Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,12,3}

Atlas Canonical Name {2,6,12,3}*1728b

Overview

Group
SmallGroup(1728,47874)
Rank
5
Schläfli Type
{2,6,12,3}
Vertices, edges, …
2, 6, 72, 36, 6
Order of s0s1s2s3s4
6
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-fold

9-fold

12-fold

18-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

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