Polytope of Type {2,66,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,66,6}*1584a
if this polytope has a name.
Group : SmallGroup(1584,675)
Rank : 4
Schlafli Type : {2,66,6}
Number of vertices, edges, etc : 2, 66, 198, 6
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,22,6}*528
   9-fold quotients : {2,22,2}*176
   11-fold quotients : {2,6,6}*144b
   18-fold quotients : {2,11,2}*88
   22-fold quotients : {2,6,3}*72
   33-fold quotients : {2,2,6}*48
   66-fold quotients : {2,2,3}*24
   99-fold quotients : {2,2,2}*16
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, 25)( 15, 35)( 16, 34)
( 17, 33)( 18, 32)( 19, 31)( 20, 30)( 21, 29)( 22, 28)( 23, 27)( 24, 26)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 47, 58)( 48, 68)( 49, 67)
( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)
( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 80, 91)( 81,101)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 96)( 87, 95)( 88, 94)( 89, 93)( 90, 92);;
s2 := (  3, 15)(  4, 14)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)
( 11, 18)( 12, 17)( 13, 16)( 25, 26)( 27, 35)( 28, 34)( 29, 33)( 30, 32)
( 36, 81)( 37, 80)( 38, 90)( 39, 89)( 40, 88)( 41, 87)( 42, 86)( 43, 85)
( 44, 84)( 45, 83)( 46, 82)( 47, 70)( 48, 69)( 49, 79)( 50, 78)( 51, 77)
( 52, 76)( 53, 75)( 54, 74)( 55, 73)( 56, 72)( 57, 71)( 58, 92)( 59, 91)
( 60,101)( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)
( 68, 93);;
s3 := (  3, 36)(  4, 37)(  5, 38)(  6, 39)(  7, 40)(  8, 41)(  9, 42)( 10, 43)
( 11, 44)( 12, 45)( 13, 46)( 14, 58)( 15, 59)( 16, 60)( 17, 61)( 18, 62)
( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23, 67)( 24, 68)( 25, 47)( 26, 48)
( 27, 49)( 28, 50)( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 34, 56)
( 35, 57)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)
( 87, 98)( 88, 99)( 89,100)( 90,101);;
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*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, 
s3*s1*s2*s3*s2*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*s3*s1*s2*s1*s2*s3*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)!(1,2);
s1 := Sym(101)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 14, 25)( 15, 35)
( 16, 34)( 17, 33)( 18, 32)( 19, 31)( 20, 30)( 21, 29)( 22, 28)( 23, 27)
( 24, 26)( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 47, 58)( 48, 68)
( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)
( 57, 59)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 80, 91)( 81,101)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 96)( 87, 95)( 88, 94)( 89, 93)
( 90, 92);
s2 := Sym(101)!(  3, 15)(  4, 14)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)
( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 25, 26)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 81)( 37, 80)( 38, 90)( 39, 89)( 40, 88)( 41, 87)( 42, 86)
( 43, 85)( 44, 84)( 45, 83)( 46, 82)( 47, 70)( 48, 69)( 49, 79)( 50, 78)
( 51, 77)( 52, 76)( 53, 75)( 54, 74)( 55, 73)( 56, 72)( 57, 71)( 58, 92)
( 59, 91)( 60,101)( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)
( 67, 94)( 68, 93);
s3 := Sym(101)!(  3, 36)(  4, 37)(  5, 38)(  6, 39)(  7, 40)(  8, 41)(  9, 42)
( 10, 43)( 11, 44)( 12, 45)( 13, 46)( 14, 58)( 15, 59)( 16, 60)( 17, 61)
( 18, 62)( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23, 67)( 24, 68)( 25, 47)
( 26, 48)( 27, 49)( 28, 50)( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)
( 34, 56)( 35, 57)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)
( 86, 97)( 87, 98)( 88, 99)( 89,100)( 90,101);
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*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, 
s3*s1*s2*s3*s2*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*s3*s1*s2*s1*s2*s3*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