Polytope of Type {4,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,20}*320
if this polytope has a name.
Group : SmallGroup(320,1221)
Rank : 4
Schlafli Type : {4,2,20}
Number of vertices, edges, etc : 4, 4, 20, 20
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,20,2} of size 640
   {4,2,20,4} of size 1280
   {4,2,20,6} of size 1920
   {4,2,20,6} of size 1920
Vertex Figure Of :
   {2,4,2,20} of size 640
   {3,4,2,20} of size 960
   {4,4,2,20} of size 1280
   {6,4,2,20} of size 1920
   {3,4,2,20} of size 1920
   {6,4,2,20} of size 1920
   {6,4,2,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,20}*160, {4,2,10}*160
   4-fold quotients : {4,2,5}*80, {2,2,10}*80
   5-fold quotients : {4,2,4}*64
   8-fold quotients : {2,2,5}*40
   10-fold quotients : {2,2,4}*32, {4,2,2}*32
   20-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,20}*640, {4,2,40}*640, {8,2,20}*640
   3-fold covers : {12,2,20}*960, {4,6,20}*960a, {4,2,60}*960
   4-fold covers : {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, {16,2,20}*1280, {4,2,80}*1280
   5-fold covers : {4,2,100}*1600, {20,2,20}*1600, {4,10,20}*1600a, {4,10,20}*1600b
   6-fold covers : {4,4,60}*1920, {4,12,20}*1920a, {12,4,20}*1920, {8,2,60}*1920, {4,2,120}*1920, {8,6,20}*1920, {4,6,40}*1920a, {12,2,40}*1920, {24,2,20}*1920
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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(24)!(2,3);
s1 := Sym(24)!(1,2)(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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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 >;

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