Polytope of Type {2,6,60}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,60}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5324)
Rank : 4
Schlafli Type : {2,6,60}
Number of vertices, edges, etc : 2, 6, 180, 60
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 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 : {2,6,30}*720a
3-fold quotients : {2,6,20}*480a
5-fold quotients : {2,6,12}*288c
6-fold quotients : {2,6,10}*240
9-fold quotients : {2,2,20}*160
10-fold quotients : {2,6,6}*144c
15-fold quotients : {2,6,4}*96a
18-fold quotients : {2,2,10}*80
20-fold quotients : {2,3,6}*72
30-fold quotients : {2,6,2}*48
36-fold quotients : {2,2,5}*40
45-fold quotients : {2,2,4}*32
60-fold quotients : {2,3,2}*24
90-fold quotients : {2,2,2}*16
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)( 4,297)( 5,296)( 6,295)( 7,294)( 8,288)( 9,292)( 10,291)
( 11,290)( 12,289)( 13,298)( 14,302)( 15,301)( 16,300)( 17,299)( 18,278)
( 19,282)( 20,281)( 21,280)( 22,279)( 23,273)( 24,277)( 25,276)( 26,275)
( 27,274)( 28,283)( 29,287)( 30,286)( 31,285)( 32,284)( 33,308)( 34,312)
( 35,311)( 36,310)( 37,309)( 38,303)( 39,307)( 40,306)( 41,305)( 42,304)
( 43,313)( 44,317)( 45,316)( 46,315)( 47,314)( 48,338)( 49,342)( 50,341)
( 51,340)( 52,339)( 53,333)( 54,337)( 55,336)( 56,335)( 57,334)( 58,343)
( 59,347)( 60,346)( 61,345)( 62,344)( 63,323)( 64,327)( 65,326)( 66,325)
( 67,324)( 68,318)( 69,322)( 70,321)( 71,320)( 72,319)( 73,328)( 74,332)
( 75,331)( 76,330)( 77,329)( 78,353)( 79,357)( 80,356)( 81,355)( 82,354)
( 83,348)( 84,352)( 85,351)( 86,350)( 87,349)( 88,358)( 89,362)( 90,361)
( 91,360)( 92,359)( 93,203)( 94,207)( 95,206)( 96,205)( 97,204)( 98,198)
( 99,202)(100,201)(101,200)(102,199)(103,208)(104,212)(105,211)(106,210)
(107,209)(108,188)(109,192)(110,191)(111,190)(112,189)(113,183)(114,187)
(115,186)(116,185)(117,184)(118,193)(119,197)(120,196)(121,195)(122,194)
(123,218)(124,222)(125,221)(126,220)(127,219)(128,213)(129,217)(130,216)
(131,215)(132,214)(133,223)(134,227)(135,226)(136,225)(137,224)(138,248)
(139,252)(140,251)(141,250)(142,249)(143,243)(144,247)(145,246)(146,245)
(147,244)(148,253)(149,257)(150,256)(151,255)(152,254)(153,233)(154,237)
(155,236)(156,235)(157,234)(158,228)(159,232)(160,231)(161,230)(162,229)
(163,238)(164,242)(165,241)(166,240)(167,239)(168,263)(169,267)(170,266)
(171,265)(172,264)(173,258)(174,262)(175,261)(176,260)(177,259)(178,268)
(179,272)(180,271)(181,270)(182,269);;
s3 := ( 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);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
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)( 4,297)( 5,296)( 6,295)( 7,294)( 8,288)( 9,292)
( 10,291)( 11,290)( 12,289)( 13,298)( 14,302)( 15,301)( 16,300)( 17,299)
( 18,278)( 19,282)( 20,281)( 21,280)( 22,279)( 23,273)( 24,277)( 25,276)
( 26,275)( 27,274)( 28,283)( 29,287)( 30,286)( 31,285)( 32,284)( 33,308)
( 34,312)( 35,311)( 36,310)( 37,309)( 38,303)( 39,307)( 40,306)( 41,305)
( 42,304)( 43,313)( 44,317)( 45,316)( 46,315)( 47,314)( 48,338)( 49,342)
( 50,341)( 51,340)( 52,339)( 53,333)( 54,337)( 55,336)( 56,335)( 57,334)
( 58,343)( 59,347)( 60,346)( 61,345)( 62,344)( 63,323)( 64,327)( 65,326)
( 66,325)( 67,324)( 68,318)( 69,322)( 70,321)( 71,320)( 72,319)( 73,328)
( 74,332)( 75,331)( 76,330)( 77,329)( 78,353)( 79,357)( 80,356)( 81,355)
( 82,354)( 83,348)( 84,352)( 85,351)( 86,350)( 87,349)( 88,358)( 89,362)
( 90,361)( 91,360)( 92,359)( 93,203)( 94,207)( 95,206)( 96,205)( 97,204)
( 98,198)( 99,202)(100,201)(101,200)(102,199)(103,208)(104,212)(105,211)
(106,210)(107,209)(108,188)(109,192)(110,191)(111,190)(112,189)(113,183)
(114,187)(115,186)(116,185)(117,184)(118,193)(119,197)(120,196)(121,195)
(122,194)(123,218)(124,222)(125,221)(126,220)(127,219)(128,213)(129,217)
(130,216)(131,215)(132,214)(133,223)(134,227)(135,226)(136,225)(137,224)
(138,248)(139,252)(140,251)(141,250)(142,249)(143,243)(144,247)(145,246)
(146,245)(147,244)(148,253)(149,257)(150,256)(151,255)(152,254)(153,233)
(154,237)(155,236)(156,235)(157,234)(158,228)(159,232)(160,231)(161,230)
(162,229)(163,238)(164,242)(165,241)(166,240)(167,239)(168,263)(169,267)
(170,266)(171,265)(172,264)(173,258)(174,262)(175,261)(176,260)(177,259)
(178,268)(179,272)(180,271)(181,270)(182,269);
s3 := 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);
poly := sub<Sym(362)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >;
to this polytope