Polytope of Type {6,60}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,60}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5901)
Rank : 3
Schlafli Type : {6,60}
Number of vertices, edges, etc : 12, 360, 120
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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}*720d
3-fold quotients : {6,20}*480c
4-fold quotients : {6,30}*360b
5-fold quotients : {6,12}*288a
6-fold quotients : {6,20}*240b
10-fold quotients : {6,12}*144d
12-fold quotients : {6,10}*120, {2,30}*120
15-fold quotients : {6,4}*96
20-fold quotients : {6,6}*72a
24-fold quotients : {2,15}*60
30-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
36-fold quotients : {2,10}*40
60-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
72-fold quotients : {2,5}*20
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 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)( 61,121)
( 62,122)( 63,124)( 64,123)( 65,125)( 66,126)( 67,128)( 68,127)( 69,129)
( 70,130)( 71,132)( 72,131)( 73,133)( 74,134)( 75,136)( 76,135)( 77,137)
( 78,138)( 79,140)( 80,139)( 81,141)( 82,142)( 83,144)( 84,143)( 85,145)
( 86,146)( 87,148)( 88,147)( 89,149)( 90,150)( 91,152)( 92,151)( 93,153)
( 94,154)( 95,156)( 96,155)( 97,157)( 98,158)( 99,160)(100,159)(101,161)
(102,162)(103,164)(104,163)(105,165)(106,166)(107,168)(108,167)(109,169)
(110,170)(111,172)(112,171)(113,173)(114,174)(115,176)(116,175)(117,177)
(118,178)(119,180)(120,179)(183,184)(187,188)(191,192)(195,196)(199,200)
(203,204)(207,208)(211,212)(215,216)(219,220)(223,224)(227,228)(231,232)
(235,236)(239,240)(241,301)(242,302)(243,304)(244,303)(245,305)(246,306)
(247,308)(248,307)(249,309)(250,310)(251,312)(252,311)(253,313)(254,314)
(255,316)(256,315)(257,317)(258,318)(259,320)(260,319)(261,321)(262,322)
(263,324)(264,323)(265,325)(266,326)(267,328)(268,327)(269,329)(270,330)
(271,332)(272,331)(273,333)(274,334)(275,336)(276,335)(277,337)(278,338)
(279,340)(280,339)(281,341)(282,342)(283,344)(284,343)(285,345)(286,346)
(287,348)(288,347)(289,349)(290,350)(291,352)(292,351)(293,353)(294,354)
(295,356)(296,355)(297,357)(298,358)(299,360)(300,359);;
s1 := ( 1, 61)( 2, 64)( 3, 63)( 4, 62)( 5, 77)( 6, 80)( 7, 79)( 8, 78)
( 9, 73)( 10, 76)( 11, 75)( 12, 74)( 13, 69)( 14, 72)( 15, 71)( 16, 70)
( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21,101)( 22,104)( 23,103)( 24,102)
( 25,117)( 26,120)( 27,119)( 28,118)( 29,113)( 30,116)( 31,115)( 32,114)
( 33,109)( 34,112)( 35,111)( 36,110)( 37,105)( 38,108)( 39,107)( 40,106)
( 41, 81)( 42, 84)( 43, 83)( 44, 82)( 45, 97)( 46,100)( 47, 99)( 48, 98)
( 49, 93)( 50, 96)( 51, 95)( 52, 94)( 53, 89)( 54, 92)( 55, 91)( 56, 90)
( 57, 85)( 58, 88)( 59, 87)( 60, 86)(122,124)(125,137)(126,140)(127,139)
(128,138)(129,133)(130,136)(131,135)(132,134)(141,161)(142,164)(143,163)
(144,162)(145,177)(146,180)(147,179)(148,178)(149,173)(150,176)(151,175)
(152,174)(153,169)(154,172)(155,171)(156,170)(157,165)(158,168)(159,167)
(160,166)(181,241)(182,244)(183,243)(184,242)(185,257)(186,260)(187,259)
(188,258)(189,253)(190,256)(191,255)(192,254)(193,249)(194,252)(195,251)
(196,250)(197,245)(198,248)(199,247)(200,246)(201,281)(202,284)(203,283)
(204,282)(205,297)(206,300)(207,299)(208,298)(209,293)(210,296)(211,295)
(212,294)(213,289)(214,292)(215,291)(216,290)(217,285)(218,288)(219,287)
(220,286)(221,261)(222,264)(223,263)(224,262)(225,277)(226,280)(227,279)
(228,278)(229,273)(230,276)(231,275)(232,274)(233,269)(234,272)(235,271)
(236,270)(237,265)(238,268)(239,267)(240,266)(302,304)(305,317)(306,320)
(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)(321,341)(322,344)
(323,343)(324,342)(325,357)(326,360)(327,359)(328,358)(329,353)(330,356)
(331,355)(332,354)(333,349)(334,352)(335,351)(336,350)(337,345)(338,348)
(339,347)(340,346);;
s2 := ( 1,206)( 2,205)( 3,208)( 4,207)( 5,202)( 6,201)( 7,204)( 8,203)
( 9,218)( 10,217)( 11,220)( 12,219)( 13,214)( 14,213)( 15,216)( 16,215)
( 17,210)( 18,209)( 19,212)( 20,211)( 21,186)( 22,185)( 23,188)( 24,187)
( 25,182)( 26,181)( 27,184)( 28,183)( 29,198)( 30,197)( 31,200)( 32,199)
( 33,194)( 34,193)( 35,196)( 36,195)( 37,190)( 38,189)( 39,192)( 40,191)
( 41,226)( 42,225)( 43,228)( 44,227)( 45,222)( 46,221)( 47,224)( 48,223)
( 49,238)( 50,237)( 51,240)( 52,239)( 53,234)( 54,233)( 55,236)( 56,235)
( 57,230)( 58,229)( 59,232)( 60,231)( 61,266)( 62,265)( 63,268)( 64,267)
( 65,262)( 66,261)( 67,264)( 68,263)( 69,278)( 70,277)( 71,280)( 72,279)
( 73,274)( 74,273)( 75,276)( 76,275)( 77,270)( 78,269)( 79,272)( 80,271)
( 81,246)( 82,245)( 83,248)( 84,247)( 85,242)( 86,241)( 87,244)( 88,243)
( 89,258)( 90,257)( 91,260)( 92,259)( 93,254)( 94,253)( 95,256)( 96,255)
( 97,250)( 98,249)( 99,252)(100,251)(101,286)(102,285)(103,288)(104,287)
(105,282)(106,281)(107,284)(108,283)(109,298)(110,297)(111,300)(112,299)
(113,294)(114,293)(115,296)(116,295)(117,290)(118,289)(119,292)(120,291)
(121,326)(122,325)(123,328)(124,327)(125,322)(126,321)(127,324)(128,323)
(129,338)(130,337)(131,340)(132,339)(133,334)(134,333)(135,336)(136,335)
(137,330)(138,329)(139,332)(140,331)(141,306)(142,305)(143,308)(144,307)
(145,302)(146,301)(147,304)(148,303)(149,318)(150,317)(151,320)(152,319)
(153,314)(154,313)(155,316)(156,315)(157,310)(158,309)(159,312)(160,311)
(161,346)(162,345)(163,348)(164,347)(165,342)(166,341)(167,344)(168,343)
(169,358)(170,357)(171,360)(172,359)(173,354)(174,353)(175,356)(176,355)
(177,350)(178,349)(179,352)(180,351);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*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*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(360)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)
( 61,121)( 62,122)( 63,124)( 64,123)( 65,125)( 66,126)( 67,128)( 68,127)
( 69,129)( 70,130)( 71,132)( 72,131)( 73,133)( 74,134)( 75,136)( 76,135)
( 77,137)( 78,138)( 79,140)( 80,139)( 81,141)( 82,142)( 83,144)( 84,143)
( 85,145)( 86,146)( 87,148)( 88,147)( 89,149)( 90,150)( 91,152)( 92,151)
( 93,153)( 94,154)( 95,156)( 96,155)( 97,157)( 98,158)( 99,160)(100,159)
(101,161)(102,162)(103,164)(104,163)(105,165)(106,166)(107,168)(108,167)
(109,169)(110,170)(111,172)(112,171)(113,173)(114,174)(115,176)(116,175)
(117,177)(118,178)(119,180)(120,179)(183,184)(187,188)(191,192)(195,196)
(199,200)(203,204)(207,208)(211,212)(215,216)(219,220)(223,224)(227,228)
(231,232)(235,236)(239,240)(241,301)(242,302)(243,304)(244,303)(245,305)
(246,306)(247,308)(248,307)(249,309)(250,310)(251,312)(252,311)(253,313)
(254,314)(255,316)(256,315)(257,317)(258,318)(259,320)(260,319)(261,321)
(262,322)(263,324)(264,323)(265,325)(266,326)(267,328)(268,327)(269,329)
(270,330)(271,332)(272,331)(273,333)(274,334)(275,336)(276,335)(277,337)
(278,338)(279,340)(280,339)(281,341)(282,342)(283,344)(284,343)(285,345)
(286,346)(287,348)(288,347)(289,349)(290,350)(291,352)(292,351)(293,353)
(294,354)(295,356)(296,355)(297,357)(298,358)(299,360)(300,359);
s1 := Sym(360)!( 1, 61)( 2, 64)( 3, 63)( 4, 62)( 5, 77)( 6, 80)( 7, 79)
( 8, 78)( 9, 73)( 10, 76)( 11, 75)( 12, 74)( 13, 69)( 14, 72)( 15, 71)
( 16, 70)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21,101)( 22,104)( 23,103)
( 24,102)( 25,117)( 26,120)( 27,119)( 28,118)( 29,113)( 30,116)( 31,115)
( 32,114)( 33,109)( 34,112)( 35,111)( 36,110)( 37,105)( 38,108)( 39,107)
( 40,106)( 41, 81)( 42, 84)( 43, 83)( 44, 82)( 45, 97)( 46,100)( 47, 99)
( 48, 98)( 49, 93)( 50, 96)( 51, 95)( 52, 94)( 53, 89)( 54, 92)( 55, 91)
( 56, 90)( 57, 85)( 58, 88)( 59, 87)( 60, 86)(122,124)(125,137)(126,140)
(127,139)(128,138)(129,133)(130,136)(131,135)(132,134)(141,161)(142,164)
(143,163)(144,162)(145,177)(146,180)(147,179)(148,178)(149,173)(150,176)
(151,175)(152,174)(153,169)(154,172)(155,171)(156,170)(157,165)(158,168)
(159,167)(160,166)(181,241)(182,244)(183,243)(184,242)(185,257)(186,260)
(187,259)(188,258)(189,253)(190,256)(191,255)(192,254)(193,249)(194,252)
(195,251)(196,250)(197,245)(198,248)(199,247)(200,246)(201,281)(202,284)
(203,283)(204,282)(205,297)(206,300)(207,299)(208,298)(209,293)(210,296)
(211,295)(212,294)(213,289)(214,292)(215,291)(216,290)(217,285)(218,288)
(219,287)(220,286)(221,261)(222,264)(223,263)(224,262)(225,277)(226,280)
(227,279)(228,278)(229,273)(230,276)(231,275)(232,274)(233,269)(234,272)
(235,271)(236,270)(237,265)(238,268)(239,267)(240,266)(302,304)(305,317)
(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)(321,341)
(322,344)(323,343)(324,342)(325,357)(326,360)(327,359)(328,358)(329,353)
(330,356)(331,355)(332,354)(333,349)(334,352)(335,351)(336,350)(337,345)
(338,348)(339,347)(340,346);
s2 := Sym(360)!( 1,206)( 2,205)( 3,208)( 4,207)( 5,202)( 6,201)( 7,204)
( 8,203)( 9,218)( 10,217)( 11,220)( 12,219)( 13,214)( 14,213)( 15,216)
( 16,215)( 17,210)( 18,209)( 19,212)( 20,211)( 21,186)( 22,185)( 23,188)
( 24,187)( 25,182)( 26,181)( 27,184)( 28,183)( 29,198)( 30,197)( 31,200)
( 32,199)( 33,194)( 34,193)( 35,196)( 36,195)( 37,190)( 38,189)( 39,192)
( 40,191)( 41,226)( 42,225)( 43,228)( 44,227)( 45,222)( 46,221)( 47,224)
( 48,223)( 49,238)( 50,237)( 51,240)( 52,239)( 53,234)( 54,233)( 55,236)
( 56,235)( 57,230)( 58,229)( 59,232)( 60,231)( 61,266)( 62,265)( 63,268)
( 64,267)( 65,262)( 66,261)( 67,264)( 68,263)( 69,278)( 70,277)( 71,280)
( 72,279)( 73,274)( 74,273)( 75,276)( 76,275)( 77,270)( 78,269)( 79,272)
( 80,271)( 81,246)( 82,245)( 83,248)( 84,247)( 85,242)( 86,241)( 87,244)
( 88,243)( 89,258)( 90,257)( 91,260)( 92,259)( 93,254)( 94,253)( 95,256)
( 96,255)( 97,250)( 98,249)( 99,252)(100,251)(101,286)(102,285)(103,288)
(104,287)(105,282)(106,281)(107,284)(108,283)(109,298)(110,297)(111,300)
(112,299)(113,294)(114,293)(115,296)(116,295)(117,290)(118,289)(119,292)
(120,291)(121,326)(122,325)(123,328)(124,327)(125,322)(126,321)(127,324)
(128,323)(129,338)(130,337)(131,340)(132,339)(133,334)(134,333)(135,336)
(136,335)(137,330)(138,329)(139,332)(140,331)(141,306)(142,305)(143,308)
(144,307)(145,302)(146,301)(147,304)(148,303)(149,318)(150,317)(151,320)
(152,319)(153,314)(154,313)(155,316)(156,315)(157,310)(158,309)(159,312)
(160,311)(161,346)(162,345)(163,348)(164,347)(165,342)(166,341)(167,344)
(168,343)(169,358)(170,357)(171,360)(172,359)(173,354)(174,353)(175,356)
(176,355)(177,350)(178,349)(179,352)(180,351);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*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*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;
References : None.
to this polytope