Polytope of Type {60,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,12}*1440c
if this polytope has a 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 : 6
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 : {60,6}*720c, {30,12}*720c
   3-fold quotients : {60,4}*480a
   4-fold quotients : {30,6}*360c
   5-fold quotients : {12,12}*288c
   6-fold quotients : {60,2}*240, {30,4}*240a
   8-fold quotients : {15,6}*180
   9-fold quotients : {20,4}*160
   10-fold quotients : {12,6}*144b, {6,12}*144c
   12-fold quotients : {30,2}*120
   15-fold quotients : {12,4}*96a
   18-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {6,6}*72c
   24-fold quotients : {15,2}*60
   30-fold quotients : {12,2}*48, {6,4}*48a
   36-fold quotients : {10,2}*40
   40-fold quotients : {3,6}*36
   45-fold quotients : {4,4}*32
   60-fold quotients : {6,2}*24
   72-fold quotients : {5,2}*20
   90-fold quotients : {2,4}*16, {4,2}*16
   120-fold quotients : {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)( 16, 31)
( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 41)( 22, 45)( 23, 44)( 24, 43)
( 25, 42)( 26, 36)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 47, 50)( 48, 49)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 76)( 62, 80)( 63, 79)
( 64, 78)( 65, 77)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)
( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 92, 95)( 93, 94)( 96,101)( 97,105)
( 98,104)( 99,103)(100,102)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,131)(112,135)(113,134)(114,133)(115,132)(116,126)(117,130)(118,129)
(119,128)(120,127)(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)
(145,147)(151,166)(152,170)(153,169)(154,168)(155,167)(156,176)(157,180)
(158,179)(159,178)(160,177)(161,171)(162,175)(163,174)(164,173)(165,172)
(181,316)(182,320)(183,319)(184,318)(185,317)(186,326)(187,330)(188,329)
(189,328)(190,327)(191,321)(192,325)(193,324)(194,323)(195,322)(196,346)
(197,350)(198,349)(199,348)(200,347)(201,356)(202,360)(203,359)(204,358)
(205,357)(206,351)(207,355)(208,354)(209,353)(210,352)(211,331)(212,335)
(213,334)(214,333)(215,332)(216,341)(217,345)(218,344)(219,343)(220,342)
(221,336)(222,340)(223,339)(224,338)(225,337)(226,271)(227,275)(228,274)
(229,273)(230,272)(231,281)(232,285)(233,284)(234,283)(235,282)(236,276)
(237,280)(238,279)(239,278)(240,277)(241,301)(242,305)(243,304)(244,303)
(245,302)(246,311)(247,315)(248,314)(249,313)(250,312)(251,306)(252,310)
(253,309)(254,308)(255,307)(256,286)(257,290)(258,289)(259,288)(260,287)
(261,296)(262,300)(263,299)(264,298)(265,297)(266,291)(267,295)(268,294)
(269,293)(270,292);;
s1 := (  1,202)(  2,201)(  3,205)(  4,204)(  5,203)(  6,197)(  7,196)(  8,200)
(  9,199)( 10,198)( 11,207)( 12,206)( 13,210)( 14,209)( 15,208)( 16,187)
( 17,186)( 18,190)( 19,189)( 20,188)( 21,182)( 22,181)( 23,185)( 24,184)
( 25,183)( 26,192)( 27,191)( 28,195)( 29,194)( 30,193)( 31,217)( 32,216)
( 33,220)( 34,219)( 35,218)( 36,212)( 37,211)( 38,215)( 39,214)( 40,213)
( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,247)( 47,246)( 48,250)
( 49,249)( 50,248)( 51,242)( 52,241)( 53,245)( 54,244)( 55,243)( 56,252)
( 57,251)( 58,255)( 59,254)( 60,253)( 61,232)( 62,231)( 63,235)( 64,234)
( 65,233)( 66,227)( 67,226)( 68,230)( 69,229)( 70,228)( 71,237)( 72,236)
( 73,240)( 74,239)( 75,238)( 76,262)( 77,261)( 78,265)( 79,264)( 80,263)
( 81,257)( 82,256)( 83,260)( 84,259)( 85,258)( 86,267)( 87,266)( 88,270)
( 89,269)( 90,268)( 91,292)( 92,291)( 93,295)( 94,294)( 95,293)( 96,287)
( 97,286)( 98,290)( 99,289)(100,288)(101,297)(102,296)(103,300)(104,299)
(105,298)(106,277)(107,276)(108,280)(109,279)(110,278)(111,272)(112,271)
(113,275)(114,274)(115,273)(116,282)(117,281)(118,285)(119,284)(120,283)
(121,307)(122,306)(123,310)(124,309)(125,308)(126,302)(127,301)(128,305)
(129,304)(130,303)(131,312)(132,311)(133,315)(134,314)(135,313)(136,337)
(137,336)(138,340)(139,339)(140,338)(141,332)(142,331)(143,335)(144,334)
(145,333)(146,342)(147,341)(148,345)(149,344)(150,343)(151,322)(152,321)
(153,325)(154,324)(155,323)(156,317)(157,316)(158,320)(159,319)(160,318)
(161,327)(162,326)(163,330)(164,329)(165,328)(166,352)(167,351)(168,355)
(169,354)(170,353)(171,347)(172,346)(173,350)(174,349)(175,348)(176,357)
(177,356)(178,360)(179,359)(180,358);;
s2 := ( 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);;
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*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*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*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)
( 16, 31)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 41)( 22, 45)( 23, 44)
( 24, 43)( 25, 42)( 26, 36)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 47, 50)
( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 76)( 62, 80)
( 63, 79)( 64, 78)( 65, 77)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)
( 71, 81)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 92, 95)( 93, 94)( 96,101)
( 97,105)( 98,104)( 99,103)(100,102)(106,121)(107,125)(108,124)(109,123)
(110,122)(111,131)(112,135)(113,134)(114,133)(115,132)(116,126)(117,130)
(118,129)(119,128)(120,127)(137,140)(138,139)(141,146)(142,150)(143,149)
(144,148)(145,147)(151,166)(152,170)(153,169)(154,168)(155,167)(156,176)
(157,180)(158,179)(159,178)(160,177)(161,171)(162,175)(163,174)(164,173)
(165,172)(181,316)(182,320)(183,319)(184,318)(185,317)(186,326)(187,330)
(188,329)(189,328)(190,327)(191,321)(192,325)(193,324)(194,323)(195,322)
(196,346)(197,350)(198,349)(199,348)(200,347)(201,356)(202,360)(203,359)
(204,358)(205,357)(206,351)(207,355)(208,354)(209,353)(210,352)(211,331)
(212,335)(213,334)(214,333)(215,332)(216,341)(217,345)(218,344)(219,343)
(220,342)(221,336)(222,340)(223,339)(224,338)(225,337)(226,271)(227,275)
(228,274)(229,273)(230,272)(231,281)(232,285)(233,284)(234,283)(235,282)
(236,276)(237,280)(238,279)(239,278)(240,277)(241,301)(242,305)(243,304)
(244,303)(245,302)(246,311)(247,315)(248,314)(249,313)(250,312)(251,306)
(252,310)(253,309)(254,308)(255,307)(256,286)(257,290)(258,289)(259,288)
(260,287)(261,296)(262,300)(263,299)(264,298)(265,297)(266,291)(267,295)
(268,294)(269,293)(270,292);
s1 := Sym(360)!(  1,202)(  2,201)(  3,205)(  4,204)(  5,203)(  6,197)(  7,196)
(  8,200)(  9,199)( 10,198)( 11,207)( 12,206)( 13,210)( 14,209)( 15,208)
( 16,187)( 17,186)( 18,190)( 19,189)( 20,188)( 21,182)( 22,181)( 23,185)
( 24,184)( 25,183)( 26,192)( 27,191)( 28,195)( 29,194)( 30,193)( 31,217)
( 32,216)( 33,220)( 34,219)( 35,218)( 36,212)( 37,211)( 38,215)( 39,214)
( 40,213)( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,247)( 47,246)
( 48,250)( 49,249)( 50,248)( 51,242)( 52,241)( 53,245)( 54,244)( 55,243)
( 56,252)( 57,251)( 58,255)( 59,254)( 60,253)( 61,232)( 62,231)( 63,235)
( 64,234)( 65,233)( 66,227)( 67,226)( 68,230)( 69,229)( 70,228)( 71,237)
( 72,236)( 73,240)( 74,239)( 75,238)( 76,262)( 77,261)( 78,265)( 79,264)
( 80,263)( 81,257)( 82,256)( 83,260)( 84,259)( 85,258)( 86,267)( 87,266)
( 88,270)( 89,269)( 90,268)( 91,292)( 92,291)( 93,295)( 94,294)( 95,293)
( 96,287)( 97,286)( 98,290)( 99,289)(100,288)(101,297)(102,296)(103,300)
(104,299)(105,298)(106,277)(107,276)(108,280)(109,279)(110,278)(111,272)
(112,271)(113,275)(114,274)(115,273)(116,282)(117,281)(118,285)(119,284)
(120,283)(121,307)(122,306)(123,310)(124,309)(125,308)(126,302)(127,301)
(128,305)(129,304)(130,303)(131,312)(132,311)(133,315)(134,314)(135,313)
(136,337)(137,336)(138,340)(139,339)(140,338)(141,332)(142,331)(143,335)
(144,334)(145,333)(146,342)(147,341)(148,345)(149,344)(150,343)(151,322)
(152,321)(153,325)(154,324)(155,323)(156,317)(157,316)(158,320)(159,319)
(160,318)(161,327)(162,326)(163,330)(164,329)(165,328)(166,352)(167,351)
(168,355)(169,354)(170,353)(171,347)(172,346)(173,350)(174,349)(175,348)
(176,357)(177,356)(178,360)(179,359)(180,358);
s2 := 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);
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*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*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*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