Polytope of Type {2,60,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60,6}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5324)
Rank : 4
Schlafli Type : {2,60,6}
Number of vertices, edges, etc : 2, 60, 180, 6
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 : {2,30,6}*720a
   3-fold quotients : {2,20,6}*480a
   5-fold quotients : {2,12,6}*288c
   6-fold quotients : {2,10,6}*240
   9-fold quotients : {2,20,2}*160
   10-fold quotients : {2,6,6}*144b
   15-fold quotients : {2,4,6}*96a
   18-fold quotients : {2,10,2}*80
   20-fold quotients : {2,6,3}*72
   30-fold quotients : {2,2,6}*48
   36-fold quotients : {2,5,2}*40
   45-fold quotients : {2,4,2}*32
   60-fold quotients : {2,2,3}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3,183)(  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);;
s2 := (  3,279)(  4,278)(  5,282)(  6,281)(  7,280)(  8,274)(  9,273)( 10,277)
( 11,276)( 12,275)( 13,284)( 14,283)( 15,287)( 16,286)( 17,285)( 18,309)
( 19,308)( 20,312)( 21,311)( 22,310)( 23,304)( 24,303)( 25,307)( 26,306)
( 27,305)( 28,314)( 29,313)( 30,317)( 31,316)( 32,315)( 33,294)( 34,293)
( 35,297)( 36,296)( 37,295)( 38,289)( 39,288)( 40,292)( 41,291)( 42,290)
( 43,299)( 44,298)( 45,302)( 46,301)( 47,300)( 48,324)( 49,323)( 50,327)
( 51,326)( 52,325)( 53,319)( 54,318)( 55,322)( 56,321)( 57,320)( 58,329)
( 59,328)( 60,332)( 61,331)( 62,330)( 63,354)( 64,353)( 65,357)( 66,356)
( 67,355)( 68,349)( 69,348)( 70,352)( 71,351)( 72,350)( 73,359)( 74,358)
( 75,362)( 76,361)( 77,360)( 78,339)( 79,338)( 80,342)( 81,341)( 82,340)
( 83,334)( 84,333)( 85,337)( 86,336)( 87,335)( 88,344)( 89,343)( 90,347)
( 91,346)( 92,345)( 93,189)( 94,188)( 95,192)( 96,191)( 97,190)( 98,184)
( 99,183)(100,187)(101,186)(102,185)(103,194)(104,193)(105,197)(106,196)
(107,195)(108,219)(109,218)(110,222)(111,221)(112,220)(113,214)(114,213)
(115,217)(116,216)(117,215)(118,224)(119,223)(120,227)(121,226)(122,225)
(123,204)(124,203)(125,207)(126,206)(127,205)(128,199)(129,198)(130,202)
(131,201)(132,200)(133,209)(134,208)(135,212)(136,211)(137,210)(138,234)
(139,233)(140,237)(141,236)(142,235)(143,229)(144,228)(145,232)(146,231)
(147,230)(148,239)(149,238)(150,242)(151,241)(152,240)(153,264)(154,263)
(155,267)(156,266)(157,265)(158,259)(159,258)(160,262)(161,261)(162,260)
(163,269)(164,268)(165,272)(166,271)(167,270)(168,249)(169,248)(170,252)
(171,251)(172,250)(173,244)(174,243)(175,247)(176,246)(177,245)(178,254)
(179,253)(180,257)(181,256)(182,255);;
s3 := (  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]);;

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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*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)!(  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);
s2 := Sym(362)!(  3,279)(  4,278)(  5,282)(  6,281)(  7,280)(  8,274)(  9,273)
( 10,277)( 11,276)( 12,275)( 13,284)( 14,283)( 15,287)( 16,286)( 17,285)
( 18,309)( 19,308)( 20,312)( 21,311)( 22,310)( 23,304)( 24,303)( 25,307)
( 26,306)( 27,305)( 28,314)( 29,313)( 30,317)( 31,316)( 32,315)( 33,294)
( 34,293)( 35,297)( 36,296)( 37,295)( 38,289)( 39,288)( 40,292)( 41,291)
( 42,290)( 43,299)( 44,298)( 45,302)( 46,301)( 47,300)( 48,324)( 49,323)
( 50,327)( 51,326)( 52,325)( 53,319)( 54,318)( 55,322)( 56,321)( 57,320)
( 58,329)( 59,328)( 60,332)( 61,331)( 62,330)( 63,354)( 64,353)( 65,357)
( 66,356)( 67,355)( 68,349)( 69,348)( 70,352)( 71,351)( 72,350)( 73,359)
( 74,358)( 75,362)( 76,361)( 77,360)( 78,339)( 79,338)( 80,342)( 81,341)
( 82,340)( 83,334)( 84,333)( 85,337)( 86,336)( 87,335)( 88,344)( 89,343)
( 90,347)( 91,346)( 92,345)( 93,189)( 94,188)( 95,192)( 96,191)( 97,190)
( 98,184)( 99,183)(100,187)(101,186)(102,185)(103,194)(104,193)(105,197)
(106,196)(107,195)(108,219)(109,218)(110,222)(111,221)(112,220)(113,214)
(114,213)(115,217)(116,216)(117,215)(118,224)(119,223)(120,227)(121,226)
(122,225)(123,204)(124,203)(125,207)(126,206)(127,205)(128,199)(129,198)
(130,202)(131,201)(132,200)(133,209)(134,208)(135,212)(136,211)(137,210)
(138,234)(139,233)(140,237)(141,236)(142,235)(143,229)(144,228)(145,232)
(146,231)(147,230)(148,239)(149,238)(150,242)(151,241)(152,240)(153,264)
(154,263)(155,267)(156,266)(157,265)(158,259)(159,258)(160,262)(161,261)
(162,260)(163,269)(164,268)(165,272)(166,271)(167,270)(168,249)(169,248)
(170,252)(171,251)(172,250)(173,244)(174,243)(175,247)(176,246)(177,245)
(178,254)(179,253)(180,257)(181,256)(182,255);
s3 := 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>;

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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*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