Polytope of Type {20,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,4}*960a
Also Known As : {{20,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(960,7430)
Rank : 4
Schlafli Type : {20,6,4}
Number of vertices, edges, etc : 20, 60, 12, 4
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,6,4,2} of size 1920
Vertex Figure Of :
{2,20,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,6,2}*480a, {10,6,4}*480a
3-fold quotients : {20,2,4}*320
4-fold quotients : {10,6,2}*240
5-fold quotients : {4,6,4}*192a
6-fold quotients : {20,2,2}*160, {10,2,4}*160
10-fold quotients : {2,6,4}*96a, {4,6,2}*96a
12-fold quotients : {5,2,4}*80, {10,2,2}*80
15-fold quotients : {4,2,4}*64
20-fold quotients : {2,6,2}*48
24-fold quotients : {5,2,2}*40
30-fold quotients : {2,2,4}*32, {4,2,2}*32
40-fold quotients : {2,3,2}*24
60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,12,4}*1920a, {20,6,8}*1920, {40,6,4}*1920a
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66, 96)( 67,100)( 68, 99)
( 69, 98)( 70, 97)( 71,101)( 72,105)( 73,104)( 74,103)( 75,102)( 76,106)
( 77,110)( 78,109)( 79,108)( 80,107)( 81,111)( 82,115)( 83,114)( 84,113)
( 85,112)( 86,116)( 87,120)( 88,119)( 89,118)( 90,117)(122,125)(123,124)
(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)(143,144)
(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)(162,165)(163,164)
(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)(181,211)(182,215)
(183,214)(184,213)(185,212)(186,216)(187,220)(188,219)(189,218)(190,217)
(191,221)(192,225)(193,224)(194,223)(195,222)(196,226)(197,230)(198,229)
(199,228)(200,227)(201,231)(202,235)(203,234)(204,233)(205,232)(206,236)
(207,240)(208,239)(209,238)(210,237);;
s1 := ( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 72)( 7, 71)( 8, 75)
( 9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)( 16, 77)
( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 87)( 22, 86)( 23, 90)( 24, 89)
( 25, 88)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31, 92)( 32, 91)
( 33, 95)( 34, 94)( 35, 93)( 36,102)( 37,101)( 38,105)( 39,104)( 40,103)
( 41, 97)( 42, 96)( 43,100)( 44, 99)( 45, 98)( 46,107)( 47,106)( 48,110)
( 49,109)( 50,108)( 51,117)( 52,116)( 53,120)( 54,119)( 55,118)( 56,112)
( 57,111)( 58,115)( 59,114)( 60,113)(121,197)(122,196)(123,200)(124,199)
(125,198)(126,207)(127,206)(128,210)(129,209)(130,208)(131,202)(132,201)
(133,205)(134,204)(135,203)(136,182)(137,181)(138,185)(139,184)(140,183)
(141,192)(142,191)(143,195)(144,194)(145,193)(146,187)(147,186)(148,190)
(149,189)(150,188)(151,227)(152,226)(153,230)(154,229)(155,228)(156,237)
(157,236)(158,240)(159,239)(160,238)(161,232)(162,231)(163,235)(164,234)
(165,233)(166,212)(167,211)(168,215)(169,214)(170,213)(171,222)(172,221)
(173,225)(174,224)(175,223)(176,217)(177,216)(178,220)(179,219)(180,218);;
s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)
( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 51)
( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 66)( 62, 67)( 63, 68)( 64, 69)
( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91, 96)( 92, 97)
( 93, 98)( 94, 99)( 95,100)(106,111)(107,112)(108,113)(109,114)(110,115)
(121,141)(122,142)(123,143)(124,144)(125,145)(126,136)(127,137)(128,138)
(129,139)(130,140)(131,146)(132,147)(133,148)(134,149)(135,150)(151,171)
(152,172)(153,173)(154,174)(155,175)(156,166)(157,167)(158,168)(159,169)
(160,170)(161,176)(162,177)(163,178)(164,179)(165,180)(181,201)(182,202)
(183,203)(184,204)(185,205)(186,196)(187,197)(188,198)(189,199)(190,200)
(191,206)(192,207)(193,208)(194,209)(195,210)(211,231)(212,232)(213,233)
(214,234)(215,235)(216,226)(217,227)(218,228)(219,229)(220,230)(221,236)
(222,237)(223,238)(224,239)(225,240);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66, 96)( 67,100)
( 68, 99)( 69, 98)( 70, 97)( 71,101)( 72,105)( 73,104)( 74,103)( 75,102)
( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)( 81,111)( 82,115)( 83,114)
( 84,113)( 85,112)( 86,116)( 87,120)( 88,119)( 89,118)( 90,117)(122,125)
(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)
(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)(162,165)
(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)(181,211)
(182,215)(183,214)(184,213)(185,212)(186,216)(187,220)(188,219)(189,218)
(190,217)(191,221)(192,225)(193,224)(194,223)(195,222)(196,226)(197,230)
(198,229)(199,228)(200,227)(201,231)(202,235)(203,234)(204,233)(205,232)
(206,236)(207,240)(208,239)(209,238)(210,237);
s1 := Sym(240)!( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 72)( 7, 71)
( 8, 75)( 9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)
( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 87)( 22, 86)( 23, 90)
( 24, 89)( 25, 88)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31, 92)
( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36,102)( 37,101)( 38,105)( 39,104)
( 40,103)( 41, 97)( 42, 96)( 43,100)( 44, 99)( 45, 98)( 46,107)( 47,106)
( 48,110)( 49,109)( 50,108)( 51,117)( 52,116)( 53,120)( 54,119)( 55,118)
( 56,112)( 57,111)( 58,115)( 59,114)( 60,113)(121,197)(122,196)(123,200)
(124,199)(125,198)(126,207)(127,206)(128,210)(129,209)(130,208)(131,202)
(132,201)(133,205)(134,204)(135,203)(136,182)(137,181)(138,185)(139,184)
(140,183)(141,192)(142,191)(143,195)(144,194)(145,193)(146,187)(147,186)
(148,190)(149,189)(150,188)(151,227)(152,226)(153,230)(154,229)(155,228)
(156,237)(157,236)(158,240)(159,239)(160,238)(161,232)(162,231)(163,235)
(164,234)(165,233)(166,212)(167,211)(168,215)(169,214)(170,213)(171,222)
(172,221)(173,225)(174,224)(175,223)(176,217)(177,216)(178,220)(179,219)
(180,218);
s2 := Sym(240)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)
( 18, 23)( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)
( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 66)( 62, 67)( 63, 68)
( 64, 69)( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91, 96)
( 92, 97)( 93, 98)( 94, 99)( 95,100)(106,111)(107,112)(108,113)(109,114)
(110,115)(121,141)(122,142)(123,143)(124,144)(125,145)(126,136)(127,137)
(128,138)(129,139)(130,140)(131,146)(132,147)(133,148)(134,149)(135,150)
(151,171)(152,172)(153,173)(154,174)(155,175)(156,166)(157,167)(158,168)
(159,169)(160,170)(161,176)(162,177)(163,178)(164,179)(165,180)(181,201)
(182,202)(183,203)(184,204)(185,205)(186,196)(187,197)(188,198)(189,199)
(190,200)(191,206)(192,207)(193,208)(194,209)(195,210)(211,231)(212,232)
(213,233)(214,234)(215,235)(216,226)(217,227)(218,228)(219,229)(220,230)
(221,236)(222,237)(223,238)(224,239)(225,240);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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