Polytope of Type {8,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,34}*544
Also Known As : {8,34|2}. if this polytope has another name.
Group : SmallGroup(544,132)
Rank : 3
Schlafli Type : {8,34}
Number of vertices, edges, etc : 8, 136, 34
Order of s₀s₁s₂ : 136
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,34,2} of size 1088
Vertex Figure Of :
   {2,8,34} of size 1088
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,34}*272
   4-fold quotients : {2,34}*136
   8-fold quotients : {2,17}*68
   17-fold quotients : {8,2}*32
   34-fold quotients : {4,2}*16
   68-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,68}*1088a, {16,34}*1088
   3-fold covers : {24,34}*1632, {8,102}*1632
Permutation Representation (GAP) :

s0 := ( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)( 41, 58)( 42, 59)
( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)( 49, 66)( 50, 67)
( 51, 68)( 69,103)( 70,104)( 71,105)( 72,106)( 73,107)( 74,108)( 75,109)
( 76,110)( 77,111)( 78,112)( 79,113)( 80,114)( 81,115)( 82,116)( 83,117)
( 84,118)( 85,119)( 86,120)( 87,121)( 88,122)( 89,123)( 90,124)( 91,125)
( 92,126)( 93,127)( 94,128)( 95,129)( 96,130)( 97,131)( 98,132)( 99,133)
(100,134)(101,135)(102,136);;
s1 := (  1, 69)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 81)(  7, 80)(  8, 79)
(  9, 78)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 71)
( 17, 70)( 18, 86)( 19,102)( 20,101)( 21,100)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)
( 33, 88)( 34, 87)( 35,120)( 36,136)( 37,135)( 38,134)( 39,133)( 40,132)
( 41,131)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,125)( 48,124)
( 49,123)( 50,122)( 51,121)( 52,103)( 53,119)( 54,118)( 55,117)( 56,116)
( 57,115)( 58,114)( 59,113)( 60,112)( 61,111)( 62,110)( 63,109)( 64,108)
( 65,107)( 66,106)( 67,105)( 68,104);;
s2 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)
( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)
( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)
( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)
(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)(111,113)
(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(136)!( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)( 41, 58)
( 42, 59)( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)( 49, 66)
( 50, 67)( 51, 68)( 69,103)( 70,104)( 71,105)( 72,106)( 73,107)( 74,108)
( 75,109)( 76,110)( 77,111)( 78,112)( 79,113)( 80,114)( 81,115)( 82,116)
( 83,117)( 84,118)( 85,119)( 86,120)( 87,121)( 88,122)( 89,123)( 90,124)
( 91,125)( 92,126)( 93,127)( 94,128)( 95,129)( 96,130)( 97,131)( 98,132)
( 99,133)(100,134)(101,135)(102,136);
s1 := Sym(136)!(  1, 69)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 81)(  7, 80)
(  8, 79)(  9, 78)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 71)( 17, 70)( 18, 86)( 19,102)( 20,101)( 21,100)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)
( 32, 89)( 33, 88)( 34, 87)( 35,120)( 36,136)( 37,135)( 38,134)( 39,133)
( 40,132)( 41,131)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,125)
( 48,124)( 49,123)( 50,122)( 51,121)( 52,103)( 53,119)( 54,118)( 55,117)
( 56,116)( 57,115)( 58,114)( 59,113)( 60,112)( 61,111)( 62,110)( 63,109)
( 64,108)( 65,107)( 66,106)( 67,105)( 68,104);
s2 := Sym(136)!(  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)
(  9, 11)( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)
( 26, 28)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 45)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)
( 60, 62)( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)
( 94, 96)(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)
(111,113)(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)
(128,130);
poly := sub<Sym(136)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 >;

References : None.
to this polytope