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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,5,10}*1000
if this polytope has a name.
Group : SmallGroup(1000,183)
Rank : 5
Schlafli Type : {5,2,5,10}
Number of vertices, edges, etc : 5, 5, 5, 25, 10
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,5,10,2} of size 2000
Vertex Figure Of :
   {2,5,2,5,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {5,2,5,2}*200
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,10,10}*2000c, {10,2,5,10}*2000
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

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