Polytope of Type {4,12,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,10}*960c
if this polytope has a name.
Group : SmallGroup(960,10951)
Rank : 4
Schlafli Type : {4,12,10}
Number of vertices, edges, etc : 4, 24, 60, 10
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,10,2} of size 1920
Vertex Figure Of :
{2,4,12,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,10}*480b
5-fold quotients : {4,12,2}*192c
10-fold quotients : {4,6,2}*96c
20-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,20}*1920c, {4,12,10}*1920b
Permutation Representation (GAP) :
s0 := ( 1, 63)( 2, 64)( 3, 61)( 4, 62)( 5, 67)( 6, 68)( 7, 65)( 8, 66)
( 9, 71)( 10, 72)( 11, 69)( 12, 70)( 13, 75)( 14, 76)( 15, 73)( 16, 74)
( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)( 24, 82)
( 25, 87)( 26, 88)( 27, 85)( 28, 86)( 29, 91)( 30, 92)( 31, 89)( 32, 90)
( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 99)( 38,100)( 39, 97)( 40, 98)
( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)( 47,105)( 48,106)
( 49,111)( 50,112)( 51,109)( 52,110)( 53,115)( 54,116)( 55,113)( 56,114)
( 57,119)( 58,120)( 59,117)( 60,118)(121,183)(122,184)(123,181)(124,182)
(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)(132,190)
(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)(140,198)
(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)(148,206)
(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)(156,214)
(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)(164,222)
(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)(172,230)
(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)(180,238);;
s1 := ( 2, 3)( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)
( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)
( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)
( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)
( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)
( 99,118)(100,120)(121,181)(122,183)(123,182)(124,184)(125,185)(126,187)
(127,186)(128,188)(129,189)(130,191)(131,190)(132,192)(133,193)(134,195)
(135,194)(136,196)(137,197)(138,199)(139,198)(140,200)(141,221)(142,223)
(143,222)(144,224)(145,225)(146,227)(147,226)(148,228)(149,229)(150,231)
(151,230)(152,232)(153,233)(154,235)(155,234)(156,236)(157,237)(158,239)
(159,238)(160,240)(161,201)(162,203)(163,202)(164,204)(165,205)(166,207)
(167,206)(168,208)(169,209)(170,211)(171,210)(172,212)(173,213)(174,215)
(175,214)(176,216)(177,217)(178,219)(179,218)(180,220);;
s2 := ( 1,161)( 2,164)( 3,163)( 4,162)( 5,177)( 6,180)( 7,179)( 8,178)
( 9,173)( 10,176)( 11,175)( 12,174)( 13,169)( 14,172)( 15,171)( 16,170)
( 17,165)( 18,168)( 19,167)( 20,166)( 21,141)( 22,144)( 23,143)( 24,142)
( 25,157)( 26,160)( 27,159)( 28,158)( 29,153)( 30,156)( 31,155)( 32,154)
( 33,149)( 34,152)( 35,151)( 36,150)( 37,145)( 38,148)( 39,147)( 40,146)
( 41,121)( 42,124)( 43,123)( 44,122)( 45,137)( 46,140)( 47,139)( 48,138)
( 49,133)( 50,136)( 51,135)( 52,134)( 53,129)( 54,132)( 55,131)( 56,130)
( 57,125)( 58,128)( 59,127)( 60,126)( 61,221)( 62,224)( 63,223)( 64,222)
( 65,237)( 66,240)( 67,239)( 68,238)( 69,233)( 70,236)( 71,235)( 72,234)
( 73,229)( 74,232)( 75,231)( 76,230)( 77,225)( 78,228)( 79,227)( 80,226)
( 81,201)( 82,204)( 83,203)( 84,202)( 85,217)( 86,220)( 87,219)( 88,218)
( 89,213)( 90,216)( 91,215)( 92,214)( 93,209)( 94,212)( 95,211)( 96,210)
( 97,205)( 98,208)( 99,207)(100,206)(101,181)(102,184)(103,183)(104,182)
(105,197)(106,200)(107,199)(108,198)(109,193)(110,196)(111,195)(112,194)
(113,189)(114,192)(115,191)(116,190)(117,185)(118,188)(119,187)(120,186);;
s3 := ( 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)
(121,125)(122,126)(123,127)(124,128)(129,137)(130,138)(131,139)(132,140)
(141,145)(142,146)(143,147)(144,148)(149,157)(150,158)(151,159)(152,160)
(161,165)(162,166)(163,167)(164,168)(169,177)(170,178)(171,179)(172,180)
(181,185)(182,186)(183,187)(184,188)(189,197)(190,198)(191,199)(192,200)
(201,205)(202,206)(203,207)(204,208)(209,217)(210,218)(211,219)(212,220)
(221,225)(222,226)(223,227)(224,228)(229,237)(230,238)(231,239)(232,240);;
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*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1,
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(240)!( 1, 63)( 2, 64)( 3, 61)( 4, 62)( 5, 67)( 6, 68)( 7, 65)
( 8, 66)( 9, 71)( 10, 72)( 11, 69)( 12, 70)( 13, 75)( 14, 76)( 15, 73)
( 16, 74)( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)
( 24, 82)( 25, 87)( 26, 88)( 27, 85)( 28, 86)( 29, 91)( 30, 92)( 31, 89)
( 32, 90)( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 99)( 38,100)( 39, 97)
( 40, 98)( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)( 47,105)
( 48,106)( 49,111)( 50,112)( 51,109)( 52,110)( 53,115)( 54,116)( 55,113)
( 56,114)( 57,119)( 58,120)( 59,117)( 60,118)(121,183)(122,184)(123,181)
(124,182)(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)
(132,190)(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)
(140,198)(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)
(148,206)(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)
(156,214)(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)
(164,222)(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)
(172,230)(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)
(180,238);
s1 := Sym(240)!( 2, 3)( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)
( 23, 42)( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)
( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)
( 39, 58)( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)
( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)
( 98,119)( 99,118)(100,120)(121,181)(122,183)(123,182)(124,184)(125,185)
(126,187)(127,186)(128,188)(129,189)(130,191)(131,190)(132,192)(133,193)
(134,195)(135,194)(136,196)(137,197)(138,199)(139,198)(140,200)(141,221)
(142,223)(143,222)(144,224)(145,225)(146,227)(147,226)(148,228)(149,229)
(150,231)(151,230)(152,232)(153,233)(154,235)(155,234)(156,236)(157,237)
(158,239)(159,238)(160,240)(161,201)(162,203)(163,202)(164,204)(165,205)
(166,207)(167,206)(168,208)(169,209)(170,211)(171,210)(172,212)(173,213)
(174,215)(175,214)(176,216)(177,217)(178,219)(179,218)(180,220);
s2 := Sym(240)!( 1,161)( 2,164)( 3,163)( 4,162)( 5,177)( 6,180)( 7,179)
( 8,178)( 9,173)( 10,176)( 11,175)( 12,174)( 13,169)( 14,172)( 15,171)
( 16,170)( 17,165)( 18,168)( 19,167)( 20,166)( 21,141)( 22,144)( 23,143)
( 24,142)( 25,157)( 26,160)( 27,159)( 28,158)( 29,153)( 30,156)( 31,155)
( 32,154)( 33,149)( 34,152)( 35,151)( 36,150)( 37,145)( 38,148)( 39,147)
( 40,146)( 41,121)( 42,124)( 43,123)( 44,122)( 45,137)( 46,140)( 47,139)
( 48,138)( 49,133)( 50,136)( 51,135)( 52,134)( 53,129)( 54,132)( 55,131)
( 56,130)( 57,125)( 58,128)( 59,127)( 60,126)( 61,221)( 62,224)( 63,223)
( 64,222)( 65,237)( 66,240)( 67,239)( 68,238)( 69,233)( 70,236)( 71,235)
( 72,234)( 73,229)( 74,232)( 75,231)( 76,230)( 77,225)( 78,228)( 79,227)
( 80,226)( 81,201)( 82,204)( 83,203)( 84,202)( 85,217)( 86,220)( 87,219)
( 88,218)( 89,213)( 90,216)( 91,215)( 92,214)( 93,209)( 94,212)( 95,211)
( 96,210)( 97,205)( 98,208)( 99,207)(100,206)(101,181)(102,184)(103,183)
(104,182)(105,197)(106,200)(107,199)(108,198)(109,193)(110,196)(111,195)
(112,194)(113,189)(114,192)(115,191)(116,190)(117,185)(118,188)(119,187)
(120,186);
s3 := 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)(121,125)(122,126)(123,127)(124,128)(129,137)(130,138)(131,139)
(132,140)(141,145)(142,146)(143,147)(144,148)(149,157)(150,158)(151,159)
(152,160)(161,165)(162,166)(163,167)(164,168)(169,177)(170,178)(171,179)
(172,180)(181,185)(182,186)(183,187)(184,188)(189,197)(190,198)(191,199)
(192,200)(201,205)(202,206)(203,207)(204,208)(209,217)(210,218)(211,219)
(212,220)(221,225)(222,226)(223,227)(224,228)(229,237)(230,238)(231,239)
(232,240);
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*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope