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Polytope of Type {6,2,4,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,4,10,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,236178)
Rank : 6
Schlafli Type : {6,2,4,10,2}
Number of vertices, edges, etc : 6, 6, 4, 20, 10, 2
Order of s0s1s2s3s4s5 : 60
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 : {3,2,4,10,2}*960, {6,2,2,10,2}*960
   3-fold quotients : {2,2,4,10,2}*640
   4-fold quotients : {3,2,2,10,2}*480, {6,2,2,5,2}*480
   5-fold quotients : {6,2,4,2,2}*384
   6-fold quotients : {2,2,2,10,2}*320
   8-fold quotients : {3,2,2,5,2}*240
   10-fold quotients : {3,2,4,2,2}*192, {6,2,2,2,2}*192
   12-fold quotients : {2,2,2,5,2}*160
   15-fold quotients : {2,2,4,2,2}*128
   20-fold quotients : {3,2,2,2,2}*96
   30-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8,11)(12,17)(13,18)(19,23)(20,24);;
s3 := ( 7, 8)( 9,13)(10,12)(11,16)(14,20)(15,19)(17,22)(18,21)(23,26)(24,25);;
s4 := ( 7, 9)( 8,12)(10,14)(11,17)(13,19)(16,21)(18,23)(22,25);;
s5 := (27,28);;
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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(28)!(3,4)(5,6);
s1 := Sym(28)!(1,5)(2,3)(4,6);
s2 := Sym(28)!( 8,11)(12,17)(13,18)(19,23)(20,24);
s3 := Sym(28)!( 7, 8)( 9,13)(10,12)(11,16)(14,20)(15,19)(17,22)(18,21)(23,26)
(24,25);
s4 := Sym(28)!( 7, 9)( 8,12)(10,14)(11,17)(13,19)(16,21)(18,23)(22,25);
s5 := Sym(28)!(27,28);
poly := sub<Sym(28)|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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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