Polytope of Type {2,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,20}*160
if this polytope has a name.
Group : SmallGroup(160,215)
Rank : 4
Schlafli Type : {2,2,20}
Number of vertices, edges, etc : 2, 2, 20, 20
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,20,2} of size 320
   {2,2,20,4} of size 640
   {2,2,20,6} of size 960
   {2,2,20,6} of size 960
   {2,2,20,8} of size 1280
   {2,2,20,8} of size 1280
   {2,2,20,4} of size 1280
   {2,2,20,6} of size 1440
   {2,2,20,10} of size 1600
   {2,2,20,10} of size 1600
   {2,2,20,10} of size 1600
   {2,2,20,12} of size 1920
   {2,2,20,6} of size 1920
   {2,2,20,6} of size 1920
   {2,2,20,6} of size 1920
   {2,2,20,10} of size 1920
   {2,2,20,10} of size 1920
   {2,2,20,3} of size 1920
   {2,2,20,5} of size 1920
Vertex Figure Of :
   {2,2,2,20} of size 320
   {3,2,2,20} of size 480
   {4,2,2,20} of size 640
   {5,2,2,20} of size 800
   {6,2,2,20} of size 960
   {7,2,2,20} of size 1120
   {8,2,2,20} of size 1280
   {9,2,2,20} of size 1440
   {10,2,2,20} of size 1600
   {11,2,2,20} of size 1760
   {12,2,2,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,10}*80
   4-fold quotients : {2,2,5}*40
   5-fold quotients : {2,2,4}*32
   10-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,20}*320, {4,2,20}*320, {2,2,40}*320
   3-fold covers : {2,6,20}*480a, {6,2,20}*480, {2,2,60}*480
   4-fold covers : {4,4,20}*640, {2,4,40}*640a, {2,4,20}*640, {2,4,40}*640b, {2,8,20}*640a, {2,8,20}*640b, {4,2,40}*640, {8,2,20}*640, {2,2,80}*640
   5-fold covers : {2,2,100}*800, {2,10,20}*800a, {2,10,20}*800b, {10,2,20}*800
   6-fold covers : {12,2,20}*960, {6,4,20}*960, {4,6,20}*960a, {2,6,40}*960, {6,2,40}*960, {2,12,20}*960, {2,4,60}*960a, {4,2,60}*960, {2,2,120}*960
   7-fold covers : {2,14,20}*1120, {14,2,20}*1120, {2,2,140}*1120
   8-fold covers : {2,8,20}*1280a, {2,4,40}*1280a, {2,8,40}*1280a, {2,8,40}*1280b, {2,8,40}*1280c, {2,8,40}*1280d, {8,2,40}*1280, {8,4,20}*1280a, {4,4,40}*1280a, {8,4,20}*1280b, {4,4,40}*1280b, {4,8,20}*1280a, {4,4,20}*1280a, {4,4,20}*1280b, {4,8,20}*1280b, {4,8,20}*1280c, {4,8,20}*1280d, {2,16,20}*1280a, {2,4,80}*1280a, {2,16,20}*1280b, {2,4,80}*1280b, {2,4,20}*1280a, {2,4,40}*1280b, {2,8,20}*1280b, {16,2,20}*1280, {4,2,80}*1280, {2,2,160}*1280
   9-fold covers : {2,18,20}*1440a, {18,2,20}*1440, {2,2,180}*1440, {6,6,20}*1440a, {6,6,20}*1440b, {6,6,20}*1440c, {2,6,60}*1440a, {2,6,60}*1440b, {2,6,60}*1440c, {6,2,60}*1440, {2,6,20}*1440
   10-fold covers : {2,4,100}*1600, {4,2,100}*1600, {2,2,200}*1600, {20,2,20}*1600, {4,10,20}*1600a, {10,4,20}*1600, {2,10,40}*1600a, {2,10,40}*1600b, {10,2,40}*1600, {2,20,20}*1600a, {2,20,20}*1600b, {4,10,20}*1600b
   11-fold covers : {2,22,20}*1760, {22,2,20}*1760, {2,2,220}*1760
   12-fold covers : {4,4,60}*1920, {4,12,20}*1920a, {12,4,20}*1920, {2,8,60}*1920a, {2,4,120}*1920a, {6,8,20}*1920a, {6,4,40}*1920a, {2,12,40}*1920a, {2,24,20}*1920a, {2,8,60}*1920b, {2,4,120}*1920b, {6,8,20}*1920b, {6,4,40}*1920b, {2,12,40}*1920b, {2,24,20}*1920b, {2,4,60}*1920a, {6,4,20}*1920a, {2,12,20}*1920a, {8,2,60}*1920, {4,2,120}*1920, {8,6,20}*1920, {4,6,40}*1920a, {12,2,40}*1920, {24,2,20}*1920, {2,2,240}*1920, {2,6,80}*1920, {6,2,80}*1920, {4,6,20}*1920a, {6,4,20}*1920b, {6,6,20}*1920, {2,6,20}*1920a, {2,6,60}*1920a, {2,4,60}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope