Polytope of Type {34,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,6,3}*1224
if this polytope has a name.
Group : SmallGroup(1224,139)
Rank : 4
Schlafli Type : {34,6,3}
Number of vertices, edges, etc : 34, 102, 9, 3
Order of s₀s₁s₂s₃ : 102
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {34,2,3}*408
   6-fold quotients : {17,2,3}*204
   17-fold quotients : {2,6,3}*72
   51-fold quotients : {2,2,3}*24
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)
(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146);;
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, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)
( 52,104)( 53,103)( 54,119)( 55,118)( 56,117)( 57,116)( 58,115)( 59,114)
( 60,113)( 61,112)( 62,111)( 63,110)( 64,109)( 65,108)( 66,107)( 67,106)
( 68,105)( 69,121)( 70,120)( 71,136)( 72,135)( 73,134)( 74,133)( 75,132)
( 76,131)( 77,130)( 78,129)( 79,128)( 80,127)( 81,126)( 82,125)( 83,124)
( 84,123)( 85,122)( 86,138)( 87,137)( 88,153)( 89,152)( 90,151)( 91,150)
( 92,149)( 93,148)( 94,147)( 95,146)( 96,145)( 97,144)( 98,143)( 99,142)
(100,141)(101,140)(102,139);;
s2 := (  1, 52)(  2, 53)(  3, 54)(  4, 55)(  5, 56)(  6, 57)(  7, 58)(  8, 59)
(  9, 60)( 10, 61)( 11, 62)( 12, 63)( 13, 64)( 14, 65)( 15, 66)( 16, 67)
( 17, 68)( 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, 69)( 36, 70)( 37, 71)( 38, 72)( 39, 73)( 40, 74)
( 41, 75)( 42, 76)( 43, 77)( 44, 78)( 45, 79)( 46, 80)( 47, 81)( 48, 82)
( 49, 83)( 50, 84)( 51, 85)(120,137)(121,138)(122,139)(123,140)(124,141)
(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)
(133,150)(134,151)(135,152)(136,153);;
s3 := (  1, 18)(  2, 19)(  3, 20)(  4, 21)(  5, 22)(  6, 23)(  7, 24)(  8, 25)
(  9, 26)( 10, 27)( 11, 28)( 12, 29)( 13, 30)( 14, 31)( 15, 32)( 16, 33)
( 17, 34)( 52,120)( 53,121)( 54,122)( 55,123)( 56,124)( 57,125)( 58,126)
( 59,127)( 60,128)( 61,129)( 62,130)( 63,131)( 64,132)( 65,133)( 66,134)
( 67,135)( 68,136)( 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)( 86,137)( 87,138)( 88,139)( 89,140)( 90,141)
( 91,142)( 92,143)( 93,144)( 94,145)( 95,146)( 96,147)( 97,148)( 98,149)
( 99,150)(100,151)(101,152)(102,153);;
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*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*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(153)!(  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)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)
(145,146);
s1 := Sym(153)!(  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)( 52,104)( 53,103)( 54,119)( 55,118)( 56,117)( 57,116)( 58,115)
( 59,114)( 60,113)( 61,112)( 62,111)( 63,110)( 64,109)( 65,108)( 66,107)
( 67,106)( 68,105)( 69,121)( 70,120)( 71,136)( 72,135)( 73,134)( 74,133)
( 75,132)( 76,131)( 77,130)( 78,129)( 79,128)( 80,127)( 81,126)( 82,125)
( 83,124)( 84,123)( 85,122)( 86,138)( 87,137)( 88,153)( 89,152)( 90,151)
( 91,150)( 92,149)( 93,148)( 94,147)( 95,146)( 96,145)( 97,144)( 98,143)
( 99,142)(100,141)(101,140)(102,139);
s2 := Sym(153)!(  1, 52)(  2, 53)(  3, 54)(  4, 55)(  5, 56)(  6, 57)(  7, 58)
(  8, 59)(  9, 60)( 10, 61)( 11, 62)( 12, 63)( 13, 64)( 14, 65)( 15, 66)
( 16, 67)( 17, 68)( 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, 69)( 36, 70)( 37, 71)( 38, 72)( 39, 73)
( 40, 74)( 41, 75)( 42, 76)( 43, 77)( 44, 78)( 45, 79)( 46, 80)( 47, 81)
( 48, 82)( 49, 83)( 50, 84)( 51, 85)(120,137)(121,138)(122,139)(123,140)
(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)
(132,149)(133,150)(134,151)(135,152)(136,153);
s3 := Sym(153)!(  1, 18)(  2, 19)(  3, 20)(  4, 21)(  5, 22)(  6, 23)(  7, 24)
(  8, 25)(  9, 26)( 10, 27)( 11, 28)( 12, 29)( 13, 30)( 14, 31)( 15, 32)
( 16, 33)( 17, 34)( 52,120)( 53,121)( 54,122)( 55,123)( 56,124)( 57,125)
( 58,126)( 59,127)( 60,128)( 61,129)( 62,130)( 63,131)( 64,132)( 65,133)
( 66,134)( 67,135)( 68,136)( 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)( 86,137)( 87,138)( 88,139)( 89,140)
( 90,141)( 91,142)( 92,143)( 93,144)( 94,145)( 95,146)( 96,147)( 97,148)
( 98,149)( 99,150)(100,151)(101,152)(102,153);
poly := sub<Sym(153)|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*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*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