Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,18,2}

Atlas Canonical Name {4,18,2}*288a

Overview

Group
SmallGroup(288,356)
Rank
4
Schläfli Type
{4,18,2}
Vertices, edges, …
4, 36, 18, 2
Order of s0s1s2s3
36
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

9-fold

12-fold

18-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

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