Polytope of Type {33,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {33,6}*396
if this polytope has a name.
Group : SmallGroup(396,22)
Rank : 3
Schlafli Type : {33,6}
Number of vertices, edges, etc : 33, 99, 6
Order of s₀s₁s₂ : 66
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {33,6,2} of size 792
   {33,6,3} of size 1188
   {33,6,4} of size 1584
Vertex Figure Of :
   {2,33,6} of size 792
   {4,33,6} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {33,2}*132
   9-fold quotients : {11,2}*44
   11-fold quotients : {3,6}*36
   33-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {66,6}*792c
   3-fold covers : {99,6}*1188, {33,6}*1188
   4-fold covers : {132,6}*1584c, {66,12}*1584c, {33,12}*1584, {33,6}*1584
   5-fold covers : {165,6}*1980
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope