Polytope of Type {4,24,2}

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

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

Permutation Representation (Magma) :

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

to this polytope