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}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240142)
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
Non-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 : {2,4,6,10}*960b
5-fold quotients : {2,4,6,4}*384c
10-fold quotients : {2,4,6,2}*192c
20-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)
(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)
(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)
(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)(176,178)
(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)
(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)(208,210)
(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)(224,226)
(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)(240,242);;
s2 := ( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)( 25, 44)
( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)( 33, 52)
( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)( 41, 60)
( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)( 92,113)
( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)(100,121)
(101,120)(102,122)(124,125)(128,129)(132,133)(136,137)(140,141)(143,163)
(144,165)(145,164)(146,166)(147,167)(148,169)(149,168)(150,170)(151,171)
(152,173)(153,172)(154,174)(155,175)(156,177)(157,176)(158,178)(159,179)
(160,181)(161,180)(162,182)(184,185)(188,189)(192,193)(196,197)(200,201)
(203,223)(204,225)(205,224)(206,226)(207,227)(208,229)(209,228)(210,230)
(211,231)(212,233)(213,232)(214,234)(215,235)(216,237)(217,236)(218,238)
(219,239)(220,241)(221,240)(222,242);;
s3 := ( 3, 43)( 4, 46)( 5, 45)( 6, 44)( 7, 59)( 8, 62)( 9, 61)( 10, 60)
( 11, 55)( 12, 58)( 13, 57)( 14, 56)( 15, 51)( 16, 54)( 17, 53)( 18, 52)
( 19, 47)( 20, 50)( 21, 49)( 22, 48)( 24, 26)( 27, 39)( 28, 42)( 29, 41)
( 30, 40)( 31, 35)( 32, 38)( 33, 37)( 34, 36)( 63,103)( 64,106)( 65,105)
( 66,104)( 67,119)( 68,122)( 69,121)( 70,120)( 71,115)( 72,118)( 73,117)
( 74,116)( 75,111)( 76,114)( 77,113)( 78,112)( 79,107)( 80,110)( 81,109)
( 82,108)( 84, 86)( 87, 99)( 88,102)( 89,101)( 90,100)( 91, 95)( 92, 98)
( 93, 97)( 94, 96)(123,223)(124,226)(125,225)(126,224)(127,239)(128,242)
(129,241)(130,240)(131,235)(132,238)(133,237)(134,236)(135,231)(136,234)
(137,233)(138,232)(139,227)(140,230)(141,229)(142,228)(143,203)(144,206)
(145,205)(146,204)(147,219)(148,222)(149,221)(150,220)(151,215)(152,218)
(153,217)(154,216)(155,211)(156,214)(157,213)(158,212)(159,207)(160,210)
(161,209)(162,208)(163,183)(164,186)(165,185)(166,184)(167,199)(168,202)
(169,201)(170,200)(171,195)(172,198)(173,197)(174,196)(175,191)(176,194)
(177,193)(178,192)(179,187)(180,190)(181,189)(182,188);;
s4 := ( 3,127)( 4,128)( 5,129)( 6,130)( 7,123)( 8,124)( 9,125)( 10,126)
( 11,139)( 12,140)( 13,141)( 14,142)( 15,135)( 16,136)( 17,137)( 18,138)
( 19,131)( 20,132)( 21,133)( 22,134)( 23,147)( 24,148)( 25,149)( 26,150)
( 27,143)( 28,144)( 29,145)( 30,146)( 31,159)( 32,160)( 33,161)( 34,162)
( 35,155)( 36,156)( 37,157)( 38,158)( 39,151)( 40,152)( 41,153)( 42,154)
( 43,167)( 44,168)( 45,169)( 46,170)( 47,163)( 48,164)( 49,165)( 50,166)
( 51,179)( 52,180)( 53,181)( 54,182)( 55,175)( 56,176)( 57,177)( 58,178)
( 59,171)( 60,172)( 61,173)( 62,174)( 63,187)( 64,188)( 65,189)( 66,190)
( 67,183)( 68,184)( 69,185)( 70,186)( 71,199)( 72,200)( 73,201)( 74,202)
( 75,195)( 76,196)( 77,197)( 78,198)( 79,191)( 80,192)( 81,193)( 82,194)
( 83,207)( 84,208)( 85,209)( 86,210)( 87,203)( 88,204)( 89,205)( 90,206)
( 91,219)( 92,220)( 93,221)( 94,222)( 95,215)( 96,216)( 97,217)( 98,218)
( 99,211)(100,212)(101,213)(102,214)(103,227)(104,228)(105,229)(106,230)
(107,223)(108,224)(109,225)(110,226)(111,239)(112,240)(113,241)(114,242)
(115,235)(116,236)(117,237)(118,238)(119,231)(120,232)(121,233)(122,234);;
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, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s3*s2*s1*s2*s3*s1*s2, 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, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)
(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)
(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)
(160,162)(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)
(176,178)(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)
(192,194)(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)
(208,210)(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)
(224,226)(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)
(240,242);
s2 := Sym(242)!( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)
( 25, 44)( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)
( 33, 52)( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)
( 41, 60)( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)
( 92,113)( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)
(100,121)(101,120)(102,122)(124,125)(128,129)(132,133)(136,137)(140,141)
(143,163)(144,165)(145,164)(146,166)(147,167)(148,169)(149,168)(150,170)
(151,171)(152,173)(153,172)(154,174)(155,175)(156,177)(157,176)(158,178)
(159,179)(160,181)(161,180)(162,182)(184,185)(188,189)(192,193)(196,197)
(200,201)(203,223)(204,225)(205,224)(206,226)(207,227)(208,229)(209,228)
(210,230)(211,231)(212,233)(213,232)(214,234)(215,235)(216,237)(217,236)
(218,238)(219,239)(220,241)(221,240)(222,242);
s3 := Sym(242)!( 3, 43)( 4, 46)( 5, 45)( 6, 44)( 7, 59)( 8, 62)( 9, 61)
( 10, 60)( 11, 55)( 12, 58)( 13, 57)( 14, 56)( 15, 51)( 16, 54)( 17, 53)
( 18, 52)( 19, 47)( 20, 50)( 21, 49)( 22, 48)( 24, 26)( 27, 39)( 28, 42)
( 29, 41)( 30, 40)( 31, 35)( 32, 38)( 33, 37)( 34, 36)( 63,103)( 64,106)
( 65,105)( 66,104)( 67,119)( 68,122)( 69,121)( 70,120)( 71,115)( 72,118)
( 73,117)( 74,116)( 75,111)( 76,114)( 77,113)( 78,112)( 79,107)( 80,110)
( 81,109)( 82,108)( 84, 86)( 87, 99)( 88,102)( 89,101)( 90,100)( 91, 95)
( 92, 98)( 93, 97)( 94, 96)(123,223)(124,226)(125,225)(126,224)(127,239)
(128,242)(129,241)(130,240)(131,235)(132,238)(133,237)(134,236)(135,231)
(136,234)(137,233)(138,232)(139,227)(140,230)(141,229)(142,228)(143,203)
(144,206)(145,205)(146,204)(147,219)(148,222)(149,221)(150,220)(151,215)
(152,218)(153,217)(154,216)(155,211)(156,214)(157,213)(158,212)(159,207)
(160,210)(161,209)(162,208)(163,183)(164,186)(165,185)(166,184)(167,199)
(168,202)(169,201)(170,200)(171,195)(172,198)(173,197)(174,196)(175,191)
(176,194)(177,193)(178,192)(179,187)(180,190)(181,189)(182,188);
s4 := Sym(242)!( 3,127)( 4,128)( 5,129)( 6,130)( 7,123)( 8,124)( 9,125)
( 10,126)( 11,139)( 12,140)( 13,141)( 14,142)( 15,135)( 16,136)( 17,137)
( 18,138)( 19,131)( 20,132)( 21,133)( 22,134)( 23,147)( 24,148)( 25,149)
( 26,150)( 27,143)( 28,144)( 29,145)( 30,146)( 31,159)( 32,160)( 33,161)
( 34,162)( 35,155)( 36,156)( 37,157)( 38,158)( 39,151)( 40,152)( 41,153)
( 42,154)( 43,167)( 44,168)( 45,169)( 46,170)( 47,163)( 48,164)( 49,165)
( 50,166)( 51,179)( 52,180)( 53,181)( 54,182)( 55,175)( 56,176)( 57,177)
( 58,178)( 59,171)( 60,172)( 61,173)( 62,174)( 63,187)( 64,188)( 65,189)
( 66,190)( 67,183)( 68,184)( 69,185)( 70,186)( 71,199)( 72,200)( 73,201)
( 74,202)( 75,195)( 76,196)( 77,197)( 78,198)( 79,191)( 80,192)( 81,193)
( 82,194)( 83,207)( 84,208)( 85,209)( 86,210)( 87,203)( 88,204)( 89,205)
( 90,206)( 91,219)( 92,220)( 93,221)( 94,222)( 95,215)( 96,216)( 97,217)
( 98,218)( 99,211)(100,212)(101,213)(102,214)(103,227)(104,228)(105,229)
(106,230)(107,223)(108,224)(109,225)(110,226)(111,239)(112,240)(113,241)
(114,242)(115,235)(116,236)(117,237)(118,238)(119,231)(120,232)(121,233)
(122,234);
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,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s3*s2*s1*s2*s3*s1*s2,
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