Polytope of Type {2,8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,12}*768e
if this polytope has a name.
Group : SmallGroup(768,1089114)
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}*384b
4-fold quotients : {2,4,12}*192b, {2,4,12}*192c, {2,8,3}*192, {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, 55)( 4, 56)( 5, 58)( 6, 57)( 7, 52)( 8, 51)( 9, 53)( 10, 54)
( 11, 63)( 12, 64)( 13, 66)( 14, 65)( 15, 60)( 16, 59)( 17, 61)( 18, 62)
( 19, 71)( 20, 72)( 21, 74)( 22, 73)( 23, 68)( 24, 67)( 25, 69)( 26, 70)
( 27, 79)( 28, 80)( 29, 82)( 30, 81)( 31, 76)( 32, 75)( 33, 77)( 34, 78)
( 35, 87)( 36, 88)( 37, 90)( 38, 89)( 39, 84)( 40, 83)( 41, 85)( 42, 86)
( 43, 95)( 44, 96)( 45, 98)( 46, 97)( 47, 92)( 48, 91)( 49, 93)( 50, 94)
( 99,151)(100,152)(101,154)(102,153)(103,148)(104,147)(105,149)(106,150)
(107,159)(108,160)(109,162)(110,161)(111,156)(112,155)(113,157)(114,158)
(115,167)(116,168)(117,170)(118,169)(119,164)(120,163)(121,165)(122,166)
(123,175)(124,176)(125,178)(126,177)(127,172)(128,171)(129,173)(130,174)
(131,183)(132,184)(133,186)(134,185)(135,180)(136,179)(137,181)(138,182)
(139,191)(140,192)(141,194)(142,193)(143,188)(144,187)(145,189)(146,190);;
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, 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)( 99,123)(100,124)(101,128)(102,127)
(103,126)(104,125)(105,130)(106,129)(107,139)(108,140)(109,144)(110,143)
(111,142)(112,141)(113,146)(114,145)(115,131)(116,132)(117,136)(118,135)
(119,134)(120,133)(121,138)(122,137)(147,172)(148,171)(149,175)(150,176)
(151,173)(152,174)(153,177)(154,178)(155,188)(156,187)(157,191)(158,192)
(159,189)(160,190)(161,193)(162,194)(163,180)(164,179)(165,183)(166,184)
(167,181)(168,182)(169,185)(170,186);;
s3 := ( 3,115)( 4,116)( 5,121)( 6,122)( 7,120)( 8,119)( 9,117)( 10,118)
( 11,107)( 12,108)( 13,113)( 14,114)( 15,112)( 16,111)( 17,109)( 18,110)
( 19, 99)( 20,100)( 21,105)( 22,106)( 23,104)( 24,103)( 25,101)( 26,102)
( 27,139)( 28,140)( 29,145)( 30,146)( 31,144)( 32,143)( 33,141)( 34,142)
( 35,131)( 36,132)( 37,137)( 38,138)( 39,136)( 40,135)( 41,133)( 42,134)
( 43,123)( 44,124)( 45,129)( 46,130)( 47,128)( 48,127)( 49,125)( 50,126)
( 51,164)( 52,163)( 53,170)( 54,169)( 55,167)( 56,168)( 57,166)( 58,165)
( 59,156)( 60,155)( 61,162)( 62,161)( 63,159)( 64,160)( 65,158)( 66,157)
( 67,148)( 68,147)( 69,154)( 70,153)( 71,151)( 72,152)( 73,150)( 74,149)
( 75,188)( 76,187)( 77,194)( 78,193)( 79,191)( 80,192)( 81,190)( 82,189)
( 83,180)( 84,179)( 85,186)( 86,185)( 87,183)( 88,184)( 89,182)( 90,181)
( 91,172)( 92,171)( 93,178)( 94,177)( 95,175)( 96,176)( 97,174)( 98,173);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*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, 55)( 4, 56)( 5, 58)( 6, 57)( 7, 52)( 8, 51)( 9, 53)
( 10, 54)( 11, 63)( 12, 64)( 13, 66)( 14, 65)( 15, 60)( 16, 59)( 17, 61)
( 18, 62)( 19, 71)( 20, 72)( 21, 74)( 22, 73)( 23, 68)( 24, 67)( 25, 69)
( 26, 70)( 27, 79)( 28, 80)( 29, 82)( 30, 81)( 31, 76)( 32, 75)( 33, 77)
( 34, 78)( 35, 87)( 36, 88)( 37, 90)( 38, 89)( 39, 84)( 40, 83)( 41, 85)
( 42, 86)( 43, 95)( 44, 96)( 45, 98)( 46, 97)( 47, 92)( 48, 91)( 49, 93)
( 50, 94)( 99,151)(100,152)(101,154)(102,153)(103,148)(104,147)(105,149)
(106,150)(107,159)(108,160)(109,162)(110,161)(111,156)(112,155)(113,157)
(114,158)(115,167)(116,168)(117,170)(118,169)(119,164)(120,163)(121,165)
(122,166)(123,175)(124,176)(125,178)(126,177)(127,172)(128,171)(129,173)
(130,174)(131,183)(132,184)(133,186)(134,185)(135,180)(136,179)(137,181)
(138,182)(139,191)(140,192)(141,194)(142,193)(143,188)(144,187)(145,189)
(146,190);
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, 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)( 99,123)(100,124)(101,128)
(102,127)(103,126)(104,125)(105,130)(106,129)(107,139)(108,140)(109,144)
(110,143)(111,142)(112,141)(113,146)(114,145)(115,131)(116,132)(117,136)
(118,135)(119,134)(120,133)(121,138)(122,137)(147,172)(148,171)(149,175)
(150,176)(151,173)(152,174)(153,177)(154,178)(155,188)(156,187)(157,191)
(158,192)(159,189)(160,190)(161,193)(162,194)(163,180)(164,179)(165,183)
(166,184)(167,181)(168,182)(169,185)(170,186);
s3 := Sym(194)!( 3,115)( 4,116)( 5,121)( 6,122)( 7,120)( 8,119)( 9,117)
( 10,118)( 11,107)( 12,108)( 13,113)( 14,114)( 15,112)( 16,111)( 17,109)
( 18,110)( 19, 99)( 20,100)( 21,105)( 22,106)( 23,104)( 24,103)( 25,101)
( 26,102)( 27,139)( 28,140)( 29,145)( 30,146)( 31,144)( 32,143)( 33,141)
( 34,142)( 35,131)( 36,132)( 37,137)( 38,138)( 39,136)( 40,135)( 41,133)
( 42,134)( 43,123)( 44,124)( 45,129)( 46,130)( 47,128)( 48,127)( 49,125)
( 50,126)( 51,164)( 52,163)( 53,170)( 54,169)( 55,167)( 56,168)( 57,166)
( 58,165)( 59,156)( 60,155)( 61,162)( 62,161)( 63,159)( 64,160)( 65,158)
( 66,157)( 67,148)( 68,147)( 69,154)( 70,153)( 71,151)( 72,152)( 73,150)
( 74,149)( 75,188)( 76,187)( 77,194)( 78,193)( 79,191)( 80,192)( 81,190)
( 82,189)( 83,180)( 84,179)( 85,186)( 86,185)( 87,183)( 88,184)( 89,182)
( 90,181)( 91,172)( 92,171)( 93,178)( 94,177)( 95,175)( 96,176)( 97,174)
( 98,173);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*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