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