Polytope of Type {15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,6}*240
if this polytope has a name.
Group : SmallGroup(240,194)
Rank : 3
Schlafli Type : {15,6}
Number of vertices, edges, etc : 20, 60, 8
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {15,6,2} of size 480
   {15,6,4} of size 960
   {15,6,3} of size 1200
   {15,6,6} of size 1440
   {15,6,4} of size 1920
   {15,6,8} of size 1920
Vertex Figure Of :
   {2,15,6} of size 480
   {4,15,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {3,6}*48
   10-fold quotients : {3,3}*24
   12-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,12}*480, {30,6}*480
   3-fold covers : {15,6}*720e
   4-fold covers : {15,6}*960, {60,6}*960a, {30,12}*960a, {30,6}*960, {60,6}*960b, {30,12}*960b
   5-fold covers : {75,6}*1200, {15,30}*1200
   6-fold covers : {15,12}*1440c, {30,6}*1440g, {30,6}*1440h
   7-fold covers : {105,6}*1680
   8-fold covers : {15,12}*1920, {30,6}*1920a, {60,12}*1920a, {60,12}*1920b, {60,6}*1920, {30,6}*1920b, {30,6}*1920c, {120,6}*1920a, {120,6}*1920b, {60,12}*1920c, {30,24}*1920a, {30,12}*1920, {60,12}*1920d, {30,24}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope