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Polytope of Type {2,14,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,6,3}*1344
if this polytope has a name.
Group : SmallGroup(1344,11695)
Rank : 5
Schlafli Type : {2,14,6,3}
Number of vertices, edges, etc : 2, 14, 56, 12, 4
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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) :
   7-fold quotients : {2,2,6,3}*192
   14-fold quotients : {2,2,3,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  7, 27)(  8, 28)(  9, 29)( 10, 30)( 11, 23)( 12, 24)( 13, 25)( 14, 26)
( 15, 19)( 16, 20)( 17, 21)( 18, 22)( 35, 55)( 36, 56)( 37, 57)( 38, 58)
( 39, 51)( 40, 52)( 41, 53)( 42, 54)( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 63, 83)( 64, 84)( 65, 85)( 66, 86)( 67, 79)( 68, 80)( 69, 81)( 70, 82)
( 71, 75)( 72, 76)( 73, 77)( 74, 78)( 91,111)( 92,112)( 93,113)( 94,114)
( 95,107)( 96,108)( 97,109)( 98,110)( 99,103)(100,104)(101,105)(102,106)
(119,139)(120,140)(121,141)(122,142)(123,135)(124,136)(125,137)(126,138)
(127,131)(128,132)(129,133)(130,134)(147,167)(148,168)(149,169)(150,170)
(151,163)(152,164)(153,165)(154,166)(155,159)(156,160)(157,161)(158,162);;
s2 := (  3,  7)(  4,  9)(  5,  8)(  6, 10)( 11, 27)( 12, 29)( 13, 28)( 14, 30)
( 15, 23)( 16, 25)( 17, 24)( 18, 26)( 20, 21)( 31, 63)( 32, 65)( 33, 64)
( 34, 66)( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 83)( 40, 85)( 41, 84)
( 42, 86)( 43, 79)( 44, 81)( 45, 80)( 46, 82)( 47, 75)( 48, 77)( 49, 76)
( 50, 78)( 51, 71)( 52, 73)( 53, 72)( 54, 74)( 55, 67)( 56, 69)( 57, 68)
( 58, 70)( 87, 91)( 88, 93)( 89, 92)( 90, 94)( 95,111)( 96,113)( 97,112)
( 98,114)( 99,107)(100,109)(101,108)(102,110)(104,105)(115,147)(116,149)
(117,148)(118,150)(119,143)(120,145)(121,144)(122,146)(123,167)(124,169)
(125,168)(126,170)(127,163)(128,165)(129,164)(130,166)(131,159)(132,161)
(133,160)(134,162)(135,155)(136,157)(137,156)(138,158)(139,151)(140,153)
(141,152)(142,154);;
s3 := (  3,115)(  4,116)(  5,118)(  6,117)(  7,119)(  8,120)(  9,122)( 10,121)
( 11,123)( 12,124)( 13,126)( 14,125)( 15,127)( 16,128)( 17,130)( 18,129)
( 19,131)( 20,132)( 21,134)( 22,133)( 23,135)( 24,136)( 25,138)( 26,137)
( 27,139)( 28,140)( 29,142)( 30,141)( 31, 87)( 32, 88)( 33, 90)( 34, 89)
( 35, 91)( 36, 92)( 37, 94)( 38, 93)( 39, 95)( 40, 96)( 41, 98)( 42, 97)
( 43, 99)( 44,100)( 45,102)( 46,101)( 47,103)( 48,104)( 49,106)( 50,105)
( 51,107)( 52,108)( 53,110)( 54,109)( 55,111)( 56,112)( 57,114)( 58,113)
( 59,143)( 60,144)( 61,146)( 62,145)( 63,147)( 64,148)( 65,150)( 66,149)
( 67,151)( 68,152)( 69,154)( 70,153)( 71,155)( 72,156)( 73,158)( 74,157)
( 75,159)( 76,160)( 77,162)( 78,161)( 79,163)( 80,164)( 81,166)( 82,165)
( 83,167)( 84,168)( 85,170)( 86,169);;
s4 := (  3, 90)(  4, 88)(  5, 89)(  6, 87)(  7, 94)(  8, 92)(  9, 93)( 10, 91)
( 11, 98)( 12, 96)( 13, 97)( 14, 95)( 15,102)( 16,100)( 17,101)( 18, 99)
( 19,106)( 20,104)( 21,105)( 22,103)( 23,110)( 24,108)( 25,109)( 26,107)
( 27,114)( 28,112)( 29,113)( 30,111)( 31,146)( 32,144)( 33,145)( 34,143)
( 35,150)( 36,148)( 37,149)( 38,147)( 39,154)( 40,152)( 41,153)( 42,151)
( 43,158)( 44,156)( 45,157)( 46,155)( 47,162)( 48,160)( 49,161)( 50,159)
( 51,166)( 52,164)( 53,165)( 54,163)( 55,170)( 56,168)( 57,169)( 58,167)
( 59,118)( 60,116)( 61,117)( 62,115)( 63,122)( 64,120)( 65,121)( 66,119)
( 67,126)( 68,124)( 69,125)( 70,123)( 71,130)( 72,128)( 73,129)( 74,127)
( 75,134)( 76,132)( 77,133)( 78,131)( 79,138)( 80,136)( 81,137)( 82,135)
( 83,142)( 84,140)( 85,141)( 86,139);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(170)!(1,2);
s1 := Sym(170)!(  7, 27)(  8, 28)(  9, 29)( 10, 30)( 11, 23)( 12, 24)( 13, 25)
( 14, 26)( 15, 19)( 16, 20)( 17, 21)( 18, 22)( 35, 55)( 36, 56)( 37, 57)
( 38, 58)( 39, 51)( 40, 52)( 41, 53)( 42, 54)( 43, 47)( 44, 48)( 45, 49)
( 46, 50)( 63, 83)( 64, 84)( 65, 85)( 66, 86)( 67, 79)( 68, 80)( 69, 81)
( 70, 82)( 71, 75)( 72, 76)( 73, 77)( 74, 78)( 91,111)( 92,112)( 93,113)
( 94,114)( 95,107)( 96,108)( 97,109)( 98,110)( 99,103)(100,104)(101,105)
(102,106)(119,139)(120,140)(121,141)(122,142)(123,135)(124,136)(125,137)
(126,138)(127,131)(128,132)(129,133)(130,134)(147,167)(148,168)(149,169)
(150,170)(151,163)(152,164)(153,165)(154,166)(155,159)(156,160)(157,161)
(158,162);
s2 := Sym(170)!(  3,  7)(  4,  9)(  5,  8)(  6, 10)( 11, 27)( 12, 29)( 13, 28)
( 14, 30)( 15, 23)( 16, 25)( 17, 24)( 18, 26)( 20, 21)( 31, 63)( 32, 65)
( 33, 64)( 34, 66)( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 83)( 40, 85)
( 41, 84)( 42, 86)( 43, 79)( 44, 81)( 45, 80)( 46, 82)( 47, 75)( 48, 77)
( 49, 76)( 50, 78)( 51, 71)( 52, 73)( 53, 72)( 54, 74)( 55, 67)( 56, 69)
( 57, 68)( 58, 70)( 87, 91)( 88, 93)( 89, 92)( 90, 94)( 95,111)( 96,113)
( 97,112)( 98,114)( 99,107)(100,109)(101,108)(102,110)(104,105)(115,147)
(116,149)(117,148)(118,150)(119,143)(120,145)(121,144)(122,146)(123,167)
(124,169)(125,168)(126,170)(127,163)(128,165)(129,164)(130,166)(131,159)
(132,161)(133,160)(134,162)(135,155)(136,157)(137,156)(138,158)(139,151)
(140,153)(141,152)(142,154);
s3 := Sym(170)!(  3,115)(  4,116)(  5,118)(  6,117)(  7,119)(  8,120)(  9,122)
( 10,121)( 11,123)( 12,124)( 13,126)( 14,125)( 15,127)( 16,128)( 17,130)
( 18,129)( 19,131)( 20,132)( 21,134)( 22,133)( 23,135)( 24,136)( 25,138)
( 26,137)( 27,139)( 28,140)( 29,142)( 30,141)( 31, 87)( 32, 88)( 33, 90)
( 34, 89)( 35, 91)( 36, 92)( 37, 94)( 38, 93)( 39, 95)( 40, 96)( 41, 98)
( 42, 97)( 43, 99)( 44,100)( 45,102)( 46,101)( 47,103)( 48,104)( 49,106)
( 50,105)( 51,107)( 52,108)( 53,110)( 54,109)( 55,111)( 56,112)( 57,114)
( 58,113)( 59,143)( 60,144)( 61,146)( 62,145)( 63,147)( 64,148)( 65,150)
( 66,149)( 67,151)( 68,152)( 69,154)( 70,153)( 71,155)( 72,156)( 73,158)
( 74,157)( 75,159)( 76,160)( 77,162)( 78,161)( 79,163)( 80,164)( 81,166)
( 82,165)( 83,167)( 84,168)( 85,170)( 86,169);
s4 := Sym(170)!(  3, 90)(  4, 88)(  5, 89)(  6, 87)(  7, 94)(  8, 92)(  9, 93)
( 10, 91)( 11, 98)( 12, 96)( 13, 97)( 14, 95)( 15,102)( 16,100)( 17,101)
( 18, 99)( 19,106)( 20,104)( 21,105)( 22,103)( 23,110)( 24,108)( 25,109)
( 26,107)( 27,114)( 28,112)( 29,113)( 30,111)( 31,146)( 32,144)( 33,145)
( 34,143)( 35,150)( 36,148)( 37,149)( 38,147)( 39,154)( 40,152)( 41,153)
( 42,151)( 43,158)( 44,156)( 45,157)( 46,155)( 47,162)( 48,160)( 49,161)
( 50,159)( 51,166)( 52,164)( 53,165)( 54,163)( 55,170)( 56,168)( 57,169)
( 58,167)( 59,118)( 60,116)( 61,117)( 62,115)( 63,122)( 64,120)( 65,121)
( 66,119)( 67,126)( 68,124)( 69,125)( 70,123)( 71,130)( 72,128)( 73,129)
( 74,127)( 75,134)( 76,132)( 77,133)( 78,131)( 79,138)( 80,136)( 81,137)
( 82,135)( 83,142)( 84,140)( 85,141)( 86,139);
poly := sub<Sym(170)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >; 
 

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