Polytope of Type {2,14,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,24}*1344
if this polytope has a name.
Group : SmallGroup(1344,8472)
Rank : 4
Schlafli Type : {2,14,24}
Number of vertices, edges, etc : 2, 14, 168, 24
Order of s₀s₁s₂s₃ : 168
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   2-fold quotients : {2,14,12}*672
   3-fold quotients : {2,14,8}*448
   4-fold quotients : {2,14,6}*336
   6-fold quotients : {2,14,4}*224
   7-fold quotients : {2,2,24}*192
   12-fold quotients : {2,14,2}*112
   14-fold quotients : {2,2,12}*96
   21-fold quotients : {2,2,8}*64
   24-fold quotients : {2,7,2}*56
   28-fold quotients : {2,2,6}*48
   42-fold quotients : {2,2,4}*32
   56-fold quotients : {2,2,3}*24
   84-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope