Polytope of Type {6,44,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,44,2}*1584
if this polytope has a name.
Group : SmallGroup(1584,672)
Rank : 4
Schlafli Type : {6,44,2}
Number of vertices, edges, etc : 9, 198, 66, 2
Order of s₀s₁s₂s₃ : 44
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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)( 2,44)( 3,43)( 4,42)( 5,41)( 6,40)( 7,39)( 8,38)( 9,37)(10,36)
(11,35)(13,22)(14,21)(15,20)(16,19)(17,18)(23,89)(24,99)(25,98)(26,97)(27,96)
(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(45,78)(46,88)(47,87)(48,86)(49,85)
(50,84)(51,83)(52,82)(53,81)(54,80)(55,79)(57,66)(58,65)(59,64)(60,63)(61,62)
(68,77)(69,76)(70,75)(71,74)(72,73);;
s2 := ( 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)(34,46)(35,45)(36,55)(37,54)(38,53)
(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(56,57)(58,66)(59,65)(60,64)(61,63)
(67,90)(68,89)(69,99)(70,98)(71,97)(72,96)(73,95)(74,94)(75,93)(76,92)(77,91)
(78,79)(80,88)(81,87)(82,86)(83,85);;
s3 := (100,101);;
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, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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(101)!(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(101)!( 1,34)( 2,44)( 3,43)( 4,42)( 5,41)( 6,40)( 7,39)( 8,38)( 9,37)
(10,36)(11,35)(13,22)(14,21)(15,20)(16,19)(17,18)(23,89)(24,99)(25,98)(26,97)
(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(45,78)(46,88)(47,87)(48,86)
(49,85)(50,84)(51,83)(52,82)(53,81)(54,80)(55,79)(57,66)(58,65)(59,64)(60,63)
(61,62)(68,77)(69,76)(70,75)(71,74)(72,73);
s2 := 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)(34,46)(35,45)(36,55)(37,54)
(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(56,57)(58,66)(59,65)(60,64)
(61,63)(67,90)(68,89)(69,99)(70,98)(71,97)(72,96)(73,95)(74,94)(75,93)(76,92)
(77,91)(78,79)(80,88)(81,87)(82,86)(83,85);
s3 := Sym(101)!(100,101);
poly := sub<Sym(101)|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, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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 >;

to this polytope