Polytope of Type {12,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10,4}*960
Also Known As : {{12,10|2},{10,4|2}}. if this polytope has another name.
Group : SmallGroup(960,7449)
Rank : 4
Schlafli Type : {12,10,4}
Number of vertices, edges, etc : 12, 60, 20, 4
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,10,4,2} of size 1920
Vertex Figure Of :
{2,12,10,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,10,2}*480, {6,10,4}*480
3-fold quotients : {4,10,4}*320
4-fold quotients : {6,10,2}*240
5-fold quotients : {12,2,4}*192
6-fold quotients : {2,10,4}*160, {4,10,2}*160
10-fold quotients : {12,2,2}*96, {6,2,4}*96
12-fold quotients : {2,10,2}*80
15-fold quotients : {4,2,4}*64
20-fold quotients : {3,2,4}*48, {6,2,2}*48
24-fold quotients : {2,5,2}*40
30-fold quotients : {2,2,4}*32, {4,2,2}*32
40-fold quotients : {3,2,2}*24
60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,20,4}*1920, {12,10,8}*1920, {24,10,4}*1920
Permutation Representation (GAP) :
s0 := ( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)
( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)
( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 91)( 62, 92)( 63, 93)( 64, 94)
( 65, 95)( 66,101)( 67,102)( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)
( 73, 98)( 74, 99)( 75,100)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)
( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)
( 89,114)( 90,115)(126,131)(127,132)(128,133)(129,134)(130,135)(141,146)
(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)(159,164)
(160,165)(171,176)(172,177)(173,178)(174,179)(175,180)(181,211)(182,212)
(183,213)(184,214)(185,215)(186,221)(187,222)(188,223)(189,224)(190,225)
(191,216)(192,217)(193,218)(194,219)(195,220)(196,226)(197,227)(198,228)
(199,229)(200,230)(201,236)(202,237)(203,238)(204,239)(205,240)(206,231)
(207,232)(208,233)(209,234)(210,235);;
s1 := ( 1, 66)( 2, 70)( 3, 69)( 4, 68)( 5, 67)( 6, 61)( 7, 65)( 8, 64)
( 9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 81)
( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)( 24, 78)
( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 96)( 32,100)
( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)
( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,111)( 47,115)( 48,114)
( 49,113)( 50,112)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,116)
( 57,120)( 58,119)( 59,118)( 60,117)(121,201)(122,205)(123,204)(124,203)
(125,202)(126,196)(127,200)(128,199)(129,198)(130,197)(131,206)(132,210)
(133,209)(134,208)(135,207)(136,186)(137,190)(138,189)(139,188)(140,187)
(141,181)(142,185)(143,184)(144,183)(145,182)(146,191)(147,195)(148,194)
(149,193)(150,192)(151,231)(152,235)(153,234)(154,233)(155,232)(156,226)
(157,230)(158,229)(159,228)(160,227)(161,236)(162,240)(163,239)(164,238)
(165,237)(166,216)(167,220)(168,219)(169,218)(170,217)(171,211)(172,215)
(173,214)(174,213)(175,212)(176,221)(177,225)(178,224)(179,223)(180,222);;
s2 := ( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)
( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)
(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120)
(121,137)(122,136)(123,140)(124,139)(125,138)(126,142)(127,141)(128,145)
(129,144)(130,143)(131,147)(132,146)(133,150)(134,149)(135,148)(151,167)
(152,166)(153,170)(154,169)(155,168)(156,172)(157,171)(158,175)(159,174)
(160,173)(161,177)(162,176)(163,180)(164,179)(165,178)(181,197)(182,196)
(183,200)(184,199)(185,198)(186,202)(187,201)(188,205)(189,204)(190,203)
(191,207)(192,206)(193,210)(194,209)(195,208)(211,227)(212,226)(213,230)
(214,229)(215,228)(216,232)(217,231)(218,235)(219,234)(220,233)(221,237)
(222,236)(223,240)(224,239)(225,238);;
s3 := ( 1,121)( 2,122)( 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)( 61,196)( 62,197)( 63,198)( 64,199)
( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)
( 73,208)( 74,209)( 75,210)( 76,181)( 77,182)( 78,183)( 79,184)( 80,185)
( 81,186)( 82,187)( 83,188)( 84,189)( 85,190)( 86,191)( 87,192)( 88,193)
( 89,194)( 90,195)( 91,226)( 92,227)( 93,228)( 94,229)( 95,230)( 96,231)
( 97,232)( 98,233)( 99,234)(100,235)(101,236)(102,237)(103,238)(104,239)
(105,240)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)
(113,218)(114,219)(115,220)(116,221)(117,222)(118,223)(119,224)(120,225);;
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*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,
s0*s1*s0*s1*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)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)
( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 91)( 62, 92)( 63, 93)
( 64, 94)( 65, 95)( 66,101)( 67,102)( 68,103)( 69,104)( 70,105)( 71, 96)
( 72, 97)( 73, 98)( 74, 99)( 75,100)( 76,106)( 77,107)( 78,108)( 79,109)
( 80,110)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,111)( 87,112)
( 88,113)( 89,114)( 90,115)(126,131)(127,132)(128,133)(129,134)(130,135)
(141,146)(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)
(159,164)(160,165)(171,176)(172,177)(173,178)(174,179)(175,180)(181,211)
(182,212)(183,213)(184,214)(185,215)(186,221)(187,222)(188,223)(189,224)
(190,225)(191,216)(192,217)(193,218)(194,219)(195,220)(196,226)(197,227)
(198,228)(199,229)(200,230)(201,236)(202,237)(203,238)(204,239)(205,240)
(206,231)(207,232)(208,233)(209,234)(210,235);
s1 := Sym(240)!( 1, 66)( 2, 70)( 3, 69)( 4, 68)( 5, 67)( 6, 61)( 7, 65)
( 8, 64)( 9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 81)( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)
( 24, 78)( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 96)
( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)
( 40, 92)( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,111)( 47,115)
( 48,114)( 49,113)( 50,112)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)
( 56,116)( 57,120)( 58,119)( 59,118)( 60,117)(121,201)(122,205)(123,204)
(124,203)(125,202)(126,196)(127,200)(128,199)(129,198)(130,197)(131,206)
(132,210)(133,209)(134,208)(135,207)(136,186)(137,190)(138,189)(139,188)
(140,187)(141,181)(142,185)(143,184)(144,183)(145,182)(146,191)(147,195)
(148,194)(149,193)(150,192)(151,231)(152,235)(153,234)(154,233)(155,232)
(156,226)(157,230)(158,229)(159,228)(160,227)(161,236)(162,240)(163,239)
(164,238)(165,237)(166,216)(167,220)(168,219)(169,218)(170,217)(171,211)
(172,215)(173,214)(174,213)(175,212)(176,221)(177,225)(178,224)(179,223)
(180,222);
s2 := Sym(240)!( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)
( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)
( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)
(118,120)(121,137)(122,136)(123,140)(124,139)(125,138)(126,142)(127,141)
(128,145)(129,144)(130,143)(131,147)(132,146)(133,150)(134,149)(135,148)
(151,167)(152,166)(153,170)(154,169)(155,168)(156,172)(157,171)(158,175)
(159,174)(160,173)(161,177)(162,176)(163,180)(164,179)(165,178)(181,197)
(182,196)(183,200)(184,199)(185,198)(186,202)(187,201)(188,205)(189,204)
(190,203)(191,207)(192,206)(193,210)(194,209)(195,208)(211,227)(212,226)
(213,230)(214,229)(215,228)(216,232)(217,231)(218,235)(219,234)(220,233)
(221,237)(222,236)(223,240)(224,239)(225,238);
s3 := Sym(240)!( 1,121)( 2,122)( 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)( 61,196)( 62,197)( 63,198)
( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)
( 72,207)( 73,208)( 74,209)( 75,210)( 76,181)( 77,182)( 78,183)( 79,184)
( 80,185)( 81,186)( 82,187)( 83,188)( 84,189)( 85,190)( 86,191)( 87,192)
( 88,193)( 89,194)( 90,195)( 91,226)( 92,227)( 93,228)( 94,229)( 95,230)
( 96,231)( 97,232)( 98,233)( 99,234)(100,235)(101,236)(102,237)(103,238)
(104,239)(105,240)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)
(112,217)(113,218)(114,219)(115,220)(116,221)(117,222)(118,223)(119,224)
(120,225);
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*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,
s0*s1*s0*s1*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