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Polytope of Type {2,3,6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,20}*1440
if this polytope has a name.
Group : SmallGroup(1440,5324)
Rank : 5
Schlafli Type : {2,3,6,20}
Number of vertices, edges, etc : 2, 3, 9, 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 : {2,3,6,10}*720
   3-fold quotients : {2,3,2,20}*480
   5-fold quotients : {2,3,6,4}*288
   6-fold quotients : {2,3,2,10}*240
   10-fold quotients : {2,3,6,2}*144
   12-fold quotients : {2,3,2,5}*120
   15-fold quotients : {2,3,2,4}*96
   30-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,273)(  4,274)(  5,275)(  6,276)(  7,277)(  8,283)(  9,284)( 10,285)
( 11,286)( 12,287)( 13,278)( 14,279)( 15,280)( 16,281)( 17,282)( 18,303)
( 19,304)( 20,305)( 21,306)( 22,307)( 23,313)( 24,314)( 25,315)( 26,316)
( 27,317)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)( 33,288)( 34,289)
( 35,290)( 36,291)( 37,292)( 38,298)( 39,299)( 40,300)( 41,301)( 42,302)
( 43,293)( 44,294)( 45,295)( 46,296)( 47,297)( 48,318)( 49,319)( 50,320)
( 51,321)( 52,322)( 53,328)( 54,329)( 55,330)( 56,331)( 57,332)( 58,323)
( 59,324)( 60,325)( 61,326)( 62,327)( 63,348)( 64,349)( 65,350)( 66,351)
( 67,352)( 68,358)( 69,359)( 70,360)( 71,361)( 72,362)( 73,353)( 74,354)
( 75,355)( 76,356)( 77,357)( 78,333)( 79,334)( 80,335)( 81,336)( 82,337)
( 83,343)( 84,344)( 85,345)( 86,346)( 87,347)( 88,338)( 89,339)( 90,340)
( 91,341)( 92,342)( 93,228)( 94,229)( 95,230)( 96,231)( 97,232)( 98,238)
( 99,239)(100,240)(101,241)(102,242)(103,233)(104,234)(105,235)(106,236)
(107,237)(108,258)(109,259)(110,260)(111,261)(112,262)(113,268)(114,269)
(115,270)(116,271)(117,272)(118,263)(119,264)(120,265)(121,266)(122,267)
(123,243)(124,244)(125,245)(126,246)(127,247)(128,253)(129,254)(130,255)
(131,256)(132,257)(133,248)(134,249)(135,250)(136,251)(137,252)(138,183)
(139,184)(140,185)(141,186)(142,187)(143,193)(144,194)(145,195)(146,196)
(147,197)(148,188)(149,189)(150,190)(151,191)(152,192)(153,213)(154,214)
(155,215)(156,216)(157,217)(158,223)(159,224)(160,225)(161,226)(162,227)
(163,218)(164,219)(165,220)(166,221)(167,222)(168,198)(169,199)(170,200)
(171,201)(172,202)(173,208)(174,209)(175,210)(176,211)(177,212)(178,203)
(179,204)(180,205)(181,206)(182,207);;
s2 := (  3,293)(  4,294)(  5,295)(  6,296)(  7,297)(  8,288)(  9,289)( 10,290)
( 11,291)( 12,292)( 13,298)( 14,299)( 15,300)( 16,301)( 17,302)( 18,278)
( 19,279)( 20,280)( 21,281)( 22,282)( 23,273)( 24,274)( 25,275)( 26,276)
( 27,277)( 28,283)( 29,284)( 30,285)( 31,286)( 32,287)( 33,308)( 34,309)
( 35,310)( 36,311)( 37,312)( 38,303)( 39,304)( 40,305)( 41,306)( 42,307)
( 43,313)( 44,314)( 45,315)( 46,316)( 47,317)( 48,338)( 49,339)( 50,340)
( 51,341)( 52,342)( 53,333)( 54,334)( 55,335)( 56,336)( 57,337)( 58,343)
( 59,344)( 60,345)( 61,346)( 62,347)( 63,323)( 64,324)( 65,325)( 66,326)
( 67,327)( 68,318)( 69,319)( 70,320)( 71,321)( 72,322)( 73,328)( 74,329)
( 75,330)( 76,331)( 77,332)( 78,353)( 79,354)( 80,355)( 81,356)( 82,357)
( 83,348)( 84,349)( 85,350)( 86,351)( 87,352)( 88,358)( 89,359)( 90,360)
( 91,361)( 92,362)( 93,248)( 94,249)( 95,250)( 96,251)( 97,252)( 98,243)
( 99,244)(100,245)(101,246)(102,247)(103,253)(104,254)(105,255)(106,256)
(107,257)(108,233)(109,234)(110,235)(111,236)(112,237)(113,228)(114,229)
(115,230)(116,231)(117,232)(118,238)(119,239)(120,240)(121,241)(122,242)
(123,263)(124,264)(125,265)(126,266)(127,267)(128,258)(129,259)(130,260)
(131,261)(132,262)(133,268)(134,269)(135,270)(136,271)(137,272)(138,203)
(139,204)(140,205)(141,206)(142,207)(143,198)(144,199)(145,200)(146,201)
(147,202)(148,208)(149,209)(150,210)(151,211)(152,212)(153,188)(154,189)
(155,190)(156,191)(157,192)(158,183)(159,184)(160,185)(161,186)(162,187)
(163,193)(164,194)(165,195)(166,196)(167,197)(168,218)(169,219)(170,220)
(171,221)(172,222)(173,213)(174,214)(175,215)(176,216)(177,217)(178,223)
(179,224)(180,225)(181,226)(182,227);;
s3 := (  3,183)(  4,187)(  5,186)(  6,185)(  7,184)(  8,193)(  9,197)( 10,196)
( 11,195)( 12,194)( 13,188)( 14,192)( 15,191)( 16,190)( 17,189)( 18,198)
( 19,202)( 20,201)( 21,200)( 22,199)( 23,208)( 24,212)( 25,211)( 26,210)
( 27,209)( 28,203)( 29,207)( 30,206)( 31,205)( 32,204)( 33,213)( 34,217)
( 35,216)( 36,215)( 37,214)( 38,223)( 39,227)( 40,226)( 41,225)( 42,224)
( 43,218)( 44,222)( 45,221)( 46,220)( 47,219)( 48,228)( 49,232)( 50,231)
( 51,230)( 52,229)( 53,238)( 54,242)( 55,241)( 56,240)( 57,239)( 58,233)
( 59,237)( 60,236)( 61,235)( 62,234)( 63,243)( 64,247)( 65,246)( 66,245)
( 67,244)( 68,253)( 69,257)( 70,256)( 71,255)( 72,254)( 73,248)( 74,252)
( 75,251)( 76,250)( 77,249)( 78,258)( 79,262)( 80,261)( 81,260)( 82,259)
( 83,268)( 84,272)( 85,271)( 86,270)( 87,269)( 88,263)( 89,267)( 90,266)
( 91,265)( 92,264)( 93,318)( 94,322)( 95,321)( 96,320)( 97,319)( 98,328)
( 99,332)(100,331)(101,330)(102,329)(103,323)(104,327)(105,326)(106,325)
(107,324)(108,333)(109,337)(110,336)(111,335)(112,334)(113,343)(114,347)
(115,346)(116,345)(117,344)(118,338)(119,342)(120,341)(121,340)(122,339)
(123,348)(124,352)(125,351)(126,350)(127,349)(128,358)(129,362)(130,361)
(131,360)(132,359)(133,353)(134,357)(135,356)(136,355)(137,354)(138,273)
(139,277)(140,276)(141,275)(142,274)(143,283)(144,287)(145,286)(146,285)
(147,284)(148,278)(149,282)(150,281)(151,280)(152,279)(153,288)(154,292)
(155,291)(156,290)(157,289)(158,298)(159,302)(160,301)(161,300)(162,299)
(163,293)(164,297)(165,296)(166,295)(167,294)(168,303)(169,307)(170,306)
(171,305)(172,304)(173,313)(174,317)(175,316)(176,315)(177,314)(178,308)
(179,312)(180,311)(181,310)(182,309);;
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, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)( 80, 82)
( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93,139)( 94,138)( 95,142)( 96,141)
( 97,140)( 98,144)( 99,143)(100,147)(101,146)(102,145)(103,149)(104,148)
(105,152)(106,151)(107,150)(108,154)(109,153)(110,157)(111,156)(112,155)
(113,159)(114,158)(115,162)(116,161)(117,160)(118,164)(119,163)(120,167)
(121,166)(122,165)(123,169)(124,168)(125,172)(126,171)(127,170)(128,174)
(129,173)(130,177)(131,176)(132,175)(133,179)(134,178)(135,182)(136,181)
(137,180)(183,229)(184,228)(185,232)(186,231)(187,230)(188,234)(189,233)
(190,237)(191,236)(192,235)(193,239)(194,238)(195,242)(196,241)(197,240)
(198,244)(199,243)(200,247)(201,246)(202,245)(203,249)(204,248)(205,252)
(206,251)(207,250)(208,254)(209,253)(210,257)(211,256)(212,255)(213,259)
(214,258)(215,262)(216,261)(217,260)(218,264)(219,263)(220,267)(221,266)
(222,265)(223,269)(224,268)(225,272)(226,271)(227,270)(273,274)(275,277)
(278,279)(280,282)(283,284)(285,287)(288,289)(290,292)(293,294)(295,297)
(298,299)(300,302)(303,304)(305,307)(308,309)(310,312)(313,314)(315,317)
(318,319)(320,322)(323,324)(325,327)(328,329)(330,332)(333,334)(335,337)
(338,339)(340,342)(343,344)(345,347)(348,349)(350,352)(353,354)(355,357)
(358,359)(360,362);;
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 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(362)!(1,2);
s1 := Sym(362)!(  3,273)(  4,274)(  5,275)(  6,276)(  7,277)(  8,283)(  9,284)
( 10,285)( 11,286)( 12,287)( 13,278)( 14,279)( 15,280)( 16,281)( 17,282)
( 18,303)( 19,304)( 20,305)( 21,306)( 22,307)( 23,313)( 24,314)( 25,315)
( 26,316)( 27,317)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)( 33,288)
( 34,289)( 35,290)( 36,291)( 37,292)( 38,298)( 39,299)( 40,300)( 41,301)
( 42,302)( 43,293)( 44,294)( 45,295)( 46,296)( 47,297)( 48,318)( 49,319)
( 50,320)( 51,321)( 52,322)( 53,328)( 54,329)( 55,330)( 56,331)( 57,332)
( 58,323)( 59,324)( 60,325)( 61,326)( 62,327)( 63,348)( 64,349)( 65,350)
( 66,351)( 67,352)( 68,358)( 69,359)( 70,360)( 71,361)( 72,362)( 73,353)
( 74,354)( 75,355)( 76,356)( 77,357)( 78,333)( 79,334)( 80,335)( 81,336)
( 82,337)( 83,343)( 84,344)( 85,345)( 86,346)( 87,347)( 88,338)( 89,339)
( 90,340)( 91,341)( 92,342)( 93,228)( 94,229)( 95,230)( 96,231)( 97,232)
( 98,238)( 99,239)(100,240)(101,241)(102,242)(103,233)(104,234)(105,235)
(106,236)(107,237)(108,258)(109,259)(110,260)(111,261)(112,262)(113,268)
(114,269)(115,270)(116,271)(117,272)(118,263)(119,264)(120,265)(121,266)
(122,267)(123,243)(124,244)(125,245)(126,246)(127,247)(128,253)(129,254)
(130,255)(131,256)(132,257)(133,248)(134,249)(135,250)(136,251)(137,252)
(138,183)(139,184)(140,185)(141,186)(142,187)(143,193)(144,194)(145,195)
(146,196)(147,197)(148,188)(149,189)(150,190)(151,191)(152,192)(153,213)
(154,214)(155,215)(156,216)(157,217)(158,223)(159,224)(160,225)(161,226)
(162,227)(163,218)(164,219)(165,220)(166,221)(167,222)(168,198)(169,199)
(170,200)(171,201)(172,202)(173,208)(174,209)(175,210)(176,211)(177,212)
(178,203)(179,204)(180,205)(181,206)(182,207);
s2 := Sym(362)!(  3,293)(  4,294)(  5,295)(  6,296)(  7,297)(  8,288)(  9,289)
( 10,290)( 11,291)( 12,292)( 13,298)( 14,299)( 15,300)( 16,301)( 17,302)
( 18,278)( 19,279)( 20,280)( 21,281)( 22,282)( 23,273)( 24,274)( 25,275)
( 26,276)( 27,277)( 28,283)( 29,284)( 30,285)( 31,286)( 32,287)( 33,308)
( 34,309)( 35,310)( 36,311)( 37,312)( 38,303)( 39,304)( 40,305)( 41,306)
( 42,307)( 43,313)( 44,314)( 45,315)( 46,316)( 47,317)( 48,338)( 49,339)
( 50,340)( 51,341)( 52,342)( 53,333)( 54,334)( 55,335)( 56,336)( 57,337)
( 58,343)( 59,344)( 60,345)( 61,346)( 62,347)( 63,323)( 64,324)( 65,325)
( 66,326)( 67,327)( 68,318)( 69,319)( 70,320)( 71,321)( 72,322)( 73,328)
( 74,329)( 75,330)( 76,331)( 77,332)( 78,353)( 79,354)( 80,355)( 81,356)
( 82,357)( 83,348)( 84,349)( 85,350)( 86,351)( 87,352)( 88,358)( 89,359)
( 90,360)( 91,361)( 92,362)( 93,248)( 94,249)( 95,250)( 96,251)( 97,252)
( 98,243)( 99,244)(100,245)(101,246)(102,247)(103,253)(104,254)(105,255)
(106,256)(107,257)(108,233)(109,234)(110,235)(111,236)(112,237)(113,228)
(114,229)(115,230)(116,231)(117,232)(118,238)(119,239)(120,240)(121,241)
(122,242)(123,263)(124,264)(125,265)(126,266)(127,267)(128,258)(129,259)
(130,260)(131,261)(132,262)(133,268)(134,269)(135,270)(136,271)(137,272)
(138,203)(139,204)(140,205)(141,206)(142,207)(143,198)(144,199)(145,200)
(146,201)(147,202)(148,208)(149,209)(150,210)(151,211)(152,212)(153,188)
(154,189)(155,190)(156,191)(157,192)(158,183)(159,184)(160,185)(161,186)
(162,187)(163,193)(164,194)(165,195)(166,196)(167,197)(168,218)(169,219)
(170,220)(171,221)(172,222)(173,213)(174,214)(175,215)(176,216)(177,217)
(178,223)(179,224)(180,225)(181,226)(182,227);
s3 := Sym(362)!(  3,183)(  4,187)(  5,186)(  6,185)(  7,184)(  8,193)(  9,197)
( 10,196)( 11,195)( 12,194)( 13,188)( 14,192)( 15,191)( 16,190)( 17,189)
( 18,198)( 19,202)( 20,201)( 21,200)( 22,199)( 23,208)( 24,212)( 25,211)
( 26,210)( 27,209)( 28,203)( 29,207)( 30,206)( 31,205)( 32,204)( 33,213)
( 34,217)( 35,216)( 36,215)( 37,214)( 38,223)( 39,227)( 40,226)( 41,225)
( 42,224)( 43,218)( 44,222)( 45,221)( 46,220)( 47,219)( 48,228)( 49,232)
( 50,231)( 51,230)( 52,229)( 53,238)( 54,242)( 55,241)( 56,240)( 57,239)
( 58,233)( 59,237)( 60,236)( 61,235)( 62,234)( 63,243)( 64,247)( 65,246)
( 66,245)( 67,244)( 68,253)( 69,257)( 70,256)( 71,255)( 72,254)( 73,248)
( 74,252)( 75,251)( 76,250)( 77,249)( 78,258)( 79,262)( 80,261)( 81,260)
( 82,259)( 83,268)( 84,272)( 85,271)( 86,270)( 87,269)( 88,263)( 89,267)
( 90,266)( 91,265)( 92,264)( 93,318)( 94,322)( 95,321)( 96,320)( 97,319)
( 98,328)( 99,332)(100,331)(101,330)(102,329)(103,323)(104,327)(105,326)
(106,325)(107,324)(108,333)(109,337)(110,336)(111,335)(112,334)(113,343)
(114,347)(115,346)(116,345)(117,344)(118,338)(119,342)(120,341)(121,340)
(122,339)(123,348)(124,352)(125,351)(126,350)(127,349)(128,358)(129,362)
(130,361)(131,360)(132,359)(133,353)(134,357)(135,356)(136,355)(137,354)
(138,273)(139,277)(140,276)(141,275)(142,274)(143,283)(144,287)(145,286)
(146,285)(147,284)(148,278)(149,282)(150,281)(151,280)(152,279)(153,288)
(154,292)(155,291)(156,290)(157,289)(158,298)(159,302)(160,301)(161,300)
(162,299)(163,293)(164,297)(165,296)(166,295)(167,294)(168,303)(169,307)
(170,306)(171,305)(172,304)(173,313)(174,317)(175,316)(176,315)(177,314)
(178,308)(179,312)(180,311)(181,310)(182,309);
s4 := Sym(362)!(  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, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)
( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93,139)( 94,138)( 95,142)
( 96,141)( 97,140)( 98,144)( 99,143)(100,147)(101,146)(102,145)(103,149)
(104,148)(105,152)(106,151)(107,150)(108,154)(109,153)(110,157)(111,156)
(112,155)(113,159)(114,158)(115,162)(116,161)(117,160)(118,164)(119,163)
(120,167)(121,166)(122,165)(123,169)(124,168)(125,172)(126,171)(127,170)
(128,174)(129,173)(130,177)(131,176)(132,175)(133,179)(134,178)(135,182)
(136,181)(137,180)(183,229)(184,228)(185,232)(186,231)(187,230)(188,234)
(189,233)(190,237)(191,236)(192,235)(193,239)(194,238)(195,242)(196,241)
(197,240)(198,244)(199,243)(200,247)(201,246)(202,245)(203,249)(204,248)
(205,252)(206,251)(207,250)(208,254)(209,253)(210,257)(211,256)(212,255)
(213,259)(214,258)(215,262)(216,261)(217,260)(218,264)(219,263)(220,267)
(221,266)(222,265)(223,269)(224,268)(225,272)(226,271)(227,270)(273,274)
(275,277)(278,279)(280,282)(283,284)(285,287)(288,289)(290,292)(293,294)
(295,297)(298,299)(300,302)(303,304)(305,307)(308,309)(310,312)(313,314)
(315,317)(318,319)(320,322)(323,324)(325,327)(328,329)(330,332)(333,334)
(335,337)(338,339)(340,342)(343,344)(345,347)(348,349)(350,352)(353,354)
(355,357)(358,359)(360,362);
poly := sub<Sym(362)|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, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
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 >; 
 

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