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