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

Overview

Group: SmallGroup(1188,41)
Rank: 3
Schläfli Type: {33,6}
Vertices, edges, …: 99, 297, 18
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

{33,6}*396

9-fold

{33,2}*132

11-fold

{3,6}*108

27-fold

{11,2}*44

33-fold

{3,6}*36

99-fold

{3,2}*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*s2*s1)^2> of order 3

6 facets

6 of {33}*66

55 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.