Polytope of Type {12,3,2}

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

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

Permutation Representation (Magma) :

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

to this polytope