Polytope of Type {6,68}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,68}*1224
if this polytope has a name.
Group : SmallGroup(1224,136)
Rank : 3
Schlafli Type : {6,68}
Number of vertices, edges, etc : 9, 306, 102
Order of s₀s₁s₂ : 68
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   17-fold quotients : {6,4}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 18, 35)( 19, 36)( 20, 37)( 21, 38)( 22, 39)( 23, 40)( 24, 41)( 25, 42)
( 26, 43)( 27, 44)( 28, 45)( 29, 46)( 30, 47)( 31, 48)( 32, 49)( 33, 50)
( 34, 51)( 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)( 69,137)( 70,138)( 71,139)( 72,140)( 73,141)( 74,142)
( 75,143)( 76,144)( 77,145)( 78,146)( 79,147)( 80,148)( 81,149)( 82,150)
( 83,151)( 84,152)( 85,153)( 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, 52)(  2, 68)(  3, 67)(  4, 66)(  5, 65)(  6, 64)(  7, 63)(  8, 62)
(  9, 61)( 10, 60)( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)
( 17, 53)( 18, 69)( 19, 85)( 20, 84)( 21, 83)( 22, 82)( 23, 81)( 24, 80)
( 25, 79)( 26, 78)( 27, 77)( 28, 76)( 29, 75)( 30, 74)( 31, 73)( 32, 72)
( 33, 71)( 34, 70)( 35, 86)( 36,102)( 37,101)( 38,100)( 39, 99)( 40, 98)
( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 91)( 48, 90)
( 49, 89)( 50, 88)( 51, 87)(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);;
s2 := (  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);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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(153)!( 18, 35)( 19, 36)( 20, 37)( 21, 38)( 22, 39)( 23, 40)( 24, 41)
( 25, 42)( 26, 43)( 27, 44)( 28, 45)( 29, 46)( 30, 47)( 31, 48)( 32, 49)
( 33, 50)( 34, 51)( 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)( 69,137)( 70,138)( 71,139)( 72,140)( 73,141)
( 74,142)( 75,143)( 76,144)( 77,145)( 78,146)( 79,147)( 80,148)( 81,149)
( 82,150)( 83,151)( 84,152)( 85,153)( 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(153)!(  1, 52)(  2, 68)(  3, 67)(  4, 66)(  5, 65)(  6, 64)(  7, 63)
(  8, 62)(  9, 61)( 10, 60)( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 55)
( 16, 54)( 17, 53)( 18, 69)( 19, 85)( 20, 84)( 21, 83)( 22, 82)( 23, 81)
( 24, 80)( 25, 79)( 26, 78)( 27, 77)( 28, 76)( 29, 75)( 30, 74)( 31, 73)
( 32, 72)( 33, 71)( 34, 70)( 35, 86)( 36,102)( 37,101)( 38,100)( 39, 99)
( 40, 98)( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 91)
( 48, 90)( 49, 89)( 50, 88)( 51, 87)(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);
s2 := 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);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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