Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,18,6,2}*864a

Overview

Group
SmallGroup(864,4032)
Rank
5
Schläfli Type
{2,18,6,2}
Vertices, edges, …
2, 18, 54, 6, 2
Order of s0s1s2s3s4
18
Order of s0s1s2s3s4s3s2s1
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

2-fold

Representations

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