Polytope of Type {3,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,2}*768
if this polytope has a name.
Group : SmallGroup(768,1086301)
Rank : 4
Schlafli Type : {3,12,2}
Number of vertices, edges, etc : 16, 96, 64, 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 : {3,6,2}*384
   4-fold quotients : {3,12,2}*192
   8-fold quotients : {3,6,2}*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, 33)(  2, 34)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 39)(  8, 40)
(  9, 47)( 10, 48)( 11, 44)( 12, 43)( 13, 46)( 14, 45)( 15, 41)( 16, 42)
( 17, 64)( 18, 63)( 19, 59)( 20, 60)( 21, 61)( 22, 62)( 23, 58)( 24, 57)
( 25, 56)( 26, 55)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 50)( 32, 49)
( 67, 70)( 68, 69)( 73, 79)( 74, 80)( 75, 76)( 77, 78)( 81, 96)( 82, 95)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 90)( 88, 89)( 97,130)( 98,129)
( 99,133)(100,134)(101,131)(102,132)(103,136)(104,135)(105,144)(106,143)
(107,139)(108,140)(109,141)(110,142)(111,138)(112,137)(113,159)(114,160)
(115,156)(116,155)(117,158)(118,157)(119,153)(120,154)(121,151)(122,152)
(123,148)(124,147)(125,150)(126,149)(127,145)(128,146)(161,162)(163,165)
(164,166)(167,168)(169,176)(170,175)(177,191)(178,192)(179,188)(180,187)
(181,190)(182,189)(183,185)(184,186);;
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, 
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*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, 33)(  2, 34)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 39)
(  8, 40)(  9, 47)( 10, 48)( 11, 44)( 12, 43)( 13, 46)( 14, 45)( 15, 41)
( 16, 42)( 17, 64)( 18, 63)( 19, 59)( 20, 60)( 21, 61)( 22, 62)( 23, 58)
( 24, 57)( 25, 56)( 26, 55)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 50)
( 32, 49)( 67, 70)( 68, 69)( 73, 79)( 74, 80)( 75, 76)( 77, 78)( 81, 96)
( 82, 95)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 90)( 88, 89)( 97,130)
( 98,129)( 99,133)(100,134)(101,131)(102,132)(103,136)(104,135)(105,144)
(106,143)(107,139)(108,140)(109,141)(110,142)(111,138)(112,137)(113,159)
(114,160)(115,156)(116,155)(117,158)(118,157)(119,153)(120,154)(121,151)
(122,152)(123,148)(124,147)(125,150)(126,149)(127,145)(128,146)(161,162)
(163,165)(164,166)(167,168)(169,176)(170,175)(177,191)(178,192)(179,188)
(180,187)(181,190)(182,189)(183,185)(184,186);
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, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 >;

to this polytope