Polytope of Type {2,12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,8}*768f
if this polytope has a name.
Group : SmallGroup(768,1089120)
Rank : 4
Schlafli Type : {2,12,8}
Number of vertices, edges, etc : 2, 24, 96, 16
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 : {2,12,4}*384b, {2,6,8}*384c
   4-fold quotients : {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
   8-fold quotients : {2,12,2}*96, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   16-fold quotients : {2,3,4}*48, {2,6,2}*48
   24-fold quotients : {2,4,2}*32
   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 := (1,2);;
s1 := (  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, 75)( 28, 76)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 82)( 34, 81)
( 35, 91)( 36, 92)( 37, 96)( 38, 95)( 39, 94)( 40, 93)( 41, 98)( 42, 97)
( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)
( 99,147)(100,148)(101,152)(102,151)(103,150)(104,149)(105,154)(106,153)
(107,163)(108,164)(109,168)(110,167)(111,166)(112,165)(113,170)(114,169)
(115,155)(116,156)(117,160)(118,159)(119,158)(120,157)(121,162)(122,161)
(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);;
s2 := (  3, 11)(  4, 12)(  5, 14)(  6, 13)(  7, 17)(  8, 18)(  9, 15)( 10, 16)
( 21, 22)( 23, 25)( 24, 26)( 27, 35)( 28, 36)( 29, 38)( 30, 37)( 31, 41)
( 32, 42)( 33, 39)( 34, 40)( 45, 46)( 47, 49)( 48, 50)( 51, 83)( 52, 84)
( 53, 86)( 54, 85)( 55, 89)( 56, 90)( 57, 87)( 58, 88)( 59, 75)( 60, 76)
( 61, 78)( 62, 77)( 63, 81)( 64, 82)( 65, 79)( 66, 80)( 67, 91)( 68, 92)
( 69, 94)( 70, 93)( 71, 97)( 72, 98)( 73, 95)( 74, 96)( 99,107)(100,108)
(101,110)(102,109)(103,113)(104,114)(105,111)(106,112)(117,118)(119,121)
(120,122)(123,131)(124,132)(125,134)(126,133)(127,137)(128,138)(129,135)
(130,136)(141,142)(143,145)(144,146)(147,179)(148,180)(149,182)(150,181)
(151,185)(152,186)(153,183)(154,184)(155,171)(156,172)(157,174)(158,173)
(159,177)(160,178)(161,175)(162,176)(163,187)(164,188)(165,190)(166,189)
(167,193)(168,194)(169,191)(170,192);;
s3 := (  3,105)(  4,106)(  5,103)(  6,104)(  7,102)(  8,101)(  9,100)( 10, 99)
( 11,113)( 12,114)( 13,111)( 14,112)( 15,110)( 16,109)( 17,108)( 18,107)
( 19,121)( 20,122)( 21,119)( 22,120)( 23,118)( 24,117)( 25,116)( 26,115)
( 27,129)( 28,130)( 29,127)( 30,128)( 31,126)( 32,125)( 33,124)( 34,123)
( 35,137)( 36,138)( 37,135)( 38,136)( 39,134)( 40,133)( 41,132)( 42,131)
( 43,145)( 44,146)( 45,143)( 46,144)( 47,142)( 48,141)( 49,140)( 50,139)
( 51,154)( 52,153)( 53,152)( 54,151)( 55,149)( 56,150)( 57,147)( 58,148)
( 59,162)( 60,161)( 61,160)( 62,159)( 63,157)( 64,158)( 65,155)( 66,156)
( 67,170)( 68,169)( 69,168)( 70,167)( 71,165)( 72,166)( 73,163)( 74,164)
( 75,178)( 76,177)( 77,176)( 78,175)( 79,173)( 80,174)( 81,171)( 82,172)
( 83,186)( 84,185)( 85,184)( 86,183)( 87,181)( 88,182)( 89,179)( 90,180)
( 91,194)( 92,193)( 93,192)( 94,191)( 95,189)( 96,190)( 97,187)( 98,188);;
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, 
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*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(194)!(1,2);
s1 := 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, 75)( 28, 76)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 82)
( 34, 81)( 35, 91)( 36, 92)( 37, 96)( 38, 95)( 39, 94)( 40, 93)( 41, 98)
( 42, 97)( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)
( 50, 89)( 99,147)(100,148)(101,152)(102,151)(103,150)(104,149)(105,154)
(106,153)(107,163)(108,164)(109,168)(110,167)(111,166)(112,165)(113,170)
(114,169)(115,155)(116,156)(117,160)(118,159)(119,158)(120,157)(121,162)
(122,161)(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);
s2 := Sym(194)!(  3, 11)(  4, 12)(  5, 14)(  6, 13)(  7, 17)(  8, 18)(  9, 15)
( 10, 16)( 21, 22)( 23, 25)( 24, 26)( 27, 35)( 28, 36)( 29, 38)( 30, 37)
( 31, 41)( 32, 42)( 33, 39)( 34, 40)( 45, 46)( 47, 49)( 48, 50)( 51, 83)
( 52, 84)( 53, 86)( 54, 85)( 55, 89)( 56, 90)( 57, 87)( 58, 88)( 59, 75)
( 60, 76)( 61, 78)( 62, 77)( 63, 81)( 64, 82)( 65, 79)( 66, 80)( 67, 91)
( 68, 92)( 69, 94)( 70, 93)( 71, 97)( 72, 98)( 73, 95)( 74, 96)( 99,107)
(100,108)(101,110)(102,109)(103,113)(104,114)(105,111)(106,112)(117,118)
(119,121)(120,122)(123,131)(124,132)(125,134)(126,133)(127,137)(128,138)
(129,135)(130,136)(141,142)(143,145)(144,146)(147,179)(148,180)(149,182)
(150,181)(151,185)(152,186)(153,183)(154,184)(155,171)(156,172)(157,174)
(158,173)(159,177)(160,178)(161,175)(162,176)(163,187)(164,188)(165,190)
(166,189)(167,193)(168,194)(169,191)(170,192);
s3 := Sym(194)!(  3,105)(  4,106)(  5,103)(  6,104)(  7,102)(  8,101)(  9,100)
( 10, 99)( 11,113)( 12,114)( 13,111)( 14,112)( 15,110)( 16,109)( 17,108)
( 18,107)( 19,121)( 20,122)( 21,119)( 22,120)( 23,118)( 24,117)( 25,116)
( 26,115)( 27,129)( 28,130)( 29,127)( 30,128)( 31,126)( 32,125)( 33,124)
( 34,123)( 35,137)( 36,138)( 37,135)( 38,136)( 39,134)( 40,133)( 41,132)
( 42,131)( 43,145)( 44,146)( 45,143)( 46,144)( 47,142)( 48,141)( 49,140)
( 50,139)( 51,154)( 52,153)( 53,152)( 54,151)( 55,149)( 56,150)( 57,147)
( 58,148)( 59,162)( 60,161)( 61,160)( 62,159)( 63,157)( 64,158)( 65,155)
( 66,156)( 67,170)( 68,169)( 69,168)( 70,167)( 71,165)( 72,166)( 73,163)
( 74,164)( 75,178)( 76,177)( 77,176)( 78,175)( 79,173)( 80,174)( 81,171)
( 82,172)( 83,186)( 84,185)( 85,184)( 86,183)( 87,181)( 88,182)( 89,179)
( 90,180)( 91,194)( 92,193)( 93,192)( 94,191)( 95,189)( 96,190)( 97,187)
( 98,188);
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, s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*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 >;

to this polytope