Polytope of Type {2,2,4,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,15}*1920
if this polytope has a name.
Group : SmallGroup(1920,240409)
Rank : 5
Schlafli Type : {2,2,4,15}
Number of vertices, edges, etc : 2, 2, 16, 120, 60
Order of s0s1s2s3s4 : 30
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) :
3-fold quotients : {2,2,4,5}*640
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)( 11, 19)( 12, 20)
( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 27, 35)( 28, 36)
( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)( 43, 51)( 44, 52)
( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)( 59, 67)( 60, 68)
( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)( 75, 83)( 76, 84)
( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)( 91, 99)( 92,100)
(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)
(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)(123,131)(124,132)
(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)(139,147)(140,148)
(149,157)(150,158)(151,159)(152,160)(153,161)(154,162)(155,163)(156,164)
(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)(171,179)(172,180)
(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)(187,195)(188,196)
(197,205)(198,206)(199,207)(200,208)(201,209)(202,210)(203,211)(204,212)
(213,221)(214,222)(215,223)(216,224)(217,225)(218,226)(219,227)(220,228)
(229,237)(230,238)(231,239)(232,240)(233,241)(234,242)(235,243)(236,244);;
s3 := ( 6, 15)( 7, 18)( 8, 12)( 10, 19)( 11, 14)( 13, 17)( 21, 69)( 22, 79)
( 23, 82)( 24, 76)( 25, 73)( 26, 83)( 27, 78)( 28, 72)( 29, 81)( 30, 75)
( 31, 70)( 32, 80)( 33, 77)( 34, 71)( 35, 74)( 36, 84)( 37, 53)( 38, 63)
( 39, 66)( 40, 60)( 41, 57)( 42, 67)( 43, 62)( 44, 56)( 45, 65)( 46, 59)
( 47, 54)( 48, 64)( 49, 61)( 50, 55)( 51, 58)( 52, 68)( 85,165)( 86,175)
( 87,178)( 88,172)( 89,169)( 90,179)( 91,174)( 92,168)( 93,177)( 94,171)
( 95,166)( 96,176)( 97,173)( 98,167)( 99,170)(100,180)(101,229)(102,239)
(103,242)(104,236)(105,233)(106,243)(107,238)(108,232)(109,241)(110,235)
(111,230)(112,240)(113,237)(114,231)(115,234)(116,244)(117,213)(118,223)
(119,226)(120,220)(121,217)(122,227)(123,222)(124,216)(125,225)(126,219)
(127,214)(128,224)(129,221)(130,215)(131,218)(132,228)(133,197)(134,207)
(135,210)(136,204)(137,201)(138,211)(139,206)(140,200)(141,209)(142,203)
(143,198)(144,208)(145,205)(146,199)(147,202)(148,212)(149,181)(150,191)
(151,194)(152,188)(153,185)(154,195)(155,190)(156,184)(157,193)(158,187)
(159,182)(160,192)(161,189)(162,183)(163,186)(164,196);;
s4 := ( 5,117)( 6,129)( 7,124)( 8,128)( 9,126)( 10,122)( 11,131)( 12,119)
( 13,125)( 14,121)( 15,132)( 16,120)( 17,118)( 18,130)( 19,123)( 20,127)
( 21,101)( 22,113)( 23,108)( 24,112)( 25,110)( 26,106)( 27,115)( 28,103)
( 29,109)( 30,105)( 31,116)( 32,104)( 33,102)( 34,114)( 35,107)( 36,111)
( 37, 85)( 38, 97)( 39, 92)( 40, 96)( 41, 94)( 42, 90)( 43, 99)( 44, 87)
( 45, 93)( 46, 89)( 47,100)( 48, 88)( 49, 86)( 50, 98)( 51, 91)( 52, 95)
( 53,149)( 54,161)( 55,156)( 56,160)( 57,158)( 58,154)( 59,163)( 60,151)
( 61,157)( 62,153)( 63,164)( 64,152)( 65,150)( 66,162)( 67,155)( 68,159)
( 69,133)( 70,145)( 71,140)( 72,144)( 73,142)( 74,138)( 75,147)( 76,135)
( 77,141)( 78,137)( 79,148)( 80,136)( 81,134)( 82,146)( 83,139)( 84,143)
(165,197)(166,209)(167,204)(168,208)(169,206)(170,202)(171,211)(172,199)
(173,205)(174,201)(175,212)(176,200)(177,198)(178,210)(179,203)(180,207)
(182,193)(183,188)(184,192)(185,190)(187,195)(191,196)(213,229)(214,241)
(215,236)(216,240)(217,238)(218,234)(219,243)(220,231)(221,237)(222,233)
(223,244)(224,232)(225,230)(226,242)(227,235)(228,239);;
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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3*s4*s2*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(244)!(1,2);
s1 := Sym(244)!(3,4);
s2 := Sym(244)!( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)( 11, 19)
( 12, 20)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 27, 35)
( 28, 36)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)( 43, 51)
( 44, 52)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)( 59, 67)
( 60, 68)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)( 75, 83)
( 76, 84)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)( 91, 99)
( 92,100)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)(107,115)
(108,116)(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)(123,131)
(124,132)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)(139,147)
(140,148)(149,157)(150,158)(151,159)(152,160)(153,161)(154,162)(155,163)
(156,164)(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)(171,179)
(172,180)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)(187,195)
(188,196)(197,205)(198,206)(199,207)(200,208)(201,209)(202,210)(203,211)
(204,212)(213,221)(214,222)(215,223)(216,224)(217,225)(218,226)(219,227)
(220,228)(229,237)(230,238)(231,239)(232,240)(233,241)(234,242)(235,243)
(236,244);
s3 := Sym(244)!( 6, 15)( 7, 18)( 8, 12)( 10, 19)( 11, 14)( 13, 17)( 21, 69)
( 22, 79)( 23, 82)( 24, 76)( 25, 73)( 26, 83)( 27, 78)( 28, 72)( 29, 81)
( 30, 75)( 31, 70)( 32, 80)( 33, 77)( 34, 71)( 35, 74)( 36, 84)( 37, 53)
( 38, 63)( 39, 66)( 40, 60)( 41, 57)( 42, 67)( 43, 62)( 44, 56)( 45, 65)
( 46, 59)( 47, 54)( 48, 64)( 49, 61)( 50, 55)( 51, 58)( 52, 68)( 85,165)
( 86,175)( 87,178)( 88,172)( 89,169)( 90,179)( 91,174)( 92,168)( 93,177)
( 94,171)( 95,166)( 96,176)( 97,173)( 98,167)( 99,170)(100,180)(101,229)
(102,239)(103,242)(104,236)(105,233)(106,243)(107,238)(108,232)(109,241)
(110,235)(111,230)(112,240)(113,237)(114,231)(115,234)(116,244)(117,213)
(118,223)(119,226)(120,220)(121,217)(122,227)(123,222)(124,216)(125,225)
(126,219)(127,214)(128,224)(129,221)(130,215)(131,218)(132,228)(133,197)
(134,207)(135,210)(136,204)(137,201)(138,211)(139,206)(140,200)(141,209)
(142,203)(143,198)(144,208)(145,205)(146,199)(147,202)(148,212)(149,181)
(150,191)(151,194)(152,188)(153,185)(154,195)(155,190)(156,184)(157,193)
(158,187)(159,182)(160,192)(161,189)(162,183)(163,186)(164,196);
s4 := Sym(244)!( 5,117)( 6,129)( 7,124)( 8,128)( 9,126)( 10,122)( 11,131)
( 12,119)( 13,125)( 14,121)( 15,132)( 16,120)( 17,118)( 18,130)( 19,123)
( 20,127)( 21,101)( 22,113)( 23,108)( 24,112)( 25,110)( 26,106)( 27,115)
( 28,103)( 29,109)( 30,105)( 31,116)( 32,104)( 33,102)( 34,114)( 35,107)
( 36,111)( 37, 85)( 38, 97)( 39, 92)( 40, 96)( 41, 94)( 42, 90)( 43, 99)
( 44, 87)( 45, 93)( 46, 89)( 47,100)( 48, 88)( 49, 86)( 50, 98)( 51, 91)
( 52, 95)( 53,149)( 54,161)( 55,156)( 56,160)( 57,158)( 58,154)( 59,163)
( 60,151)( 61,157)( 62,153)( 63,164)( 64,152)( 65,150)( 66,162)( 67,155)
( 68,159)( 69,133)( 70,145)( 71,140)( 72,144)( 73,142)( 74,138)( 75,147)
( 76,135)( 77,141)( 78,137)( 79,148)( 80,136)( 81,134)( 82,146)( 83,139)
( 84,143)(165,197)(166,209)(167,204)(168,208)(169,206)(170,202)(171,211)
(172,199)(173,205)(174,201)(175,212)(176,200)(177,198)(178,210)(179,203)
(180,207)(182,193)(183,188)(184,192)(185,190)(187,195)(191,196)(213,229)
(214,241)(215,236)(216,240)(217,238)(218,234)(219,243)(220,231)(221,237)
(222,233)(223,244)(224,232)(225,230)(226,242)(227,235)(228,239);
poly := sub<Sym(244)|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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3*s4*s2*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope