Polytope of Type {22,6,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,6,3,2}*1584
if this polytope has a name.
Group : SmallGroup(1584,675)
Rank : 5
Schlafli Type : {22,6,3,2}
Number of vertices, edges, etc : 22, 66, 9, 3, 2
Order of s₀s₁s₂s₃s₄ : 66
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {22,2,3,2}*528
   6-fold quotients : {11,2,3,2}*264
   11-fold quotients : {2,6,3,2}*144
   33-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)
(24,33)(25,32)(26,31)(27,30)(28,29)(35,44)(36,43)(37,42)(38,41)(39,40)(46,55)
(47,54)(48,53)(49,52)(50,51)(57,66)(58,65)(59,64)(60,63)(61,62)(68,77)(69,76)
(70,75)(71,74)(72,73)(79,88)(80,87)(81,86)(82,85)(83,84)(90,99)(91,98)(92,97)
(93,96)(94,95);;
s1 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24)(13,23)(14,33)(15,32)(16,31)
(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(34,35)(36,44)(37,43)(38,42)(39,41)
(45,57)(46,56)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)
(67,68)(69,77)(70,76)(71,75)(72,74)(78,90)(79,89)(80,99)(81,98)(82,97)(83,96)
(84,95)(85,94)(86,93)(87,92)(88,91);;
s2 := ( 1,12)( 2,13)( 3,14)( 4,15)( 5,16)( 6,17)( 7,18)( 8,19)( 9,20)(10,21)
(11,22)(34,78)(35,79)(36,80)(37,81)(38,82)(39,83)(40,84)(41,85)(42,86)(43,87)
(44,88)(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)
(55,77)(56,89)(57,90)(58,91)(59,92)(60,93)(61,94)(62,95)(63,96)(64,97)(65,98)
(66,99);;
s3 := ( 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);;
s4 := (100,101);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*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*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(101)!( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)
(17,18)(24,33)(25,32)(26,31)(27,30)(28,29)(35,44)(36,43)(37,42)(38,41)(39,40)
(46,55)(47,54)(48,53)(49,52)(50,51)(57,66)(58,65)(59,64)(60,63)(61,62)(68,77)
(69,76)(70,75)(71,74)(72,73)(79,88)(80,87)(81,86)(82,85)(83,84)(90,99)(91,98)
(92,97)(93,96)(94,95);
s1 := Sym(101)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24)(13,23)(14,33)(15,32)
(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(34,35)(36,44)(37,43)(38,42)
(39,41)(45,57)(46,56)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)
(55,58)(67,68)(69,77)(70,76)(71,75)(72,74)(78,90)(79,89)(80,99)(81,98)(82,97)
(83,96)(84,95)(85,94)(86,93)(87,92)(88,91);
s2 := Sym(101)!( 1,12)( 2,13)( 3,14)( 4,15)( 5,16)( 6,17)( 7,18)( 8,19)( 9,20)
(10,21)(11,22)(34,78)(35,79)(36,80)(37,81)(38,82)(39,83)(40,84)(41,85)(42,86)
(43,87)(44,88)(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)
(54,76)(55,77)(56,89)(57,90)(58,91)(59,92)(60,93)(61,94)(62,95)(63,96)(64,97)
(65,98)(66,99);
s3 := Sym(101)!( 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);
s4 := Sym(101)!(100,101);
poly := sub<Sym(101)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope