Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,2,18,6}

Atlas Canonical Name {2,2,2,18,6}*1728b

Overview

Group
SmallGroup(1728,46164)
Rank
6
Schläfli Type
{2,2,2,18,6}
Vertices, edges, …
2, 2, 2, 18, 54, 6
Order of s0s1s2s3s4s5
18
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 := (5,6);;
s3 := ( 8, 9)(10,13)(11,15)(12,14)(16,26)(17,25)(18,27)(19,32)(20,31)(21,33)(22,29)(23,28)(24,30)(35,36)(37,40)(38,42)(39,41)(43,53)(44,52)(45,54)(46,59)(47,58)(48,60)(49,56)(50,55)(51,57);;
s4 := ( 7,46)( 8,48)( 9,47)(10,43)(11,45)(12,44)(13,49)(14,51)(15,50)(16,37)(17,39)(18,38)(19,34)(20,36)(21,35)(22,40)(23,42)(24,41)(25,56)(26,55)(27,57)(28,53)(29,52)(30,54)(31,59)(32,58)(33,60);;
s5 := (10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)(29,32)(30,33)(37,40)(38,41)(39,42)(46,49)(47,50)(48,51)(55,58)(56,59)(57,60);;
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, s2*s3*s2*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, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(60)!(1,2);
s1 := Sym(60)!(3,4);
s2 := Sym(60)!(5,6);
s3 := Sym(60)!( 8, 9)(10,13)(11,15)(12,14)(16,26)(17,25)(18,27)(19,32)(20,31)(21,33)(22,29)(23,28)(24,30)(35,36)(37,40)(38,42)(39,41)(43,53)(44,52)(45,54)(46,59)(47,58)(48,60)(49,56)(50,55)(51,57);
s4 := Sym(60)!( 7,46)( 8,48)( 9,47)(10,43)(11,45)(12,44)(13,49)(14,51)(15,50)(16,37)(17,39)(18,38)(19,34)(20,36)(21,35)(22,40)(23,42)(24,41)(25,56)(26,55)(27,57)(28,53)(29,52)(30,54)(31,59)(32,58)(33,60);
s5 := Sym(60)!(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)(29,32)(30,33)(37,40)(38,41)(39,42)(46,49)(47,50)(48,51)(55,58)(56,59)(57,60);
poly := sub<Sym(60)|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, 
s2*s3*s2*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, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;