Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,9}

Atlas Canonical Name {2,4,9}*144

Overview

Group
SmallGroup(144,109)
Rank
4
Schläfli Type
{2,4,9}
Vertices, edges, …
2, 4, 18, 9
Order of s0s1s2s3
18
Order of s0s1s2s3s2s1
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

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

Representations

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