Polytope of Type {2,20,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,4,3}*1920
if this polytope has a name.
Group : SmallGroup(1920,240142)
Rank : 5
Schlafli Type : {2,20,4,3}
Number of vertices, edges, etc : 2, 20, 80, 12, 6
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 : {2,10,4,3}*960
4-fold quotients : {2,20,2,3}*480
5-fold quotients : {2,4,4,3}*384b
8-fold quotients : {2,10,2,3}*240
10-fold quotients : {2,2,4,3}*192
16-fold quotients : {2,5,2,3}*120
20-fold quotients : {2,4,2,3}*96, {2,2,4,3}*96
40-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)( 34, 38)
( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)( 54, 58)
( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)( 74, 78)
( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)(114,118)
(123,183)(124,184)(125,185)(126,186)(127,199)(128,200)(129,201)(130,202)
(131,195)(132,196)(133,197)(134,198)(135,191)(136,192)(137,193)(138,194)
(139,187)(140,188)(141,189)(142,190)(143,203)(144,204)(145,205)(146,206)
(147,219)(148,220)(149,221)(150,222)(151,215)(152,216)(153,217)(154,218)
(155,211)(156,212)(157,213)(158,214)(159,207)(160,208)(161,209)(162,210)
(163,223)(164,224)(165,225)(166,226)(167,239)(168,240)(169,241)(170,242)
(171,235)(172,236)(173,237)(174,238)(175,231)(176,232)(177,233)(178,234)
(179,227)(180,228)(181,229)(182,230);;
s2 := ( 3,129)( 4,130)( 5,127)( 6,128)( 7,125)( 8,126)( 9,123)( 10,124)
( 11,141)( 12,142)( 13,139)( 14,140)( 15,137)( 16,138)( 17,135)( 18,136)
( 19,133)( 20,134)( 21,131)( 22,132)( 23,149)( 24,150)( 25,147)( 26,148)
( 27,145)( 28,146)( 29,143)( 30,144)( 31,161)( 32,162)( 33,159)( 34,160)
( 35,157)( 36,158)( 37,155)( 38,156)( 39,153)( 40,154)( 41,151)( 42,152)
( 43,169)( 44,170)( 45,167)( 46,168)( 47,165)( 48,166)( 49,163)( 50,164)
( 51,181)( 52,182)( 53,179)( 54,180)( 55,177)( 56,178)( 57,175)( 58,176)
( 59,173)( 60,174)( 61,171)( 62,172)( 63,189)( 64,190)( 65,187)( 66,188)
( 67,185)( 68,186)( 69,183)( 70,184)( 71,201)( 72,202)( 73,199)( 74,200)
( 75,197)( 76,198)( 77,195)( 78,196)( 79,193)( 80,194)( 81,191)( 82,192)
( 83,209)( 84,210)( 85,207)( 86,208)( 87,205)( 88,206)( 89,203)( 90,204)
( 91,221)( 92,222)( 93,219)( 94,220)( 95,217)( 96,218)( 97,215)( 98,216)
( 99,213)(100,214)(101,211)(102,212)(103,229)(104,230)(105,227)(106,228)
(107,225)(108,226)(109,223)(110,224)(111,241)(112,242)(113,239)(114,240)
(115,237)(116,238)(117,235)(118,236)(119,233)(120,234)(121,231)(122,232);;
s3 := ( 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);;
s4 := ( 3, 43)( 4, 46)( 5, 45)( 6, 44)( 7, 47)( 8, 50)( 9, 49)( 10, 48)
( 11, 51)( 12, 54)( 13, 53)( 14, 52)( 15, 55)( 16, 58)( 17, 57)( 18, 56)
( 19, 59)( 20, 62)( 21, 61)( 22, 60)( 24, 26)( 28, 30)( 32, 34)( 36, 38)
( 40, 42)( 63,103)( 64,106)( 65,105)( 66,104)( 67,107)( 68,110)( 69,109)
( 70,108)( 71,111)( 72,114)( 73,113)( 74,112)( 75,115)( 76,118)( 77,117)
( 78,116)( 79,119)( 80,122)( 81,121)( 82,120)( 84, 86)( 88, 90)( 92, 94)
( 96, 98)(100,102)(123,163)(124,166)(125,165)(126,164)(127,167)(128,170)
(129,169)(130,168)(131,171)(132,174)(133,173)(134,172)(135,175)(136,178)
(137,177)(138,176)(139,179)(140,182)(141,181)(142,180)(144,146)(148,150)
(152,154)(156,158)(160,162)(183,223)(184,226)(185,225)(186,224)(187,227)
(188,230)(189,229)(190,228)(191,231)(192,234)(193,233)(194,232)(195,235)
(196,238)(197,237)(198,236)(199,239)(200,242)(201,241)(202,240)(204,206)
(208,210)(212,214)(216,218)(220,222);;
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,
s3*s4*s3*s4*s3*s4, 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*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)!( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)
( 14, 18)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)
( 34, 38)( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)
( 54, 58)( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)
( 74, 78)( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)
(114,118)(123,183)(124,184)(125,185)(126,186)(127,199)(128,200)(129,201)
(130,202)(131,195)(132,196)(133,197)(134,198)(135,191)(136,192)(137,193)
(138,194)(139,187)(140,188)(141,189)(142,190)(143,203)(144,204)(145,205)
(146,206)(147,219)(148,220)(149,221)(150,222)(151,215)(152,216)(153,217)
(154,218)(155,211)(156,212)(157,213)(158,214)(159,207)(160,208)(161,209)
(162,210)(163,223)(164,224)(165,225)(166,226)(167,239)(168,240)(169,241)
(170,242)(171,235)(172,236)(173,237)(174,238)(175,231)(176,232)(177,233)
(178,234)(179,227)(180,228)(181,229)(182,230);
s2 := Sym(242)!( 3,129)( 4,130)( 5,127)( 6,128)( 7,125)( 8,126)( 9,123)
( 10,124)( 11,141)( 12,142)( 13,139)( 14,140)( 15,137)( 16,138)( 17,135)
( 18,136)( 19,133)( 20,134)( 21,131)( 22,132)( 23,149)( 24,150)( 25,147)
( 26,148)( 27,145)( 28,146)( 29,143)( 30,144)( 31,161)( 32,162)( 33,159)
( 34,160)( 35,157)( 36,158)( 37,155)( 38,156)( 39,153)( 40,154)( 41,151)
( 42,152)( 43,169)( 44,170)( 45,167)( 46,168)( 47,165)( 48,166)( 49,163)
( 50,164)( 51,181)( 52,182)( 53,179)( 54,180)( 55,177)( 56,178)( 57,175)
( 58,176)( 59,173)( 60,174)( 61,171)( 62,172)( 63,189)( 64,190)( 65,187)
( 66,188)( 67,185)( 68,186)( 69,183)( 70,184)( 71,201)( 72,202)( 73,199)
( 74,200)( 75,197)( 76,198)( 77,195)( 78,196)( 79,193)( 80,194)( 81,191)
( 82,192)( 83,209)( 84,210)( 85,207)( 86,208)( 87,205)( 88,206)( 89,203)
( 90,204)( 91,221)( 92,222)( 93,219)( 94,220)( 95,217)( 96,218)( 97,215)
( 98,216)( 99,213)(100,214)(101,211)(102,212)(103,229)(104,230)(105,227)
(106,228)(107,225)(108,226)(109,223)(110,224)(111,241)(112,242)(113,239)
(114,240)(115,237)(116,238)(117,235)(118,236)(119,233)(120,234)(121,231)
(122,232);
s3 := 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);
s4 := Sym(242)!( 3, 43)( 4, 46)( 5, 45)( 6, 44)( 7, 47)( 8, 50)( 9, 49)
( 10, 48)( 11, 51)( 12, 54)( 13, 53)( 14, 52)( 15, 55)( 16, 58)( 17, 57)
( 18, 56)( 19, 59)( 20, 62)( 21, 61)( 22, 60)( 24, 26)( 28, 30)( 32, 34)
( 36, 38)( 40, 42)( 63,103)( 64,106)( 65,105)( 66,104)( 67,107)( 68,110)
( 69,109)( 70,108)( 71,111)( 72,114)( 73,113)( 74,112)( 75,115)( 76,118)
( 77,117)( 78,116)( 79,119)( 80,122)( 81,121)( 82,120)( 84, 86)( 88, 90)
( 92, 94)( 96, 98)(100,102)(123,163)(124,166)(125,165)(126,164)(127,167)
(128,170)(129,169)(130,168)(131,171)(132,174)(133,173)(134,172)(135,175)
(136,178)(137,177)(138,176)(139,179)(140,182)(141,181)(142,180)(144,146)
(148,150)(152,154)(156,158)(160,162)(183,223)(184,226)(185,225)(186,224)
(187,227)(188,230)(189,229)(190,228)(191,231)(192,234)(193,233)(194,232)
(195,235)(196,238)(197,237)(198,236)(199,239)(200,242)(201,241)(202,240)
(204,206)(208,210)(212,214)(216,218)(220,222);
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, s3*s4*s3*s4*s3*s4,
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope