Polytope of Type {3,2,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,20}*480
if this polytope has a name.
Group : SmallGroup(480,1088)
Rank : 5
Schlafli Type : {3,2,2,20}
Number of vertices, edges, etc : 3, 3, 2, 20, 20
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,20,2} of size 960
   {3,2,2,20,4} of size 1920
Vertex Figure Of :
   {2,3,2,2,20} of size 960
   {3,3,2,2,20} of size 1920
   {4,3,2,2,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,10}*240
   4-fold quotients : {3,2,2,5}*120
   5-fold quotients : {3,2,2,4}*96
   10-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,20}*960, {3,2,2,40}*960, {6,2,2,20}*960
   3-fold covers : {9,2,2,20}*1440, {3,2,6,20}*1440a, {3,6,2,20}*1440, {3,2,2,60}*1440
   4-fold covers : {3,2,8,20}*1920a, {3,2,4,40}*1920a, {3,2,8,20}*1920b, {3,2,4,40}*1920b, {3,2,4,20}*1920, {3,2,2,80}*1920, {6,2,4,20}*1920, {6,4,2,20}*1920a, {12,2,2,20}*1920, {6,2,2,40}*1920, {3,4,2,20}*1920
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10)(12,15)(13,14)(16,17)(18,19)(20,23)(21,22)(24,25);;
s4 := ( 6,12)( 7, 9)( 8,18)(10,20)(11,14)(13,16)(15,24)(17,21)(19,22)(23,25);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(25)!(2,3);
s1 := Sym(25)!(1,2);
s2 := Sym(25)!(4,5);
s3 := Sym(25)!( 7, 8)( 9,10)(12,15)(13,14)(16,17)(18,19)(20,23)(21,22)(24,25);
s4 := Sym(25)!( 6,12)( 7, 9)( 8,18)(10,20)(11,14)(13,16)(15,24)(17,21)(19,22)
(23,25);
poly := sub<Sym(25)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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