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