Polytope of Type {6,20,2}

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

to this polytope