Polytope of Type {2,4,60,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,60,2}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240289)
Rank : 5
Schlafli Type : {2,4,60,2}
Number of vertices, edges, etc : 2, 4, 120, 60, 2
Order of s0s1s2s3s4 : 60
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 : {2,4,30,2}*960b
4-fold quotients : {2,4,15,2}*480
5-fold quotients : {2,4,12,2}*384b
10-fold quotients : {2,4,6,2}*192c
20-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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)
(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)(208,210)
(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)(224,226)
(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)(240,242);;
s2 := ( 4, 5)( 7, 19)( 8, 21)( 9, 20)( 10, 22)( 11, 15)( 12, 17)( 13, 16)
( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)( 29, 60)
( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)( 37, 52)
( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)( 68, 81)
( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)( 92,117)
( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)(100,109)
(101,108)(102,110)(123,183)(124,185)(125,184)(126,186)(127,199)(128,201)
(129,200)(130,202)(131,195)(132,197)(133,196)(134,198)(135,191)(136,193)
(137,192)(138,194)(139,187)(140,189)(141,188)(142,190)(143,223)(144,225)
(145,224)(146,226)(147,239)(148,241)(149,240)(150,242)(151,235)(152,237)
(153,236)(154,238)(155,231)(156,233)(157,232)(158,234)(159,227)(160,229)
(161,228)(162,230)(163,203)(164,205)(165,204)(166,206)(167,219)(168,221)
(169,220)(170,222)(171,215)(172,217)(173,216)(174,218)(175,211)(176,213)
(177,212)(178,214)(179,207)(180,209)(181,208)(182,210);;
s3 := ( 3,167)( 4,170)( 5,169)( 6,168)( 7,163)( 8,166)( 9,165)( 10,164)
( 11,179)( 12,182)( 13,181)( 14,180)( 15,175)( 16,178)( 17,177)( 18,176)
( 19,171)( 20,174)( 21,173)( 22,172)( 23,147)( 24,150)( 25,149)( 26,148)
( 27,143)( 28,146)( 29,145)( 30,144)( 31,159)( 32,162)( 33,161)( 34,160)
( 35,155)( 36,158)( 37,157)( 38,156)( 39,151)( 40,154)( 41,153)( 42,152)
( 43,127)( 44,130)( 45,129)( 46,128)( 47,123)( 48,126)( 49,125)( 50,124)
( 51,139)( 52,142)( 53,141)( 54,140)( 55,135)( 56,138)( 57,137)( 58,136)
( 59,131)( 60,134)( 61,133)( 62,132)( 63,227)( 64,230)( 65,229)( 66,228)
( 67,223)( 68,226)( 69,225)( 70,224)( 71,239)( 72,242)( 73,241)( 74,240)
( 75,235)( 76,238)( 77,237)( 78,236)( 79,231)( 80,234)( 81,233)( 82,232)
( 83,207)( 84,210)( 85,209)( 86,208)( 87,203)( 88,206)( 89,205)( 90,204)
( 91,219)( 92,222)( 93,221)( 94,220)( 95,215)( 96,218)( 97,217)( 98,216)
( 99,211)(100,214)(101,213)(102,212)(103,187)(104,190)(105,189)(106,188)
(107,183)(108,186)(109,185)(110,184)(111,199)(112,202)(113,201)(114,200)
(115,195)(116,198)(117,197)(118,196)(119,191)(120,194)(121,193)(122,192);;
s4 := (243,244);;
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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s1*s2, 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*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*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*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, 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)(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)
(208,210)(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)
(224,226)(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)
(240,242);
s2 := Sym(244)!( 4, 5)( 7, 19)( 8, 21)( 9, 20)( 10, 22)( 11, 15)( 12, 17)
( 13, 16)( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)
( 29, 60)( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)
( 37, 52)( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)
( 68, 81)( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)
( 92,117)( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)
(100,109)(101,108)(102,110)(123,183)(124,185)(125,184)(126,186)(127,199)
(128,201)(129,200)(130,202)(131,195)(132,197)(133,196)(134,198)(135,191)
(136,193)(137,192)(138,194)(139,187)(140,189)(141,188)(142,190)(143,223)
(144,225)(145,224)(146,226)(147,239)(148,241)(149,240)(150,242)(151,235)
(152,237)(153,236)(154,238)(155,231)(156,233)(157,232)(158,234)(159,227)
(160,229)(161,228)(162,230)(163,203)(164,205)(165,204)(166,206)(167,219)
(168,221)(169,220)(170,222)(171,215)(172,217)(173,216)(174,218)(175,211)
(176,213)(177,212)(178,214)(179,207)(180,209)(181,208)(182,210);
s3 := Sym(244)!( 3,167)( 4,170)( 5,169)( 6,168)( 7,163)( 8,166)( 9,165)
( 10,164)( 11,179)( 12,182)( 13,181)( 14,180)( 15,175)( 16,178)( 17,177)
( 18,176)( 19,171)( 20,174)( 21,173)( 22,172)( 23,147)( 24,150)( 25,149)
( 26,148)( 27,143)( 28,146)( 29,145)( 30,144)( 31,159)( 32,162)( 33,161)
( 34,160)( 35,155)( 36,158)( 37,157)( 38,156)( 39,151)( 40,154)( 41,153)
( 42,152)( 43,127)( 44,130)( 45,129)( 46,128)( 47,123)( 48,126)( 49,125)
( 50,124)( 51,139)( 52,142)( 53,141)( 54,140)( 55,135)( 56,138)( 57,137)
( 58,136)( 59,131)( 60,134)( 61,133)( 62,132)( 63,227)( 64,230)( 65,229)
( 66,228)( 67,223)( 68,226)( 69,225)( 70,224)( 71,239)( 72,242)( 73,241)
( 74,240)( 75,235)( 76,238)( 77,237)( 78,236)( 79,231)( 80,234)( 81,233)
( 82,232)( 83,207)( 84,210)( 85,209)( 86,208)( 87,203)( 88,206)( 89,205)
( 90,204)( 91,219)( 92,222)( 93,221)( 94,220)( 95,215)( 96,218)( 97,217)
( 98,216)( 99,211)(100,214)(101,213)(102,212)(103,187)(104,190)(105,189)
(106,188)(107,183)(108,186)(109,185)(110,184)(111,199)(112,202)(113,201)
(114,200)(115,195)(116,198)(117,197)(118,196)(119,191)(120,194)(121,193)
(122,192);
s4 := Sym(244)!(243,244);
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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2,
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*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*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*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