Polytope of Type {6,66}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,66}*1188
if this polytope has a name.
Group : SmallGroup(1188,41)
Rank : 3
Schlafli Type : {6,66}
Number of vertices, edges, etc : 9, 297, 99
Order of s₀s₁s₂ : 33
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   11-fold quotients : {6,6}*108
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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, 6)( 3, 5)( 7,31)( 8,33)( 9,32)(10,28)(11,30)(12,29)(13,25)
(14,27)(15,26)(16,22)(17,24)(18,23)(20,21)(34,38)(35,37)(36,39)(40,65)(41,64)
(42,66)(43,62)(44,61)(45,63)(46,59)(47,58)(48,60)(49,56)(50,55)(51,57)(52,53)
(67,72)(68,71)(69,70)(73,99)(74,98)(75,97)(76,96)(77,95)(78,94)(79,93)(80,92)
(81,91)(82,90)(83,89)(84,88)(85,87);;
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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, 6)( 3, 5)( 7,31)( 8,33)( 9,32)(10,28)(11,30)(12,29)
(13,25)(14,27)(15,26)(16,22)(17,24)(18,23)(20,21)(34,38)(35,37)(36,39)(40,65)
(41,64)(42,66)(43,62)(44,61)(45,63)(46,59)(47,58)(48,60)(49,56)(50,55)(51,57)
(52,53)(67,72)(68,71)(69,70)(73,99)(74,98)(75,97)(76,96)(77,95)(78,94)(79,93)
(80,92)(81,91)(82,90)(83,89)(84,88)(85,87);
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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