Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,46116)
Rank
6
Schläfli Type
{2,2,6,6,4}
Vertices, edges, …
2, 2, 9, 27, 18, 4
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

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 9,13)(10,14)(11,15)(12,16)(17,29)(18,30)(19,31)(20,32)(21,37)(22,38)(23,39)(24,40)(25,33)(26,34)(27,35)(28,36);;
s3 := ( 5,17)( 6,19)( 7,18)( 8,20)( 9,21)(10,23)(11,22)(12,24)(13,25)(14,27)(15,26)(16,28)(30,31)(34,35)(38,39);;
s4 := ( 7, 8)( 9,13)(10,14)(11,16)(12,15)(17,21)(18,22)(19,24)(20,23)(27,28)(29,37)(30,38)(31,40)(32,39)(35,36);;
s5 := ( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39);;
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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*s4*s5*s4*s5, s2*s3*s4*s2*s3*s4*s2*s3*s4, 
s5*s4*s3*s5*s4*s5*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!( 9,13)(10,14)(11,15)(12,16)(17,29)(18,30)(19,31)(20,32)(21,37)(22,38)(23,39)(24,40)(25,33)(26,34)(27,35)(28,36);
s3 := Sym(40)!( 5,17)( 6,19)( 7,18)( 8,20)( 9,21)(10,23)(11,22)(12,24)(13,25)(14,27)(15,26)(16,28)(30,31)(34,35)(38,39);
s4 := Sym(40)!( 7, 8)( 9,13)(10,14)(11,16)(12,15)(17,21)(18,22)(19,24)(20,23)(27,28)(29,37)(30,38)(31,40)(32,39)(35,36);
s5 := Sym(40)!( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39);
poly := sub<Sym(40)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*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*s4*s5*s4*s5, 
s2*s3*s4*s2*s3*s4*s2*s3*s4, s5*s4*s3*s5*s4*s5*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;