Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,3,6,20}*1440

Overview

Group
SmallGroup(1440,5324)
Rank
5
Schläfli Type
{2,3,6,20}
Vertices, edges, …
2, 3, 9, 60, 20
Order of s0s1s2s3s4
60
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

5-fold

6-fold

10-fold

12-fold

15-fold

30-fold

Covers minimal covers in bold

None in this atlas.

Representations

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 >;