Polytope of Type {2,34,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,34,8}*1088
if this polytope has a name.
Group : SmallGroup(1088,1317)
Rank : 4
Schlafli Type : {2,34,8}
Number of vertices, edges, etc : 2, 34, 136, 8
Order of s₀s₁s₂s₃ : 136
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) :
   2-fold quotients : {2,34,4}*544
   4-fold quotients : {2,34,2}*272
   8-fold quotients : {2,17,2}*136
   17-fold quotients : {2,2,8}*64
   34-fold quotients : {2,2,4}*32
   68-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)
(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)
(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131);;
s2 := (  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)( 11, 13)
( 20, 21)( 22, 36)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 37, 55)( 38, 54)( 39, 70)( 40, 69)( 41, 68)( 42, 67)( 43, 66)( 44, 65)
( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)( 52, 57)
( 53, 56)( 71,106)( 72,105)( 73,121)( 74,120)( 75,119)( 76,118)( 77,117)
( 78,116)( 79,115)( 80,114)( 81,113)( 82,112)( 83,111)( 84,110)( 85,109)
( 86,108)( 87,107)( 88,123)( 89,122)( 90,138)( 91,137)( 92,136)( 93,135)
( 94,134)( 95,133)( 96,132)( 97,131)( 98,130)( 99,129)(100,128)(101,127)
(102,126)(103,125)(104,124);;
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, 88)( 21, 89)( 22, 90)( 23, 91)( 24, 92)( 25, 93)( 26, 94)
( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31, 99)( 32,100)( 33,101)( 34,102)
( 35,103)( 36,104)( 37,122)( 38,123)( 39,124)( 40,125)( 41,126)( 42,127)
( 43,128)( 44,129)( 45,130)( 46,131)( 47,132)( 48,133)( 49,134)( 50,135)
( 51,136)( 52,137)( 53,138)( 54,105)( 55,106)( 56,107)( 57,108)( 58,109)
( 59,110)( 60,111)( 61,112)( 62,113)( 63,114)( 64,115)( 65,116)( 66,117)
( 67,118)( 68,119)( 69,120)( 70,121);;
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*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(138)!(1,2);
s1 := Sym(138)!(  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)(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)
(113,114)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)
(130,131);
s2 := Sym(138)!(  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)
( 11, 13)( 20, 21)( 22, 36)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)
( 28, 30)( 37, 55)( 38, 54)( 39, 70)( 40, 69)( 41, 68)( 42, 67)( 43, 66)
( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)
( 52, 57)( 53, 56)( 71,106)( 72,105)( 73,121)( 74,120)( 75,119)( 76,118)
( 77,117)( 78,116)( 79,115)( 80,114)( 81,113)( 82,112)( 83,111)( 84,110)
( 85,109)( 86,108)( 87,107)( 88,123)( 89,122)( 90,138)( 91,137)( 92,136)
( 93,135)( 94,134)( 95,133)( 96,132)( 97,131)( 98,130)( 99,129)(100,128)
(101,127)(102,126)(103,125)(104,124);
s3 := Sym(138)!(  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, 88)( 21, 89)( 22, 90)( 23, 91)( 24, 92)( 25, 93)
( 26, 94)( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31, 99)( 32,100)( 33,101)
( 34,102)( 35,103)( 36,104)( 37,122)( 38,123)( 39,124)( 40,125)( 41,126)
( 42,127)( 43,128)( 44,129)( 45,130)( 46,131)( 47,132)( 48,133)( 49,134)
( 50,135)( 51,136)( 52,137)( 53,138)( 54,105)( 55,106)( 56,107)( 57,108)
( 58,109)( 59,110)( 60,111)( 61,112)( 62,113)( 63,114)( 64,115)( 65,116)
( 66,117)( 67,118)( 68,119)( 69,120)( 70,121);
poly := sub<Sym(138)|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*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