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Polytope of Type {6,15,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,15,2}*480
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 4
Schlafli Type : {6,15,2}
Number of vertices, edges, etc : 8, 60, 20, 2
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,15,2,2} of size 960
   {6,15,2,3} of size 1440
   {6,15,2,4} of size 1920
Vertex Figure Of :
   {2,6,15,2} of size 960
   {4,6,15,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {6,3,2}*96
   10-fold quotients : {3,3,2}*48
   12-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,15,2}*960, {6,30,2}*960
   3-fold covers : {6,15,2}*1440e
   4-fold covers : {6,15,2}*1920, {6,15,4}*1920, {6,60,2}*1920a, {6,30,4}*1920, {12,30,2}*1920a, {6,30,2}*1920, {6,60,2}*1920b, {12,30,2}*1920b
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)(11,12)(15,16)(19,20);;
s1 := ( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16);;
s2 := ( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,18)(10,17)(11,19)(12,20)(13,14);;
s3 := (21,22);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(22)!( 3, 4)( 7, 8)(11,12)(15,16)(19,20);
s1 := Sym(22)!( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16);
s2 := Sym(22)!( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,18)(10,17)(11,19)(12,20)(13,14);
s3 := Sym(22)!(21,22);
poly := sub<Sym(22)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >; 
 

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