Polytope of Type {20,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,3}*720
if this polytope has a name.
Group : SmallGroup(720,500)
Rank : 4
Schlafli Type : {20,6,3}
Number of vertices, edges, etc : 20, 60, 9, 3
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,6,3,2} of size 1440
Vertex Figure Of :
{2,20,6,3} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,6,3}*360
3-fold quotients : {20,2,3}*240
5-fold quotients : {4,6,3}*144
6-fold quotients : {10,2,3}*120
10-fold quotients : {2,6,3}*72
12-fold quotients : {5,2,3}*60
15-fold quotients : {4,2,3}*48
30-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {40,6,3}*1440, {20,6,6}*1440c
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 91,136)( 92,140)( 93,139)( 94,138)
( 95,137)( 96,141)( 97,145)( 98,144)( 99,143)(100,142)(101,146)(102,150)
(103,149)(104,148)(105,147)(106,151)(107,155)(108,154)(109,153)(110,152)
(111,156)(112,160)(113,159)(114,158)(115,157)(116,161)(117,165)(118,164)
(119,163)(120,162)(121,166)(122,170)(123,169)(124,168)(125,167)(126,171)
(127,175)(128,174)(129,173)(130,172)(131,176)(132,180)(133,179)(134,178)
(135,177)(181,226)(182,230)(183,229)(184,228)(185,227)(186,231)(187,235)
(188,234)(189,233)(190,232)(191,236)(192,240)(193,239)(194,238)(195,237)
(196,241)(197,245)(198,244)(199,243)(200,242)(201,246)(202,250)(203,249)
(204,248)(205,247)(206,251)(207,255)(208,254)(209,253)(210,252)(211,256)
(212,260)(213,259)(214,258)(215,257)(216,261)(217,265)(218,264)(219,263)
(220,262)(221,266)(222,270)(223,269)(224,268)(225,267)(272,275)(273,274)
(277,280)(278,279)(282,285)(283,284)(287,290)(288,289)(292,295)(293,294)
(297,300)(298,299)(302,305)(303,304)(307,310)(308,309)(312,315)(313,314)
(317,320)(318,319)(322,325)(323,324)(327,330)(328,329)(332,335)(333,334)
(337,340)(338,339)(342,345)(343,344)(347,350)(348,349)(352,355)(353,354)
(357,360)(358,359);;
s1 := ( 1,182)( 2,181)( 3,185)( 4,184)( 5,183)( 6,192)( 7,191)( 8,195)
( 9,194)( 10,193)( 11,187)( 12,186)( 13,190)( 14,189)( 15,188)( 16,197)
( 17,196)( 18,200)( 19,199)( 20,198)( 21,207)( 22,206)( 23,210)( 24,209)
( 25,208)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,212)( 32,211)
( 33,215)( 34,214)( 35,213)( 36,222)( 37,221)( 38,225)( 39,224)( 40,223)
( 41,217)( 42,216)( 43,220)( 44,219)( 45,218)( 46,227)( 47,226)( 48,230)
( 49,229)( 50,228)( 51,237)( 52,236)( 53,240)( 54,239)( 55,238)( 56,232)
( 57,231)( 58,235)( 59,234)( 60,233)( 61,242)( 62,241)( 63,245)( 64,244)
( 65,243)( 66,252)( 67,251)( 68,255)( 69,254)( 70,253)( 71,247)( 72,246)
( 73,250)( 74,249)( 75,248)( 76,257)( 77,256)( 78,260)( 79,259)( 80,258)
( 81,267)( 82,266)( 83,270)( 84,269)( 85,268)( 86,262)( 87,261)( 88,265)
( 89,264)( 90,263)( 91,317)( 92,316)( 93,320)( 94,319)( 95,318)( 96,327)
( 97,326)( 98,330)( 99,329)(100,328)(101,322)(102,321)(103,325)(104,324)
(105,323)(106,332)(107,331)(108,335)(109,334)(110,333)(111,342)(112,341)
(113,345)(114,344)(115,343)(116,337)(117,336)(118,340)(119,339)(120,338)
(121,347)(122,346)(123,350)(124,349)(125,348)(126,357)(127,356)(128,360)
(129,359)(130,358)(131,352)(132,351)(133,355)(134,354)(135,353)(136,272)
(137,271)(138,275)(139,274)(140,273)(141,282)(142,281)(143,285)(144,284)
(145,283)(146,277)(147,276)(148,280)(149,279)(150,278)(151,287)(152,286)
(153,290)(154,289)(155,288)(156,297)(157,296)(158,300)(159,299)(160,298)
(161,292)(162,291)(163,295)(164,294)(165,293)(166,302)(167,301)(168,305)
(169,304)(170,303)(171,312)(172,311)(173,315)(174,314)(175,313)(176,307)
(177,306)(178,310)(179,309)(180,308);;
s2 := ( 1,276)( 2,277)( 3,278)( 4,279)( 5,280)( 6,271)( 7,272)( 8,273)
( 9,274)( 10,275)( 11,281)( 12,282)( 13,283)( 14,284)( 15,285)( 16,306)
( 17,307)( 18,308)( 19,309)( 20,310)( 21,301)( 22,302)( 23,303)( 24,304)
( 25,305)( 26,311)( 27,312)( 28,313)( 29,314)( 30,315)( 31,291)( 32,292)
( 33,293)( 34,294)( 35,295)( 36,286)( 37,287)( 38,288)( 39,289)( 40,290)
( 41,296)( 42,297)( 43,298)( 44,299)( 45,300)( 46,321)( 47,322)( 48,323)
( 49,324)( 50,325)( 51,316)( 52,317)( 53,318)( 54,319)( 55,320)( 56,326)
( 57,327)( 58,328)( 59,329)( 60,330)( 61,351)( 62,352)( 63,353)( 64,354)
( 65,355)( 66,346)( 67,347)( 68,348)( 69,349)( 70,350)( 71,356)( 72,357)
( 73,358)( 74,359)( 75,360)( 76,336)( 77,337)( 78,338)( 79,339)( 80,340)
( 81,331)( 82,332)( 83,333)( 84,334)( 85,335)( 86,341)( 87,342)( 88,343)
( 89,344)( 90,345)( 91,231)( 92,232)( 93,233)( 94,234)( 95,235)( 96,226)
( 97,227)( 98,228)( 99,229)(100,230)(101,236)(102,237)(103,238)(104,239)
(105,240)(106,261)(107,262)(108,263)(109,264)(110,265)(111,256)(112,257)
(113,258)(114,259)(115,260)(116,266)(117,267)(118,268)(119,269)(120,270)
(121,246)(122,247)(123,248)(124,249)(125,250)(126,241)(127,242)(128,243)
(129,244)(130,245)(131,251)(132,252)(133,253)(134,254)(135,255)(136,186)
(137,187)(138,188)(139,189)(140,190)(141,181)(142,182)(143,183)(144,184)
(145,185)(146,191)(147,192)(148,193)(149,194)(150,195)(151,216)(152,217)
(153,218)(154,219)(155,220)(156,211)(157,212)(158,213)(159,214)(160,215)
(161,221)(162,222)(163,223)(164,224)(165,225)(166,201)(167,202)(168,203)
(169,204)(170,205)(171,196)(172,197)(173,198)(174,199)(175,200)(176,206)
(177,207)(178,208)(179,209)(180,210);;
s3 := ( 1,286)( 2,287)( 3,288)( 4,289)( 5,290)( 6,296)( 7,297)( 8,298)
( 9,299)( 10,300)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,271)
( 17,272)( 18,273)( 19,274)( 20,275)( 21,281)( 22,282)( 23,283)( 24,284)
( 25,285)( 26,276)( 27,277)( 28,278)( 29,279)( 30,280)( 31,301)( 32,302)
( 33,303)( 34,304)( 35,305)( 36,311)( 37,312)( 38,313)( 39,314)( 40,315)
( 41,306)( 42,307)( 43,308)( 44,309)( 45,310)( 46,331)( 47,332)( 48,333)
( 49,334)( 50,335)( 51,341)( 52,342)( 53,343)( 54,344)( 55,345)( 56,336)
( 57,337)( 58,338)( 59,339)( 60,340)( 61,316)( 62,317)( 63,318)( 64,319)
( 65,320)( 66,326)( 67,327)( 68,328)( 69,329)( 70,330)( 71,321)( 72,322)
( 73,323)( 74,324)( 75,325)( 76,346)( 77,347)( 78,348)( 79,349)( 80,350)
( 81,356)( 82,357)( 83,358)( 84,359)( 85,360)( 86,351)( 87,352)( 88,353)
( 89,354)( 90,355)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,251)
( 97,252)( 98,253)( 99,254)(100,255)(101,246)(102,247)(103,248)(104,249)
(105,250)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)(112,237)
(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)(120,235)
(121,256)(122,257)(123,258)(124,259)(125,260)(126,266)(127,267)(128,268)
(129,269)(130,270)(131,261)(132,262)(133,263)(134,264)(135,265)(136,196)
(137,197)(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)(144,209)
(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,181)(152,182)
(153,183)(154,184)(155,185)(156,191)(157,192)(158,193)(159,194)(160,195)
(161,186)(162,187)(163,188)(164,189)(165,190)(166,211)(167,212)(168,213)
(169,214)(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)(176,216)
(177,217)(178,218)(179,219)(180,220);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(360)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 91,136)( 92,140)( 93,139)
( 94,138)( 95,137)( 96,141)( 97,145)( 98,144)( 99,143)(100,142)(101,146)
(102,150)(103,149)(104,148)(105,147)(106,151)(107,155)(108,154)(109,153)
(110,152)(111,156)(112,160)(113,159)(114,158)(115,157)(116,161)(117,165)
(118,164)(119,163)(120,162)(121,166)(122,170)(123,169)(124,168)(125,167)
(126,171)(127,175)(128,174)(129,173)(130,172)(131,176)(132,180)(133,179)
(134,178)(135,177)(181,226)(182,230)(183,229)(184,228)(185,227)(186,231)
(187,235)(188,234)(189,233)(190,232)(191,236)(192,240)(193,239)(194,238)
(195,237)(196,241)(197,245)(198,244)(199,243)(200,242)(201,246)(202,250)
(203,249)(204,248)(205,247)(206,251)(207,255)(208,254)(209,253)(210,252)
(211,256)(212,260)(213,259)(214,258)(215,257)(216,261)(217,265)(218,264)
(219,263)(220,262)(221,266)(222,270)(223,269)(224,268)(225,267)(272,275)
(273,274)(277,280)(278,279)(282,285)(283,284)(287,290)(288,289)(292,295)
(293,294)(297,300)(298,299)(302,305)(303,304)(307,310)(308,309)(312,315)
(313,314)(317,320)(318,319)(322,325)(323,324)(327,330)(328,329)(332,335)
(333,334)(337,340)(338,339)(342,345)(343,344)(347,350)(348,349)(352,355)
(353,354)(357,360)(358,359);
s1 := Sym(360)!( 1,182)( 2,181)( 3,185)( 4,184)( 5,183)( 6,192)( 7,191)
( 8,195)( 9,194)( 10,193)( 11,187)( 12,186)( 13,190)( 14,189)( 15,188)
( 16,197)( 17,196)( 18,200)( 19,199)( 20,198)( 21,207)( 22,206)( 23,210)
( 24,209)( 25,208)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,212)
( 32,211)( 33,215)( 34,214)( 35,213)( 36,222)( 37,221)( 38,225)( 39,224)
( 40,223)( 41,217)( 42,216)( 43,220)( 44,219)( 45,218)( 46,227)( 47,226)
( 48,230)( 49,229)( 50,228)( 51,237)( 52,236)( 53,240)( 54,239)( 55,238)
( 56,232)( 57,231)( 58,235)( 59,234)( 60,233)( 61,242)( 62,241)( 63,245)
( 64,244)( 65,243)( 66,252)( 67,251)( 68,255)( 69,254)( 70,253)( 71,247)
( 72,246)( 73,250)( 74,249)( 75,248)( 76,257)( 77,256)( 78,260)( 79,259)
( 80,258)( 81,267)( 82,266)( 83,270)( 84,269)( 85,268)( 86,262)( 87,261)
( 88,265)( 89,264)( 90,263)( 91,317)( 92,316)( 93,320)( 94,319)( 95,318)
( 96,327)( 97,326)( 98,330)( 99,329)(100,328)(101,322)(102,321)(103,325)
(104,324)(105,323)(106,332)(107,331)(108,335)(109,334)(110,333)(111,342)
(112,341)(113,345)(114,344)(115,343)(116,337)(117,336)(118,340)(119,339)
(120,338)(121,347)(122,346)(123,350)(124,349)(125,348)(126,357)(127,356)
(128,360)(129,359)(130,358)(131,352)(132,351)(133,355)(134,354)(135,353)
(136,272)(137,271)(138,275)(139,274)(140,273)(141,282)(142,281)(143,285)
(144,284)(145,283)(146,277)(147,276)(148,280)(149,279)(150,278)(151,287)
(152,286)(153,290)(154,289)(155,288)(156,297)(157,296)(158,300)(159,299)
(160,298)(161,292)(162,291)(163,295)(164,294)(165,293)(166,302)(167,301)
(168,305)(169,304)(170,303)(171,312)(172,311)(173,315)(174,314)(175,313)
(176,307)(177,306)(178,310)(179,309)(180,308);
s2 := Sym(360)!( 1,276)( 2,277)( 3,278)( 4,279)( 5,280)( 6,271)( 7,272)
( 8,273)( 9,274)( 10,275)( 11,281)( 12,282)( 13,283)( 14,284)( 15,285)
( 16,306)( 17,307)( 18,308)( 19,309)( 20,310)( 21,301)( 22,302)( 23,303)
( 24,304)( 25,305)( 26,311)( 27,312)( 28,313)( 29,314)( 30,315)( 31,291)
( 32,292)( 33,293)( 34,294)( 35,295)( 36,286)( 37,287)( 38,288)( 39,289)
( 40,290)( 41,296)( 42,297)( 43,298)( 44,299)( 45,300)( 46,321)( 47,322)
( 48,323)( 49,324)( 50,325)( 51,316)( 52,317)( 53,318)( 54,319)( 55,320)
( 56,326)( 57,327)( 58,328)( 59,329)( 60,330)( 61,351)( 62,352)( 63,353)
( 64,354)( 65,355)( 66,346)( 67,347)( 68,348)( 69,349)( 70,350)( 71,356)
( 72,357)( 73,358)( 74,359)( 75,360)( 76,336)( 77,337)( 78,338)( 79,339)
( 80,340)( 81,331)( 82,332)( 83,333)( 84,334)( 85,335)( 86,341)( 87,342)
( 88,343)( 89,344)( 90,345)( 91,231)( 92,232)( 93,233)( 94,234)( 95,235)
( 96,226)( 97,227)( 98,228)( 99,229)(100,230)(101,236)(102,237)(103,238)
(104,239)(105,240)(106,261)(107,262)(108,263)(109,264)(110,265)(111,256)
(112,257)(113,258)(114,259)(115,260)(116,266)(117,267)(118,268)(119,269)
(120,270)(121,246)(122,247)(123,248)(124,249)(125,250)(126,241)(127,242)
(128,243)(129,244)(130,245)(131,251)(132,252)(133,253)(134,254)(135,255)
(136,186)(137,187)(138,188)(139,189)(140,190)(141,181)(142,182)(143,183)
(144,184)(145,185)(146,191)(147,192)(148,193)(149,194)(150,195)(151,216)
(152,217)(153,218)(154,219)(155,220)(156,211)(157,212)(158,213)(159,214)
(160,215)(161,221)(162,222)(163,223)(164,224)(165,225)(166,201)(167,202)
(168,203)(169,204)(170,205)(171,196)(172,197)(173,198)(174,199)(175,200)
(176,206)(177,207)(178,208)(179,209)(180,210);
s3 := Sym(360)!( 1,286)( 2,287)( 3,288)( 4,289)( 5,290)( 6,296)( 7,297)
( 8,298)( 9,299)( 10,300)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)
( 16,271)( 17,272)( 18,273)( 19,274)( 20,275)( 21,281)( 22,282)( 23,283)
( 24,284)( 25,285)( 26,276)( 27,277)( 28,278)( 29,279)( 30,280)( 31,301)
( 32,302)( 33,303)( 34,304)( 35,305)( 36,311)( 37,312)( 38,313)( 39,314)
( 40,315)( 41,306)( 42,307)( 43,308)( 44,309)( 45,310)( 46,331)( 47,332)
( 48,333)( 49,334)( 50,335)( 51,341)( 52,342)( 53,343)( 54,344)( 55,345)
( 56,336)( 57,337)( 58,338)( 59,339)( 60,340)( 61,316)( 62,317)( 63,318)
( 64,319)( 65,320)( 66,326)( 67,327)( 68,328)( 69,329)( 70,330)( 71,321)
( 72,322)( 73,323)( 74,324)( 75,325)( 76,346)( 77,347)( 78,348)( 79,349)
( 80,350)( 81,356)( 82,357)( 83,358)( 84,359)( 85,360)( 86,351)( 87,352)
( 88,353)( 89,354)( 90,355)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,251)( 97,252)( 98,253)( 99,254)(100,255)(101,246)(102,247)(103,248)
(104,249)(105,250)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)
(112,237)(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)
(120,235)(121,256)(122,257)(123,258)(124,259)(125,260)(126,266)(127,267)
(128,268)(129,269)(130,270)(131,261)(132,262)(133,263)(134,264)(135,265)
(136,196)(137,197)(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)
(144,209)(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,181)
(152,182)(153,183)(154,184)(155,185)(156,191)(157,192)(158,193)(159,194)
(160,195)(161,186)(162,187)(163,188)(164,189)(165,190)(166,211)(167,212)
(168,213)(169,214)(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)
(176,216)(177,217)(178,218)(179,219)(180,220);
poly := sub<Sym(360)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope