Polytope of Type {4,3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,12}*768a
if this polytope has a name.
Group : SmallGroup(768,1086320)
Rank : 4
Schlafli Type : {4,3,12}
Number of vertices, edges, etc : 8, 16, 48, 16
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 : {4,3,6}*384b
4-fold quotients : {4,3,3}*192, {2,3,12}*192
8-fold quotients : {2,3,6}*96
16-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s0*s1*s0*s1> of order 2.
16 facets:
16 of 2-fold non-regular quotient of {4,3}*48
4 vertex figures:
4 of {3,12}*96
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)(105,107)(106,108)(109,111)(110,112)(113,117)(114,118)(115,119)(116,120)(121,127)(122,128)(123,125)(124,126)(137,139)(138,140)(141,143)(142,144)(145,149)(146,150)(147,151)(148,152)(153,159)(154,160)(155,157)(156,158)(169,171)(170,172)(173,175)(174,176)(177,181)(178,182)(179,183)(180,184)(185,191)(186,192)(187,189)(188,190);;
s1 := ( 1, 10)( 2, 9)( 3, 12)( 4, 11)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 21, 23)( 22, 24)( 25, 26)( 27, 28)( 29, 32)( 30, 31)( 33, 74)( 34, 73)( 35, 76)( 36, 75)( 37, 80)( 38, 79)( 39, 78)( 40, 77)( 41, 66)( 42, 65)( 43, 68)( 44, 67)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 81)( 50, 82)( 51, 83)( 52, 84)( 53, 87)( 54, 88)( 55, 85)( 56, 86)( 57, 90)( 58, 89)( 59, 92)( 60, 91)( 61, 96)( 62, 95)( 63, 94)( 64, 93)( 97,105)( 98,106)( 99,107)(100,108)(101,111)(102,112)(103,109)(104,110)(113,114)(115,116)(117,120)(118,119)(125,127)(126,128)(129,169)(130,170)(131,171)(132,172)(133,175)(134,176)(135,173)(136,174)(137,161)(138,162)(139,163)(140,164)(141,167)(142,168)(143,165)(144,166)(145,178)(146,177)(147,180)(148,179)(149,184)(150,183)(151,182)(152,181)(153,185)(154,186)(155,187)(156,188)(157,191)(158,192)(159,189)(160,190);;
s2 := ( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)( 8, 72)( 9, 82)( 10, 81)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 88)( 16, 87)( 17, 74)( 18, 73)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 80)( 24, 79)( 25, 90)( 26, 89)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 96)( 32, 95)( 35, 37)( 36, 38)( 41, 50)( 42, 49)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 56)( 48, 55)( 57, 58)( 59, 62)( 60, 61)( 63, 64)( 97,162)( 98,161)( 99,166)(100,165)(101,164)(102,163)(103,168)(104,167)(105,177)(106,178)(107,181)(108,182)(109,179)(110,180)(111,183)(112,184)(113,169)(114,170)(115,173)(116,174)(117,171)(118,172)(119,175)(120,176)(121,185)(122,186)(123,189)(124,190)(125,187)(126,188)(127,191)(128,192)(129,130)(131,134)(132,133)(135,136)(137,145)(138,146)(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(155,157)(156,158);;
s3 := ( 1, 98)( 2, 97)( 3,100)( 4, 99)( 5,104)( 6,103)( 7,102)( 8,101)( 9,105)( 10,106)( 11,107)( 12,108)( 13,111)( 14,112)( 15,109)( 16,110)( 17,122)( 18,121)( 19,124)( 20,123)( 21,128)( 22,127)( 23,126)( 24,125)( 25,114)( 26,113)( 27,116)( 28,115)( 29,120)( 30,119)( 31,118)( 32,117)( 33,162)( 34,161)( 35,164)( 36,163)( 37,168)( 38,167)( 39,166)( 40,165)( 41,169)( 42,170)( 43,171)( 44,172)( 45,175)( 46,176)( 47,173)( 48,174)( 49,186)( 50,185)( 51,188)( 52,187)( 53,192)( 54,191)( 55,190)( 56,189)( 57,178)( 58,177)( 59,180)( 60,179)( 61,184)( 62,183)( 63,182)( 64,181)( 65,130)( 66,129)( 67,132)( 68,131)( 69,136)( 70,135)( 71,134)( 72,133)( 73,137)( 74,138)( 75,139)( 76,140)( 77,143)( 78,144)( 79,141)( 80,142)( 81,154)( 82,153)( 83,156)( 84,155)( 85,160)( 86,159)( 87,158)( 88,157)( 89,146)( 90,145)( 91,148)( 92,147)( 93,152)( 94,151)( 95,150)( 96,149);;
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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2,
s0*s2*s1*s0*s1*s2*s1*s3*s2*s0*s1*s0*s1*s2*s3*s1 ];;
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)(105,107)(106,108)(109,111)(110,112)(113,117)(114,118)(115,119)(116,120)(121,127)(122,128)(123,125)(124,126)(137,139)(138,140)(141,143)(142,144)(145,149)(146,150)(147,151)(148,152)(153,159)(154,160)(155,157)(156,158)(169,171)(170,172)(173,175)(174,176)(177,181)(178,182)(179,183)(180,184)(185,191)(186,192)(187,189)(188,190);
s1 := Sym(192)!( 1, 10)( 2, 9)( 3, 12)( 4, 11)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 21, 23)( 22, 24)( 25, 26)( 27, 28)( 29, 32)( 30, 31)( 33, 74)( 34, 73)( 35, 76)( 36, 75)( 37, 80)( 38, 79)( 39, 78)( 40, 77)( 41, 66)( 42, 65)( 43, 68)( 44, 67)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 81)( 50, 82)( 51, 83)( 52, 84)( 53, 87)( 54, 88)( 55, 85)( 56, 86)( 57, 90)( 58, 89)( 59, 92)( 60, 91)( 61, 96)( 62, 95)( 63, 94)( 64, 93)( 97,105)( 98,106)( 99,107)(100,108)(101,111)(102,112)(103,109)(104,110)(113,114)(115,116)(117,120)(118,119)(125,127)(126,128)(129,169)(130,170)(131,171)(132,172)(133,175)(134,176)(135,173)(136,174)(137,161)(138,162)(139,163)(140,164)(141,167)(142,168)(143,165)(144,166)(145,178)(146,177)(147,180)(148,179)(149,184)(150,183)(151,182)(152,181)(153,185)(154,186)(155,187)(156,188)(157,191)(158,192)(159,189)(160,190);
s2 := Sym(192)!( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)( 8, 72)( 9, 82)( 10, 81)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 88)( 16, 87)( 17, 74)( 18, 73)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 80)( 24, 79)( 25, 90)( 26, 89)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 96)( 32, 95)( 35, 37)( 36, 38)( 41, 50)( 42, 49)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 56)( 48, 55)( 57, 58)( 59, 62)( 60, 61)( 63, 64)( 97,162)( 98,161)( 99,166)(100,165)(101,164)(102,163)(103,168)(104,167)(105,177)(106,178)(107,181)(108,182)(109,179)(110,180)(111,183)(112,184)(113,169)(114,170)(115,173)(116,174)(117,171)(118,172)(119,175)(120,176)(121,185)(122,186)(123,189)(124,190)(125,187)(126,188)(127,191)(128,192)(129,130)(131,134)(132,133)(135,136)(137,145)(138,146)(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(155,157)(156,158);
s3 := Sym(192)!( 1, 98)( 2, 97)( 3,100)( 4, 99)( 5,104)( 6,103)( 7,102)( 8,101)( 9,105)( 10,106)( 11,107)( 12,108)( 13,111)( 14,112)( 15,109)( 16,110)( 17,122)( 18,121)( 19,124)( 20,123)( 21,128)( 22,127)( 23,126)( 24,125)( 25,114)( 26,113)( 27,116)( 28,115)( 29,120)( 30,119)( 31,118)( 32,117)( 33,162)( 34,161)( 35,164)( 36,163)( 37,168)( 38,167)( 39,166)( 40,165)( 41,169)( 42,170)( 43,171)( 44,172)( 45,175)( 46,176)( 47,173)( 48,174)( 49,186)( 50,185)( 51,188)( 52,187)( 53,192)( 54,191)( 55,190)( 56,189)( 57,178)( 58,177)( 59,180)( 60,179)( 61,184)( 62,183)( 63,182)( 64,181)( 65,130)( 66,129)( 67,132)( 68,131)( 69,136)( 70,135)( 71,134)( 72,133)( 73,137)( 74,138)( 75,139)( 76,140)( 77,143)( 78,144)( 79,141)( 80,142)( 81,154)( 82,153)( 83,156)( 84,155)( 85,160)( 86,159)( 87,158)( 88,157)( 89,146)( 90,145)( 91,148)( 92,147)( 93,152)( 94,151)( 95,150)( 96,149);
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,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2,
s0*s2*s1*s0*s1*s2*s1*s3*s2*s0*s1*s0*s1*s2*s3*s1 >;
References : None.
to this polytope