Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,47874)
Rank
6
Schläfli Type
{4,6,6,3,2}
Vertices, edges, …
4, 12, 18, 9, 3, 2
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, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36);;
s1 := ( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35);;
s2 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16)(17,21)(18,24)(19,23)(20,22)(26,28)(29,33)(30,36)(31,35)(32,34);;
s3 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)(13,29)(14,30)(15,31)(16,32)(17,25)(18,26)(19,27)(20,28)(21,33)(22,34)(23,35)(24,36);;
s4 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,21)( 6,22)( 7,23)( 8,24)( 9,17)(10,18)(11,19)(12,20)(29,33)(30,34)(31,35)(32,36);;
s5 := (37,38);;
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*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, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(38)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36);
s1 := Sym(38)!( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35);
s2 := Sym(38)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16)(17,21)(18,24)(19,23)(20,22)(26,28)(29,33)(30,36)(31,35)(32,34);
s3 := Sym(38)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)(13,29)(14,30)(15,31)(16,32)(17,25)(18,26)(19,27)(20,28)(21,33)(22,34)(23,35)(24,36);
s4 := Sym(38)!( 1,13)( 2,14)( 3,15)( 4,16)( 5,21)( 6,22)( 7,23)( 8,24)( 9,17)(10,18)(11,19)(12,20)(29,33)(30,34)(31,35)(32,36);
s5 := Sym(38)!(37,38);
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*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, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;