Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,9,2,2}

Atlas Canonical Name {3,2,4,9,2,2}*1728

Overview

Group
SmallGroup(1728,46115)
Rank
7
Schläfli Type
{3,2,4,9,2,2}
Vertices, edges, …
3, 3, 4, 18, 9, 2, 2
Order of s0s1s2s3s4s5s6
18
Order of s0s1s2s3s4s5s6s5s4s3s2s1
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

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5,10)( 6,12)( 7,14)( 8,16)(11,21)(13,23)(17,27)(24,33)(26,35)(28,36)(30,37)(32,38);;
s3 := ( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)(21,27)(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38);;
s4 := ( 4, 9)( 5, 7)( 6,17)( 8,13)(10,14)(11,26)(12,27)(15,22)(16,23)(18,19)(20,34)(21,35)(24,30)(25,31)(28,32)(29,39)(33,37)(36,38);;
s5 := (40,41);;
s6 := (42,43);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, 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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, 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(43)!(2,3);
s1 := Sym(43)!(1,2);
s2 := Sym(43)!( 5,10)( 6,12)( 7,14)( 8,16)(11,21)(13,23)(17,27)(24,33)(26,35)(28,36)(30,37)(32,38);
s3 := Sym(43)!( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)(21,27)(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38);
s4 := Sym(43)!( 4, 9)( 5, 7)( 6,17)( 8,13)(10,14)(11,26)(12,27)(15,22)(16,23)(18,19)(20,34)(21,35)(24,30)(25,31)(28,32)(29,39)(33,37)(36,38);
s5 := Sym(43)!(40,41);
s6 := Sym(43)!(42,43);
poly := sub<Sym(43)|s0,s1,s2,s3,s4,s5,s6>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s5*s6*s5*s6, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;