Polytope of Type {2,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,3}*768
if this polytope has a name.
Group : SmallGroup(768,1086301)
Rank : 4
Schlafli Type : {2,12,3}
Number of vertices, edges, etc : 2, 64, 96, 16
Order of s₀s₁s₂s₃ : 8
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 : {2,6,3}*384
   4-fold quotients : {2,12,3}*192
   8-fold quotients : {2,6,3}*96
   16-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope