Polytope of Type {15,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,6,2}*480
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 4
Schlafli Type : {15,6,2}
Number of vertices, edges, etc : 20, 60, 8, 2
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {15,6,2,2} of size 960
   {15,6,2,3} of size 1440
   {15,6,2,4} of size 1920
Vertex Figure Of :
   {2,15,6,2} of size 960
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {3,6,2}*96
   10-fold quotients : {3,3,2}*48
   12-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,12,2}*960, {15,6,4}*960, {30,6,2}*960
   3-fold covers : {15,6,6}*1440, {15,6,2}*1440e
   4-fold covers : {15,6,2}*1920, {15,6,4}*1920, {15,6,8}*1920, {15,12,4}*1920, {60,6,2}*1920a, {30,12,2}*1920a, {30,6,2}*1920, {60,6,2}*1920b, {30,6,4}*1920, {30,12,2}*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);;
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*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(22)!( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,13)(10,14)(11,16)(12,15);
s1 := Sym(22)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,17)(10,19)(11,18)(12,20)(14,15);
s2 := Sym(22)!( 1, 2)( 5, 6)( 9,10)(13,14)(17,18);
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*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 >;

to this polytope