Polytope of Type {2,4,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,4}*768g
if this polytope has a name.
Group : SmallGroup(768,1090188)
Rank : 5
Schlafli Type : {2,4,12,4}
Number of vertices, edges, etc : 2, 4, 24, 24, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,4,6,4}*384d
4-fold quotients : {2,4,3,4}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)
( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)
( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)
( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)
(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)
(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)
(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(153,161)(154,162)
(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)
(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194);;
s2 := ( 3, 19)( 4, 22)( 5, 21)( 6, 20)( 7, 27)( 8, 30)( 9, 29)( 10, 28)
( 11, 23)( 12, 26)( 13, 25)( 14, 24)( 15, 31)( 16, 34)( 17, 33)( 18, 32)
( 36, 38)( 39, 43)( 40, 46)( 41, 45)( 42, 44)( 48, 50)( 51, 67)( 52, 70)
( 53, 69)( 54, 68)( 55, 75)( 56, 78)( 57, 77)( 58, 76)( 59, 71)( 60, 74)
( 61, 73)( 62, 72)( 63, 79)( 64, 82)( 65, 81)( 66, 80)( 84, 86)( 87, 91)
( 88, 94)( 89, 93)( 90, 92)( 96, 98)( 99,163)(100,166)(101,165)(102,164)
(103,171)(104,174)(105,173)(106,172)(107,167)(108,170)(109,169)(110,168)
(111,175)(112,178)(113,177)(114,176)(115,147)(116,150)(117,149)(118,148)
(119,155)(120,158)(121,157)(122,156)(123,151)(124,154)(125,153)(126,152)
(127,159)(128,162)(129,161)(130,160)(131,179)(132,182)(133,181)(134,180)
(135,187)(136,190)(137,189)(138,188)(139,183)(140,186)(141,185)(142,184)
(143,191)(144,194)(145,193)(146,192);;
s3 := ( 3, 99)( 4,100)( 5,102)( 6,101)( 7,111)( 8,112)( 9,114)( 10,113)
( 11,107)( 12,108)( 13,110)( 14,109)( 15,103)( 16,104)( 17,106)( 18,105)
( 19,131)( 20,132)( 21,134)( 22,133)( 23,143)( 24,144)( 25,146)( 26,145)
( 27,139)( 28,140)( 29,142)( 30,141)( 31,135)( 32,136)( 33,138)( 34,137)
( 35,115)( 36,116)( 37,118)( 38,117)( 39,127)( 40,128)( 41,130)( 42,129)
( 43,123)( 44,124)( 45,126)( 46,125)( 47,119)( 48,120)( 49,122)( 50,121)
( 51,147)( 52,148)( 53,150)( 54,149)( 55,159)( 56,160)( 57,162)( 58,161)
( 59,155)( 60,156)( 61,158)( 62,157)( 63,151)( 64,152)( 65,154)( 66,153)
( 67,179)( 68,180)( 69,182)( 70,181)( 71,191)( 72,192)( 73,194)( 74,193)
( 75,187)( 76,188)( 77,190)( 78,189)( 79,183)( 80,184)( 81,186)( 82,185)
( 83,163)( 84,164)( 85,166)( 86,165)( 87,175)( 88,176)( 89,178)( 90,177)
( 91,171)( 92,172)( 93,174)( 94,173)( 95,167)( 96,168)( 97,170)( 98,169);;
s4 := ( 3, 53)( 4, 54)( 5, 51)( 6, 52)( 7, 57)( 8, 58)( 9, 55)( 10, 56)
( 11, 61)( 12, 62)( 13, 59)( 14, 60)( 15, 65)( 16, 66)( 17, 63)( 18, 64)
( 19, 69)( 20, 70)( 21, 67)( 22, 68)( 23, 73)( 24, 74)( 25, 71)( 26, 72)
( 27, 77)( 28, 78)( 29, 75)( 30, 76)( 31, 81)( 32, 82)( 33, 79)( 34, 80)
( 35, 85)( 36, 86)( 37, 83)( 38, 84)( 39, 89)( 40, 90)( 41, 87)( 42, 88)
( 43, 93)( 44, 94)( 45, 91)( 46, 92)( 47, 97)( 48, 98)( 49, 95)( 50, 96)
( 99,149)(100,150)(101,147)(102,148)(103,153)(104,154)(105,151)(106,152)
(107,157)(108,158)(109,155)(110,156)(111,161)(112,162)(113,159)(114,160)
(115,165)(116,166)(117,163)(118,164)(119,169)(120,170)(121,167)(122,168)
(123,173)(124,174)(125,171)(126,172)(127,177)(128,178)(129,175)(130,176)
(131,181)(132,182)(133,179)(134,180)(135,185)(136,186)(137,183)(138,184)
(139,189)(140,190)(141,187)(142,188)(143,193)(144,194)(145,191)(146,192);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)
( 10, 18)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)
( 26, 34)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)
( 42, 50)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)
( 58, 66)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)
( 74, 82)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)
(106,114)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)
(122,130)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)
(138,146)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(153,161)
(154,162)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(169,177)
(170,178)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)
(186,194);
s2 := Sym(194)!( 3, 19)( 4, 22)( 5, 21)( 6, 20)( 7, 27)( 8, 30)( 9, 29)
( 10, 28)( 11, 23)( 12, 26)( 13, 25)( 14, 24)( 15, 31)( 16, 34)( 17, 33)
( 18, 32)( 36, 38)( 39, 43)( 40, 46)( 41, 45)( 42, 44)( 48, 50)( 51, 67)
( 52, 70)( 53, 69)( 54, 68)( 55, 75)( 56, 78)( 57, 77)( 58, 76)( 59, 71)
( 60, 74)( 61, 73)( 62, 72)( 63, 79)( 64, 82)( 65, 81)( 66, 80)( 84, 86)
( 87, 91)( 88, 94)( 89, 93)( 90, 92)( 96, 98)( 99,163)(100,166)(101,165)
(102,164)(103,171)(104,174)(105,173)(106,172)(107,167)(108,170)(109,169)
(110,168)(111,175)(112,178)(113,177)(114,176)(115,147)(116,150)(117,149)
(118,148)(119,155)(120,158)(121,157)(122,156)(123,151)(124,154)(125,153)
(126,152)(127,159)(128,162)(129,161)(130,160)(131,179)(132,182)(133,181)
(134,180)(135,187)(136,190)(137,189)(138,188)(139,183)(140,186)(141,185)
(142,184)(143,191)(144,194)(145,193)(146,192);
s3 := Sym(194)!( 3, 99)( 4,100)( 5,102)( 6,101)( 7,111)( 8,112)( 9,114)
( 10,113)( 11,107)( 12,108)( 13,110)( 14,109)( 15,103)( 16,104)( 17,106)
( 18,105)( 19,131)( 20,132)( 21,134)( 22,133)( 23,143)( 24,144)( 25,146)
( 26,145)( 27,139)( 28,140)( 29,142)( 30,141)( 31,135)( 32,136)( 33,138)
( 34,137)( 35,115)( 36,116)( 37,118)( 38,117)( 39,127)( 40,128)( 41,130)
( 42,129)( 43,123)( 44,124)( 45,126)( 46,125)( 47,119)( 48,120)( 49,122)
( 50,121)( 51,147)( 52,148)( 53,150)( 54,149)( 55,159)( 56,160)( 57,162)
( 58,161)( 59,155)( 60,156)( 61,158)( 62,157)( 63,151)( 64,152)( 65,154)
( 66,153)( 67,179)( 68,180)( 69,182)( 70,181)( 71,191)( 72,192)( 73,194)
( 74,193)( 75,187)( 76,188)( 77,190)( 78,189)( 79,183)( 80,184)( 81,186)
( 82,185)( 83,163)( 84,164)( 85,166)( 86,165)( 87,175)( 88,176)( 89,178)
( 90,177)( 91,171)( 92,172)( 93,174)( 94,173)( 95,167)( 96,168)( 97,170)
( 98,169);
s4 := Sym(194)!( 3, 53)( 4, 54)( 5, 51)( 6, 52)( 7, 57)( 8, 58)( 9, 55)
( 10, 56)( 11, 61)( 12, 62)( 13, 59)( 14, 60)( 15, 65)( 16, 66)( 17, 63)
( 18, 64)( 19, 69)( 20, 70)( 21, 67)( 22, 68)( 23, 73)( 24, 74)( 25, 71)
( 26, 72)( 27, 77)( 28, 78)( 29, 75)( 30, 76)( 31, 81)( 32, 82)( 33, 79)
( 34, 80)( 35, 85)( 36, 86)( 37, 83)( 38, 84)( 39, 89)( 40, 90)( 41, 87)
( 42, 88)( 43, 93)( 44, 94)( 45, 91)( 46, 92)( 47, 97)( 48, 98)( 49, 95)
( 50, 96)( 99,149)(100,150)(101,147)(102,148)(103,153)(104,154)(105,151)
(106,152)(107,157)(108,158)(109,155)(110,156)(111,161)(112,162)(113,159)
(114,160)(115,165)(116,166)(117,163)(118,164)(119,169)(120,170)(121,167)
(122,168)(123,173)(124,174)(125,171)(126,172)(127,177)(128,178)(129,175)
(130,176)(131,181)(132,182)(133,179)(134,180)(135,185)(136,186)(137,183)
(138,184)(139,189)(140,190)(141,187)(142,188)(143,193)(144,194)(145,191)
(146,192);
poly := sub<Sym(194)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2 >;
to this polytope