Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {9,2,4,9}*1296

Overview

Group
SmallGroup(1296,1782)
Rank
5
Schläfli Type
{9,2,4,9}
Vertices, edges, …
9, 9, 4, 18, 9
Order of s0s1s2s3s4
9
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

9-fold

Covers minimal covers in bold

None in this atlas.

Representations

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 >;