Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,12,6,6}*1728h

Overview

Group
SmallGroup(1728,47874)
Rank
5
Schläfli Type
{2,12,6,6}
Vertices, edges, …
2, 12, 36, 18, 6
Order of s0s1s2s3s4
6
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

3-fold

6-fold

9-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

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