Polytope of Type {2,2,5,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5,10,5}*2000
if this polytope has a name.
Group : SmallGroup(2000,501)
Rank : 6
Schlafli Type : {2,2,5,10,5}
Number of vertices, edges, etc : 2, 2, 5, 25, 25, 5
Order of s₀s₁s₂s₃s₄s₅ : 10
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,2,5,2,5}*400
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(10,25)(11,29)(12,28)(13,27)(14,26)(15,20)(16,24)(17,23)
(18,22)(19,21);;
s3 := ( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(15,25)(16,29)(17,28)(18,27)(19,26)
(21,24)(22,23);;
s4 := ( 6, 9)( 7, 8)(10,11)(12,14)(15,17)(18,19)(20,23)(21,22)(25,29)(26,28);;
s5 := ( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28);;
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*s2*s3*s4*s3*s4*s2*s3*s4*s3, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!(1,2);
s1 := Sym(29)!(3,4);
s2 := Sym(29)!( 6, 9)( 7, 8)(10,25)(11,29)(12,28)(13,27)(14,26)(15,20)(16,24)
(17,23)(18,22)(19,21);
s3 := Sym(29)!( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(15,25)(16,29)(17,28)(18,27)
(19,26)(21,24)(22,23);
s4 := Sym(29)!( 6, 9)( 7, 8)(10,11)(12,14)(15,17)(18,19)(20,23)(21,22)(25,29)
(26,28);
s5 := Sym(29)!( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)
(27,28);
poly := sub<Sym(29)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*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*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope