Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1728,47887)
Rank
5
Schläfli Type
{2,4,6,6}
Vertices, edges, …
2, 12, 36, 54, 6
Order of s0s1s2s3s4
12
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

9-fold

18-fold

27-fold

36-fold

54-fold

Covers minimal covers in bold

None in this atlas.

Representations

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