Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,6,6,3}

Atlas Canonical Name {2,4,6,6,3}*1728e

Overview

Group
SmallGroup(1728,47874)
Rank
6
Schläfli Type
{2,4,6,6,3}
Vertices, edges, …
2, 4, 12, 18, 9, 3
Order of s0s1s2s3s4s5
6
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

6-fold

Covers minimal covers in bold

None in this atlas.

Representations

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