Polytope of Type {6,33} with group SmallGroup(1188,41)

Overview

Group: SmallGroup(1188,41)
Rank: 3
Schläfli Type: {6,33}
Vertices, edges, …: 18, 297, 99
Order of s₀s₁s₂: 66
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

3-fold

{6,33}*396

9-fold

{2,33}*132

11-fold

{6,3}*108

27-fold

{2,11}*44

33-fold

{6,3}*36

99-fold

{2,3}*12

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2> of order 3

55 facets

33 of {2}*4
22 of {6}*12

6 vertex figures

6 of {33}*66

Representations

Permutation Representation (GAP)

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

Finitely Presented Group Representation (GAP)

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

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
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 >;

References

None.

to this polytope.