Polytope of Type {2,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6}*480b
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 4
Schlafli Type : {2,20,6}
Number of vertices, edges, etc : 2, 20, 60, 6
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,20,6,2} of size 960
   {2,20,6,4} of size 1920
Vertex Figure Of :
   {2,2,20,6} of size 960
   {3,2,20,6} of size 1440
   {4,2,20,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,4,6}*96b
   10-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,20,6}*960c
   3-fold covers : {2,20,18}*1440b, {2,60,6}*1440d
   4-fold covers : {2,40,6}*1920a, {4,20,6}*1920b, {2,20,12}*1920b, {2,20,6}*1920a, {4,20,6}*1920c, {2,40,6}*1920b, {2,40,6}*1920c, {2,20,12}*1920c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3, 4)( 5, 6)( 7,20)( 8,19)( 9,22)(10,21)(11,16)(12,15)(13,18)(14,17);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,19)(12,21)(13,20)(14,22)(16,17);;
s3 := ( 5, 6)( 9,10)(13,14)(17,18)(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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(22)!(1,2);
s1 := Sym(22)!( 3, 4)( 5, 6)( 7,20)( 8,19)( 9,22)(10,21)(11,16)(12,15)(13,18)
(14,17);
s2 := Sym(22)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,19)(12,21)(13,20)(14,22)(16,17);
s3 := Sym(22)!( 5, 6)( 9,10)(13,14)(17,18)(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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1 >;

to this polytope