Polytope of Type {6,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,20}*480
if this polytope has a name.
Group : SmallGroup(480,1088)
Rank : 4
Schlafli Type : {6,2,20}
Number of vertices, edges, etc : 6, 6, 20, 20
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,20,2} of size 960
   {6,2,20,4} of size 1920
Vertex Figure Of :
   {2,6,2,20} of size 960
   {3,6,2,20} of size 1440
   {4,6,2,20} of size 1920
   {3,6,2,20} of size 1920
   {4,6,2,20} of size 1920
   {4,6,2,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,20}*240, {6,2,10}*240
   3-fold quotients : {2,2,20}*160
   4-fold quotients : {3,2,10}*120, {6,2,5}*120
   5-fold quotients : {6,2,4}*96
   6-fold quotients : {2,2,10}*80
   8-fold quotients : {3,2,5}*60
   10-fold quotients : {3,2,4}*48, {6,2,2}*48
   12-fold quotients : {2,2,5}*40
   15-fold quotients : {2,2,4}*32
   20-fold quotients : {3,2,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,20}*960, {6,4,20}*960, {6,2,40}*960
   3-fold covers : {18,2,20}*1440, {6,6,20}*1440a, {6,6,20}*1440c, {6,2,60}*1440
   4-fold covers : {12,4,20}*1920, {6,8,20}*1920a, {6,4,40}*1920a, {6,8,20}*1920b, {6,4,40}*1920b, {6,4,20}*1920a, {12,2,40}*1920, {24,2,20}*1920, {6,2,80}*1920, {6,4,20}*1920b
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26);;
s3 := ( 7,13)( 8,10)( 9,19)(11,21)(12,15)(14,17)(16,25)(18,22)(20,23)(24,26);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(26)!(3,4)(5,6);
s1 := Sym(26)!(1,5)(2,3)(4,6);
s2 := Sym(26)!( 8, 9)(10,11)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26);
s3 := Sym(26)!( 7,13)( 8,10)( 9,19)(11,21)(12,15)(14,17)(16,25)(18,22)(20,23)
(24,26);
poly := sub<Sym(26)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope