Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,33,2}

Atlas Canonical Name {6,33,2}*792

Overview

Group
SmallGroup(792,129)
Rank
4
Schläfli Type
{6,33,2}
Vertices, edges, …
6, 99, 33, 2
Order of s0s1s2s3
66
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

9-fold

11-fold

33-fold

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP) 
s0 := (34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)(48,81)(49,82)(50,83)(51,84)(52,85)(53,86)(54,87)(55,88)(56,89)(57,90)(58,91)(59,92)(60,93)(61,94)(62,95)(63,96)(64,97)(65,98)(66,99);;
s1 := ( 1,34)( 2,44)( 3,43)( 4,42)( 5,41)( 6,40)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,56)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,45)(24,55)(25,54)(26,53)(27,52)(28,51)(29,50)(30,49)(31,48)(32,47)(33,46)(68,77)(69,76)(70,75)(71,74)(72,73)(78,89)(79,99)(80,98)(81,97)(82,96)(83,95)(84,94)(85,93)(86,92)(87,91)(88,90);;
s2 := ( 1,13)( 2,12)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(23,24)(25,33)(26,32)(27,31)(28,30)(34,79)(35,78)(36,88)(37,87)(38,86)(39,85)(40,84)(41,83)(42,82)(43,81)(44,80)(45,68)(46,67)(47,77)(48,76)(49,75)(50,74)(51,73)(52,72)(53,71)(54,70)(55,69)(56,90)(57,89)(58,99)(59,98)(60,97)(61,96)(62,95)(63,94)(64,93)(65,92)(66,91);;
s3 := (100,101);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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(101)!(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)(48,81)(49,82)(50,83)(51,84)(52,85)(53,86)(54,87)(55,88)(56,89)(57,90)(58,91)(59,92)(60,93)(61,94)(62,95)(63,96)(64,97)(65,98)(66,99);
s1 := Sym(101)!( 1,34)( 2,44)( 3,43)( 4,42)( 5,41)( 6,40)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,56)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,45)(24,55)(25,54)(26,53)(27,52)(28,51)(29,50)(30,49)(31,48)(32,47)(33,46)(68,77)(69,76)(70,75)(71,74)(72,73)(78,89)(79,99)(80,98)(81,97)(82,96)(83,95)(84,94)(85,93)(86,92)(87,91)(88,90);
s2 := Sym(101)!( 1,13)( 2,12)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(23,24)(25,33)(26,32)(27,31)(28,30)(34,79)(35,78)(36,88)(37,87)(38,86)(39,85)(40,84)(41,83)(42,82)(43,81)(44,80)(45,68)(46,67)(47,77)(48,76)(49,75)(50,74)(51,73)(52,72)(53,71)(54,70)(55,69)(56,90)(57,89)(58,99)(59,98)(60,97)(61,96)(62,95)(63,94)(64,93)(65,92)(66,91);
s3 := Sym(101)!(100,101);
poly := sub<Sym(101)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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 >;