Polytope of Type {6,76}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,76}*1368
if this polytope has a name.
Group : SmallGroup(1368,179)
Rank : 3
Schlafli Type : {6,76}
Number of vertices, edges, etc : 9, 342, 114
Order of s₀s₁s₂ : 76
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) :
   19-fold quotients : {6,4}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)( 27, 46)
( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)( 35, 54)
( 36, 55)( 37, 56)( 38, 57)( 58,115)( 59,116)( 60,117)( 61,118)( 62,119)
( 63,120)( 64,121)( 65,122)( 66,123)( 67,124)( 68,125)( 69,126)( 70,127)
( 71,128)( 72,129)( 73,130)( 74,131)( 75,132)( 76,133)( 77,153)( 78,154)
( 79,155)( 80,156)( 81,157)( 82,158)( 83,159)( 84,160)( 85,161)( 86,162)
( 87,163)( 88,164)( 89,165)( 90,166)( 91,167)( 92,168)( 93,169)( 94,170)
( 95,171)( 96,134)( 97,135)( 98,136)( 99,137)(100,138)(101,139)(102,140)
(103,141)(104,142)(105,143)(106,144)(107,145)(108,146)(109,147)(110,148)
(111,149)(112,150)(113,151)(114,152);;
s1 := (  1, 58)(  2, 76)(  3, 75)(  4, 74)(  5, 73)(  6, 72)(  7, 71)(  8, 70)
(  9, 69)( 10, 68)( 11, 67)( 12, 66)( 13, 65)( 14, 64)( 15, 63)( 16, 62)
( 17, 61)( 18, 60)( 19, 59)( 20, 77)( 21, 95)( 22, 94)( 23, 93)( 24, 92)
( 25, 91)( 26, 90)( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)( 32, 84)
( 33, 83)( 34, 82)( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 96)( 40,114)
( 41,113)( 42,112)( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)( 48,106)
( 49,105)( 50,104)( 51,103)( 52,102)( 53,101)( 54,100)( 55, 99)( 56, 98)
( 57, 97)(116,133)(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)
(123,126)(124,125)(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)
(141,146)(142,145)(143,144)(154,171)(155,170)(156,169)(157,168)(158,167)
(159,166)(160,165)(161,164)(162,163);;
s2 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20, 59)( 21, 58)( 22, 76)( 23, 75)( 24, 74)( 25, 73)( 26, 72)
( 27, 71)( 28, 70)( 29, 69)( 30, 68)( 31, 67)( 32, 66)( 33, 65)( 34, 64)
( 35, 63)( 36, 62)( 37, 61)( 38, 60)( 39,116)( 40,115)( 41,133)( 42,132)
( 43,131)( 44,130)( 45,129)( 46,128)( 47,127)( 48,126)( 49,125)( 50,124)
( 51,123)( 52,122)( 53,121)( 54,120)( 55,119)( 56,118)( 57,117)( 77, 78)
( 79, 95)( 80, 94)( 81, 93)( 82, 92)( 83, 91)( 84, 90)( 85, 89)( 86, 88)
( 96,135)( 97,134)( 98,152)( 99,151)(100,150)(101,149)(102,148)(103,147)
(104,146)(105,145)(106,144)(107,143)(108,142)(109,141)(110,140)(111,139)
(112,138)(113,137)(114,136)(153,154)(155,171)(156,170)(157,169)(158,168)
(159,167)(160,166)(161,165)(162,164);;
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(171)!( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)
( 27, 46)( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)
( 35, 54)( 36, 55)( 37, 56)( 38, 57)( 58,115)( 59,116)( 60,117)( 61,118)
( 62,119)( 63,120)( 64,121)( 65,122)( 66,123)( 67,124)( 68,125)( 69,126)
( 70,127)( 71,128)( 72,129)( 73,130)( 74,131)( 75,132)( 76,133)( 77,153)
( 78,154)( 79,155)( 80,156)( 81,157)( 82,158)( 83,159)( 84,160)( 85,161)
( 86,162)( 87,163)( 88,164)( 89,165)( 90,166)( 91,167)( 92,168)( 93,169)
( 94,170)( 95,171)( 96,134)( 97,135)( 98,136)( 99,137)(100,138)(101,139)
(102,140)(103,141)(104,142)(105,143)(106,144)(107,145)(108,146)(109,147)
(110,148)(111,149)(112,150)(113,151)(114,152);
s1 := Sym(171)!(  1, 58)(  2, 76)(  3, 75)(  4, 74)(  5, 73)(  6, 72)(  7, 71)
(  8, 70)(  9, 69)( 10, 68)( 11, 67)( 12, 66)( 13, 65)( 14, 64)( 15, 63)
( 16, 62)( 17, 61)( 18, 60)( 19, 59)( 20, 77)( 21, 95)( 22, 94)( 23, 93)
( 24, 92)( 25, 91)( 26, 90)( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)
( 32, 84)( 33, 83)( 34, 82)( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 96)
( 40,114)( 41,113)( 42,112)( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)
( 48,106)( 49,105)( 50,104)( 51,103)( 52,102)( 53,101)( 54,100)( 55, 99)
( 56, 98)( 57, 97)(116,133)(117,132)(118,131)(119,130)(120,129)(121,128)
(122,127)(123,126)(124,125)(135,152)(136,151)(137,150)(138,149)(139,148)
(140,147)(141,146)(142,145)(143,144)(154,171)(155,170)(156,169)(157,168)
(158,167)(159,166)(160,165)(161,164)(162,163);
s2 := Sym(171)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20, 59)( 21, 58)( 22, 76)( 23, 75)( 24, 74)( 25, 73)
( 26, 72)( 27, 71)( 28, 70)( 29, 69)( 30, 68)( 31, 67)( 32, 66)( 33, 65)
( 34, 64)( 35, 63)( 36, 62)( 37, 61)( 38, 60)( 39,116)( 40,115)( 41,133)
( 42,132)( 43,131)( 44,130)( 45,129)( 46,128)( 47,127)( 48,126)( 49,125)
( 50,124)( 51,123)( 52,122)( 53,121)( 54,120)( 55,119)( 56,118)( 57,117)
( 77, 78)( 79, 95)( 80, 94)( 81, 93)( 82, 92)( 83, 91)( 84, 90)( 85, 89)
( 86, 88)( 96,135)( 97,134)( 98,152)( 99,151)(100,150)(101,149)(102,148)
(103,147)(104,146)(105,145)(106,144)(107,143)(108,142)(109,141)(110,140)
(111,139)(112,138)(113,137)(114,136)(153,154)(155,171)(156,170)(157,169)
(158,168)(159,167)(160,166)(161,165)(162,164);
poly := sub<Sym(171)|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*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope