Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,46115)
Rank
7
Schläfli Type
{3,2,2,4,9,2}
Vertices, edges, …
3, 3, 2, 4, 18, 9, 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 := (4,5);;
s3 := ( 7,12)( 8,14)( 9,16)(10,18)(13,23)(15,25)(19,29)(26,35)(28,37)(30,38)(32,39)(34,40);;
s4 := ( 6, 7)( 8,11)( 9,10)(12,20)(13,19)(14,21)(15,17)(16,18)(22,28)(23,29)(24,26)(25,27)(30,36)(31,37)(32,34)(33,35)(38,41)(39,40);;
s5 := ( 6,11)( 7, 9)( 8,19)(10,15)(12,16)(13,28)(14,29)(17,24)(18,25)(20,21)(22,36)(23,37)(26,32)(27,33)(30,34)(31,41)(35,39)(38,40);;
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, s2*s3*s2*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, 
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(43)!(2,3);
s1 := Sym(43)!(1,2);
s2 := Sym(43)!(4,5);
s3 := Sym(43)!( 7,12)( 8,14)( 9,16)(10,18)(13,23)(15,25)(19,29)(26,35)(28,37)(30,38)(32,39)(34,40);
s4 := Sym(43)!( 6, 7)( 8,11)( 9,10)(12,20)(13,19)(14,21)(15,17)(16,18)(22,28)(23,29)(24,26)(25,27)(30,36)(31,37)(32,34)(33,35)(38,41)(39,40);
s5 := Sym(43)!( 6,11)( 7, 9)( 8,19)(10,15)(12,16)(13,28)(14,29)(17,24)(18,25)(20,21)(22,36)(23,37)(26,32)(27,33)(30,34)(31,41)(35,39)(38,40);
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, 
s2*s3*s2*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, 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, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;