Polytope of Type {2,4,6,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,14}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11695)
Rank : 5
Schlafli Type : {2,4,6,14}
Number of vertices, edges, etc : 2, 4, 12, 42, 14
Order of s₀s₁s₂s₃s₄ : 42
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,4,6,2}*192c
   14-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3,  5)(  4,  6)(  7,  9)(  8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)
(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)
(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)
(163,165)(164,166)(167,169)(168,170);;
s2 := (  4,  5)(  8,  9)( 12, 13)( 16, 17)( 20, 21)( 24, 25)( 28, 29)( 31, 59)
( 32, 61)( 33, 60)( 34, 62)( 35, 63)( 36, 65)( 37, 64)( 38, 66)( 39, 67)
( 40, 69)( 41, 68)( 42, 70)( 43, 71)( 44, 73)( 45, 72)( 46, 74)( 47, 75)
( 48, 77)( 49, 76)( 50, 78)( 51, 79)( 52, 81)( 53, 80)( 54, 82)( 55, 83)
( 56, 85)( 57, 84)( 58, 86)( 88, 89)( 92, 93)( 96, 97)(100,101)(104,105)
(108,109)(112,113)(115,143)(116,145)(117,144)(118,146)(119,147)(120,149)
(121,148)(122,150)(123,151)(124,153)(125,152)(126,154)(127,155)(128,157)
(129,156)(130,158)(131,159)(132,161)(133,160)(134,162)(135,163)(136,165)
(137,164)(138,166)(139,167)(140,169)(141,168)(142,170);;
s3 := (  3, 59)(  4, 62)(  5, 61)(  6, 60)(  7, 83)(  8, 86)(  9, 85)( 10, 84)
( 11, 79)( 12, 82)( 13, 81)( 14, 80)( 15, 75)( 16, 78)( 17, 77)( 18, 76)
( 19, 71)( 20, 74)( 21, 73)( 22, 72)( 23, 67)( 24, 70)( 25, 69)( 26, 68)
( 27, 63)( 28, 66)( 29, 65)( 30, 64)( 32, 34)( 35, 55)( 36, 58)( 37, 57)
( 38, 56)( 39, 51)( 40, 54)( 41, 53)( 42, 52)( 43, 47)( 44, 50)( 45, 49)
( 46, 48)( 87,143)( 88,146)( 89,145)( 90,144)( 91,167)( 92,170)( 93,169)
( 94,168)( 95,163)( 96,166)( 97,165)( 98,164)( 99,159)(100,162)(101,161)
(102,160)(103,155)(104,158)(105,157)(106,156)(107,151)(108,154)(109,153)
(110,152)(111,147)(112,150)(113,149)(114,148)(116,118)(119,139)(120,142)
(121,141)(122,140)(123,135)(124,138)(125,137)(126,136)(127,131)(128,134)
(129,133)(130,132);;
s4 := (  3, 91)(  4, 92)(  5, 93)(  6, 94)(  7, 87)(  8, 88)(  9, 89)( 10, 90)
( 11,111)( 12,112)( 13,113)( 14,114)( 15,107)( 16,108)( 17,109)( 18,110)
( 19,103)( 20,104)( 21,105)( 22,106)( 23, 99)( 24,100)( 25,101)( 26,102)
( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31,119)( 32,120)( 33,121)( 34,122)
( 35,115)( 36,116)( 37,117)( 38,118)( 39,139)( 40,140)( 41,141)( 42,142)
( 43,135)( 44,136)( 45,137)( 46,138)( 47,131)( 48,132)( 49,133)( 50,134)
( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)( 58,126)
( 59,147)( 60,148)( 61,149)( 62,150)( 63,143)( 64,144)( 65,145)( 66,146)
( 67,167)( 68,168)( 69,169)( 70,170)( 71,163)( 72,164)( 73,165)( 74,166)
( 75,159)( 76,160)( 77,161)( 78,162)( 79,155)( 80,156)( 81,157)( 82,158)
( 83,151)( 84,152)( 85,153)( 86,154);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(170)!(1,2);
s1 := Sym(170)!(  3,  5)(  4,  6)(  7,  9)(  8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)
(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)
(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)
(160,162)(163,165)(164,166)(167,169)(168,170);
s2 := Sym(170)!(  4,  5)(  8,  9)( 12, 13)( 16, 17)( 20, 21)( 24, 25)( 28, 29)
( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 63)( 36, 65)( 37, 64)( 38, 66)
( 39, 67)( 40, 69)( 41, 68)( 42, 70)( 43, 71)( 44, 73)( 45, 72)( 46, 74)
( 47, 75)( 48, 77)( 49, 76)( 50, 78)( 51, 79)( 52, 81)( 53, 80)( 54, 82)
( 55, 83)( 56, 85)( 57, 84)( 58, 86)( 88, 89)( 92, 93)( 96, 97)(100,101)
(104,105)(108,109)(112,113)(115,143)(116,145)(117,144)(118,146)(119,147)
(120,149)(121,148)(122,150)(123,151)(124,153)(125,152)(126,154)(127,155)
(128,157)(129,156)(130,158)(131,159)(132,161)(133,160)(134,162)(135,163)
(136,165)(137,164)(138,166)(139,167)(140,169)(141,168)(142,170);
s3 := Sym(170)!(  3, 59)(  4, 62)(  5, 61)(  6, 60)(  7, 83)(  8, 86)(  9, 85)
( 10, 84)( 11, 79)( 12, 82)( 13, 81)( 14, 80)( 15, 75)( 16, 78)( 17, 77)
( 18, 76)( 19, 71)( 20, 74)( 21, 73)( 22, 72)( 23, 67)( 24, 70)( 25, 69)
( 26, 68)( 27, 63)( 28, 66)( 29, 65)( 30, 64)( 32, 34)( 35, 55)( 36, 58)
( 37, 57)( 38, 56)( 39, 51)( 40, 54)( 41, 53)( 42, 52)( 43, 47)( 44, 50)
( 45, 49)( 46, 48)( 87,143)( 88,146)( 89,145)( 90,144)( 91,167)( 92,170)
( 93,169)( 94,168)( 95,163)( 96,166)( 97,165)( 98,164)( 99,159)(100,162)
(101,161)(102,160)(103,155)(104,158)(105,157)(106,156)(107,151)(108,154)
(109,153)(110,152)(111,147)(112,150)(113,149)(114,148)(116,118)(119,139)
(120,142)(121,141)(122,140)(123,135)(124,138)(125,137)(126,136)(127,131)
(128,134)(129,133)(130,132);
s4 := Sym(170)!(  3, 91)(  4, 92)(  5, 93)(  6, 94)(  7, 87)(  8, 88)(  9, 89)
( 10, 90)( 11,111)( 12,112)( 13,113)( 14,114)( 15,107)( 16,108)( 17,109)
( 18,110)( 19,103)( 20,104)( 21,105)( 22,106)( 23, 99)( 24,100)( 25,101)
( 26,102)( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31,119)( 32,120)( 33,121)
( 34,122)( 35,115)( 36,116)( 37,117)( 38,118)( 39,139)( 40,140)( 41,141)
( 42,142)( 43,135)( 44,136)( 45,137)( 46,138)( 47,131)( 48,132)( 49,133)
( 50,134)( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)
( 58,126)( 59,147)( 60,148)( 61,149)( 62,150)( 63,143)( 64,144)( 65,145)
( 66,146)( 67,167)( 68,168)( 69,169)( 70,170)( 71,163)( 72,164)( 73,165)
( 74,166)( 75,159)( 76,160)( 77,161)( 78,162)( 79,155)( 80,156)( 81,157)
( 82,158)( 83,151)( 84,152)( 85,153)( 86,154);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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