Polytope of Type {9,2,4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,4,9}*1296
if this polytope has a name.
Group : SmallGroup(1296,1782)
Rank : 5
Schlafli Type : {9,2,4,9}
Number of vertices, edges, etc : 9, 9, 4, 18, 9
Order of s₀s₁s₂s₃s₄ : 9
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {9,2,4,3}*432, {3,2,4,9}*432
   9-fold quotients : {3,2,4,3}*144
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 := (11,16)(12,18)(13,20)(14,22)(17,27)(19,29)(23,33)(30,39)(32,41)(34,42)
(36,43)(38,44);;
s3 := (10,11)(12,15)(13,14)(16,24)(17,23)(18,25)(19,21)(20,22)(26,32)(27,33)
(28,30)(29,31)(34,40)(35,41)(36,38)(37,39)(42,45)(43,44);;
s4 := (10,15)(11,13)(12,23)(14,19)(16,20)(17,32)(18,33)(21,28)(22,29)(24,25)
(26,40)(27,41)(30,36)(31,37)(34,38)(35,45)(39,43)(42,44);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(45)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(45)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(45)!(11,16)(12,18)(13,20)(14,22)(17,27)(19,29)(23,33)(30,39)(32,41)
(34,42)(36,43)(38,44);
s3 := Sym(45)!(10,11)(12,15)(13,14)(16,24)(17,23)(18,25)(19,21)(20,22)(26,32)
(27,33)(28,30)(29,31)(34,40)(35,41)(36,38)(37,39)(42,45)(43,44);
s4 := Sym(45)!(10,15)(11,13)(12,23)(14,19)(16,20)(17,32)(18,33)(21,28)(22,29)
(24,25)(26,40)(27,41)(30,36)(31,37)(34,38)(35,45)(39,43)(42,44);
poly := sub<Sym(45)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope