Polytope of Type {2,4,24}

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

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

Permutation Representation (Magma) :

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

to this polytope