Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,6,6}

Atlas Canonical Name {12,6,6}*864h

Overview

Group
SmallGroup(864,4673)
Rank
4
Schläfli Type
{12,6,6}
Vertices, edges, …
12, 36, 18, 6
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

6-fold

9-fold

18-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.