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