)( 4, 9)( 7,14)( 8,13)(11,20)(12,19)(15,16)(17,26)(18,25)(21,22)
(23,30)(24,29)(27,28)(31,32);;
s3 := ( 3,11)( 4, 7)( 5,19)( 6,21)( 8,23)( 9,13)(10,15)(12,17)(14,29)(16,31)
(18,24)(20,25)(22,27)(26,30)(28,32);;
s4 := (34,35);;
s5 := (33,34);;
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, 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*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(35)!(1,2);
s1 := Sym(35)!( 5, 6)( 9,10)(13,15)(14,16)(19,21)(20,22)(25,27)(26,28)(29,31)
(30,32);
s2 := Sym(35)!( 3, 5)( 4, 9)( 7,14)( 8,13)(11,20)(12,19)(15,16)(17,26)(18,25)
(21,22)(23,30)(24,29)(27,28)(31,32);
s3 := Sym(35)!( 3,11)( 4, 7)( 5,19)( 6,21)( 8,23)( 9,13)(10,15)(12,17)(14,29)
(16,31)(18,24)(20,25)(22,27)(26,30)(28,32);
s4 := Sym(35)!(34,35);
s5 := Sym(35)!(33,34);
poly := sub<Sym(35)|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, 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*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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