Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,36}

Atlas Canonical Name {2,6,36}*1296b

Overview

Group
SmallGroup(1296,2978)
Rank
4
Schläfli Type
{2,6,36}
Vertices, edges, …
2, 9, 162, 54
Order of s0s1s2s3
36
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

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (12,23)(13,21)(14,22)(15,26)(16,24)(17,25)(18,29)(19,27)(20,28)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,77)(40,75)(41,76)(42,80)(43,78)(44,79)(45,83)(46,81)(47,82)(48,67)(49,68)(50,66)(51,70)(52,71)(53,69)(54,73)(55,74)(56,72);;
s2 := ( 3,30)( 4,32)( 5,31)( 6,37)( 7,36)( 8,38)( 9,34)(10,33)(11,35)(13,14)(15,19)(16,18)(17,20)(21,77)(22,76)(23,75)(24,81)(25,83)(26,82)(27,78)(28,80)(29,79)(39,66)(40,68)(41,67)(42,73)(43,72)(44,74)(45,70)(46,69)(47,71)(48,50)(51,54)(52,56)(53,55)(58,59)(60,64)(61,63)(62,65);;
s3 := ( 3, 6)( 4, 8)( 5, 7)( 9,10)(12,16)(13,15)(14,17)(18,20)(21,26)(22,25)(23,24)(28,29)(30,78)(31,80)(32,79)(33,75)(34,77)(35,76)(36,82)(37,81)(38,83)(39,61)(40,60)(41,62)(42,58)(43,57)(44,59)(45,65)(46,64)(47,63)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,72)(55,74)(56,73);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, 
s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(83)!(1,2);
s1 := Sym(83)!(12,23)(13,21)(14,22)(15,26)(16,24)(17,25)(18,29)(19,27)(20,28)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,77)(40,75)(41,76)(42,80)(43,78)(44,79)(45,83)(46,81)(47,82)(48,67)(49,68)(50,66)(51,70)(52,71)(53,69)(54,73)(55,74)(56,72);
s2 := Sym(83)!( 3,30)( 4,32)( 5,31)( 6,37)( 7,36)( 8,38)( 9,34)(10,33)(11,35)(13,14)(15,19)(16,18)(17,20)(21,77)(22,76)(23,75)(24,81)(25,83)(26,82)(27,78)(28,80)(29,79)(39,66)(40,68)(41,67)(42,73)(43,72)(44,74)(45,70)(46,69)(47,71)(48,50)(51,54)(52,56)(53,55)(58,59)(60,64)(61,63)(62,65);
s3 := Sym(83)!( 3, 6)( 4, 8)( 5, 7)( 9,10)(12,16)(13,15)(14,17)(18,20)(21,26)(22,25)(23,24)(28,29)(30,78)(31,80)(32,79)(33,75)(34,77)(35,76)(36,82)(37,81)(38,83)(39,61)(40,60)(41,62)(42,58)(43,57)(44,59)(45,65)(46,64)(47,63)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,72)(55,74)(56,73);
poly := sub<Sym(83)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, 
s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2 >;