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Polytope of Type {114,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {114,6}*1368a
if this polytope has a name.
Group : SmallGroup(1368,182)
Rank : 3
Schlafli Type : {114,6}
Number of vertices, edges, etc : 114, 342, 6
Order of s0s1s2 : 114
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   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) :
   3-fold quotients : {38,6}*456
   9-fold quotients : {38,2}*152
   18-fold quotients : {19,2}*76
   19-fold quotients : {6,6}*72b
   38-fold quotients : {6,3}*36
   57-fold quotients : {2,6}*24
   114-fold quotients : {2,3}*12
   171-fold quotients : {2,2}*8
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, 59)(  2, 58)(  3, 76)(  4, 75)(  5, 74)(  6, 73)(  7, 72)(  8, 71)
(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 64)( 16, 63)
( 17, 62)( 18, 61)( 19, 60)( 20, 97)( 21, 96)( 22,114)( 23,113)( 24,112)
( 25,111)( 26,110)( 27,109)( 28,108)( 29,107)( 30,106)( 31,105)( 32,104)
( 33,103)( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 98)( 39, 78)( 40, 77)
( 41, 95)( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)
( 49, 87)( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)(115,116)(117,133)(118,132)(119,131)(120,130)(121,129)(122,128)
(123,127)(124,126)(134,154)(135,153)(136,171)(137,170)(138,169)(139,168)
(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)(146,161)(147,160)
(148,159)(149,158)(150,157)(151,156)(152,155);;
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, 
s2*s0*s1*s2*s1*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*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*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 ];;
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, 59)(  2, 58)(  3, 76)(  4, 75)(  5, 74)(  6, 73)(  7, 72)
(  8, 71)(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 64)
( 16, 63)( 17, 62)( 18, 61)( 19, 60)( 20, 97)( 21, 96)( 22,114)( 23,113)
( 24,112)( 25,111)( 26,110)( 27,109)( 28,108)( 29,107)( 30,106)( 31,105)
( 32,104)( 33,103)( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 98)( 39, 78)
( 40, 77)( 41, 95)( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)
( 48, 88)( 49, 87)( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)
( 56, 80)( 57, 79)(115,116)(117,133)(118,132)(119,131)(120,130)(121,129)
(122,128)(123,127)(124,126)(134,154)(135,153)(136,171)(137,170)(138,169)
(139,168)(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)(146,161)
(147,160)(148,159)(149,158)(150,157)(151,156)(152,155);
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, 
s2*s0*s1*s2*s1*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*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*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 >; 
 
References : None.
to this polytope