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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5,10,2}*800
if this polytope has a name.
Group : SmallGroup(800,1208)
Rank : 6
Schlafli Type : {2,2,5,10,2}
Number of vertices, edges, etc : 2, 2, 5, 25, 10, 2
Order of s₀s₁s₂s₃s₄s₅ : 10
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,5,10,2,2} of size 1600
Vertex Figure Of :
   {2,2,2,5,10,2} of size 1600
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,2,5,2,2}*160
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,5,10,2}*1600, {2,2,5,10,4}*1600, {2,2,10,10,2}*1600c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,22)(20,25)(21,24)
(26,29)(27,28);;
s3 := ( 5,11)( 6, 8)( 7,18)( 9,20)(10,14)(12,16)(13,22)(15,26)(17,21)(19,24)
(23,28)(25,27);;
s4 := ( 8, 9)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29);;
s5 := (30,31);;
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*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(31)!(1,2);
s1 := Sym(31)!(3,4);
s2 := Sym(31)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,22)(20,25)
(21,24)(26,29)(27,28);
s3 := Sym(31)!( 5,11)( 6, 8)( 7,18)( 9,20)(10,14)(12,16)(13,22)(15,26)(17,21)
(19,24)(23,28)(25,27);
s4 := Sym(31)!( 8, 9)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)
(28,29);
s5 := Sym(31)!(30,31);
poly := sub<Sym(31)|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*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope