Polytope of Type {34,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,6}*408
Also Known As : {34,6|2}. if this polytope has another name.
Group : SmallGroup(408,41)
Rank : 3
Schlafli Type : {34,6}
Number of vertices, edges, etc : 34, 102, 6
Order of s₀s₁s₂ : 102
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {34,6,2} of size 816
   {34,6,3} of size 1224
   {34,6,4} of size 1632
   {34,6,3} of size 1632
   {34,6,4} of size 1632
Vertex Figure Of :
   {2,34,6} of size 816
   {4,34,6} of size 1632
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {34,2}*136
   6-fold quotients : {17,2}*68
   17-fold quotients : {2,6}*24
   34-fold quotients : {2,3}*12
   51-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {34,12}*816, {68,6}*816a
   3-fold covers : {34,18}*1224, {102,6}*1224a, {102,6}*1224b
   4-fold covers : {34,24}*1632, {136,6}*1632, {68,12}*1632, {68,6}*1632
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope