Polytope of Type {2,15,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,4}*960
if this polytope has a name.
Group : SmallGroup(960,11375)
Rank : 4
Schlafli Type : {2,15,4}
Number of vertices, edges, etc : 2, 60, 120, 16
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,15,4,2} of size 1920
Vertex Figure Of :
{2,2,15,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,5,4}*320
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,15,8}*1920b, {2,15,8}*1920c, {2,15,4}*1920, {2,30,4}*1920c, {2,30,4}*1920d
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 13)( 5, 16)( 6, 10)( 8, 17)( 9, 12)( 11, 15)( 19, 67)( 20, 77)
( 21, 80)( 22, 74)( 23, 71)( 24, 81)( 25, 76)( 26, 70)( 27, 79)( 28, 73)
( 29, 68)( 30, 78)( 31, 75)( 32, 69)( 33, 72)( 34, 82)( 35, 51)( 36, 61)
( 37, 64)( 38, 58)( 39, 55)( 40, 65)( 41, 60)( 42, 54)( 43, 63)( 44, 57)
( 45, 52)( 46, 62)( 47, 59)( 48, 53)( 49, 56)( 50, 66)( 83,163)( 84,173)
( 85,176)( 86,170)( 87,167)( 88,177)( 89,172)( 90,166)( 91,175)( 92,169)
( 93,164)( 94,174)( 95,171)( 96,165)( 97,168)( 98,178)( 99,227)(100,237)
(101,240)(102,234)(103,231)(104,241)(105,236)(106,230)(107,239)(108,233)
(109,228)(110,238)(111,235)(112,229)(113,232)(114,242)(115,211)(116,221)
(117,224)(118,218)(119,215)(120,225)(121,220)(122,214)(123,223)(124,217)
(125,212)(126,222)(127,219)(128,213)(129,216)(130,226)(131,195)(132,205)
(133,208)(134,202)(135,199)(136,209)(137,204)(138,198)(139,207)(140,201)
(141,196)(142,206)(143,203)(144,197)(145,200)(146,210)(147,179)(148,189)
(149,192)(150,186)(151,183)(152,193)(153,188)(154,182)(155,191)(156,185)
(157,180)(158,190)(159,187)(160,181)(161,184)(162,194);;
s2 := ( 3, 99)( 4,100)( 5,102)( 6,101)( 7,104)( 8,103)( 9,105)( 10,106)
( 11,114)( 12,113)( 13,111)( 14,112)( 15,109)( 16,110)( 17,108)( 18,107)
( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 88)( 24, 87)( 25, 89)( 26, 90)
( 27, 98)( 28, 97)( 29, 95)( 30, 96)( 31, 93)( 32, 94)( 33, 92)( 34, 91)
( 35,147)( 36,148)( 37,150)( 38,149)( 39,152)( 40,151)( 41,153)( 42,154)
( 43,162)( 44,161)( 45,159)( 46,160)( 47,157)( 48,158)( 49,156)( 50,155)
( 51,131)( 52,132)( 53,134)( 54,133)( 55,136)( 56,135)( 57,137)( 58,138)
( 59,146)( 60,145)( 61,143)( 62,144)( 63,141)( 64,142)( 65,140)( 66,139)
( 67,115)( 68,116)( 69,118)( 70,117)( 71,120)( 72,119)( 73,121)( 74,122)
( 75,130)( 76,129)( 77,127)( 78,128)( 79,125)( 80,126)( 81,124)( 82,123)
(163,179)(164,180)(165,182)(166,181)(167,184)(168,183)(169,185)(170,186)
(171,194)(172,193)(173,191)(174,192)(175,189)(176,190)(177,188)(178,187)
(195,227)(196,228)(197,230)(198,229)(199,232)(200,231)(201,233)(202,234)
(203,242)(204,241)(205,239)(206,240)(207,237)(208,238)(209,236)(210,235)
(213,214)(215,216)(219,226)(220,225)(221,223)(222,224);;
s3 := ( 3, 7)( 4, 8)( 5, 9)( 6, 10)( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 19, 23)( 20, 24)( 21, 25)( 22, 26)( 27, 31)( 28, 32)( 29, 33)( 30, 34)
( 35, 39)( 36, 40)( 37, 41)( 38, 42)( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 51, 55)( 52, 56)( 53, 57)( 54, 58)( 59, 63)( 60, 64)( 61, 65)( 62, 66)
( 67, 71)( 68, 72)( 69, 73)( 70, 74)( 75, 79)( 76, 80)( 77, 81)( 78, 82)
( 83, 87)( 84, 88)( 85, 89)( 86, 90)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
( 99,103)(100,104)(101,105)(102,106)(107,111)(108,112)(109,113)(110,114)
(115,119)(116,120)(117,121)(118,122)(123,127)(124,128)(125,129)(126,130)
(131,135)(132,136)(133,137)(134,138)(139,143)(140,144)(141,145)(142,146)
(147,151)(148,152)(149,153)(150,154)(155,159)(156,160)(157,161)(158,162)
(163,167)(164,168)(165,169)(166,170)(171,175)(172,176)(173,177)(174,178)
(179,183)(180,184)(181,185)(182,186)(187,191)(188,192)(189,193)(190,194)
(195,199)(196,200)(197,201)(198,202)(203,207)(204,208)(205,209)(206,210)
(211,215)(212,216)(213,217)(214,218)(219,223)(220,224)(221,225)(222,226)
(227,231)(228,232)(229,233)(230,234)(235,239)(236,240)(237,241)(238,242);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!( 4, 13)( 5, 16)( 6, 10)( 8, 17)( 9, 12)( 11, 15)( 19, 67)
( 20, 77)( 21, 80)( 22, 74)( 23, 71)( 24, 81)( 25, 76)( 26, 70)( 27, 79)
( 28, 73)( 29, 68)( 30, 78)( 31, 75)( 32, 69)( 33, 72)( 34, 82)( 35, 51)
( 36, 61)( 37, 64)( 38, 58)( 39, 55)( 40, 65)( 41, 60)( 42, 54)( 43, 63)
( 44, 57)( 45, 52)( 46, 62)( 47, 59)( 48, 53)( 49, 56)( 50, 66)( 83,163)
( 84,173)( 85,176)( 86,170)( 87,167)( 88,177)( 89,172)( 90,166)( 91,175)
( 92,169)( 93,164)( 94,174)( 95,171)( 96,165)( 97,168)( 98,178)( 99,227)
(100,237)(101,240)(102,234)(103,231)(104,241)(105,236)(106,230)(107,239)
(108,233)(109,228)(110,238)(111,235)(112,229)(113,232)(114,242)(115,211)
(116,221)(117,224)(118,218)(119,215)(120,225)(121,220)(122,214)(123,223)
(124,217)(125,212)(126,222)(127,219)(128,213)(129,216)(130,226)(131,195)
(132,205)(133,208)(134,202)(135,199)(136,209)(137,204)(138,198)(139,207)
(140,201)(141,196)(142,206)(143,203)(144,197)(145,200)(146,210)(147,179)
(148,189)(149,192)(150,186)(151,183)(152,193)(153,188)(154,182)(155,191)
(156,185)(157,180)(158,190)(159,187)(160,181)(161,184)(162,194);
s2 := Sym(242)!( 3, 99)( 4,100)( 5,102)( 6,101)( 7,104)( 8,103)( 9,105)
( 10,106)( 11,114)( 12,113)( 13,111)( 14,112)( 15,109)( 16,110)( 17,108)
( 18,107)( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 88)( 24, 87)( 25, 89)
( 26, 90)( 27, 98)( 28, 97)( 29, 95)( 30, 96)( 31, 93)( 32, 94)( 33, 92)
( 34, 91)( 35,147)( 36,148)( 37,150)( 38,149)( 39,152)( 40,151)( 41,153)
( 42,154)( 43,162)( 44,161)( 45,159)( 46,160)( 47,157)( 48,158)( 49,156)
( 50,155)( 51,131)( 52,132)( 53,134)( 54,133)( 55,136)( 56,135)( 57,137)
( 58,138)( 59,146)( 60,145)( 61,143)( 62,144)( 63,141)( 64,142)( 65,140)
( 66,139)( 67,115)( 68,116)( 69,118)( 70,117)( 71,120)( 72,119)( 73,121)
( 74,122)( 75,130)( 76,129)( 77,127)( 78,128)( 79,125)( 80,126)( 81,124)
( 82,123)(163,179)(164,180)(165,182)(166,181)(167,184)(168,183)(169,185)
(170,186)(171,194)(172,193)(173,191)(174,192)(175,189)(176,190)(177,188)
(178,187)(195,227)(196,228)(197,230)(198,229)(199,232)(200,231)(201,233)
(202,234)(203,242)(204,241)(205,239)(206,240)(207,237)(208,238)(209,236)
(210,235)(213,214)(215,216)(219,226)(220,225)(221,223)(222,224);
s3 := Sym(242)!( 3, 7)( 4, 8)( 5, 9)( 6, 10)( 11, 15)( 12, 16)( 13, 17)
( 14, 18)( 19, 23)( 20, 24)( 21, 25)( 22, 26)( 27, 31)( 28, 32)( 29, 33)
( 30, 34)( 35, 39)( 36, 40)( 37, 41)( 38, 42)( 43, 47)( 44, 48)( 45, 49)
( 46, 50)( 51, 55)( 52, 56)( 53, 57)( 54, 58)( 59, 63)( 60, 64)( 61, 65)
( 62, 66)( 67, 71)( 68, 72)( 69, 73)( 70, 74)( 75, 79)( 76, 80)( 77, 81)
( 78, 82)( 83, 87)( 84, 88)( 85, 89)( 86, 90)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)( 99,103)(100,104)(101,105)(102,106)(107,111)(108,112)(109,113)
(110,114)(115,119)(116,120)(117,121)(118,122)(123,127)(124,128)(125,129)
(126,130)(131,135)(132,136)(133,137)(134,138)(139,143)(140,144)(141,145)
(142,146)(147,151)(148,152)(149,153)(150,154)(155,159)(156,160)(157,161)
(158,162)(163,167)(164,168)(165,169)(166,170)(171,175)(172,176)(173,177)
(174,178)(179,183)(180,184)(181,185)(182,186)(187,191)(188,192)(189,193)
(190,194)(195,199)(196,200)(197,201)(198,202)(203,207)(204,208)(205,209)
(206,210)(211,215)(212,216)(213,217)(214,218)(219,223)(220,224)(221,225)
(222,226)(227,231)(228,232)(229,233)(230,234)(235,239)(236,240)(237,241)
(238,242);
poly := sub<Sym(242)|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, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*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*s1*s2*s1*s2*s1*s2 >;
to this polytope