Polytope of Type {2,20,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6,3}*1920
if this polytope has a name.
Group : SmallGroup(1920,240142)
Rank : 5
Schlafli Type : {2,20,6,3}
Number of vertices, edges, etc : 2, 20, 80, 12, 4
Order of s0s1s2s3s4 : 20
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 : {2,10,6,3}*960
5-fold quotients : {2,4,6,3}*384
10-fold quotients : {2,2,6,3}*192
20-fold quotients : {2,2,3,3}*96
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 := ( 3,127)( 4,129)( 5,128)( 6,130)( 7,123)( 8,125)( 9,124)( 10,126)
( 11,139)( 12,141)( 13,140)( 14,142)( 15,135)( 16,137)( 17,136)( 18,138)
( 19,131)( 20,133)( 21,132)( 22,134)( 23,167)( 24,169)( 25,168)( 26,170)
( 27,163)( 28,165)( 29,164)( 30,166)( 31,179)( 32,181)( 33,180)( 34,182)
( 35,175)( 36,177)( 37,176)( 38,178)( 39,171)( 40,173)( 41,172)( 42,174)
( 43,147)( 44,149)( 45,148)( 46,150)( 47,143)( 48,145)( 49,144)( 50,146)
( 51,159)( 52,161)( 53,160)( 54,162)( 55,155)( 56,157)( 57,156)( 58,158)
( 59,151)( 60,153)( 61,152)( 62,154)( 63,187)( 64,189)( 65,188)( 66,190)
( 67,183)( 68,185)( 69,184)( 70,186)( 71,199)( 72,201)( 73,200)( 74,202)
( 75,195)( 76,197)( 77,196)( 78,198)( 79,191)( 80,193)( 81,192)( 82,194)
( 83,227)( 84,229)( 85,228)( 86,230)( 87,223)( 88,225)( 89,224)( 90,226)
( 91,239)( 92,241)( 93,240)( 94,242)( 95,235)( 96,237)( 97,236)( 98,238)
( 99,231)(100,233)(101,232)(102,234)(103,207)(104,209)(105,208)(106,210)
(107,203)(108,205)(109,204)(110,206)(111,219)(112,221)(113,220)(114,222)
(115,215)(116,217)(117,216)(118,218)(119,211)(120,213)(121,212)(122,214);;
s3 := ( 3, 23)( 4, 24)( 5, 26)( 6, 25)( 7, 27)( 8, 28)( 9, 30)( 10, 29)
( 11, 31)( 12, 32)( 13, 34)( 14, 33)( 15, 35)( 16, 36)( 17, 38)( 18, 37)
( 19, 39)( 20, 40)( 21, 42)( 22, 41)( 45, 46)( 49, 50)( 53, 54)( 57, 58)
( 61, 62)( 63, 83)( 64, 84)( 65, 86)( 66, 85)( 67, 87)( 68, 88)( 69, 90)
( 70, 89)( 71, 91)( 72, 92)( 73, 94)( 74, 93)( 75, 95)( 76, 96)( 77, 98)
( 78, 97)( 79, 99)( 80,100)( 81,102)( 82,101)(105,106)(109,110)(113,114)
(117,118)(121,122)(123,143)(124,144)(125,146)(126,145)(127,147)(128,148)
(129,150)(130,149)(131,151)(132,152)(133,154)(134,153)(135,155)(136,156)
(137,158)(138,157)(139,159)(140,160)(141,162)(142,161)(165,166)(169,170)
(173,174)(177,178)(181,182)(183,203)(184,204)(185,206)(186,205)(187,207)
(188,208)(189,210)(190,209)(191,211)(192,212)(193,214)(194,213)(195,215)
(196,216)(197,218)(198,217)(199,219)(200,220)(201,222)(202,221)(225,226)
(229,230)(233,234)(237,238)(241,242);;
s4 := ( 3, 6)( 7, 10)( 11, 14)( 15, 18)( 19, 22)( 23, 46)( 24, 44)( 25, 45)
( 26, 43)( 27, 50)( 28, 48)( 29, 49)( 30, 47)( 31, 54)( 32, 52)( 33, 53)
( 34, 51)( 35, 58)( 36, 56)( 37, 57)( 38, 55)( 39, 62)( 40, 60)( 41, 61)
( 42, 59)( 63, 66)( 67, 70)( 71, 74)( 75, 78)( 79, 82)( 83,106)( 84,104)
( 85,105)( 86,103)( 87,110)( 88,108)( 89,109)( 90,107)( 91,114)( 92,112)
( 93,113)( 94,111)( 95,118)( 96,116)( 97,117)( 98,115)( 99,122)(100,120)
(101,121)(102,119)(123,126)(127,130)(131,134)(135,138)(139,142)(143,166)
(144,164)(145,165)(146,163)(147,170)(148,168)(149,169)(150,167)(151,174)
(152,172)(153,173)(154,171)(155,178)(156,176)(157,177)(158,175)(159,182)
(160,180)(161,181)(162,179)(183,186)(187,190)(191,194)(195,198)(199,202)
(203,226)(204,224)(205,225)(206,223)(207,230)(208,228)(209,229)(210,227)
(211,234)(212,232)(213,233)(214,231)(215,238)(216,236)(217,237)(218,235)
(219,242)(220,240)(221,241)(222,239);;
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*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
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)!( 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)!( 3,127)( 4,129)( 5,128)( 6,130)( 7,123)( 8,125)( 9,124)
( 10,126)( 11,139)( 12,141)( 13,140)( 14,142)( 15,135)( 16,137)( 17,136)
( 18,138)( 19,131)( 20,133)( 21,132)( 22,134)( 23,167)( 24,169)( 25,168)
( 26,170)( 27,163)( 28,165)( 29,164)( 30,166)( 31,179)( 32,181)( 33,180)
( 34,182)( 35,175)( 36,177)( 37,176)( 38,178)( 39,171)( 40,173)( 41,172)
( 42,174)( 43,147)( 44,149)( 45,148)( 46,150)( 47,143)( 48,145)( 49,144)
( 50,146)( 51,159)( 52,161)( 53,160)( 54,162)( 55,155)( 56,157)( 57,156)
( 58,158)( 59,151)( 60,153)( 61,152)( 62,154)( 63,187)( 64,189)( 65,188)
( 66,190)( 67,183)( 68,185)( 69,184)( 70,186)( 71,199)( 72,201)( 73,200)
( 74,202)( 75,195)( 76,197)( 77,196)( 78,198)( 79,191)( 80,193)( 81,192)
( 82,194)( 83,227)( 84,229)( 85,228)( 86,230)( 87,223)( 88,225)( 89,224)
( 90,226)( 91,239)( 92,241)( 93,240)( 94,242)( 95,235)( 96,237)( 97,236)
( 98,238)( 99,231)(100,233)(101,232)(102,234)(103,207)(104,209)(105,208)
(106,210)(107,203)(108,205)(109,204)(110,206)(111,219)(112,221)(113,220)
(114,222)(115,215)(116,217)(117,216)(118,218)(119,211)(120,213)(121,212)
(122,214);
s3 := Sym(242)!( 3, 23)( 4, 24)( 5, 26)( 6, 25)( 7, 27)( 8, 28)( 9, 30)
( 10, 29)( 11, 31)( 12, 32)( 13, 34)( 14, 33)( 15, 35)( 16, 36)( 17, 38)
( 18, 37)( 19, 39)( 20, 40)( 21, 42)( 22, 41)( 45, 46)( 49, 50)( 53, 54)
( 57, 58)( 61, 62)( 63, 83)( 64, 84)( 65, 86)( 66, 85)( 67, 87)( 68, 88)
( 69, 90)( 70, 89)( 71, 91)( 72, 92)( 73, 94)( 74, 93)( 75, 95)( 76, 96)
( 77, 98)( 78, 97)( 79, 99)( 80,100)( 81,102)( 82,101)(105,106)(109,110)
(113,114)(117,118)(121,122)(123,143)(124,144)(125,146)(126,145)(127,147)
(128,148)(129,150)(130,149)(131,151)(132,152)(133,154)(134,153)(135,155)
(136,156)(137,158)(138,157)(139,159)(140,160)(141,162)(142,161)(165,166)
(169,170)(173,174)(177,178)(181,182)(183,203)(184,204)(185,206)(186,205)
(187,207)(188,208)(189,210)(190,209)(191,211)(192,212)(193,214)(194,213)
(195,215)(196,216)(197,218)(198,217)(199,219)(200,220)(201,222)(202,221)
(225,226)(229,230)(233,234)(237,238)(241,242);
s4 := Sym(242)!( 3, 6)( 7, 10)( 11, 14)( 15, 18)( 19, 22)( 23, 46)( 24, 44)
( 25, 45)( 26, 43)( 27, 50)( 28, 48)( 29, 49)( 30, 47)( 31, 54)( 32, 52)
( 33, 53)( 34, 51)( 35, 58)( 36, 56)( 37, 57)( 38, 55)( 39, 62)( 40, 60)
( 41, 61)( 42, 59)( 63, 66)( 67, 70)( 71, 74)( 75, 78)( 79, 82)( 83,106)
( 84,104)( 85,105)( 86,103)( 87,110)( 88,108)( 89,109)( 90,107)( 91,114)
( 92,112)( 93,113)( 94,111)( 95,118)( 96,116)( 97,117)( 98,115)( 99,122)
(100,120)(101,121)(102,119)(123,126)(127,130)(131,134)(135,138)(139,142)
(143,166)(144,164)(145,165)(146,163)(147,170)(148,168)(149,169)(150,167)
(151,174)(152,172)(153,173)(154,171)(155,178)(156,176)(157,177)(158,175)
(159,182)(160,180)(161,181)(162,179)(183,186)(187,190)(191,194)(195,198)
(199,202)(203,226)(204,224)(205,225)(206,223)(207,230)(208,228)(209,229)
(210,227)(211,234)(212,232)(213,233)(214,231)(215,238)(216,236)(217,237)
(218,235)(219,242)(220,240)(221,241)(222,239);
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*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
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