Polytope of Type {5,2,2,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,2,5,2}*400
if this polytope has a name.
Group : SmallGroup(400,218)
Rank : 6
Schlafli Type : {5,2,2,5,2}
Number of vertices, edges, etc : 5, 5, 2, 5, 5, 2
Order of s₀s₁s₂s₃s₄s₅ : 10
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,2,5,2,2} of size 800
   {5,2,2,5,2,3} of size 1200
   {5,2,2,5,2,4} of size 1600
   {5,2,2,5,2,5} of size 2000
Vertex Figure Of :
   {2,5,2,2,5,2} of size 800
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,2,10,2}*800, {10,2,2,5,2}*800
   3-fold covers : {5,2,2,15,2}*1200, {15,2,2,5,2}*1200
   4-fold covers : {5,2,2,20,2}*1600, {20,2,2,5,2}*1600, {5,2,2,10,4}*1600, {5,2,4,10,2}*1600, {10,4,2,5,2}*1600, {10,2,2,10,2}*1600
   5-fold covers : {5,2,2,25,2}*2000, {25,2,2,5,2}*2000, {5,2,2,5,10}*2000, {5,2,10,5,2}*2000, {5,10,2,5,2}*2000
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := ( 9,10)(11,12);;
s4 := ( 8, 9)(10,11);;
s5 := (13,14);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!(2,3)(4,5);
s1 := Sym(14)!(1,2)(3,4);
s2 := Sym(14)!(6,7);
s3 := Sym(14)!( 9,10)(11,12);
s4 := Sym(14)!( 8, 9)(10,11);
s5 := Sym(14)!(13,14);
poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope