Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*768c
if this polytope has a name.
Group : SmallGroup(768,1089263)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 16, 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 : {2,6,12}*384a, {2,12,6}*384b
   4-fold quotients : {2,12,3}*192, {2,6,6}*192
   8-fold quotients : {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,3}*48
   24-fold quotients : {2,2,4}*32
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope