Polytope of Type {4,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,3}*768b
if this polytope has a name.
Group : SmallGroup(768,1086329)
Rank : 4
Schlafli Type : {4,12,3}
Number of vertices, edges, etc : 8, 64, 48, 4
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 4
Special Properties :
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 : {4,6,3}*384b
4-fold quotients : {4,3,3}*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 := ( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 21)( 18, 22)( 19, 23)( 20, 24)
( 25, 31)( 26, 32)( 27, 29)( 28, 30)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 63)( 58, 64)( 59, 61)( 60, 62)
( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)
( 89, 95)( 90, 96)( 91, 93)( 92, 94)( 97, 98)( 99,100)(101,102)(103,104)
(105,108)(106,107)(109,112)(110,111)(113,118)(114,117)(115,120)(116,119)
(121,128)(122,127)(123,126)(124,125)(129,130)(131,132)(133,134)(135,136)
(137,140)(138,139)(141,144)(142,143)(145,150)(146,149)(147,152)(148,151)
(153,160)(154,159)(155,158)(156,157)(161,162)(163,164)(165,166)(167,168)
(169,172)(170,171)(173,176)(174,175)(177,182)(178,181)(179,184)(180,183)
(185,192)(186,191)(187,190)(188,189);;
s1 := ( 1,112)( 2,111)( 3,110)( 4,109)( 5,106)( 6,105)( 7,108)( 8,107)
( 9,102)( 10,101)( 11,104)( 12,103)( 13,100)( 14, 99)( 15, 98)( 16, 97)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,119)( 22,120)( 23,117)( 24,118)
( 25,124)( 26,123)( 27,122)( 28,121)( 29,126)( 30,125)( 31,128)( 32,127)
( 33,176)( 34,175)( 35,174)( 36,173)( 37,170)( 38,169)( 39,172)( 40,171)
( 41,166)( 42,165)( 43,168)( 44,167)( 45,164)( 46,163)( 47,162)( 48,161)
( 49,177)( 50,178)( 51,179)( 52,180)( 53,183)( 54,184)( 55,181)( 56,182)
( 57,188)( 58,187)( 59,186)( 60,185)( 61,190)( 62,189)( 63,192)( 64,191)
( 65,144)( 66,143)( 67,142)( 68,141)( 69,138)( 70,137)( 71,140)( 72,139)
( 73,134)( 74,133)( 75,136)( 76,135)( 77,132)( 78,131)( 79,130)( 80,129)
( 81,145)( 82,146)( 83,147)( 84,148)( 85,151)( 86,152)( 87,149)( 88,150)
( 89,156)( 90,155)( 91,154)( 92,153)( 93,158)( 94,157)( 95,160)( 96,159);;
s2 := ( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)( 8, 72)
( 9, 86)( 10, 85)( 11, 82)( 12, 81)( 13, 88)( 14, 87)( 15, 84)( 16, 83)
( 17, 76)( 18, 75)( 19, 80)( 20, 79)( 21, 74)( 22, 73)( 23, 78)( 24, 77)
( 25, 96)( 26, 95)( 27, 92)( 28, 91)( 29, 94)( 30, 93)( 31, 90)( 32, 89)
( 35, 37)( 36, 38)( 41, 54)( 42, 53)( 43, 50)( 44, 49)( 45, 56)( 46, 55)
( 47, 52)( 48, 51)( 57, 64)( 58, 63)( 59, 60)( 61, 62)( 97,162)( 98,161)
( 99,166)(100,165)(101,164)(102,163)(103,168)(104,167)(105,181)(106,182)
(107,177)(108,178)(109,183)(110,184)(111,179)(112,180)(113,171)(114,172)
(115,175)(116,176)(117,169)(118,170)(119,173)(120,174)(121,191)(122,192)
(123,187)(124,188)(125,189)(126,190)(127,185)(128,186)(129,130)(131,134)
(132,133)(135,136)(137,149)(138,150)(139,145)(140,146)(141,151)(142,152)
(143,147)(144,148)(153,159)(154,160);;
s3 := ( 5, 7)( 6, 8)( 9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 31)( 18, 32)
( 19, 29)( 20, 30)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 65)( 34, 66)
( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 76)( 42, 75)
( 43, 74)( 44, 73)( 45, 78)( 46, 77)( 47, 80)( 48, 79)( 49, 95)( 50, 96)
( 51, 93)( 52, 94)( 53, 89)( 54, 90)( 55, 91)( 56, 92)( 57, 85)( 58, 86)
( 59, 87)( 60, 88)( 61, 83)( 62, 84)( 63, 81)( 64, 82)( 97, 98)( 99,100)
(101,104)(102,103)(105,107)(106,108)(113,128)(114,127)(115,126)(116,125)
(117,122)(118,121)(119,124)(120,123)(129,162)(130,161)(131,164)(132,163)
(133,168)(134,167)(135,166)(136,165)(137,171)(138,172)(139,169)(140,170)
(141,173)(142,174)(143,175)(144,176)(145,192)(146,191)(147,190)(148,189)
(149,186)(150,185)(151,188)(152,187)(153,182)(154,181)(155,184)(156,183)
(157,180)(158,179)(159,178)(160,177);;
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*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s1*s2*s1*s0*s1*s2*s3*s0*s1*s2*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(192)!( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 21)( 18, 22)( 19, 23)
( 20, 24)( 25, 31)( 26, 32)( 27, 29)( 28, 30)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 63)( 58, 64)( 59, 61)
( 60, 62)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 85)( 82, 86)( 83, 87)
( 84, 88)( 89, 95)( 90, 96)( 91, 93)( 92, 94)( 97, 98)( 99,100)(101,102)
(103,104)(105,108)(106,107)(109,112)(110,111)(113,118)(114,117)(115,120)
(116,119)(121,128)(122,127)(123,126)(124,125)(129,130)(131,132)(133,134)
(135,136)(137,140)(138,139)(141,144)(142,143)(145,150)(146,149)(147,152)
(148,151)(153,160)(154,159)(155,158)(156,157)(161,162)(163,164)(165,166)
(167,168)(169,172)(170,171)(173,176)(174,175)(177,182)(178,181)(179,184)
(180,183)(185,192)(186,191)(187,190)(188,189);
s1 := Sym(192)!( 1,112)( 2,111)( 3,110)( 4,109)( 5,106)( 6,105)( 7,108)
( 8,107)( 9,102)( 10,101)( 11,104)( 12,103)( 13,100)( 14, 99)( 15, 98)
( 16, 97)( 17,113)( 18,114)( 19,115)( 20,116)( 21,119)( 22,120)( 23,117)
( 24,118)( 25,124)( 26,123)( 27,122)( 28,121)( 29,126)( 30,125)( 31,128)
( 32,127)( 33,176)( 34,175)( 35,174)( 36,173)( 37,170)( 38,169)( 39,172)
( 40,171)( 41,166)( 42,165)( 43,168)( 44,167)( 45,164)( 46,163)( 47,162)
( 48,161)( 49,177)( 50,178)( 51,179)( 52,180)( 53,183)( 54,184)( 55,181)
( 56,182)( 57,188)( 58,187)( 59,186)( 60,185)( 61,190)( 62,189)( 63,192)
( 64,191)( 65,144)( 66,143)( 67,142)( 68,141)( 69,138)( 70,137)( 71,140)
( 72,139)( 73,134)( 74,133)( 75,136)( 76,135)( 77,132)( 78,131)( 79,130)
( 80,129)( 81,145)( 82,146)( 83,147)( 84,148)( 85,151)( 86,152)( 87,149)
( 88,150)( 89,156)( 90,155)( 91,154)( 92,153)( 93,158)( 94,157)( 95,160)
( 96,159);
s2 := Sym(192)!( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)
( 8, 72)( 9, 86)( 10, 85)( 11, 82)( 12, 81)( 13, 88)( 14, 87)( 15, 84)
( 16, 83)( 17, 76)( 18, 75)( 19, 80)( 20, 79)( 21, 74)( 22, 73)( 23, 78)
( 24, 77)( 25, 96)( 26, 95)( 27, 92)( 28, 91)( 29, 94)( 30, 93)( 31, 90)
( 32, 89)( 35, 37)( 36, 38)( 41, 54)( 42, 53)( 43, 50)( 44, 49)( 45, 56)
( 46, 55)( 47, 52)( 48, 51)( 57, 64)( 58, 63)( 59, 60)( 61, 62)( 97,162)
( 98,161)( 99,166)(100,165)(101,164)(102,163)(103,168)(104,167)(105,181)
(106,182)(107,177)(108,178)(109,183)(110,184)(111,179)(112,180)(113,171)
(114,172)(115,175)(116,176)(117,169)(118,170)(119,173)(120,174)(121,191)
(122,192)(123,187)(124,188)(125,189)(126,190)(127,185)(128,186)(129,130)
(131,134)(132,133)(135,136)(137,149)(138,150)(139,145)(140,146)(141,151)
(142,152)(143,147)(144,148)(153,159)(154,160);
s3 := Sym(192)!( 5, 7)( 6, 8)( 9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 31)
( 18, 32)( 19, 29)( 20, 30)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 65)
( 34, 66)( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 76)
( 42, 75)( 43, 74)( 44, 73)( 45, 78)( 46, 77)( 47, 80)( 48, 79)( 49, 95)
( 50, 96)( 51, 93)( 52, 94)( 53, 89)( 54, 90)( 55, 91)( 56, 92)( 57, 85)
( 58, 86)( 59, 87)( 60, 88)( 61, 83)( 62, 84)( 63, 81)( 64, 82)( 97, 98)
( 99,100)(101,104)(102,103)(105,107)(106,108)(113,128)(114,127)(115,126)
(116,125)(117,122)(118,121)(119,124)(120,123)(129,162)(130,161)(131,164)
(132,163)(133,168)(134,167)(135,166)(136,165)(137,171)(138,172)(139,169)
(140,170)(141,173)(142,174)(143,175)(144,176)(145,192)(146,191)(147,190)
(148,189)(149,186)(150,185)(151,188)(152,187)(153,182)(154,181)(155,184)
(156,183)(157,180)(158,179)(159,178)(160,177);
poly := sub<Sym(192)|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*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s1*s2*s1*s0*s1*s2*s3*s0*s1*s2*s0*s1*s0 >;
References : None.
to this polytope