Polytope of Type {2,33,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,33,6}*792
if this polytope has a name.
Group : SmallGroup(792,129)
Rank : 4
Schlafli Type : {2,33,6}
Number of vertices, edges, etc : 2, 33, 99, 6
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,33,6,2} of size 1584
Vertex Figure Of :
   {2,2,33,6} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,33,2}*264
   9-fold quotients : {2,11,2}*88
   11-fold quotients : {2,3,6}*72
   33-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,66,6}*1584c
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)
( 36, 69)( 37, 79)( 38, 78)( 39, 77)( 40, 76)( 41, 75)( 42, 74)( 43, 73)
( 44, 72)( 45, 71)( 46, 70)( 47, 91)( 48,101)( 49,100)( 50, 99)( 51, 98)
( 52, 97)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 92)( 58, 80)( 59, 90)
( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 85)( 65, 84)( 66, 83)( 67, 82)
( 68, 81);;
s2 := (  3, 48)(  4, 47)(  5, 57)(  6, 56)(  7, 55)(  8, 54)(  9, 53)( 10, 52)
( 11, 51)( 12, 50)( 13, 49)( 14, 37)( 15, 36)( 16, 46)( 17, 45)( 18, 44)
( 19, 43)( 20, 42)( 21, 41)( 22, 40)( 23, 39)( 24, 38)( 25, 59)( 26, 58)
( 27, 68)( 28, 67)( 29, 66)( 30, 65)( 31, 64)( 32, 63)( 33, 62)( 34, 61)
( 35, 60)( 69, 81)( 70, 80)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)
( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 91, 92)( 93,101)( 94,100)( 95, 99)
( 96, 98);;
s3 := ( 36, 69)( 37, 70)( 38, 71)( 39, 72)( 40, 73)( 41, 74)( 42, 75)( 43, 76)
( 44, 77)( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)( 50, 83)( 51, 84)
( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 89)( 57, 90)( 58, 91)( 59, 92)
( 60, 93)( 61, 94)( 62, 95)( 63, 96)( 64, 97)( 65, 98)( 66, 99)( 67,100)
( 68,101);;
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, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*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*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*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)( 36, 69)( 37, 79)( 38, 78)( 39, 77)( 40, 76)( 41, 75)( 42, 74)
( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 47, 91)( 48,101)( 49,100)( 50, 99)
( 51, 98)( 52, 97)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 92)( 58, 80)
( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 85)( 65, 84)( 66, 83)
( 67, 82)( 68, 81);
s2 := Sym(101)!(  3, 48)(  4, 47)(  5, 57)(  6, 56)(  7, 55)(  8, 54)(  9, 53)
( 10, 52)( 11, 51)( 12, 50)( 13, 49)( 14, 37)( 15, 36)( 16, 46)( 17, 45)
( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)( 23, 39)( 24, 38)( 25, 59)
( 26, 58)( 27, 68)( 28, 67)( 29, 66)( 30, 65)( 31, 64)( 32, 63)( 33, 62)
( 34, 61)( 35, 60)( 69, 81)( 70, 80)( 71, 90)( 72, 89)( 73, 88)( 74, 87)
( 75, 86)( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 91, 92)( 93,101)( 94,100)
( 95, 99)( 96, 98);
s3 := Sym(101)!( 36, 69)( 37, 70)( 38, 71)( 39, 72)( 40, 73)( 41, 74)( 42, 75)
( 43, 76)( 44, 77)( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)( 50, 83)
( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 89)( 57, 90)( 58, 91)
( 59, 92)( 60, 93)( 61, 94)( 62, 95)( 63, 96)( 64, 97)( 65, 98)( 66, 99)
( 67,100)( 68,101);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*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*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*s1*s2*s1*s2*s1*s2 >;

to this polytope