Polytope of Type {12,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,60}*1440c
if this polytope has a 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 : 6
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 : {6,60}*720c, {12,30}*720c
   3-fold quotients : {4,60}*480a
   4-fold quotients : {6,30}*360c
   5-fold quotients : {12,12}*288b
   6-fold quotients : {2,60}*240, {4,30}*240a
   8-fold quotients : {6,15}*180
   9-fold quotients : {4,20}*160
   10-fold quotients : {6,12}*144b, {12,6}*144c
   12-fold quotients : {2,30}*120
   15-fold quotients : {4,12}*96a
   18-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {6,6}*72b
   24-fold quotients : {2,15}*60
   30-fold quotients : {2,12}*48, {4,6}*48a
   36-fold quotients : {2,10}*40
   40-fold quotients : {6,3}*36
   45-fold quotients : {4,4}*32
   60-fold quotients : {2,6}*24
   72-fold quotients : {2,5}*20
   90-fold quotients : {2,4}*16, {4,2}*16
   120-fold quotients : {2,3}*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, 37)
( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)
( 25, 33)( 26, 42)( 27, 41)( 28, 45)( 29, 44)( 30, 43)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)( 63, 85)
( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)
( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91, 97)( 92, 96)( 93,100)( 94, 99)
( 95, 98)(101,102)(103,105)(106,127)(107,126)(108,130)(109,129)(110,128)
(111,122)(112,121)(113,125)(114,124)(115,123)(116,132)(117,131)(118,135)
(119,134)(120,133)(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)
(148,150)(151,172)(152,171)(153,175)(154,174)(155,173)(156,167)(157,166)
(158,170)(159,169)(160,168)(161,177)(162,176)(163,180)(164,179)(165,178)
(181,322)(182,321)(183,325)(184,324)(185,323)(186,317)(187,316)(188,320)
(189,319)(190,318)(191,327)(192,326)(193,330)(194,329)(195,328)(196,352)
(197,351)(198,355)(199,354)(200,353)(201,347)(202,346)(203,350)(204,349)
(205,348)(206,357)(207,356)(208,360)(209,359)(210,358)(211,337)(212,336)
(213,340)(214,339)(215,338)(216,332)(217,331)(218,335)(219,334)(220,333)
(221,342)(222,341)(223,345)(224,344)(225,343)(226,277)(227,276)(228,280)
(229,279)(230,278)(231,272)(232,271)(233,275)(234,274)(235,273)(236,282)
(237,281)(238,285)(239,284)(240,283)(241,307)(242,306)(243,310)(244,309)
(245,308)(246,302)(247,301)(248,305)(249,304)(250,303)(251,312)(252,311)
(253,315)(254,314)(255,313)(256,292)(257,291)(258,295)(259,294)(260,293)
(261,287)(262,286)(263,290)(264,289)(265,288)(266,297)(267,296)(268,300)
(269,299)(270,298);;
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, s2*s0*s1*s0*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, 
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, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)
( 24, 34)( 25, 33)( 26, 42)( 27, 41)( 28, 45)( 29, 44)( 30, 43)( 46, 52)
( 47, 51)( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)
( 63, 85)( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)
( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91, 97)( 92, 96)( 93,100)
( 94, 99)( 95, 98)(101,102)(103,105)(106,127)(107,126)(108,130)(109,129)
(110,128)(111,122)(112,121)(113,125)(114,124)(115,123)(116,132)(117,131)
(118,135)(119,134)(120,133)(136,142)(137,141)(138,145)(139,144)(140,143)
(146,147)(148,150)(151,172)(152,171)(153,175)(154,174)(155,173)(156,167)
(157,166)(158,170)(159,169)(160,168)(161,177)(162,176)(163,180)(164,179)
(165,178)(181,322)(182,321)(183,325)(184,324)(185,323)(186,317)(187,316)
(188,320)(189,319)(190,318)(191,327)(192,326)(193,330)(194,329)(195,328)
(196,352)(197,351)(198,355)(199,354)(200,353)(201,347)(202,346)(203,350)
(204,349)(205,348)(206,357)(207,356)(208,360)(209,359)(210,358)(211,337)
(212,336)(213,340)(214,339)(215,338)(216,332)(217,331)(218,335)(219,334)
(220,333)(221,342)(222,341)(223,345)(224,344)(225,343)(226,277)(227,276)
(228,280)(229,279)(230,278)(231,272)(232,271)(233,275)(234,274)(235,273)
(236,282)(237,281)(238,285)(239,284)(240,283)(241,307)(242,306)(243,310)
(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)(250,303)(251,312)
(252,311)(253,315)(254,314)(255,313)(256,292)(257,291)(258,295)(259,294)
(260,293)(261,287)(262,286)(263,290)(264,289)(265,288)(266,297)(267,296)
(268,300)(269,299)(270,298);
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, s2*s0*s1*s0*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, 
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