Polytope of Type {2,20,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208136)
Rank : 5
Schlafli Type : {2,20,6,4}
Number of vertices, edges, etc : 2, 20, 60, 12, 4
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 : {2,20,6,2}*960a, {2,10,6,4}*960a
3-fold quotients : {2,20,2,4}*640
4-fold quotients : {2,10,6,2}*480
5-fold quotients : {2,4,6,4}*384a
6-fold quotients : {2,20,2,2}*320, {2,10,2,4}*320
10-fold quotients : {2,2,6,4}*192a, {2,4,6,2}*192a
12-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
15-fold quotients : {2,4,2,4}*128
20-fold quotients : {2,2,6,2}*96
24-fold quotients : {2,5,2,2}*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 := ( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 63, 93)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 98)( 69,102)( 70,101)
( 71,100)( 72, 99)( 73,103)( 74,107)( 75,106)( 76,105)( 77,104)( 78,108)
( 79,112)( 80,111)( 81,110)( 82,109)( 83,113)( 84,117)( 85,116)( 86,115)
( 87,114)( 88,118)( 89,122)( 90,121)( 91,120)( 92,119)(124,127)(125,126)
(129,132)(130,131)(134,137)(135,136)(139,142)(140,141)(144,147)(145,146)
(149,152)(150,151)(154,157)(155,156)(159,162)(160,161)(164,167)(165,166)
(169,172)(170,171)(174,177)(175,176)(179,182)(180,181)(183,213)(184,217)
(185,216)(186,215)(187,214)(188,218)(189,222)(190,221)(191,220)(192,219)
(193,223)(194,227)(195,226)(196,225)(197,224)(198,228)(199,232)(200,231)
(201,230)(202,229)(203,233)(204,237)(205,236)(206,235)(207,234)(208,238)
(209,242)(210,241)(211,240)(212,239);;
s2 := ( 3, 64)( 4, 63)( 5, 67)( 6, 66)( 7, 65)( 8, 74)( 9, 73)( 10, 77)
( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)( 18, 79)
( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 89)( 24, 88)( 25, 92)( 26, 91)
( 27, 90)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 94)( 34, 93)
( 35, 97)( 36, 96)( 37, 95)( 38,104)( 39,103)( 40,107)( 41,106)( 42,105)
( 43, 99)( 44, 98)( 45,102)( 46,101)( 47,100)( 48,109)( 49,108)( 50,112)
( 51,111)( 52,110)( 53,119)( 54,118)( 55,122)( 56,121)( 57,120)( 58,114)
( 59,113)( 60,117)( 61,116)( 62,115)(123,199)(124,198)(125,202)(126,201)
(127,200)(128,209)(129,208)(130,212)(131,211)(132,210)(133,204)(134,203)
(135,207)(136,206)(137,205)(138,184)(139,183)(140,187)(141,186)(142,185)
(143,194)(144,193)(145,197)(146,196)(147,195)(148,189)(149,188)(150,192)
(151,191)(152,190)(153,229)(154,228)(155,232)(156,231)(157,230)(158,239)
(159,238)(160,242)(161,241)(162,240)(163,234)(164,233)(165,237)(166,236)
(167,235)(168,214)(169,213)(170,217)(171,216)(172,215)(173,224)(174,223)
(175,227)(176,226)(177,225)(178,219)(179,218)(180,222)(181,221)(182,220);;
s3 := ( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)( 20, 25)
( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)( 48, 53)
( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 68)( 64, 69)( 65, 70)( 66, 71)
( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)( 94, 99)
( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)(112,117)
(123,143)(124,144)(125,145)(126,146)(127,147)(128,138)(129,139)(130,140)
(131,141)(132,142)(133,148)(134,149)(135,150)(136,151)(137,152)(153,173)
(154,174)(155,175)(156,176)(157,177)(158,168)(159,169)(160,170)(161,171)
(162,172)(163,178)(164,179)(165,180)(166,181)(167,182)(183,203)(184,204)
(185,205)(186,206)(187,207)(188,198)(189,199)(190,200)(191,201)(192,202)
(193,208)(194,209)(195,210)(196,211)(197,212)(213,233)(214,234)(215,235)
(216,236)(217,237)(218,228)(219,229)(220,230)(221,231)(222,232)(223,238)
(224,239)(225,240)(226,241)(227,242);;
s4 := ( 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);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 63, 93)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 98)( 69,102)
( 70,101)( 71,100)( 72, 99)( 73,103)( 74,107)( 75,106)( 76,105)( 77,104)
( 78,108)( 79,112)( 80,111)( 81,110)( 82,109)( 83,113)( 84,117)( 85,116)
( 86,115)( 87,114)( 88,118)( 89,122)( 90,121)( 91,120)( 92,119)(124,127)
(125,126)(129,132)(130,131)(134,137)(135,136)(139,142)(140,141)(144,147)
(145,146)(149,152)(150,151)(154,157)(155,156)(159,162)(160,161)(164,167)
(165,166)(169,172)(170,171)(174,177)(175,176)(179,182)(180,181)(183,213)
(184,217)(185,216)(186,215)(187,214)(188,218)(189,222)(190,221)(191,220)
(192,219)(193,223)(194,227)(195,226)(196,225)(197,224)(198,228)(199,232)
(200,231)(201,230)(202,229)(203,233)(204,237)(205,236)(206,235)(207,234)
(208,238)(209,242)(210,241)(211,240)(212,239);
s2 := Sym(242)!( 3, 64)( 4, 63)( 5, 67)( 6, 66)( 7, 65)( 8, 74)( 9, 73)
( 10, 77)( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)
( 18, 79)( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 89)( 24, 88)( 25, 92)
( 26, 91)( 27, 90)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 94)
( 34, 93)( 35, 97)( 36, 96)( 37, 95)( 38,104)( 39,103)( 40,107)( 41,106)
( 42,105)( 43, 99)( 44, 98)( 45,102)( 46,101)( 47,100)( 48,109)( 49,108)
( 50,112)( 51,111)( 52,110)( 53,119)( 54,118)( 55,122)( 56,121)( 57,120)
( 58,114)( 59,113)( 60,117)( 61,116)( 62,115)(123,199)(124,198)(125,202)
(126,201)(127,200)(128,209)(129,208)(130,212)(131,211)(132,210)(133,204)
(134,203)(135,207)(136,206)(137,205)(138,184)(139,183)(140,187)(141,186)
(142,185)(143,194)(144,193)(145,197)(146,196)(147,195)(148,189)(149,188)
(150,192)(151,191)(152,190)(153,229)(154,228)(155,232)(156,231)(157,230)
(158,239)(159,238)(160,242)(161,241)(162,240)(163,234)(164,233)(165,237)
(166,236)(167,235)(168,214)(169,213)(170,217)(171,216)(172,215)(173,224)
(174,223)(175,227)(176,226)(177,225)(178,219)(179,218)(180,222)(181,221)
(182,220);
s3 := Sym(242)!( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)
( 20, 25)( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)
( 48, 53)( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 68)( 64, 69)( 65, 70)
( 66, 71)( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)
( 94, 99)( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)
(112,117)(123,143)(124,144)(125,145)(126,146)(127,147)(128,138)(129,139)
(130,140)(131,141)(132,142)(133,148)(134,149)(135,150)(136,151)(137,152)
(153,173)(154,174)(155,175)(156,176)(157,177)(158,168)(159,169)(160,170)
(161,171)(162,172)(163,178)(164,179)(165,180)(166,181)(167,182)(183,203)
(184,204)(185,205)(186,206)(187,207)(188,198)(189,199)(190,200)(191,201)
(192,202)(193,208)(194,209)(195,210)(196,211)(197,212)(213,233)(214,234)
(215,235)(216,236)(217,237)(218,228)(219,229)(220,230)(221,231)(222,232)
(223,238)(224,239)(225,240)(226,241)(227,242);
s4 := 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);
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*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope