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

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

s0 := (2,3);;
s1 := (1,2)(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);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, 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(29)!(2,3);
s1 := Sym(29)!(1,2)(3,4);
s2 := Sym(29)!( 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(29)!( 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(29)!( 8, 9)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(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, 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*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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