Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,47915)
Rank
6
Schläfli Type
{2,6,6,6,2}
Vertices, edges, …
2, 6, 18, 18, 6, 2
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

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