Polytope of Type {4,10,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,4,3}*1920
Also Known As : {{4,10|2},{10,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(1920,240151)
Rank : 5
Schlafli Type : {4,10,4,3}
Number of vertices, edges, etc : 4, 20, 40, 12, 6
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
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 : {2,10,4,3}*960
4-fold quotients : {4,10,2,3}*480
5-fold quotients : {4,2,4,3}*384
8-fold quotients : {2,10,2,3}*240
10-fold quotients : {4,2,4,3}*192, {2,2,4,3}*192
16-fold quotients : {2,5,2,3}*120
20-fold quotients : {4,2,2,3}*96, {2,2,4,3}*96
40-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (121,181)(122,182)(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);;
s1 := ( 1,121)( 2,122)( 3,123)( 4,124)( 5,137)( 6,138)( 7,139)( 8,140)
( 9,133)( 10,134)( 11,135)( 12,136)( 13,129)( 14,130)( 15,131)( 16,132)
( 17,125)( 18,126)( 19,127)( 20,128)( 21,141)( 22,142)( 23,143)( 24,144)
( 25,157)( 26,158)( 27,159)( 28,160)( 29,153)( 30,154)( 31,155)( 32,156)
( 33,149)( 34,150)( 35,151)( 36,152)( 37,145)( 38,146)( 39,147)( 40,148)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,177)( 46,178)( 47,179)( 48,180)
( 49,173)( 50,174)( 51,175)( 52,176)( 53,169)( 54,170)( 55,171)( 56,172)
( 57,165)( 58,166)( 59,167)( 60,168)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,197)( 66,198)( 67,199)( 68,200)( 69,193)( 70,194)( 71,195)( 72,196)
( 73,189)( 74,190)( 75,191)( 76,192)( 77,185)( 78,186)( 79,187)( 80,188)
( 81,201)( 82,202)( 83,203)( 84,204)( 85,217)( 86,218)( 87,219)( 88,220)
( 89,213)( 90,214)( 91,215)( 92,216)( 93,209)( 94,210)( 95,211)( 96,212)
( 97,205)( 98,206)( 99,207)(100,208)(101,221)(102,222)(103,223)(104,224)
(105,237)(106,238)(107,239)(108,240)(109,233)(110,234)(111,235)(112,236)
(113,229)(114,230)(115,231)(116,232)(117,225)(118,226)(119,227)(120,228);;
s2 := ( 1, 7)( 2, 8)( 3, 5)( 4, 6)( 9, 19)( 10, 20)( 11, 17)( 12, 18)
( 13, 15)( 14, 16)( 21, 27)( 22, 28)( 23, 25)( 24, 26)( 29, 39)( 30, 40)
( 31, 37)( 32, 38)( 33, 35)( 34, 36)( 41, 47)( 42, 48)( 43, 45)( 44, 46)
( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 55)( 54, 56)( 61, 67)( 62, 68)
( 63, 65)( 64, 66)( 69, 79)( 70, 80)( 71, 77)( 72, 78)( 73, 75)( 74, 76)
( 81, 87)( 82, 88)( 83, 85)( 84, 86)( 89, 99)( 90,100)( 91, 97)( 92, 98)
( 93, 95)( 94, 96)(101,107)(102,108)(103,105)(104,106)(109,119)(110,120)
(111,117)(112,118)(113,115)(114,116)(121,127)(122,128)(123,125)(124,126)
(129,139)(130,140)(131,137)(132,138)(133,135)(134,136)(141,147)(142,148)
(143,145)(144,146)(149,159)(150,160)(151,157)(152,158)(153,155)(154,156)
(161,167)(162,168)(163,165)(164,166)(169,179)(170,180)(171,177)(172,178)
(173,175)(174,176)(181,187)(182,188)(183,185)(184,186)(189,199)(190,200)
(191,197)(192,198)(193,195)(194,196)(201,207)(202,208)(203,205)(204,206)
(209,219)(210,220)(211,217)(212,218)(213,215)(214,216)(221,227)(222,228)
(223,225)(224,226)(229,239)(230,240)(231,237)(232,238)(233,235)(234,236);;
s3 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)( 23, 44)
( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)( 31, 52)
( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)( 39, 60)
( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)( 98,118)
( 99,120)(100,119)(123,124)(127,128)(131,132)(135,136)(139,140)(141,161)
(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)(149,169)
(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)(157,177)
(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)(199,200)
(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)(208,227)
(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)(216,235)
(217,237)(218,238)(219,240)(220,239);;
s4 := ( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)( 8, 26)
( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)
( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)
( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)
( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)
(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)
(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)
(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)
(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)
(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)
(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)
(226,228)(230,232)(234,236)(238,240);;
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*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*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(240)!(121,181)(122,182)(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);
s1 := Sym(240)!( 1,121)( 2,122)( 3,123)( 4,124)( 5,137)( 6,138)( 7,139)
( 8,140)( 9,133)( 10,134)( 11,135)( 12,136)( 13,129)( 14,130)( 15,131)
( 16,132)( 17,125)( 18,126)( 19,127)( 20,128)( 21,141)( 22,142)( 23,143)
( 24,144)( 25,157)( 26,158)( 27,159)( 28,160)( 29,153)( 30,154)( 31,155)
( 32,156)( 33,149)( 34,150)( 35,151)( 36,152)( 37,145)( 38,146)( 39,147)
( 40,148)( 41,161)( 42,162)( 43,163)( 44,164)( 45,177)( 46,178)( 47,179)
( 48,180)( 49,173)( 50,174)( 51,175)( 52,176)( 53,169)( 54,170)( 55,171)
( 56,172)( 57,165)( 58,166)( 59,167)( 60,168)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,197)( 66,198)( 67,199)( 68,200)( 69,193)( 70,194)( 71,195)
( 72,196)( 73,189)( 74,190)( 75,191)( 76,192)( 77,185)( 78,186)( 79,187)
( 80,188)( 81,201)( 82,202)( 83,203)( 84,204)( 85,217)( 86,218)( 87,219)
( 88,220)( 89,213)( 90,214)( 91,215)( 92,216)( 93,209)( 94,210)( 95,211)
( 96,212)( 97,205)( 98,206)( 99,207)(100,208)(101,221)(102,222)(103,223)
(104,224)(105,237)(106,238)(107,239)(108,240)(109,233)(110,234)(111,235)
(112,236)(113,229)(114,230)(115,231)(116,232)(117,225)(118,226)(119,227)
(120,228);
s2 := Sym(240)!( 1, 7)( 2, 8)( 3, 5)( 4, 6)( 9, 19)( 10, 20)( 11, 17)
( 12, 18)( 13, 15)( 14, 16)( 21, 27)( 22, 28)( 23, 25)( 24, 26)( 29, 39)
( 30, 40)( 31, 37)( 32, 38)( 33, 35)( 34, 36)( 41, 47)( 42, 48)( 43, 45)
( 44, 46)( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 55)( 54, 56)( 61, 67)
( 62, 68)( 63, 65)( 64, 66)( 69, 79)( 70, 80)( 71, 77)( 72, 78)( 73, 75)
( 74, 76)( 81, 87)( 82, 88)( 83, 85)( 84, 86)( 89, 99)( 90,100)( 91, 97)
( 92, 98)( 93, 95)( 94, 96)(101,107)(102,108)(103,105)(104,106)(109,119)
(110,120)(111,117)(112,118)(113,115)(114,116)(121,127)(122,128)(123,125)
(124,126)(129,139)(130,140)(131,137)(132,138)(133,135)(134,136)(141,147)
(142,148)(143,145)(144,146)(149,159)(150,160)(151,157)(152,158)(153,155)
(154,156)(161,167)(162,168)(163,165)(164,166)(169,179)(170,180)(171,177)
(172,178)(173,175)(174,176)(181,187)(182,188)(183,185)(184,186)(189,199)
(190,200)(191,197)(192,198)(193,195)(194,196)(201,207)(202,208)(203,205)
(204,206)(209,219)(210,220)(211,217)(212,218)(213,215)(214,216)(221,227)
(222,228)(223,225)(224,226)(229,239)(230,240)(231,237)(232,238)(233,235)
(234,236);
s3 := Sym(240)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)
( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)
( 31, 52)( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)
( 39, 60)( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)
( 98,118)( 99,120)(100,119)(123,124)(127,128)(131,132)(135,136)(139,140)
(141,161)(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)
(149,169)(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)
(157,177)(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)
(199,200)(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)
(208,227)(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)
(216,235)(217,237)(218,238)(219,240)(220,239);
s4 := Sym(240)!( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)
( 8, 26)( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)
( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)
( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)
( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)
(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)
(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)
(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)
(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)
(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)
(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)
(222,224)(226,228)(230,232)(234,236)(238,240);
poly := sub<Sym(240)|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*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*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope