Polytope of Type {10,5,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,5,2,4}*800
if this polytope has a name.
Group : SmallGroup(800,1134)
Rank : 5
Schlafli Type : {10,5,2,4}
Number of vertices, edges, etc : 10, 25, 5, 4, 4
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,5,2,4,2} of size 1600
Vertex Figure Of :
   {2,10,5,2,4} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,5,2,2}*400
   5-fold quotients : {2,5,2,4}*160
   10-fold quotients : {2,5,2,2}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,5,2,8}*1600, {10,10,2,4}*1600b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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