Polytope of Type {10,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,240151)
Rank : 4
Schlafli Type : {10,4,6}
Number of vertices, edges, etc : 10, 80, 48, 24
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 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 : {10,4,6}*960
4-fold quotients : {10,4,6}*480, {10,4,3}*480
5-fold quotients : {2,4,6}*384b
8-fold quotients : {10,2,6}*240
10-fold quotients : {2,4,6}*192
12-fold quotients : {10,4,2}*160
16-fold quotients : {5,2,6}*120, {10,2,3}*120
20-fold quotients : {2,4,6}*96a, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
24-fold quotients : {10,2,2}*80
32-fold quotients : {5,2,3}*60
40-fold quotients : {2,4,3}*48, {2,2,6}*48
48-fold quotients : {5,2,2}*40
60-fold quotients : {2,4,2}*32
80-fold quotients : {2,2,3}*24
120-fold quotients : {2,2,2}*16
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, 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)(121,187)(122,188)(123,185)(124,186)
(125,183)(126,184)(127,181)(128,182)(129,199)(130,200)(131,197)(132,198)
(133,195)(134,196)(135,193)(136,194)(137,191)(138,192)(139,189)(140,190)
(141,207)(142,208)(143,205)(144,206)(145,203)(146,204)(147,201)(148,202)
(149,219)(150,220)(151,217)(152,218)(153,215)(154,216)(155,213)(156,214)
(157,211)(158,212)(159,209)(160,210)(161,227)(162,228)(163,225)(164,226)
(165,223)(166,224)(167,221)(168,222)(169,239)(170,240)(171,237)(172,238)
(173,235)(174,236)(175,233)(176,234)(177,231)(178,232)(179,229)(180,230);;
s2 := ( 1,121)( 2,122)( 3,124)( 4,123)( 5,125)( 6,126)( 7,128)( 8,127)
( 9,129)( 10,130)( 11,132)( 12,131)( 13,133)( 14,134)( 15,136)( 16,135)
( 17,137)( 18,138)( 19,140)( 20,139)( 21,161)( 22,162)( 23,164)( 24,163)
( 25,165)( 26,166)( 27,168)( 28,167)( 29,169)( 30,170)( 31,172)( 32,171)
( 33,173)( 34,174)( 35,176)( 36,175)( 37,177)( 38,178)( 39,180)( 40,179)
( 41,141)( 42,142)( 43,144)( 44,143)( 45,145)( 46,146)( 47,148)( 48,147)
( 49,149)( 50,150)( 51,152)( 52,151)( 53,153)( 54,154)( 55,156)( 56,155)
( 57,157)( 58,158)( 59,160)( 60,159)( 61,181)( 62,182)( 63,184)( 64,183)
( 65,185)( 66,186)( 67,188)( 68,187)( 69,189)( 70,190)( 71,192)( 72,191)
( 73,193)( 74,194)( 75,196)( 76,195)( 77,197)( 78,198)( 79,200)( 80,199)
( 81,221)( 82,222)( 83,224)( 84,223)( 85,225)( 86,226)( 87,228)( 88,227)
( 89,229)( 90,230)( 91,232)( 92,231)( 93,233)( 94,234)( 95,236)( 96,235)
( 97,237)( 98,238)( 99,240)(100,239)(101,201)(102,202)(103,204)(104,203)
(105,205)(106,206)(107,208)(108,207)(109,209)(110,210)(111,212)(112,211)
(113,213)(114,214)(115,216)(116,215)(117,217)(118,218)(119,220)(120,219);;
s3 := ( 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]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
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, 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)(121,187)(122,188)(123,185)
(124,186)(125,183)(126,184)(127,181)(128,182)(129,199)(130,200)(131,197)
(132,198)(133,195)(134,196)(135,193)(136,194)(137,191)(138,192)(139,189)
(140,190)(141,207)(142,208)(143,205)(144,206)(145,203)(146,204)(147,201)
(148,202)(149,219)(150,220)(151,217)(152,218)(153,215)(154,216)(155,213)
(156,214)(157,211)(158,212)(159,209)(160,210)(161,227)(162,228)(163,225)
(164,226)(165,223)(166,224)(167,221)(168,222)(169,239)(170,240)(171,237)
(172,238)(173,235)(174,236)(175,233)(176,234)(177,231)(178,232)(179,229)
(180,230);
s2 := Sym(240)!( 1,121)( 2,122)( 3,124)( 4,123)( 5,125)( 6,126)( 7,128)
( 8,127)( 9,129)( 10,130)( 11,132)( 12,131)( 13,133)( 14,134)( 15,136)
( 16,135)( 17,137)( 18,138)( 19,140)( 20,139)( 21,161)( 22,162)( 23,164)
( 24,163)( 25,165)( 26,166)( 27,168)( 28,167)( 29,169)( 30,170)( 31,172)
( 32,171)( 33,173)( 34,174)( 35,176)( 36,175)( 37,177)( 38,178)( 39,180)
( 40,179)( 41,141)( 42,142)( 43,144)( 44,143)( 45,145)( 46,146)( 47,148)
( 48,147)( 49,149)( 50,150)( 51,152)( 52,151)( 53,153)( 54,154)( 55,156)
( 56,155)( 57,157)( 58,158)( 59,160)( 60,159)( 61,181)( 62,182)( 63,184)
( 64,183)( 65,185)( 66,186)( 67,188)( 68,187)( 69,189)( 70,190)( 71,192)
( 72,191)( 73,193)( 74,194)( 75,196)( 76,195)( 77,197)( 78,198)( 79,200)
( 80,199)( 81,221)( 82,222)( 83,224)( 84,223)( 85,225)( 86,226)( 87,228)
( 88,227)( 89,229)( 90,230)( 91,232)( 92,231)( 93,233)( 94,234)( 95,236)
( 96,235)( 97,237)( 98,238)( 99,240)(100,239)(101,201)(102,202)(103,204)
(104,203)(105,205)(106,206)(107,208)(108,207)(109,209)(110,210)(111,212)
(112,211)(113,213)(114,214)(115,216)(116,215)(117,217)(118,218)(119,220)
(120,219);
s3 := 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>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
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