Polytope of Type {9,2,5,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,5,10}*1800
if this polytope has a name.
Group : SmallGroup(1800,296)
Rank : 5
Schlafli Type : {9,2,5,10}
Number of vertices, edges, etc : 9, 9, 5, 25, 10
Order of s₀s₁s₂s₃s₄ : 90
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   3-fold quotients : {3,2,5,10}*600
   5-fold quotients : {9,2,5,2}*360
   15-fold quotients : {3,2,5,2}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,18)(16,20)(17,19)(21,22)(23,28)(24,27)(25,30)(26,29)
(31,34)(32,33);;
s3 := (10,16)(11,13)(12,23)(14,25)(15,19)(17,21)(18,27)(20,31)(22,26)(24,29)
(28,33)(30,32);;
s4 := (13,14)(16,17)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(34)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(34)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(34)!(11,12)(13,14)(15,18)(16,20)(17,19)(21,22)(23,28)(24,27)(25,30)
(26,29)(31,34)(32,33);
s3 := Sym(34)!(10,16)(11,13)(12,23)(14,25)(15,19)(17,21)(18,27)(20,31)(22,26)
(24,29)(28,33)(30,32);
s4 := Sym(34)!(13,14)(16,17)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)
(33,34);
poly := sub<Sym(34)|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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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