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}*768h
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, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)( 8, 64)( 9, 65)( 10, 66)
( 11, 51)( 12, 52)( 13, 53)( 14, 54)( 15, 55)( 16, 56)( 17, 57)( 18, 58)
( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)( 26, 82)
( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 71)( 32, 72)( 33, 73)( 34, 74)
( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)( 42, 98)
( 43, 83)( 44, 84)( 45, 85)( 46, 86)( 47, 87)( 48, 88)( 49, 89)( 50, 90)
( 99,155)(100,156)(101,157)(102,158)(103,159)(104,160)(105,161)(106,162)
(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)(113,153)(114,154)
(115,171)(116,172)(117,173)(118,174)(119,175)(120,176)(121,177)(122,178)
(123,163)(124,164)(125,165)(126,166)(127,167)(128,168)(129,169)(130,170)
(131,187)(132,188)(133,189)(134,190)(135,191)(136,192)(137,193)(138,194)
(139,179)(140,180)(141,181)(142,182)(143,183)(144,184)(145,185)(146,186);;
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, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)
(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)
(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)
(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)(176,178)
(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194);;
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,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)( 8, 64)( 9, 65)
( 10, 66)( 11, 51)( 12, 52)( 13, 53)( 14, 54)( 15, 55)( 16, 56)( 17, 57)
( 18, 58)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)
( 26, 82)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 71)( 32, 72)( 33, 73)
( 34, 74)( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)
( 42, 98)( 43, 83)( 44, 84)( 45, 85)( 46, 86)( 47, 87)( 48, 88)( 49, 89)
( 50, 90)( 99,155)(100,156)(101,157)(102,158)(103,159)(104,160)(105,161)
(106,162)(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)(113,153)
(114,154)(115,171)(116,172)(117,173)(118,174)(119,175)(120,176)(121,177)
(122,178)(123,163)(124,164)(125,165)(126,166)(127,167)(128,168)(129,169)
(130,170)(131,187)(132,188)(133,189)(134,190)(135,191)(136,192)(137,193)
(138,194)(139,179)(140,180)(141,181)(142,182)(143,183)(144,184)(145,185)
(146,186);
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, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)
(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)
(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)
(160,162)(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)
(176,178)(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)
(192,194);
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, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2 >;
to this polytope