Polytope of Type {2,44,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,44,6}*1584
if this polytope has a name.
Group : SmallGroup(1584,672)
Rank : 4
Schlafli Type : {2,44,6}
Number of vertices, edges, etc : 2, 66, 198, 9
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 : {2,4,6}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope