Polytope of Type {60,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,12}*1440b
Also Known As : {60,12|2}. if this polytope has another name.
Group : SmallGroup(1440,3806)
Rank : 3
Schlafli Type : {60,12}
Number of vertices, edges, etc : 60, 360, 12
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,12}*720b, {60,6}*720b
   3-fold quotients : {20,12}*480, {60,4}*480a
   4-fold quotients : {30,6}*360b
   5-fold quotients : {12,12}*288a
   6-fold quotients : {10,12}*240, {20,6}*240a, {60,2}*240, {30,4}*240a
   9-fold quotients : {20,4}*160
   10-fold quotients : {6,12}*144a, {12,6}*144a
   12-fold quotients : {10,6}*120, {30,2}*120
   15-fold quotients : {4,12}*96a, {12,4}*96a
   18-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {6,6}*72a
   24-fold quotients : {15,2}*60
   30-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
   36-fold quotients : {10,2}*40
   45-fold quotients : {4,4}*32
   60-fold quotients : {2,6}*24, {6,2}*24
   72-fold quotients : {5,2}*20
   90-fold quotients : {2,4}*16, {4,2}*16
   120-fold quotients : {2,3}*12, {3,2}*12
   180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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