Polytope of Type {2,4,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,30,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 5
Schlafli Type : {2,4,30,4}
Number of vertices, edges, etc : 2, 4, 60, 60, 4
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 : {2,4,6,4}*384c
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)(124,125)(127,139)(128,141)(129,140)(130,142)(131,135)
(132,137)(133,136)(134,138)(143,163)(144,165)(145,164)(146,166)(147,179)
(148,181)(149,180)(150,182)(151,175)(152,177)(153,176)(154,178)(155,171)
(156,173)(157,172)(158,174)(159,167)(160,169)(161,168)(162,170)(184,185)
(187,199)(188,201)(189,200)(190,202)(191,195)(192,197)(193,196)(194,198)
(203,223)(204,225)(205,224)(206,226)(207,239)(208,241)(209,240)(210,242)
(211,235)(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)(218,234)
(219,227)(220,229)(221,228)(222,230);;
s3 := ( 3, 47)( 4, 50)( 5, 49)( 6, 48)( 7, 43)( 8, 46)( 9, 45)( 10, 44)
( 11, 59)( 12, 62)( 13, 61)( 14, 60)( 15, 55)( 16, 58)( 17, 57)( 18, 56)
( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 27)( 24, 30)( 25, 29)( 26, 28)
( 31, 39)( 32, 42)( 33, 41)( 34, 40)( 36, 38)( 63,107)( 64,110)( 65,109)
( 66,108)( 67,103)( 68,106)( 69,105)( 70,104)( 71,119)( 72,122)( 73,121)
( 74,120)( 75,115)( 76,118)( 77,117)( 78,116)( 79,111)( 80,114)( 81,113)
( 82,112)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 99)( 92,102)( 93,101)
( 94,100)( 96, 98)(123,227)(124,230)(125,229)(126,228)(127,223)(128,226)
(129,225)(130,224)(131,239)(132,242)(133,241)(134,240)(135,235)(136,238)
(137,237)(138,236)(139,231)(140,234)(141,233)(142,232)(143,207)(144,210)
(145,209)(146,208)(147,203)(148,206)(149,205)(150,204)(151,219)(152,222)
(153,221)(154,220)(155,215)(156,218)(157,217)(158,216)(159,211)(160,214)
(161,213)(162,212)(163,187)(164,190)(165,189)(166,188)(167,183)(168,186)
(169,185)(170,184)(171,199)(172,202)(173,201)(174,200)(175,195)(176,198)
(177,197)(178,196)(179,191)(180,194)(181,193)(182,192);;
s4 := ( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)( 9,129)( 10,130)
( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)
( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)
( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)
( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)
( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)
( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)
( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)
( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,193)( 74,194)
( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)( 81,201)( 82,202)
( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)
( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)( 97,217)( 98,218)
( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,226)
(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)(114,234)
(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)(121,241)(122,242);;
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, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, 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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!( 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(242)!( 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)(124,125)(127,139)(128,141)(129,140)(130,142)
(131,135)(132,137)(133,136)(134,138)(143,163)(144,165)(145,164)(146,166)
(147,179)(148,181)(149,180)(150,182)(151,175)(152,177)(153,176)(154,178)
(155,171)(156,173)(157,172)(158,174)(159,167)(160,169)(161,168)(162,170)
(184,185)(187,199)(188,201)(189,200)(190,202)(191,195)(192,197)(193,196)
(194,198)(203,223)(204,225)(205,224)(206,226)(207,239)(208,241)(209,240)
(210,242)(211,235)(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)
(218,234)(219,227)(220,229)(221,228)(222,230);
s3 := Sym(242)!( 3, 47)( 4, 50)( 5, 49)( 6, 48)( 7, 43)( 8, 46)( 9, 45)
( 10, 44)( 11, 59)( 12, 62)( 13, 61)( 14, 60)( 15, 55)( 16, 58)( 17, 57)
( 18, 56)( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 27)( 24, 30)( 25, 29)
( 26, 28)( 31, 39)( 32, 42)( 33, 41)( 34, 40)( 36, 38)( 63,107)( 64,110)
( 65,109)( 66,108)( 67,103)( 68,106)( 69,105)( 70,104)( 71,119)( 72,122)
( 73,121)( 74,120)( 75,115)( 76,118)( 77,117)( 78,116)( 79,111)( 80,114)
( 81,113)( 82,112)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 99)( 92,102)
( 93,101)( 94,100)( 96, 98)(123,227)(124,230)(125,229)(126,228)(127,223)
(128,226)(129,225)(130,224)(131,239)(132,242)(133,241)(134,240)(135,235)
(136,238)(137,237)(138,236)(139,231)(140,234)(141,233)(142,232)(143,207)
(144,210)(145,209)(146,208)(147,203)(148,206)(149,205)(150,204)(151,219)
(152,222)(153,221)(154,220)(155,215)(156,218)(157,217)(158,216)(159,211)
(160,214)(161,213)(162,212)(163,187)(164,190)(165,189)(166,188)(167,183)
(168,186)(169,185)(170,184)(171,199)(172,202)(173,201)(174,200)(175,195)
(176,198)(177,197)(178,196)(179,191)(180,194)(181,193)(182,192);
s4 := Sym(242)!( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)( 9,129)
( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)
( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)
( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)
( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)
( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)
( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)
( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)
( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,193)
( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)( 81,201)
( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)( 89,209)
( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)( 97,217)
( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)
(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)
(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)(121,241)
(122,242);
poly := sub<Sym(242)|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,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
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 >;
to this polytope