Polytope of Type {20,2,6}

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

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

Permutation Representation (Magma) :

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

to this polytope