Polytope of Type {20,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope