Polytope of Type {60,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,4764)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 180, 360, 12
Order of s0s1s2 : 20
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {30,4}*720
5-fold quotients : {12,4}*288
9-fold quotients : {20,4}*160
10-fold quotients : {6,4}*144
18-fold quotients : {20,2}*80, {10,4}*80
20-fold quotients : {6,4}*72
36-fold quotients : {10,2}*40
45-fold quotients : {4,4}*32
72-fold quotients : {5,2}*20
90-fold quotients : {2,4}*16, {4,2}*16
180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 91)( 2, 95)( 3, 94)( 4, 93)( 5, 92)( 6,101)( 7,105)( 8,104)
( 9,103)( 10,102)( 11, 96)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16,121)
( 17,125)( 18,124)( 19,123)( 20,122)( 21,131)( 22,135)( 23,134)( 24,133)
( 25,132)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,106)( 32,110)
( 33,109)( 34,108)( 35,107)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,111)( 42,115)( 43,114)( 44,113)( 45,112)( 46,136)( 47,140)( 48,139)
( 49,138)( 50,137)( 51,146)( 52,150)( 53,149)( 54,148)( 55,147)( 56,141)
( 57,145)( 58,144)( 59,143)( 60,142)( 61,166)( 62,170)( 63,169)( 64,168)
( 65,167)( 66,176)( 67,180)( 68,179)( 69,178)( 70,177)( 71,171)( 72,175)
( 73,174)( 74,173)( 75,172)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)
( 81,161)( 82,165)( 83,164)( 84,163)( 85,162)( 86,156)( 87,160)( 88,159)
( 89,158)( 90,157)(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 := ( 1,277)( 2,276)( 3,280)( 4,279)( 5,278)( 6,272)( 7,271)( 8,275)
( 9,274)( 10,273)( 11,282)( 12,281)( 13,285)( 14,284)( 15,283)( 16,297)
( 17,296)( 18,300)( 19,299)( 20,298)( 21,292)( 22,291)( 23,295)( 24,294)
( 25,293)( 26,287)( 27,286)( 28,290)( 29,289)( 30,288)( 31,302)( 32,301)
( 33,305)( 34,304)( 35,303)( 36,312)( 37,311)( 38,315)( 39,314)( 40,313)
( 41,307)( 42,306)( 43,310)( 44,309)( 45,308)( 46,322)( 47,321)( 48,325)
( 49,324)( 50,323)( 51,317)( 52,316)( 53,320)( 54,319)( 55,318)( 56,327)
( 57,326)( 58,330)( 59,329)( 60,328)( 61,342)( 62,341)( 63,345)( 64,344)
( 65,343)( 66,337)( 67,336)( 68,340)( 69,339)( 70,338)( 71,332)( 72,331)
( 73,335)( 74,334)( 75,333)( 76,347)( 77,346)( 78,350)( 79,349)( 80,348)
( 81,357)( 82,356)( 83,360)( 84,359)( 85,358)( 86,352)( 87,351)( 88,355)
( 89,354)( 90,353)( 91,187)( 92,186)( 93,190)( 94,189)( 95,188)( 96,182)
( 97,181)( 98,185)( 99,184)(100,183)(101,192)(102,191)(103,195)(104,194)
(105,193)(106,207)(107,206)(108,210)(109,209)(110,208)(111,202)(112,201)
(113,205)(114,204)(115,203)(116,197)(117,196)(118,200)(119,199)(120,198)
(121,212)(122,211)(123,215)(124,214)(125,213)(126,222)(127,221)(128,225)
(129,224)(130,223)(131,217)(132,216)(133,220)(134,219)(135,218)(136,232)
(137,231)(138,235)(139,234)(140,233)(141,227)(142,226)(143,230)(144,229)
(145,228)(146,237)(147,236)(148,240)(149,239)(150,238)(151,252)(152,251)
(153,255)(154,254)(155,253)(156,247)(157,246)(158,250)(159,249)(160,248)
(161,242)(162,241)(163,245)(164,244)(165,243)(166,257)(167,256)(168,260)
(169,259)(170,258)(171,267)(172,266)(173,270)(174,269)(175,268)(176,262)
(177,261)(178,265)(179,264)(180,263);;
s2 := ( 6, 36)( 7, 37)( 8, 38)( 9, 39)( 10, 40)( 11, 26)( 12, 27)( 13, 28)
( 14, 29)( 15, 30)( 16, 31)( 17, 32)( 18, 33)( 19, 34)( 20, 35)( 51, 81)
( 52, 82)( 53, 83)( 54, 84)( 55, 85)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 96,126)( 97,127)
( 98,128)( 99,129)(100,130)(101,116)(102,117)(103,118)(104,119)(105,120)
(106,121)(107,122)(108,123)(109,124)(110,125)(141,171)(142,172)(143,173)
(144,174)(145,175)(146,161)(147,162)(148,163)(149,164)(150,165)(151,166)
(152,167)(153,168)(154,169)(155,170)(181,271)(182,272)(183,273)(184,274)
(185,275)(186,306)(187,307)(188,308)(189,309)(190,310)(191,296)(192,297)
(193,298)(194,299)(195,300)(196,301)(197,302)(198,303)(199,304)(200,305)
(201,291)(202,292)(203,293)(204,294)(205,295)(206,281)(207,282)(208,283)
(209,284)(210,285)(211,286)(212,287)(213,288)(214,289)(215,290)(216,276)
(217,277)(218,278)(219,279)(220,280)(221,311)(222,312)(223,313)(224,314)
(225,315)(226,316)(227,317)(228,318)(229,319)(230,320)(231,351)(232,352)
(233,353)(234,354)(235,355)(236,341)(237,342)(238,343)(239,344)(240,345)
(241,346)(242,347)(243,348)(244,349)(245,350)(246,336)(247,337)(248,338)
(249,339)(250,340)(251,326)(252,327)(253,328)(254,329)(255,330)(256,331)
(257,332)(258,333)(259,334)(260,335)(261,321)(262,322)(263,323)(264,324)
(265,325)(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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*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*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(360)!( 1, 91)( 2, 95)( 3, 94)( 4, 93)( 5, 92)( 6,101)( 7,105)
( 8,104)( 9,103)( 10,102)( 11, 96)( 12,100)( 13, 99)( 14, 98)( 15, 97)
( 16,121)( 17,125)( 18,124)( 19,123)( 20,122)( 21,131)( 22,135)( 23,134)
( 24,133)( 25,132)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,106)
( 32,110)( 33,109)( 34,108)( 35,107)( 36,116)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,111)( 42,115)( 43,114)( 44,113)( 45,112)( 46,136)( 47,140)
( 48,139)( 49,138)( 50,137)( 51,146)( 52,150)( 53,149)( 54,148)( 55,147)
( 56,141)( 57,145)( 58,144)( 59,143)( 60,142)( 61,166)( 62,170)( 63,169)
( 64,168)( 65,167)( 66,176)( 67,180)( 68,179)( 69,178)( 70,177)( 71,171)
( 72,175)( 73,174)( 74,173)( 75,172)( 76,151)( 77,155)( 78,154)( 79,153)
( 80,152)( 81,161)( 82,165)( 83,164)( 84,163)( 85,162)( 86,156)( 87,160)
( 88,159)( 89,158)( 90,157)(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)!( 1,277)( 2,276)( 3,280)( 4,279)( 5,278)( 6,272)( 7,271)
( 8,275)( 9,274)( 10,273)( 11,282)( 12,281)( 13,285)( 14,284)( 15,283)
( 16,297)( 17,296)( 18,300)( 19,299)( 20,298)( 21,292)( 22,291)( 23,295)
( 24,294)( 25,293)( 26,287)( 27,286)( 28,290)( 29,289)( 30,288)( 31,302)
( 32,301)( 33,305)( 34,304)( 35,303)( 36,312)( 37,311)( 38,315)( 39,314)
( 40,313)( 41,307)( 42,306)( 43,310)( 44,309)( 45,308)( 46,322)( 47,321)
( 48,325)( 49,324)( 50,323)( 51,317)( 52,316)( 53,320)( 54,319)( 55,318)
( 56,327)( 57,326)( 58,330)( 59,329)( 60,328)( 61,342)( 62,341)( 63,345)
( 64,344)( 65,343)( 66,337)( 67,336)( 68,340)( 69,339)( 70,338)( 71,332)
( 72,331)( 73,335)( 74,334)( 75,333)( 76,347)( 77,346)( 78,350)( 79,349)
( 80,348)( 81,357)( 82,356)( 83,360)( 84,359)( 85,358)( 86,352)( 87,351)
( 88,355)( 89,354)( 90,353)( 91,187)( 92,186)( 93,190)( 94,189)( 95,188)
( 96,182)( 97,181)( 98,185)( 99,184)(100,183)(101,192)(102,191)(103,195)
(104,194)(105,193)(106,207)(107,206)(108,210)(109,209)(110,208)(111,202)
(112,201)(113,205)(114,204)(115,203)(116,197)(117,196)(118,200)(119,199)
(120,198)(121,212)(122,211)(123,215)(124,214)(125,213)(126,222)(127,221)
(128,225)(129,224)(130,223)(131,217)(132,216)(133,220)(134,219)(135,218)
(136,232)(137,231)(138,235)(139,234)(140,233)(141,227)(142,226)(143,230)
(144,229)(145,228)(146,237)(147,236)(148,240)(149,239)(150,238)(151,252)
(152,251)(153,255)(154,254)(155,253)(156,247)(157,246)(158,250)(159,249)
(160,248)(161,242)(162,241)(163,245)(164,244)(165,243)(166,257)(167,256)
(168,260)(169,259)(170,258)(171,267)(172,266)(173,270)(174,269)(175,268)
(176,262)(177,261)(178,265)(179,264)(180,263);
s2 := Sym(360)!( 6, 36)( 7, 37)( 8, 38)( 9, 39)( 10, 40)( 11, 26)( 12, 27)
( 13, 28)( 14, 29)( 15, 30)( 16, 31)( 17, 32)( 18, 33)( 19, 34)( 20, 35)
( 51, 81)( 52, 82)( 53, 83)( 54, 84)( 55, 85)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 96,126)
( 97,127)( 98,128)( 99,129)(100,130)(101,116)(102,117)(103,118)(104,119)
(105,120)(106,121)(107,122)(108,123)(109,124)(110,125)(141,171)(142,172)
(143,173)(144,174)(145,175)(146,161)(147,162)(148,163)(149,164)(150,165)
(151,166)(152,167)(153,168)(154,169)(155,170)(181,271)(182,272)(183,273)
(184,274)(185,275)(186,306)(187,307)(188,308)(189,309)(190,310)(191,296)
(192,297)(193,298)(194,299)(195,300)(196,301)(197,302)(198,303)(199,304)
(200,305)(201,291)(202,292)(203,293)(204,294)(205,295)(206,281)(207,282)
(208,283)(209,284)(210,285)(211,286)(212,287)(213,288)(214,289)(215,290)
(216,276)(217,277)(218,278)(219,279)(220,280)(221,311)(222,312)(223,313)
(224,314)(225,315)(226,316)(227,317)(228,318)(229,319)(230,320)(231,351)
(232,352)(233,353)(234,354)(235,355)(236,341)(237,342)(238,343)(239,344)
(240,345)(241,346)(242,347)(243,348)(244,349)(245,350)(246,336)(247,337)
(248,338)(249,339)(250,340)(251,326)(252,327)(253,328)(254,329)(255,330)
(256,331)(257,332)(258,333)(259,334)(260,335)(261,321)(262,322)(263,323)
(264,324)(265,325)(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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*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*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope