Polytope of Type {2,15,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,6,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240232)
Rank : 5
Schlafli Type : {2,15,6,4}
Number of vertices, edges, etc : 2, 20, 60, 16, 4
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,15,6,2}*960
5-fold quotients : {2,3,6,4}*384
10-fold quotients : {2,3,6,2}*192
12-fold quotients : {2,5,2,4}*160
20-fold quotients : {2,3,3,2}*96
24-fold quotients : {2,5,2,2}*80
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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);;
s2 := ( 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);;
s3 := ( 3, 6)( 7, 10)( 11, 14)( 15, 18)( 19, 22)( 23, 46)( 24, 44)( 25, 45)
( 26, 43)( 27, 50)( 28, 48)( 29, 49)( 30, 47)( 31, 54)( 32, 52)( 33, 53)
( 34, 51)( 35, 58)( 36, 56)( 37, 57)( 38, 55)( 39, 62)( 40, 60)( 41, 61)
( 42, 59)( 63, 66)( 67, 70)( 71, 74)( 75, 78)( 79, 82)( 83,106)( 84,104)
( 85,105)( 86,103)( 87,110)( 88,108)( 89,109)( 90,107)( 91,114)( 92,112)
( 93,113)( 94,111)( 95,118)( 96,116)( 97,117)( 98,115)( 99,122)(100,120)
(101,121)(102,119)(123,186)(124,184)(125,185)(126,183)(127,190)(128,188)
(129,189)(130,187)(131,194)(132,192)(133,193)(134,191)(135,198)(136,196)
(137,197)(138,195)(139,202)(140,200)(141,201)(142,199)(143,226)(144,224)
(145,225)(146,223)(147,230)(148,228)(149,229)(150,227)(151,234)(152,232)
(153,233)(154,231)(155,238)(156,236)(157,237)(158,235)(159,242)(160,240)
(161,241)(162,239)(163,206)(164,204)(165,205)(166,203)(167,210)(168,208)
(169,209)(170,207)(171,214)(172,212)(173,213)(174,211)(175,218)(176,216)
(177,217)(178,215)(179,222)(180,220)(181,221)(182,219);;
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,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := 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);
s2 := 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);
s3 := Sym(242)!( 3, 6)( 7, 10)( 11, 14)( 15, 18)( 19, 22)( 23, 46)( 24, 44)
( 25, 45)( 26, 43)( 27, 50)( 28, 48)( 29, 49)( 30, 47)( 31, 54)( 32, 52)
( 33, 53)( 34, 51)( 35, 58)( 36, 56)( 37, 57)( 38, 55)( 39, 62)( 40, 60)
( 41, 61)( 42, 59)( 63, 66)( 67, 70)( 71, 74)( 75, 78)( 79, 82)( 83,106)
( 84,104)( 85,105)( 86,103)( 87,110)( 88,108)( 89,109)( 90,107)( 91,114)
( 92,112)( 93,113)( 94,111)( 95,118)( 96,116)( 97,117)( 98,115)( 99,122)
(100,120)(101,121)(102,119)(123,186)(124,184)(125,185)(126,183)(127,190)
(128,188)(129,189)(130,187)(131,194)(132,192)(133,193)(134,191)(135,198)
(136,196)(137,197)(138,195)(139,202)(140,200)(141,201)(142,199)(143,226)
(144,224)(145,225)(146,223)(147,230)(148,228)(149,229)(150,227)(151,234)
(152,232)(153,233)(154,231)(155,238)(156,236)(157,237)(158,235)(159,242)
(160,240)(161,241)(162,239)(163,206)(164,204)(165,205)(166,203)(167,210)
(168,208)(169,209)(170,207)(171,214)(172,212)(173,213)(174,211)(175,218)
(176,216)(177,217)(178,215)(179,222)(180,220)(181,221)(182,219);
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, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3*s1*s2 >;
to this polytope