Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,6,6,4}*1728i

Overview

Group
SmallGroup(1728,47874)
Rank
5
Schläfli Type
{2,6,6,4}
Vertices, edges, …
2, 18, 54, 36, 4
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 := ( 7,11)( 8,12)( 9,13)(10,14)(15,27)(16,28)(17,29)(18,30)(19,35)(20,36)(21,37)(22,38)(23,31)(24,32)(25,33)(26,34);;
s2 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,15)( 8,17)( 9,16)(10,18)(11,23)(12,25)(13,24)(14,26)(27,31)(28,33)(29,32)(30,34)(36,37);;
s3 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,23)(20,24)(21,26)(22,25)(29,30)(31,35)(32,36)(33,38)(34,37);;
s4 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37);;
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*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 7,11)( 8,12)( 9,13)(10,14)(15,27)(16,28)(17,29)(18,30)(19,35)(20,36)(21,37)(22,38)(23,31)(24,32)(25,33)(26,34);
s2 := Sym(38)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,15)( 8,17)( 9,16)(10,18)(11,23)(12,25)(13,24)(14,26)(27,31)(28,33)(29,32)(30,34)(36,37);
s3 := Sym(38)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,23)(20,24)(21,26)(22,25)(29,30)(31,35)(32,36)(33,38)(34,37);
s4 := Sym(38)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37);
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*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2 >;