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