Polytope of Type {2,34,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,34,6}*816
if this polytope has a name.
Group : SmallGroup(816,199)
Rank : 4
Schlafli Type : {2,34,6}
Number of vertices, edges, etc : 2, 34, 102, 6
Order of s₀s₁s₂s₃ : 102
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,34,6,2} of size 1632
Vertex Figure Of :
   {2,2,34,6} of size 1632
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,34,2}*272
   6-fold quotients : {2,17,2}*136
   17-fold quotients : {2,2,6}*48
   34-fold quotients : {2,2,3}*24
   51-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,34,12}*1632, {2,68,6}*1632a, {4,34,6}*1632
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 19)(  5, 18)(  6, 17)(  7, 16)(  8, 15)(  9, 14)( 10, 13)( 11, 12)
( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 45, 46)
( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)( 62, 63)
( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)( 79, 80)
( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97);;
s2 := (  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)( 11, 13)
( 20, 38)( 21, 37)( 22, 53)( 23, 52)( 24, 51)( 25, 50)( 26, 49)( 27, 48)
( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)( 33, 42)( 34, 41)( 35, 40)
( 36, 39)( 54, 55)( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)( 61, 65)
( 62, 64)( 71, 89)( 72, 88)( 73,104)( 74,103)( 75,102)( 76,101)( 77,100)
( 78, 99)( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)
( 86, 91)( 87, 90);;
s3 := (  3, 71)(  4, 72)(  5, 73)(  6, 74)(  7, 75)(  8, 76)(  9, 77)( 10, 78)
( 11, 79)( 12, 80)( 13, 81)( 14, 82)( 15, 83)( 16, 84)( 17, 85)( 18, 86)
( 19, 87)( 20, 54)( 21, 55)( 22, 56)( 23, 57)( 24, 58)( 25, 59)( 26, 60)
( 27, 61)( 28, 62)( 29, 63)( 30, 64)( 31, 65)( 32, 66)( 33, 67)( 34, 68)
( 35, 69)( 36, 70)( 37, 88)( 38, 89)( 39, 90)( 40, 91)( 41, 92)( 42, 93)
( 43, 94)( 44, 95)( 45, 96)( 46, 97)( 47, 98)( 48, 99)( 49,100)( 50,101)
( 51,102)( 52,103)( 53,104);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*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(104)!(1,2);
s1 := Sym(104)!(  4, 19)(  5, 18)(  6, 17)(  7, 16)(  8, 15)(  9, 14)( 10, 13)
( 11, 12)( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)
( 28, 29)( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)
( 45, 46)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)
( 62, 63)( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)
( 79, 80)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)
( 96, 97);
s2 := Sym(104)!(  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)
( 11, 13)( 20, 38)( 21, 37)( 22, 53)( 23, 52)( 24, 51)( 25, 50)( 26, 49)
( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)( 33, 42)( 34, 41)
( 35, 40)( 36, 39)( 54, 55)( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)
( 61, 65)( 62, 64)( 71, 89)( 72, 88)( 73,104)( 74,103)( 75,102)( 76,101)
( 77,100)( 78, 99)( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 83, 94)( 84, 93)
( 85, 92)( 86, 91)( 87, 90);
s3 := Sym(104)!(  3, 71)(  4, 72)(  5, 73)(  6, 74)(  7, 75)(  8, 76)(  9, 77)
( 10, 78)( 11, 79)( 12, 80)( 13, 81)( 14, 82)( 15, 83)( 16, 84)( 17, 85)
( 18, 86)( 19, 87)( 20, 54)( 21, 55)( 22, 56)( 23, 57)( 24, 58)( 25, 59)
( 26, 60)( 27, 61)( 28, 62)( 29, 63)( 30, 64)( 31, 65)( 32, 66)( 33, 67)
( 34, 68)( 35, 69)( 36, 70)( 37, 88)( 38, 89)( 39, 90)( 40, 91)( 41, 92)
( 42, 93)( 43, 94)( 44, 95)( 45, 96)( 46, 97)( 47, 98)( 48, 99)( 49,100)
( 50,101)( 51,102)( 52,103)( 53,104);
poly := sub<Sym(104)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*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