Polytope of Type {34,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,8,2}*1088
if this polytope has a name.
Group : SmallGroup(1088,1317)
Rank : 4
Schlafli Type : {34,8,2}
Number of vertices, edges, etc : 34, 136, 8, 2
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 : {34,4,2}*544
   4-fold quotients : {34,2,2}*272
   8-fold quotients : {17,2,2}*136
   17-fold quotients : {2,8,2}*64
   34-fold quotients : {2,4,2}*32
   68-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)
(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)
(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129);;
s1 := (  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, 53)( 36, 52)( 37, 68)( 38, 67)( 39, 66)( 40, 65)( 41, 64)( 42, 63)
( 43, 62)( 44, 61)( 45, 60)( 46, 59)( 47, 58)( 48, 57)( 49, 56)( 50, 55)
( 51, 54)( 69,104)( 70,103)( 71,119)( 72,118)( 73,117)( 74,116)( 75,115)
( 76,114)( 77,113)( 78,112)( 79,111)( 80,110)( 81,109)( 82,108)( 83,107)
( 84,106)( 85,105)( 86,121)( 87,120)( 88,136)( 89,135)( 90,134)( 91,133)
( 92,132)( 93,131)( 94,130)( 95,129)( 96,128)( 97,127)( 98,126)( 99,125)
(100,124)(101,123)(102,122);;
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, 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)( 35,120)( 36,121)( 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)( 52,103)( 53,104)( 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);;
s3 := (137,138);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*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(138)!(  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)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)
(111,112)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)
(128,129);
s1 := Sym(138)!(  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, 53)( 36, 52)( 37, 68)( 38, 67)( 39, 66)( 40, 65)( 41, 64)
( 42, 63)( 43, 62)( 44, 61)( 45, 60)( 46, 59)( 47, 58)( 48, 57)( 49, 56)
( 50, 55)( 51, 54)( 69,104)( 70,103)( 71,119)( 72,118)( 73,117)( 74,116)
( 75,115)( 76,114)( 77,113)( 78,112)( 79,111)( 80,110)( 81,109)( 82,108)
( 83,107)( 84,106)( 85,105)( 86,121)( 87,120)( 88,136)( 89,135)( 90,134)
( 91,133)( 92,132)( 93,131)( 94,130)( 95,129)( 96,128)( 97,127)( 98,126)
( 99,125)(100,124)(101,123)(102,122);
s2 := Sym(138)!(  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, 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)( 35,120)( 36,121)( 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)( 52,103)( 53,104)( 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);
s3 := Sym(138)!(137,138);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*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 >;

to this polytope