Polytope of Type {6,4,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,22}*1584
if this polytope has a name.
Group : SmallGroup(1584,657)
Rank : 4
Schlafli Type : {6,4,22}
Number of vertices, edges, etc : 9, 18, 66, 22
Order of s₀s₁s₂s₃ : 44
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-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) :
   11-fold quotients : {6,4,2}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope