Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,36,6}

Atlas Canonical Name {2,36,6}*864c

Overview

Group
SmallGroup(864,3998)
Rank
4
Schläfli Type
{2,36,6}
Vertices, edges, …
2, 36, 108, 6
Order of s0s1s2s3
18
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

9-fold

18-fold

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,33)(16,34)(17,31)(18,32)(19,29)(20,30)(21,27)(22,28)(23,37)(24,38)(25,35)(26,36);;
s2 := ( 3,15)( 4,17)( 5,16)( 6,18)( 7,23)( 8,25)( 9,24)(10,26)(11,19)(12,21)(13,20)(14,22)(27,31)(28,33)(29,32)(30,34)(36,37);;
s3 := ( 4, 6)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30)(32,34)(36,38);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,33)(16,34)(17,31)(18,32)(19,29)(20,30)(21,27)(22,28)(23,37)(24,38)(25,35)(26,36);
s2 := Sym(38)!( 3,15)( 4,17)( 5,16)( 6,18)( 7,23)( 8,25)( 9,24)(10,26)(11,19)(12,21)(13,20)(14,22)(27,31)(28,33)(29,32)(30,34)(36,37);
s3 := Sym(38)!( 4, 6)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30)(32,34)(36,38);
poly := sub<Sym(38)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3 >;