Polytope of Type {24,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,2}*768f
if this polytope has a name.
Group : SmallGroup(768,1089367)
Rank : 4
Schlafli Type : {24,4,2}
Number of vertices, edges, etc : 48, 96, 8, 2
Order of s₀s₁s₂s₃ : 12
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 : {12,4,2}*384c
   4-fold quotients : {6,4,2}*192
   8-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,4,2}*48, {6,2,2}*48
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1, 97)(  2, 98)(  3,102)(  4,101)(  5,100)(  6, 99)(  7,104)(  8,103)
(  9,113)( 10,114)( 11,118)( 12,117)( 13,116)( 14,115)( 15,120)( 16,119)
( 17,105)( 18,106)( 19,110)( 20,109)( 21,108)( 22,107)( 23,112)( 24,111)
( 25,122)( 26,121)( 27,125)( 28,126)( 29,123)( 30,124)( 31,127)( 32,128)
( 33,138)( 34,137)( 35,141)( 36,142)( 37,139)( 38,140)( 39,143)( 40,144)
( 41,130)( 42,129)( 43,133)( 44,134)( 45,131)( 46,132)( 47,135)( 48,136)
( 49,170)( 50,169)( 51,173)( 52,174)( 53,171)( 54,172)( 55,175)( 56,176)
( 57,186)( 58,185)( 59,189)( 60,190)( 61,187)( 62,188)( 63,191)( 64,192)
( 65,178)( 66,177)( 67,181)( 68,182)( 69,179)( 70,180)( 71,183)( 72,184)
( 73,146)( 74,145)( 75,149)( 76,150)( 77,147)( 78,148)( 79,151)( 80,152)
( 81,162)( 82,161)( 83,165)( 84,166)( 85,163)( 86,164)( 87,167)( 88,168)
( 89,154)( 90,153)( 91,157)( 92,158)( 93,155)( 94,156)( 95,159)( 96,160);;
s1 := (  1, 57)(  2, 58)(  3, 60)(  4, 59)(  5, 63)(  6, 64)(  7, 61)(  8, 62)
(  9, 49)( 10, 50)( 11, 52)( 12, 51)( 13, 55)( 14, 56)( 15, 53)( 16, 54)
( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 71)( 22, 72)( 23, 69)( 24, 70)
( 25, 82)( 26, 81)( 27, 83)( 28, 84)( 29, 88)( 30, 87)( 31, 86)( 32, 85)
( 33, 74)( 34, 73)( 35, 75)( 36, 76)( 37, 80)( 38, 79)( 39, 78)( 40, 77)
( 41, 90)( 42, 89)( 43, 91)( 44, 92)( 45, 96)( 46, 95)( 47, 94)( 48, 93)
( 97,154)( 98,153)( 99,155)(100,156)(101,160)(102,159)(103,158)(104,157)
(105,146)(106,145)(107,147)(108,148)(109,152)(110,151)(111,150)(112,149)
(113,162)(114,161)(115,163)(116,164)(117,168)(118,167)(119,166)(120,165)
(121,177)(122,178)(123,180)(124,179)(125,183)(126,184)(127,181)(128,182)
(129,169)(130,170)(131,172)(132,171)(133,175)(134,176)(135,173)(136,174)
(137,185)(138,186)(139,188)(140,187)(141,191)(142,192)(143,189)(144,190);;
s2 := (  1,103)(  2,104)(  3,101)(  4,102)(  5,100)(  6, 99)(  7, 98)(  8, 97)
(  9,111)( 10,112)( 11,109)( 12,110)( 13,108)( 14,107)( 15,106)( 16,105)
( 17,119)( 18,120)( 19,117)( 20,118)( 21,116)( 22,115)( 23,114)( 24,113)
( 25,128)( 26,127)( 27,126)( 28,125)( 29,123)( 30,124)( 31,121)( 32,122)
( 33,136)( 34,135)( 35,134)( 36,133)( 37,131)( 38,132)( 39,129)( 40,130)
( 41,144)( 42,143)( 43,142)( 44,141)( 45,139)( 46,140)( 47,137)( 48,138)
( 49,175)( 50,176)( 51,173)( 52,174)( 53,172)( 54,171)( 55,170)( 56,169)
( 57,183)( 58,184)( 59,181)( 60,182)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,191)( 66,192)( 67,189)( 68,190)( 69,188)( 70,187)( 71,186)( 72,185)
( 73,151)( 74,152)( 75,149)( 76,150)( 77,148)( 78,147)( 79,146)( 80,145)
( 81,159)( 82,160)( 83,157)( 84,158)( 85,156)( 86,155)( 87,154)( 88,153)
( 89,167)( 90,168)( 91,165)( 92,166)( 93,164)( 94,163)( 95,162)( 96,161);;
s3 := (193,194);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(194)!(  1, 97)(  2, 98)(  3,102)(  4,101)(  5,100)(  6, 99)(  7,104)
(  8,103)(  9,113)( 10,114)( 11,118)( 12,117)( 13,116)( 14,115)( 15,120)
( 16,119)( 17,105)( 18,106)( 19,110)( 20,109)( 21,108)( 22,107)( 23,112)
( 24,111)( 25,122)( 26,121)( 27,125)( 28,126)( 29,123)( 30,124)( 31,127)
( 32,128)( 33,138)( 34,137)( 35,141)( 36,142)( 37,139)( 38,140)( 39,143)
( 40,144)( 41,130)( 42,129)( 43,133)( 44,134)( 45,131)( 46,132)( 47,135)
( 48,136)( 49,170)( 50,169)( 51,173)( 52,174)( 53,171)( 54,172)( 55,175)
( 56,176)( 57,186)( 58,185)( 59,189)( 60,190)( 61,187)( 62,188)( 63,191)
( 64,192)( 65,178)( 66,177)( 67,181)( 68,182)( 69,179)( 70,180)( 71,183)
( 72,184)( 73,146)( 74,145)( 75,149)( 76,150)( 77,147)( 78,148)( 79,151)
( 80,152)( 81,162)( 82,161)( 83,165)( 84,166)( 85,163)( 86,164)( 87,167)
( 88,168)( 89,154)( 90,153)( 91,157)( 92,158)( 93,155)( 94,156)( 95,159)
( 96,160);
s1 := Sym(194)!(  1, 57)(  2, 58)(  3, 60)(  4, 59)(  5, 63)(  6, 64)(  7, 61)
(  8, 62)(  9, 49)( 10, 50)( 11, 52)( 12, 51)( 13, 55)( 14, 56)( 15, 53)
( 16, 54)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 71)( 22, 72)( 23, 69)
( 24, 70)( 25, 82)( 26, 81)( 27, 83)( 28, 84)( 29, 88)( 30, 87)( 31, 86)
( 32, 85)( 33, 74)( 34, 73)( 35, 75)( 36, 76)( 37, 80)( 38, 79)( 39, 78)
( 40, 77)( 41, 90)( 42, 89)( 43, 91)( 44, 92)( 45, 96)( 46, 95)( 47, 94)
( 48, 93)( 97,154)( 98,153)( 99,155)(100,156)(101,160)(102,159)(103,158)
(104,157)(105,146)(106,145)(107,147)(108,148)(109,152)(110,151)(111,150)
(112,149)(113,162)(114,161)(115,163)(116,164)(117,168)(118,167)(119,166)
(120,165)(121,177)(122,178)(123,180)(124,179)(125,183)(126,184)(127,181)
(128,182)(129,169)(130,170)(131,172)(132,171)(133,175)(134,176)(135,173)
(136,174)(137,185)(138,186)(139,188)(140,187)(141,191)(142,192)(143,189)
(144,190);
s2 := Sym(194)!(  1,103)(  2,104)(  3,101)(  4,102)(  5,100)(  6, 99)(  7, 98)
(  8, 97)(  9,111)( 10,112)( 11,109)( 12,110)( 13,108)( 14,107)( 15,106)
( 16,105)( 17,119)( 18,120)( 19,117)( 20,118)( 21,116)( 22,115)( 23,114)
( 24,113)( 25,128)( 26,127)( 27,126)( 28,125)( 29,123)( 30,124)( 31,121)
( 32,122)( 33,136)( 34,135)( 35,134)( 36,133)( 37,131)( 38,132)( 39,129)
( 40,130)( 41,144)( 42,143)( 43,142)( 44,141)( 45,139)( 46,140)( 47,137)
( 48,138)( 49,175)( 50,176)( 51,173)( 52,174)( 53,172)( 54,171)( 55,170)
( 56,169)( 57,183)( 58,184)( 59,181)( 60,182)( 61,180)( 62,179)( 63,178)
( 64,177)( 65,191)( 66,192)( 67,189)( 68,190)( 69,188)( 70,187)( 71,186)
( 72,185)( 73,151)( 74,152)( 75,149)( 76,150)( 77,148)( 78,147)( 79,146)
( 80,145)( 81,159)( 82,160)( 83,157)( 84,158)( 85,156)( 86,155)( 87,154)
( 88,153)( 89,167)( 90,168)( 91,165)( 92,166)( 93,164)( 94,163)( 95,162)
( 96,161);
s3 := Sym(194)!(193,194);
poly := sub<Sym(194)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >;

to this polytope