Polytope of Type {2,8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,12}*768f
if this polytope has a name.
Group : SmallGroup(768,1089120)
Rank : 4
Schlafli Type : {2,8,12}
Number of vertices, edges, etc : 2, 16, 96, 24
Order of s0s1s2s3 : 12
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 : {2,4,12}*384b, {2,8,6}*384c
4-fold quotients : {2,4,12}*192b, {2,4,12}*192c, {2,4,6}*192
8-fold quotients : {2,2,12}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
16-fold quotients : {2,4,3}*48, {2,2,6}*48
24-fold quotients : {2,2,4}*32
32-fold quotients : {2,2,3}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,103)( 4,104)( 5,106)( 6,105)( 7,100)( 8, 99)( 9,101)( 10,102)
( 11,111)( 12,112)( 13,114)( 14,113)( 15,108)( 16,107)( 17,109)( 18,110)
( 19,119)( 20,120)( 21,122)( 22,121)( 23,116)( 24,115)( 25,117)( 26,118)
( 27,127)( 28,128)( 29,130)( 30,129)( 31,124)( 32,123)( 33,125)( 34,126)
( 35,135)( 36,136)( 37,138)( 38,137)( 39,132)( 40,131)( 41,133)( 42,134)
( 43,143)( 44,144)( 45,146)( 46,145)( 47,140)( 48,139)( 49,141)( 50,142)
( 51,152)( 52,151)( 53,153)( 54,154)( 55,147)( 56,148)( 57,150)( 58,149)
( 59,160)( 60,159)( 61,161)( 62,162)( 63,155)( 64,156)( 65,158)( 66,157)
( 67,168)( 68,167)( 69,169)( 70,170)( 71,163)( 72,164)( 73,166)( 74,165)
( 75,176)( 76,175)( 77,177)( 78,178)( 79,171)( 80,172)( 81,174)( 82,173)
( 83,184)( 84,183)( 85,185)( 86,186)( 87,179)( 88,180)( 89,182)( 90,181)
( 91,192)( 92,191)( 93,193)( 94,194)( 95,187)( 96,188)( 97,190)( 98,189);;
s2 := ( 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, 75)( 52, 76)
( 53, 80)( 54, 79)( 55, 78)( 56, 77)( 57, 82)( 58, 81)( 59, 91)( 60, 92)
( 61, 96)( 62, 95)( 63, 94)( 64, 93)( 65, 98)( 66, 97)( 67, 83)( 68, 84)
( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 90)( 74, 89)(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)(147,171)(148,172)(149,176)(150,175)
(151,174)(152,173)(153,178)(154,177)(155,187)(156,188)(157,192)(158,191)
(159,190)(160,189)(161,194)(162,193)(163,179)(164,180)(165,184)(166,183)
(167,182)(168,181)(169,186)(170,185);;
s3 := ( 3, 67)( 4, 68)( 5, 73)( 6, 74)( 7, 72)( 8, 71)( 9, 69)( 10, 70)
( 11, 59)( 12, 60)( 13, 65)( 14, 66)( 15, 64)( 16, 63)( 17, 61)( 18, 62)
( 19, 51)( 20, 52)( 21, 57)( 22, 58)( 23, 56)( 24, 55)( 25, 53)( 26, 54)
( 27, 91)( 28, 92)( 29, 97)( 30, 98)( 31, 96)( 32, 95)( 33, 93)( 34, 94)
( 35, 83)( 36, 84)( 37, 89)( 38, 90)( 39, 88)( 40, 87)( 41, 85)( 42, 86)
( 43, 75)( 44, 76)( 45, 81)( 46, 82)( 47, 80)( 48, 79)( 49, 77)( 50, 78)
( 99,163)(100,164)(101,169)(102,170)(103,168)(104,167)(105,165)(106,166)
(107,155)(108,156)(109,161)(110,162)(111,160)(112,159)(113,157)(114,158)
(115,147)(116,148)(117,153)(118,154)(119,152)(120,151)(121,149)(122,150)
(123,187)(124,188)(125,193)(126,194)(127,192)(128,191)(129,189)(130,190)
(131,179)(132,180)(133,185)(134,186)(135,184)(136,183)(137,181)(138,182)
(139,171)(140,172)(141,177)(142,178)(143,176)(144,175)(145,173)(146,174);;
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,
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3,103)( 4,104)( 5,106)( 6,105)( 7,100)( 8, 99)( 9,101)
( 10,102)( 11,111)( 12,112)( 13,114)( 14,113)( 15,108)( 16,107)( 17,109)
( 18,110)( 19,119)( 20,120)( 21,122)( 22,121)( 23,116)( 24,115)( 25,117)
( 26,118)( 27,127)( 28,128)( 29,130)( 30,129)( 31,124)( 32,123)( 33,125)
( 34,126)( 35,135)( 36,136)( 37,138)( 38,137)( 39,132)( 40,131)( 41,133)
( 42,134)( 43,143)( 44,144)( 45,146)( 46,145)( 47,140)( 48,139)( 49,141)
( 50,142)( 51,152)( 52,151)( 53,153)( 54,154)( 55,147)( 56,148)( 57,150)
( 58,149)( 59,160)( 60,159)( 61,161)( 62,162)( 63,155)( 64,156)( 65,158)
( 66,157)( 67,168)( 68,167)( 69,169)( 70,170)( 71,163)( 72,164)( 73,166)
( 74,165)( 75,176)( 76,175)( 77,177)( 78,178)( 79,171)( 80,172)( 81,174)
( 82,173)( 83,184)( 84,183)( 85,185)( 86,186)( 87,179)( 88,180)( 89,182)
( 90,181)( 91,192)( 92,191)( 93,193)( 94,194)( 95,187)( 96,188)( 97,190)
( 98,189);
s2 := 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, 75)
( 52, 76)( 53, 80)( 54, 79)( 55, 78)( 56, 77)( 57, 82)( 58, 81)( 59, 91)
( 60, 92)( 61, 96)( 62, 95)( 63, 94)( 64, 93)( 65, 98)( 66, 97)( 67, 83)
( 68, 84)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 90)( 74, 89)(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)(147,171)(148,172)(149,176)
(150,175)(151,174)(152,173)(153,178)(154,177)(155,187)(156,188)(157,192)
(158,191)(159,190)(160,189)(161,194)(162,193)(163,179)(164,180)(165,184)
(166,183)(167,182)(168,181)(169,186)(170,185);
s3 := Sym(194)!( 3, 67)( 4, 68)( 5, 73)( 6, 74)( 7, 72)( 8, 71)( 9, 69)
( 10, 70)( 11, 59)( 12, 60)( 13, 65)( 14, 66)( 15, 64)( 16, 63)( 17, 61)
( 18, 62)( 19, 51)( 20, 52)( 21, 57)( 22, 58)( 23, 56)( 24, 55)( 25, 53)
( 26, 54)( 27, 91)( 28, 92)( 29, 97)( 30, 98)( 31, 96)( 32, 95)( 33, 93)
( 34, 94)( 35, 83)( 36, 84)( 37, 89)( 38, 90)( 39, 88)( 40, 87)( 41, 85)
( 42, 86)( 43, 75)( 44, 76)( 45, 81)( 46, 82)( 47, 80)( 48, 79)( 49, 77)
( 50, 78)( 99,163)(100,164)(101,169)(102,170)(103,168)(104,167)(105,165)
(106,166)(107,155)(108,156)(109,161)(110,162)(111,160)(112,159)(113,157)
(114,158)(115,147)(116,148)(117,153)(118,154)(119,152)(120,151)(121,149)
(122,150)(123,187)(124,188)(125,193)(126,194)(127,192)(128,191)(129,189)
(130,190)(131,179)(132,180)(133,185)(134,186)(135,184)(136,183)(137,181)
(138,182)(139,171)(140,172)(141,177)(142,178)(143,176)(144,175)(145,173)
(146,174);
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, s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope