Polytope of Type {66,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {66,6}*792a
if this polytope has a name.
Group : SmallGroup(792,116)
Rank : 3
Schlafli Type : {66,6}
Number of vertices, edges, etc : 66, 198, 6
Order of s₀s₁s₂ : 66
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {66,6,2} of size 1584
Vertex Figure Of :
   {2,66,6} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {22,6}*264
   9-fold quotients : {22,2}*88
   11-fold quotients : {6,6}*72b
   18-fold quotients : {11,2}*44
   22-fold quotients : {6,3}*36
   33-fold quotients : {2,6}*24
   66-fold quotients : {2,3}*12
   99-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {132,6}*1584a, {66,12}*1584a
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)(35,44)(36,43)(37,42)(38,41)(39,40)
(45,56)(46,66)(47,65)(48,64)(49,63)(50,62)(51,61)(52,60)(53,59)(54,58)(55,57)
(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);;
s1 := ( 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);;
s2 := ( 1,34)( 2,35)( 3,36)( 4,37)( 5,38)( 6,39)( 7,40)( 8,41)( 9,42)(10,43)
(11,44)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)
(22,66)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(29,51)(30,52)(31,53)(32,54)
(33,55)(78,89)(79,90)(80,91)(81,92)(82,93)(83,94)(84,95)(85,96)(86,97)(87,98)
(88,99);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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)(35,44)(36,43)(37,42)(38,41)
(39,40)(45,56)(46,66)(47,65)(48,64)(49,63)(50,62)(51,61)(52,60)(53,59)(54,58)
(55,57)(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);
s1 := Sym(99)!( 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);
s2 := Sym(99)!( 1,34)( 2,35)( 3,36)( 4,37)( 5,38)( 6,39)( 7,40)( 8,41)( 9,42)
(10,43)(11,44)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)
(21,65)(22,66)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(29,51)(30,52)(31,53)
(32,54)(33,55)(78,89)(79,90)(80,91)(81,92)(82,93)(83,94)(84,95)(85,96)(86,97)
(87,98)(88,99);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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