Polytope of Type {4,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,44}*1584
if this polytope has a name.
Group : SmallGroup(1584,657)
Rank : 3
Schlafli Type : {4,44}
Number of vertices, edges, etc : 18, 396, 198
Order of s₀s₁s₂ : 66
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,4}*144
   18-fold quotients : {2,22}*88
   22-fold quotients : {4,4}*72
   36-fold quotients : {2,11}*44
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope