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Polytope of Type {2,6,20}

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

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