Polytope of Type {12,60}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,60}*1440b
Also Known As : {12,60|2}. if this polytope has another name.
Group : SmallGroup(1440,3806)
Rank : 3
Schlafli Type : {12,60}
Number of vertices, edges, etc : 12, 360, 60
Order of s0s1s2 : 60
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {12,30}*720b, {6,60}*720b
3-fold quotients : {12,20}*480, {4,60}*480a
4-fold quotients : {6,30}*360b
5-fold quotients : {12,12}*288a
6-fold quotients : {12,10}*240, {6,20}*240a, {2,60}*240, {4,30}*240a
9-fold quotients : {4,20}*160
10-fold quotients : {6,12}*144a, {12,6}*144a
12-fold quotients : {6,10}*120, {2,30}*120
15-fold quotients : {4,12}*96a, {12,4}*96a
18-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {6,6}*72a
24-fold quotients : {2,15}*60
30-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
36-fold quotients : {2,10}*40
45-fold quotients : {4,4}*32
60-fold quotients : {2,6}*24, {6,2}*24
72-fold quotients : {2,5}*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 := ( 16, 31)( 17, 32)( 18, 33)( 19, 34)( 20, 35)( 21, 36)( 22, 37)( 23, 38)
( 24, 39)( 25, 40)( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 61, 76)
( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)
( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)(106,121)(107,122)
(108,123)(109,124)(110,125)(111,126)(112,127)(113,128)(114,129)(115,130)
(116,131)(117,132)(118,133)(119,134)(120,135)(151,166)(152,167)(153,168)
(154,169)(155,170)(156,171)(157,172)(158,173)(159,174)(160,175)(161,176)
(162,177)(163,178)(164,179)(165,180)(181,271)(182,272)(183,273)(184,274)
(185,275)(186,276)(187,277)(188,278)(189,279)(190,280)(191,281)(192,282)
(193,283)(194,284)(195,285)(196,301)(197,302)(198,303)(199,304)(200,305)
(201,306)(202,307)(203,308)(204,309)(205,310)(206,311)(207,312)(208,313)
(209,314)(210,315)(211,286)(212,287)(213,288)(214,289)(215,290)(216,291)
(217,292)(218,293)(219,294)(220,295)(221,296)(222,297)(223,298)(224,299)
(225,300)(226,316)(227,317)(228,318)(229,319)(230,320)(231,321)(232,322)
(233,323)(234,324)(235,325)(236,326)(237,327)(238,328)(239,329)(240,330)
(241,346)(242,347)(243,348)(244,349)(245,350)(246,351)(247,352)(248,353)
(249,354)(250,355)(251,356)(252,357)(253,358)(254,359)(255,360)(256,331)
(257,332)(258,333)(259,334)(260,335)(261,336)(262,337)(263,338)(264,339)
(265,340)(266,341)(267,342)(268,343)(269,344)(270,345);;
s1 := ( 1,196)( 2,200)( 3,199)( 4,198)( 5,197)( 6,206)( 7,210)( 8,209)
( 9,208)( 10,207)( 11,201)( 12,205)( 13,204)( 14,203)( 15,202)( 16,181)
( 17,185)( 18,184)( 19,183)( 20,182)( 21,191)( 22,195)( 23,194)( 24,193)
( 25,192)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,211)( 32,215)
( 33,214)( 34,213)( 35,212)( 36,221)( 37,225)( 38,224)( 39,223)( 40,222)
( 41,216)( 42,220)( 43,219)( 44,218)( 45,217)( 46,241)( 47,245)( 48,244)
( 49,243)( 50,242)( 51,251)( 52,255)( 53,254)( 54,253)( 55,252)( 56,246)
( 57,250)( 58,249)( 59,248)( 60,247)( 61,226)( 62,230)( 63,229)( 64,228)
( 65,227)( 66,236)( 67,240)( 68,239)( 69,238)( 70,237)( 71,231)( 72,235)
( 73,234)( 74,233)( 75,232)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,266)( 82,270)( 83,269)( 84,268)( 85,267)( 86,261)( 87,265)( 88,264)
( 89,263)( 90,262)( 91,286)( 92,290)( 93,289)( 94,288)( 95,287)( 96,296)
( 97,300)( 98,299)( 99,298)(100,297)(101,291)(102,295)(103,294)(104,293)
(105,292)(106,271)(107,275)(108,274)(109,273)(110,272)(111,281)(112,285)
(113,284)(114,283)(115,282)(116,276)(117,280)(118,279)(119,278)(120,277)
(121,301)(122,305)(123,304)(124,303)(125,302)(126,311)(127,315)(128,314)
(129,313)(130,312)(131,306)(132,310)(133,309)(134,308)(135,307)(136,331)
(137,335)(138,334)(139,333)(140,332)(141,341)(142,345)(143,344)(144,343)
(145,342)(146,336)(147,340)(148,339)(149,338)(150,337)(151,316)(152,320)
(153,319)(154,318)(155,317)(156,326)(157,330)(158,329)(159,328)(160,327)
(161,321)(162,325)(163,324)(164,323)(165,322)(166,346)(167,350)(168,349)
(169,348)(170,347)(171,356)(172,360)(173,359)(174,358)(175,357)(176,351)
(177,355)(178,354)(179,353)(180,352);;
s2 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 67)( 62, 66)( 63, 70)( 64, 69)
( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)
( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,102)
(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)(118,120)
(121,127)(122,126)(123,130)(124,129)(125,128)(131,132)(133,135)(136,142)
(137,141)(138,145)(139,144)(140,143)(146,147)(148,150)(151,157)(152,156)
(153,160)(154,159)(155,158)(161,162)(163,165)(166,172)(167,171)(168,175)
(169,174)(170,173)(176,177)(178,180)(181,232)(182,231)(183,235)(184,234)
(185,233)(186,227)(187,226)(188,230)(189,229)(190,228)(191,237)(192,236)
(193,240)(194,239)(195,238)(196,247)(197,246)(198,250)(199,249)(200,248)
(201,242)(202,241)(203,245)(204,244)(205,243)(206,252)(207,251)(208,255)
(209,254)(210,253)(211,262)(212,261)(213,265)(214,264)(215,263)(216,257)
(217,256)(218,260)(219,259)(220,258)(221,267)(222,266)(223,270)(224,269)
(225,268)(271,322)(272,321)(273,325)(274,324)(275,323)(276,317)(277,316)
(278,320)(279,319)(280,318)(281,327)(282,326)(283,330)(284,329)(285,328)
(286,337)(287,336)(288,340)(289,339)(290,338)(291,332)(292,331)(293,335)
(294,334)(295,333)(296,342)(297,341)(298,345)(299,344)(300,343)(301,352)
(302,351)(303,355)(304,354)(305,353)(306,347)(307,346)(308,350)(309,349)
(310,348)(311,357)(312,356)(313,360)(314,359)(315,358);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(360)!( 16, 31)( 17, 32)( 18, 33)( 19, 34)( 20, 35)( 21, 36)( 22, 37)
( 23, 38)( 24, 39)( 25, 40)( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)
( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)
( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)(106,121)
(107,122)(108,123)(109,124)(110,125)(111,126)(112,127)(113,128)(114,129)
(115,130)(116,131)(117,132)(118,133)(119,134)(120,135)(151,166)(152,167)
(153,168)(154,169)(155,170)(156,171)(157,172)(158,173)(159,174)(160,175)
(161,176)(162,177)(163,178)(164,179)(165,180)(181,271)(182,272)(183,273)
(184,274)(185,275)(186,276)(187,277)(188,278)(189,279)(190,280)(191,281)
(192,282)(193,283)(194,284)(195,285)(196,301)(197,302)(198,303)(199,304)
(200,305)(201,306)(202,307)(203,308)(204,309)(205,310)(206,311)(207,312)
(208,313)(209,314)(210,315)(211,286)(212,287)(213,288)(214,289)(215,290)
(216,291)(217,292)(218,293)(219,294)(220,295)(221,296)(222,297)(223,298)
(224,299)(225,300)(226,316)(227,317)(228,318)(229,319)(230,320)(231,321)
(232,322)(233,323)(234,324)(235,325)(236,326)(237,327)(238,328)(239,329)
(240,330)(241,346)(242,347)(243,348)(244,349)(245,350)(246,351)(247,352)
(248,353)(249,354)(250,355)(251,356)(252,357)(253,358)(254,359)(255,360)
(256,331)(257,332)(258,333)(259,334)(260,335)(261,336)(262,337)(263,338)
(264,339)(265,340)(266,341)(267,342)(268,343)(269,344)(270,345);
s1 := Sym(360)!( 1,196)( 2,200)( 3,199)( 4,198)( 5,197)( 6,206)( 7,210)
( 8,209)( 9,208)( 10,207)( 11,201)( 12,205)( 13,204)( 14,203)( 15,202)
( 16,181)( 17,185)( 18,184)( 19,183)( 20,182)( 21,191)( 22,195)( 23,194)
( 24,193)( 25,192)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,211)
( 32,215)( 33,214)( 34,213)( 35,212)( 36,221)( 37,225)( 38,224)( 39,223)
( 40,222)( 41,216)( 42,220)( 43,219)( 44,218)( 45,217)( 46,241)( 47,245)
( 48,244)( 49,243)( 50,242)( 51,251)( 52,255)( 53,254)( 54,253)( 55,252)
( 56,246)( 57,250)( 58,249)( 59,248)( 60,247)( 61,226)( 62,230)( 63,229)
( 64,228)( 65,227)( 66,236)( 67,240)( 68,239)( 69,238)( 70,237)( 71,231)
( 72,235)( 73,234)( 74,233)( 75,232)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,266)( 82,270)( 83,269)( 84,268)( 85,267)( 86,261)( 87,265)
( 88,264)( 89,263)( 90,262)( 91,286)( 92,290)( 93,289)( 94,288)( 95,287)
( 96,296)( 97,300)( 98,299)( 99,298)(100,297)(101,291)(102,295)(103,294)
(104,293)(105,292)(106,271)(107,275)(108,274)(109,273)(110,272)(111,281)
(112,285)(113,284)(114,283)(115,282)(116,276)(117,280)(118,279)(119,278)
(120,277)(121,301)(122,305)(123,304)(124,303)(125,302)(126,311)(127,315)
(128,314)(129,313)(130,312)(131,306)(132,310)(133,309)(134,308)(135,307)
(136,331)(137,335)(138,334)(139,333)(140,332)(141,341)(142,345)(143,344)
(144,343)(145,342)(146,336)(147,340)(148,339)(149,338)(150,337)(151,316)
(152,320)(153,319)(154,318)(155,317)(156,326)(157,330)(158,329)(159,328)
(160,327)(161,321)(162,325)(163,324)(164,323)(165,322)(166,346)(167,350)
(168,349)(169,348)(170,347)(171,356)(172,360)(173,359)(174,358)(175,357)
(176,351)(177,355)(178,354)(179,353)(180,352);
s2 := Sym(360)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 67)( 62, 66)( 63, 70)
( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,102)(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)
(118,120)(121,127)(122,126)(123,130)(124,129)(125,128)(131,132)(133,135)
(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)(148,150)(151,157)
(152,156)(153,160)(154,159)(155,158)(161,162)(163,165)(166,172)(167,171)
(168,175)(169,174)(170,173)(176,177)(178,180)(181,232)(182,231)(183,235)
(184,234)(185,233)(186,227)(187,226)(188,230)(189,229)(190,228)(191,237)
(192,236)(193,240)(194,239)(195,238)(196,247)(197,246)(198,250)(199,249)
(200,248)(201,242)(202,241)(203,245)(204,244)(205,243)(206,252)(207,251)
(208,255)(209,254)(210,253)(211,262)(212,261)(213,265)(214,264)(215,263)
(216,257)(217,256)(218,260)(219,259)(220,258)(221,267)(222,266)(223,270)
(224,269)(225,268)(271,322)(272,321)(273,325)(274,324)(275,323)(276,317)
(277,316)(278,320)(279,319)(280,318)(281,327)(282,326)(283,330)(284,329)
(285,328)(286,337)(287,336)(288,340)(289,339)(290,338)(291,332)(292,331)
(293,335)(294,334)(295,333)(296,342)(297,341)(298,345)(299,344)(300,343)
(301,352)(302,351)(303,355)(304,354)(305,353)(306,347)(307,346)(308,350)
(309,349)(310,348)(311,357)(312,356)(313,360)(314,359)(315,358);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope