Polytope of Type {2,4,6,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208136)
Rank : 5
Schlafli Type : {2,4,6,20}
Number of vertices, edges, etc : 2, 4, 12, 60, 20
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,2,6,20}*960a, {2,4,6,10}*960a
3-fold quotients : {2,4,2,20}*640
4-fold quotients : {2,2,6,10}*480
5-fold quotients : {2,4,6,4}*384a
6-fold quotients : {2,2,2,20}*320, {2,4,2,10}*320
10-fold quotients : {2,2,6,4}*192a, {2,4,6,2}*192a
12-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
15-fold quotients : {2,4,2,4}*128
20-fold quotients : {2,2,6,2}*96
24-fold quotients : {2,2,2,5}*80
30-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
40-fold quotients : {2,2,3,2}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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)( 61,181)( 62,182)( 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)( 76,211)( 77,212)( 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)
( 91,196)( 92,197)( 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)(106,241)
(107,242)(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)(121,226)(122,227);;
s2 := ( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)( 25, 30)
( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 58)
( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)( 71, 76)
( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)( 99,104)
(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)(117,122)
(123,138)(124,139)(125,140)(126,141)(127,142)(128,148)(129,149)(130,150)
(131,151)(132,152)(133,143)(134,144)(135,145)(136,146)(137,147)(153,168)
(154,169)(155,170)(156,171)(157,172)(158,178)(159,179)(160,180)(161,181)
(162,182)(163,173)(164,174)(165,175)(166,176)(167,177)(183,198)(184,199)
(185,200)(186,201)(187,202)(188,208)(189,209)(190,210)(191,211)(192,212)
(193,203)(194,204)(195,205)(196,206)(197,207)(213,228)(214,229)(215,230)
(216,231)(217,232)(218,238)(219,239)(220,240)(221,241)(222,242)(223,233)
(224,234)(225,235)(226,236)(227,237);;
s3 := ( 3, 68)( 4, 72)( 5, 71)( 6, 70)( 7, 69)( 8, 63)( 9, 67)( 10, 66)
( 11, 65)( 12, 64)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 83)
( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 78)( 24, 82)( 25, 81)( 26, 80)
( 27, 79)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 98)( 34,102)
( 35,101)( 36,100)( 37, 99)( 38, 93)( 39, 97)( 40, 96)( 41, 95)( 42, 94)
( 43,103)( 44,107)( 45,106)( 46,105)( 47,104)( 48,113)( 49,117)( 50,116)
( 51,115)( 52,114)( 53,108)( 54,112)( 55,111)( 56,110)( 57,109)( 58,118)
( 59,122)( 60,121)( 61,120)( 62,119)(123,203)(124,207)(125,206)(126,205)
(127,204)(128,198)(129,202)(130,201)(131,200)(132,199)(133,208)(134,212)
(135,211)(136,210)(137,209)(138,188)(139,192)(140,191)(141,190)(142,189)
(143,183)(144,187)(145,186)(146,185)(147,184)(148,193)(149,197)(150,196)
(151,195)(152,194)(153,233)(154,237)(155,236)(156,235)(157,234)(158,228)
(159,232)(160,231)(161,230)(162,229)(163,238)(164,242)(165,241)(166,240)
(167,239)(168,218)(169,222)(170,221)(171,220)(172,219)(173,213)(174,217)
(175,216)(176,215)(177,214)(178,223)(179,227)(180,226)(181,225)(182,224);;
s4 := ( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)( 20, 22)
( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)( 40, 42)
( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)
( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 99)( 69, 98)( 70,102)
( 71,101)( 72,100)( 73,104)( 74,103)( 75,107)( 76,106)( 77,105)( 78,109)
( 79,108)( 80,112)( 81,111)( 82,110)( 83,114)( 84,113)( 85,117)( 86,116)
( 87,115)( 88,119)( 89,118)( 90,122)( 91,121)( 92,120)(123,124)(125,127)
(128,129)(130,132)(133,134)(135,137)(138,139)(140,142)(143,144)(145,147)
(148,149)(150,152)(153,154)(155,157)(158,159)(160,162)(163,164)(165,167)
(168,169)(170,172)(173,174)(175,177)(178,179)(180,182)(183,214)(184,213)
(185,217)(186,216)(187,215)(188,219)(189,218)(190,222)(191,221)(192,220)
(193,224)(194,223)(195,227)(196,226)(197,225)(198,229)(199,228)(200,232)
(201,231)(202,230)(203,234)(204,233)(205,237)(206,236)(207,235)(208,239)
(209,238)(210,242)(211,241)(212,240);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!( 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)( 61,181)( 62,182)( 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)( 76,211)( 77,212)( 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)( 91,196)( 92,197)( 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)
(106,241)(107,242)(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)(121,226)
(122,227);
s2 := Sym(242)!( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)
( 53, 58)( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)
( 71, 76)( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)
( 99,104)(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)
(117,122)(123,138)(124,139)(125,140)(126,141)(127,142)(128,148)(129,149)
(130,150)(131,151)(132,152)(133,143)(134,144)(135,145)(136,146)(137,147)
(153,168)(154,169)(155,170)(156,171)(157,172)(158,178)(159,179)(160,180)
(161,181)(162,182)(163,173)(164,174)(165,175)(166,176)(167,177)(183,198)
(184,199)(185,200)(186,201)(187,202)(188,208)(189,209)(190,210)(191,211)
(192,212)(193,203)(194,204)(195,205)(196,206)(197,207)(213,228)(214,229)
(215,230)(216,231)(217,232)(218,238)(219,239)(220,240)(221,241)(222,242)
(223,233)(224,234)(225,235)(226,236)(227,237);
s3 := Sym(242)!( 3, 68)( 4, 72)( 5, 71)( 6, 70)( 7, 69)( 8, 63)( 9, 67)
( 10, 66)( 11, 65)( 12, 64)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)
( 18, 83)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 78)( 24, 82)( 25, 81)
( 26, 80)( 27, 79)( 28, 88)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 98)
( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 93)( 39, 97)( 40, 96)( 41, 95)
( 42, 94)( 43,103)( 44,107)( 45,106)( 46,105)( 47,104)( 48,113)( 49,117)
( 50,116)( 51,115)( 52,114)( 53,108)( 54,112)( 55,111)( 56,110)( 57,109)
( 58,118)( 59,122)( 60,121)( 61,120)( 62,119)(123,203)(124,207)(125,206)
(126,205)(127,204)(128,198)(129,202)(130,201)(131,200)(132,199)(133,208)
(134,212)(135,211)(136,210)(137,209)(138,188)(139,192)(140,191)(141,190)
(142,189)(143,183)(144,187)(145,186)(146,185)(147,184)(148,193)(149,197)
(150,196)(151,195)(152,194)(153,233)(154,237)(155,236)(156,235)(157,234)
(158,228)(159,232)(160,231)(161,230)(162,229)(163,238)(164,242)(165,241)
(166,240)(167,239)(168,218)(169,222)(170,221)(171,220)(172,219)(173,213)
(174,217)(175,216)(176,215)(177,214)(178,223)(179,227)(180,226)(181,225)
(182,224);
s4 := Sym(242)!( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)
( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)
( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)
( 60, 62)( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 99)( 69, 98)
( 70,102)( 71,101)( 72,100)( 73,104)( 74,103)( 75,107)( 76,106)( 77,105)
( 78,109)( 79,108)( 80,112)( 81,111)( 82,110)( 83,114)( 84,113)( 85,117)
( 86,116)( 87,115)( 88,119)( 89,118)( 90,122)( 91,121)( 92,120)(123,124)
(125,127)(128,129)(130,132)(133,134)(135,137)(138,139)(140,142)(143,144)
(145,147)(148,149)(150,152)(153,154)(155,157)(158,159)(160,162)(163,164)
(165,167)(168,169)(170,172)(173,174)(175,177)(178,179)(180,182)(183,214)
(184,213)(185,217)(186,216)(187,215)(188,219)(189,218)(190,222)(191,221)
(192,220)(193,224)(194,223)(195,227)(196,226)(197,225)(198,229)(199,228)
(200,232)(201,231)(202,230)(203,234)(204,233)(205,237)(206,236)(207,235)
(208,239)(209,238)(210,242)(211,241)(212,240);
poly := sub<Sym(242)|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*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope