Polytope of Type {76,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope