Polytope of Type {68,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {68,6}*1224
if this polytope has a name.
Group : SmallGroup(1224,136)
Rank : 3
Schlafli Type : {68,6}
Number of vertices, edges, etc : 102, 306, 9
Order of s₀s₁s₂ : 68
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   17-fold quotients : {4,6}*72
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)
( 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)( 69,120)( 70,136)( 71,135)( 72,134)( 73,133)( 74,132)( 75,131)
( 76,130)( 77,129)( 78,128)( 79,127)( 80,126)( 81,125)( 82,124)( 83,123)
( 84,122)( 85,121)( 86,137)( 87,153)( 88,152)( 89,151)( 90,150)( 91,149)
( 92,148)( 93,147)( 94,146)( 95,145)( 96,144)( 97,143)( 98,142)( 99,141)
(100,140)(101,139)(102,138);;
s1 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 18, 53)( 19, 52)( 20, 68)( 21, 67)( 22, 66)( 23, 65)( 24, 64)( 25, 63)
( 26, 62)( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)( 33, 55)
( 34, 54)( 35,104)( 36,103)( 37,119)( 38,118)( 39,117)( 40,116)( 41,115)
( 42,114)( 43,113)( 44,112)( 45,111)( 46,110)( 47,109)( 48,108)( 49,107)
( 50,106)( 51,105)( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)
( 76, 80)( 77, 79)( 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)(137,138)(139,153)(140,152)(141,151)(142,150)
(143,149)(144,148)(145,147);;
s2 := (  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]);;

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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*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)( 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)( 69,120)( 70,136)( 71,135)( 72,134)( 73,133)( 74,132)
( 75,131)( 76,130)( 77,129)( 78,128)( 79,127)( 80,126)( 81,125)( 82,124)
( 83,123)( 84,122)( 85,121)( 86,137)( 87,153)( 88,152)( 89,151)( 90,150)
( 91,149)( 92,148)( 93,147)( 94,146)( 95,145)( 96,144)( 97,143)( 98,142)
( 99,141)(100,140)(101,139)(102,138);
s1 := Sym(153)!(  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)
(  9, 11)( 18, 53)( 19, 52)( 20, 68)( 21, 67)( 22, 66)( 23, 65)( 24, 64)
( 25, 63)( 26, 62)( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)
( 33, 55)( 34, 54)( 35,104)( 36,103)( 37,119)( 38,118)( 39,117)( 40,116)
( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)( 46,110)( 47,109)( 48,108)
( 49,107)( 50,106)( 51,105)( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)
( 75, 81)( 76, 80)( 77, 79)( 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)(137,138)(139,153)(140,152)(141,151)
(142,150)(143,149)(144,148)(145,147);
s2 := 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>;

Finitely Presented Group Representation (Magma) :

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