Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,47915)
Rank
6
Schläfli Type
{2,2,6,6,6}
Vertices, edges, …
2, 2, 6, 18, 18, 6
Order of s0s1s2s3s4s5
6
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

9-fold

18-fold

27-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58);;
s3 := ( 5, 6)( 8,12)( 9,11)(10,13)(14,24)(15,23)(16,25)(17,30)(18,29)(19,31)(20,27)(21,26)(22,28)(32,33)(35,39)(36,38)(37,40)(41,51)(42,50)(43,52)(44,57)(45,56)(46,58)(47,54)(48,53)(49,55);;
s4 := ( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,35)(15,37)(16,36)(17,32)(18,34)(19,33)(20,38)(21,40)(22,39)(23,53)(24,55)(25,54)(26,50)(27,52)(28,51)(29,56)(30,58)(31,57);;
s5 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)(36,39)(37,40)(44,47)(45,48)(46,49)(53,56)(54,57)(55,58);;
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, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s5*s3*s4*s5*s4*s5*s3*s4*s5*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, 
s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(58)!(1,2);
s1 := Sym(58)!(3,4);
s2 := Sym(58)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58);
s3 := Sym(58)!( 5, 6)( 8,12)( 9,11)(10,13)(14,24)(15,23)(16,25)(17,30)(18,29)(19,31)(20,27)(21,26)(22,28)(32,33)(35,39)(36,38)(37,40)(41,51)(42,50)(43,52)(44,57)(45,56)(46,58)(47,54)(48,53)(49,55);
s4 := Sym(58)!( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,35)(15,37)(16,36)(17,32)(18,34)(19,33)(20,38)(21,40)(22,39)(23,53)(24,55)(25,54)(26,50)(27,52)(28,51)(29,56)(30,58)(31,57);
s5 := Sym(58)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)(36,39)(37,40)(44,47)(45,48)(46,49)(53,56)(54,57)(55,58);
poly := sub<Sym(58)|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, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*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, 
s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*s4 >;