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Polytope of Type {2,24,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,14}*1344
if this polytope has a name.
Group : SmallGroup(1344,8472)
Rank : 4
Schlafli Type : {2,24,14}
Number of vertices, edges, etc : 2, 24, 168, 14
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 : {2,12,14}*672
   3-fold quotients : {2,8,14}*448
   4-fold quotients : {2,6,14}*336
   6-fold quotients : {2,4,14}*224
   7-fold quotients : {2,24,2}*192
   12-fold quotients : {2,2,14}*112
   14-fold quotients : {2,12,2}*96
   21-fold quotients : {2,8,2}*64
   24-fold quotients : {2,2,7}*56
   28-fold quotients : {2,6,2}*48
   42-fold quotients : {2,4,2}*32
   56-fold quotients : {2,3,2}*24
   84-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 10, 17)( 11, 18)( 12, 19)( 13, 20)( 14, 21)( 15, 22)( 16, 23)( 31, 38)
( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)( 45, 66)( 46, 67)
( 47, 68)( 48, 69)( 49, 70)( 50, 71)( 51, 72)( 52, 80)( 53, 81)( 54, 82)
( 55, 83)( 56, 84)( 57, 85)( 58, 86)( 59, 73)( 60, 74)( 61, 75)( 62, 76)
( 63, 77)( 64, 78)( 65, 79)( 87,129)( 88,130)( 89,131)( 90,132)( 91,133)
( 92,134)( 93,135)( 94,143)( 95,144)( 96,145)( 97,146)( 98,147)( 99,148)
(100,149)(101,136)(102,137)(103,138)(104,139)(105,140)(106,141)(107,142)
(108,150)(109,151)(110,152)(111,153)(112,154)(113,155)(114,156)(115,164)
(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)(122,157)(123,158)
(124,159)(125,160)(126,161)(127,162)(128,163);;
s2 := (  3, 94)(  4,100)(  5, 99)(  6, 98)(  7, 97)(  8, 96)(  9, 95)( 10, 87)
( 11, 93)( 12, 92)( 13, 91)( 14, 90)( 15, 89)( 16, 88)( 17,101)( 18,107)
( 19,106)( 20,105)( 21,104)( 22,103)( 23,102)( 24,115)( 25,121)( 26,120)
( 27,119)( 28,118)( 29,117)( 30,116)( 31,108)( 32,114)( 33,113)( 34,112)
( 35,111)( 36,110)( 37,109)( 38,122)( 39,128)( 40,127)( 41,126)( 42,125)
( 43,124)( 44,123)( 45,157)( 46,163)( 47,162)( 48,161)( 49,160)( 50,159)
( 51,158)( 52,150)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)( 58,151)
( 59,164)( 60,170)( 61,169)( 62,168)( 63,167)( 64,166)( 65,165)( 66,136)
( 67,142)( 68,141)( 69,140)( 70,139)( 71,138)( 72,137)( 73,129)( 74,135)
( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)( 80,143)( 81,149)( 82,148)
( 83,147)( 84,146)( 85,145)( 86,144);;
s3 := (  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)( 19, 23)
( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 32)( 33, 37)( 34, 36)( 38, 39)
( 40, 44)( 41, 43)( 45, 46)( 47, 51)( 48, 50)( 52, 53)( 54, 58)( 55, 57)
( 59, 60)( 61, 65)( 62, 64)( 66, 67)( 68, 72)( 69, 71)( 73, 74)( 75, 79)
( 76, 78)( 80, 81)( 82, 86)( 83, 85)( 87, 88)( 89, 93)( 90, 92)( 94, 95)
( 96,100)( 97, 99)(101,102)(103,107)(104,106)(108,109)(110,114)(111,113)
(115,116)(117,121)(118,120)(122,123)(124,128)(125,127)(129,130)(131,135)
(132,134)(136,137)(138,142)(139,141)(143,144)(145,149)(146,148)(150,151)
(152,156)(153,155)(157,158)(159,163)(160,162)(164,165)(166,170)(167,169);;
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, 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, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(170)!(1,2);
s1 := Sym(170)!( 10, 17)( 11, 18)( 12, 19)( 13, 20)( 14, 21)( 15, 22)( 16, 23)
( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)( 45, 66)
( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 71)( 51, 72)( 52, 80)( 53, 81)
( 54, 82)( 55, 83)( 56, 84)( 57, 85)( 58, 86)( 59, 73)( 60, 74)( 61, 75)
( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 87,129)( 88,130)( 89,131)( 90,132)
( 91,133)( 92,134)( 93,135)( 94,143)( 95,144)( 96,145)( 97,146)( 98,147)
( 99,148)(100,149)(101,136)(102,137)(103,138)(104,139)(105,140)(106,141)
(107,142)(108,150)(109,151)(110,152)(111,153)(112,154)(113,155)(114,156)
(115,164)(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)(122,157)
(123,158)(124,159)(125,160)(126,161)(127,162)(128,163);
s2 := Sym(170)!(  3, 94)(  4,100)(  5, 99)(  6, 98)(  7, 97)(  8, 96)(  9, 95)
( 10, 87)( 11, 93)( 12, 92)( 13, 91)( 14, 90)( 15, 89)( 16, 88)( 17,101)
( 18,107)( 19,106)( 20,105)( 21,104)( 22,103)( 23,102)( 24,115)( 25,121)
( 26,120)( 27,119)( 28,118)( 29,117)( 30,116)( 31,108)( 32,114)( 33,113)
( 34,112)( 35,111)( 36,110)( 37,109)( 38,122)( 39,128)( 40,127)( 41,126)
( 42,125)( 43,124)( 44,123)( 45,157)( 46,163)( 47,162)( 48,161)( 49,160)
( 50,159)( 51,158)( 52,150)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)
( 58,151)( 59,164)( 60,170)( 61,169)( 62,168)( 63,167)( 64,166)( 65,165)
( 66,136)( 67,142)( 68,141)( 69,140)( 70,139)( 71,138)( 72,137)( 73,129)
( 74,135)( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)( 80,143)( 81,149)
( 82,148)( 83,147)( 84,146)( 85,145)( 86,144);
s3 := Sym(170)!(  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)
( 19, 23)( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 32)( 33, 37)( 34, 36)
( 38, 39)( 40, 44)( 41, 43)( 45, 46)( 47, 51)( 48, 50)( 52, 53)( 54, 58)
( 55, 57)( 59, 60)( 61, 65)( 62, 64)( 66, 67)( 68, 72)( 69, 71)( 73, 74)
( 75, 79)( 76, 78)( 80, 81)( 82, 86)( 83, 85)( 87, 88)( 89, 93)( 90, 92)
( 94, 95)( 96,100)( 97, 99)(101,102)(103,107)(104,106)(108,109)(110,114)
(111,113)(115,116)(117,121)(118,120)(122,123)(124,128)(125,127)(129,130)
(131,135)(132,134)(136,137)(138,142)(139,141)(143,144)(145,149)(146,148)
(150,151)(152,156)(153,155)(157,158)(159,163)(160,162)(164,165)(166,170)
(167,169);
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, 
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, 
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 >; 
 

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