Polytope of Type {24,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,14}*672
Also Known As : {24,14|2}. if this polytope has another name.
Group : SmallGroup(672,392)
Rank : 3
Schlafli Type : {24,14}
Number of vertices, edges, etc : 24, 168, 14
Order of s₀s₁s₂ : 168
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {24,14,2} of size 1344
Vertex Figure Of :
   {2,24,14} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,14}*336
   3-fold quotients : {8,14}*224
   4-fold quotients : {6,14}*168
   6-fold quotients : {4,14}*112
   7-fold quotients : {24,2}*96
   12-fold quotients : {2,14}*56
   14-fold quotients : {12,2}*48
   21-fold quotients : {8,2}*32
   24-fold quotients : {2,7}*28
   28-fold quotients : {6,2}*24
   42-fold quotients : {4,2}*16
   56-fold quotients : {3,2}*12
   84-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,14}*1344, {24,28}*1344a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope