Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,9,4,2}*288

Overview

Group
SmallGroup(288,835)
Rank
5
Schläfli Type
{2,9,4,2}
Vertices, edges, …
2, 9, 18, 4, 2
Order of s0s1s2s3s4
18
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

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

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