Polytope of Type {2,15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,6}*480
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 4
Schlafli Type : {2,15,6}
Number of vertices, edges, etc : 2, 20, 60, 8
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,15,6,2} of size 960
   {2,15,6,4} of size 1920
Vertex Figure Of :
   {2,2,15,6} of size 960
   {3,2,15,6} of size 1440
   {4,2,15,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,3,6}*96
   10-fold quotients : {2,3,3}*48
   12-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,15,12}*960, {2,30,6}*960
   3-fold covers : {2,15,6}*1440e
   4-fold covers : {2,15,6}*1920, {4,15,6}*1920, {2,60,6}*1920a, {4,30,6}*1920, {2,30,12}*1920a, {2,30,6}*1920, {2,60,6}*1920b, {2,30,12}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope