Polytope of Type {5,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,20}*400
if this polytope has a name.
Group : SmallGroup(400,170)
Rank : 4
Schlafli Type : {5,2,20}
Number of vertices, edges, etc : 5, 5, 20, 20
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,20,2} of size 800
   {5,2,20,4} of size 1600
Vertex Figure Of :
   {2,5,2,20} of size 800
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,10}*200
   4-fold quotients : {5,2,5}*100
   5-fold quotients : {5,2,4}*80
   10-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,40}*800, {10,2,20}*800
   3-fold covers : {15,2,20}*1200, {5,2,60}*1200
   4-fold covers : {5,2,80}*1600, {20,2,20}*1600, {10,4,20}*1600, {10,2,40}*1600
   5-fold covers : {25,2,20}*2000, {5,2,100}*2000, {5,10,20}*2000a, {5,10,20}*2000b
Permutation Representation (GAP) :

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

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

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, 
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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