Polytope of Type {6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20}*240b
if this polytope has a name.
Group : SmallGroup(240,194)
Rank : 3
Schlafli Type : {6,20}
Number of vertices, edges, etc : 6, 60, 20
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,20,2} of size 480
   {6,20,4} of size 1920
Vertex Figure Of :
   {2,6,20} of size 480
   {4,6,20} of size 960
   {6,6,20} of size 1440
   {4,6,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {6,4}*48b
   10-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,20}*480c
   3-fold covers : {18,20}*720b, {6,60}*720d
   4-fold covers : {6,40}*960c, {12,20}*960b, {6,20}*960e, {6,40}*960d, {6,40}*960e, {12,20}*960c
   5-fold covers : {6,100}*1200b, {30,20}*1200d
   6-fold covers : {18,20}*1440, {6,60}*1440c, {6,60}*1440d
   7-fold covers : {42,20}*1680b, {6,140}*1680b
   8-fold covers : {12,40}*1920c, {12,40}*1920d, {6,40}*1920a, {12,40}*1920e, {12,40}*1920f, {6,40}*1920b, {6,20}*1920a, {6,40}*1920c, {24,20}*1920c, {24,20}*1920d, {6,40}*1920d, {6,20}*1920b, {12,20}*1920b, {12,20}*1920c, {12,40}*1920g, {12,40}*1920h, {24,20}*1920e, {24,20}*1920f
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(20)!( 3, 4)( 7, 8)(11,12)(15,16)(19,20);
s1 := Sym(20)!( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16);
s2 := Sym(20)!( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,18)(10,17)(11,20)(12,19)(13,14)
(15,16);
poly := sub<Sym(20)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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 >;

References : None.
to this polytope