Polytope of Type {4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4}*200
Also Known As : {4,4}_(5,0), {4,4|5}. if this polytope has another name.
Group : SmallGroup(200,43)
Rank : 3
Schlafli Type : {4,4}
Number of vertices, edges, etc : 25, 50, 25
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 5
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
   Skewing Operation
Facet Of :
   {4,4,2} of size 400
Vertex Figure Of :
   {2,4,4} of size 400
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4}*400
   4-fold covers : {4,4}*800
   5-fold covers : {4,20}*1000, {20,4}*1000
   6-fold covers : {4,12}*1200, {12,4}*1200
   8-fold covers : {4,4}*1600, {4,8}*1600a, {8,4}*1600a, {4,8}*1600b, {8,4}*1600b
   9-fold covers : {4,4}*1800
   10-fold covers : {4,20}*2000a, {20,4}*2000a, {4,20}*2000b, {20,4}*2000b
Permutation Representation (GAP) :

s0 := ( 7,10)( 8, 9);;
s1 := ( 1, 6)( 2, 8)( 3,10)( 4, 7)( 5, 9);;
s2 := (1,2)(3,5);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(10)!( 7,10)( 8, 9);
s1 := Sym(10)!( 1, 6)( 2, 8)( 3,10)( 4, 7)( 5, 9);
s2 := Sym(10)!(1,2)(3,5);
poly := sub<Sym(10)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope