Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,2,9,4}

Atlas Canonical Name {6,2,9,4}*864

Overview

Group
SmallGroup(864,3999)
Rank
5
Schläfli Type
{6,2,9,4}
Vertices, edges, …
6, 6, 9, 18, 4
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

2-fold

3-fold

6-fold

9-fold

Covers minimal covers in bold

2-fold

Representations

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