Polytope of Type {6,114}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,114}*1368a
if this polytope has a name.
Group : SmallGroup(1368,182)
Rank : 3
Schlafli Type : {6,114}
Number of vertices, edges, etc : 6, 342, 114
Order of s₀s₁s₂ : 114
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {6,38}*456
   9-fold quotients : {2,38}*152
   18-fold quotients : {2,19}*76
   19-fold quotients : {6,6}*72c
   38-fold quotients : {3,6}*36
   57-fold quotients : {6,2}*24
   114-fold quotients : {3,2}*12
   171-fold quotients : {2,2}*8
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, 77)(  2, 95)(  3, 94)(  4, 93)(  5, 92)(  6, 91)(  7, 90)(  8, 89)
(  9, 88)( 10, 87)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 82)( 16, 81)
( 17, 80)( 18, 79)( 19, 78)( 20, 58)( 21, 76)( 22, 75)( 23, 74)( 24, 73)
( 25, 72)( 26, 71)( 27, 70)( 28, 69)( 29, 68)( 30, 67)( 31, 66)( 32, 65)
( 33, 64)( 34, 63)( 35, 62)( 36, 61)( 37, 60)( 38, 59)( 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)(115,134)(116,152)(117,151)(118,150)(119,149)(120,148)(121,147)
(122,146)(123,145)(124,144)(125,143)(126,142)(127,141)(128,140)(129,139)
(130,138)(131,137)(132,136)(133,135)(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, 21)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)( 27, 33)
( 28, 32)( 29, 31)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)( 45, 53)
( 46, 52)( 47, 51)( 48, 50)( 58,116)( 59,115)( 60,133)( 61,132)( 62,131)
( 63,130)( 64,129)( 65,128)( 66,127)( 67,126)( 68,125)( 69,124)( 70,123)
( 71,122)( 72,121)( 73,120)( 74,119)( 75,118)( 76,117)( 77,135)( 78,134)
( 79,152)( 80,151)( 81,150)( 82,149)( 83,148)( 84,147)( 85,146)( 86,145)
( 87,144)( 88,143)( 89,142)( 90,141)( 91,140)( 92,139)( 93,138)( 94,137)
( 95,136)( 96,154)( 97,153)( 98,171)( 99,170)(100,169)(101,168)(102,167)
(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)(110,159)
(111,158)(112,157)(113,156)(114,155);;
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*s1*s0*s1*s2*s0*s1*s2*s1*s0*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*s0*s1*s2*s1*s2*s1*s2*s1 ];;
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, 77)(  2, 95)(  3, 94)(  4, 93)(  5, 92)(  6, 91)(  7, 90)
(  8, 89)(  9, 88)( 10, 87)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 82)
( 16, 81)( 17, 80)( 18, 79)( 19, 78)( 20, 58)( 21, 76)( 22, 75)( 23, 74)
( 24, 73)( 25, 72)( 26, 71)( 27, 70)( 28, 69)( 29, 68)( 30, 67)( 31, 66)
( 32, 65)( 33, 64)( 34, 63)( 35, 62)( 36, 61)( 37, 60)( 38, 59)( 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)(115,134)(116,152)(117,151)(118,150)(119,149)(120,148)
(121,147)(122,146)(123,145)(124,144)(125,143)(126,142)(127,141)(128,140)
(129,139)(130,138)(131,137)(132,136)(133,135)(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, 21)( 22, 38)( 23, 37)( 24, 36)( 25, 35)( 26, 34)
( 27, 33)( 28, 32)( 29, 31)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)
( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58,116)( 59,115)( 60,133)( 61,132)
( 62,131)( 63,130)( 64,129)( 65,128)( 66,127)( 67,126)( 68,125)( 69,124)
( 70,123)( 71,122)( 72,121)( 73,120)( 74,119)( 75,118)( 76,117)( 77,135)
( 78,134)( 79,152)( 80,151)( 81,150)( 82,149)( 83,148)( 84,147)( 85,146)
( 86,145)( 87,144)( 88,143)( 89,142)( 90,141)( 91,140)( 92,139)( 93,138)
( 94,137)( 95,136)( 96,154)( 97,153)( 98,171)( 99,170)(100,169)(101,168)
(102,167)(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)
(110,159)(111,158)(112,157)(113,156)(114,155);
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*s1*s0*s1*s2*s0*s1*s2*s1*s0*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*s0*s1*s2*s1*s2*s1*s2*s1 >;

References : None.
to this polytope