Part of the Atlas of Small Regular Polytopes

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

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

Overview

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

9-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

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