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# Polytope of Type {60,4}

Atlas Canonical Name : {60,4}*960b
if this polytope has a name.
Group : SmallGroup(960,11090)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 120, 240, 8
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{60,4,2} of size 1920
Vertex Figure Of :
{2,60,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {60,4}*480b, {60,4}*480c, {30,4}*480
4-fold quotients : {60,2}*240, {15,4}*240, {30,4}*240b, {30,4}*240c
5-fold quotients : {12,4}*192b
8-fold quotients : {15,4}*120, {30,2}*120
10-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
12-fold quotients : {20,2}*80
16-fold quotients : {15,2}*60
20-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
24-fold quotients : {10,2}*40
40-fold quotients : {3,4}*24, {6,2}*24
48-fold quotients : {5,2}*20
60-fold quotients : {4,2}*16
80-fold quotients : {3,2}*12
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {120,4}*1920c, {120,4}*1920d
Permutation Representation (GAP) :
```s0 := (  2,  3)(  5, 17)(  6, 19)(  7, 18)(  8, 20)(  9, 13)( 10, 15)( 11, 14)
( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)( 27, 58)
( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)( 35, 50)
( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)( 66, 79)
( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)( 90,115)
( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)( 98,107)
( 99,106)(100,108)(121,181)(122,183)(123,182)(124,184)(125,197)(126,199)
(127,198)(128,200)(129,193)(130,195)(131,194)(132,196)(133,189)(134,191)
(135,190)(136,192)(137,185)(138,187)(139,186)(140,188)(141,221)(142,223)
(143,222)(144,224)(145,237)(146,239)(147,238)(148,240)(149,233)(150,235)
(151,234)(152,236)(153,229)(154,231)(155,230)(156,232)(157,225)(158,227)
(159,226)(160,228)(161,201)(162,203)(163,202)(164,204)(165,217)(166,219)
(167,218)(168,220)(169,213)(170,215)(171,214)(172,216)(173,209)(174,211)
(175,210)(176,212)(177,205)(178,207)(179,206)(180,208)(242,243)(245,257)
(246,259)(247,258)(248,260)(249,253)(250,255)(251,254)(252,256)(261,281)
(262,283)(263,282)(264,284)(265,297)(266,299)(267,298)(268,300)(269,293)
(270,295)(271,294)(272,296)(273,289)(274,291)(275,290)(276,292)(277,285)
(278,287)(279,286)(280,288)(302,303)(305,317)(306,319)(307,318)(308,320)
(309,313)(310,315)(311,314)(312,316)(321,341)(322,343)(323,342)(324,344)
(325,357)(326,359)(327,358)(328,360)(329,353)(330,355)(331,354)(332,356)
(333,349)(334,351)(335,350)(336,352)(337,345)(338,347)(339,346)(340,348)
(361,421)(362,423)(363,422)(364,424)(365,437)(366,439)(367,438)(368,440)
(369,433)(370,435)(371,434)(372,436)(373,429)(374,431)(375,430)(376,432)
(377,425)(378,427)(379,426)(380,428)(381,461)(382,463)(383,462)(384,464)
(385,477)(386,479)(387,478)(388,480)(389,473)(390,475)(391,474)(392,476)
(393,469)(394,471)(395,470)(396,472)(397,465)(398,467)(399,466)(400,468)
(401,441)(402,443)(403,442)(404,444)(405,457)(406,459)(407,458)(408,460)
(409,453)(410,455)(411,454)(412,456)(413,449)(414,451)(415,450)(416,452)
(417,445)(418,447)(419,446)(420,448);;
s1 := (  1,145)(  2,146)(  3,148)(  4,147)(  5,141)(  6,142)(  7,144)(  8,143)
(  9,157)( 10,158)( 11,160)( 12,159)( 13,153)( 14,154)( 15,156)( 16,155)
( 17,149)( 18,150)( 19,152)( 20,151)( 21,125)( 22,126)( 23,128)( 24,127)
( 25,121)( 26,122)( 27,124)( 28,123)( 29,137)( 30,138)( 31,140)( 32,139)
( 33,133)( 34,134)( 35,136)( 36,135)( 37,129)( 38,130)( 39,132)( 40,131)
( 41,165)( 42,166)( 43,168)( 44,167)( 45,161)( 46,162)( 47,164)( 48,163)
( 49,177)( 50,178)( 51,180)( 52,179)( 53,173)( 54,174)( 55,176)( 56,175)
( 57,169)( 58,170)( 59,172)( 60,171)( 61,205)( 62,206)( 63,208)( 64,207)
( 65,201)( 66,202)( 67,204)( 68,203)( 69,217)( 70,218)( 71,220)( 72,219)
( 73,213)( 74,214)( 75,216)( 76,215)( 77,209)( 78,210)( 79,212)( 80,211)
( 81,185)( 82,186)( 83,188)( 84,187)( 85,181)( 86,182)( 87,184)( 88,183)
( 89,197)( 90,198)( 91,200)( 92,199)( 93,193)( 94,194)( 95,196)( 96,195)
( 97,189)( 98,190)( 99,192)(100,191)(101,225)(102,226)(103,228)(104,227)
(105,221)(106,222)(107,224)(108,223)(109,237)(110,238)(111,240)(112,239)
(113,233)(114,234)(115,236)(116,235)(117,229)(118,230)(119,232)(120,231)
(241,385)(242,386)(243,388)(244,387)(245,381)(246,382)(247,384)(248,383)
(249,397)(250,398)(251,400)(252,399)(253,393)(254,394)(255,396)(256,395)
(257,389)(258,390)(259,392)(260,391)(261,365)(262,366)(263,368)(264,367)
(265,361)(266,362)(267,364)(268,363)(269,377)(270,378)(271,380)(272,379)
(273,373)(274,374)(275,376)(276,375)(277,369)(278,370)(279,372)(280,371)
(281,405)(282,406)(283,408)(284,407)(285,401)(286,402)(287,404)(288,403)
(289,417)(290,418)(291,420)(292,419)(293,413)(294,414)(295,416)(296,415)
(297,409)(298,410)(299,412)(300,411)(301,445)(302,446)(303,448)(304,447)
(305,441)(306,442)(307,444)(308,443)(309,457)(310,458)(311,460)(312,459)
(313,453)(314,454)(315,456)(316,455)(317,449)(318,450)(319,452)(320,451)
(321,425)(322,426)(323,428)(324,427)(325,421)(326,422)(327,424)(328,423)
(329,437)(330,438)(331,440)(332,439)(333,433)(334,434)(335,436)(336,435)
(337,429)(338,430)(339,432)(340,431)(341,465)(342,466)(343,468)(344,467)
(345,461)(346,462)(347,464)(348,463)(349,477)(350,478)(351,480)(352,479)
(353,473)(354,474)(355,476)(356,475)(357,469)(358,470)(359,472)(360,471);;
s2 := (  1,244)(  2,243)(  3,242)(  4,241)(  5,248)(  6,247)(  7,246)(  8,245)
(  9,252)( 10,251)( 11,250)( 12,249)( 13,256)( 14,255)( 15,254)( 16,253)
( 17,260)( 18,259)( 19,258)( 20,257)( 21,264)( 22,263)( 23,262)( 24,261)
( 25,268)( 26,267)( 27,266)( 28,265)( 29,272)( 30,271)( 31,270)( 32,269)
( 33,276)( 34,275)( 35,274)( 36,273)( 37,280)( 38,279)( 39,278)( 40,277)
( 41,284)( 42,283)( 43,282)( 44,281)( 45,288)( 46,287)( 47,286)( 48,285)
( 49,292)( 50,291)( 51,290)( 52,289)( 53,296)( 54,295)( 55,294)( 56,293)
( 57,300)( 58,299)( 59,298)( 60,297)( 61,304)( 62,303)( 63,302)( 64,301)
( 65,308)( 66,307)( 67,306)( 68,305)( 69,312)( 70,311)( 71,310)( 72,309)
( 73,316)( 74,315)( 75,314)( 76,313)( 77,320)( 78,319)( 79,318)( 80,317)
( 81,324)( 82,323)( 83,322)( 84,321)( 85,328)( 86,327)( 87,326)( 88,325)
( 89,332)( 90,331)( 91,330)( 92,329)( 93,336)( 94,335)( 95,334)( 96,333)
( 97,340)( 98,339)( 99,338)(100,337)(101,344)(102,343)(103,342)(104,341)
(105,348)(106,347)(107,346)(108,345)(109,352)(110,351)(111,350)(112,349)
(113,356)(114,355)(115,354)(116,353)(117,360)(118,359)(119,358)(120,357)
(121,364)(122,363)(123,362)(124,361)(125,368)(126,367)(127,366)(128,365)
(129,372)(130,371)(131,370)(132,369)(133,376)(134,375)(135,374)(136,373)
(137,380)(138,379)(139,378)(140,377)(141,384)(142,383)(143,382)(144,381)
(145,388)(146,387)(147,386)(148,385)(149,392)(150,391)(151,390)(152,389)
(153,396)(154,395)(155,394)(156,393)(157,400)(158,399)(159,398)(160,397)
(161,404)(162,403)(163,402)(164,401)(165,408)(166,407)(167,406)(168,405)
(169,412)(170,411)(171,410)(172,409)(173,416)(174,415)(175,414)(176,413)
(177,420)(178,419)(179,418)(180,417)(181,424)(182,423)(183,422)(184,421)
(185,428)(186,427)(187,426)(188,425)(189,432)(190,431)(191,430)(192,429)
(193,436)(194,435)(195,434)(196,433)(197,440)(198,439)(199,438)(200,437)
(201,444)(202,443)(203,442)(204,441)(205,448)(206,447)(207,446)(208,445)
(209,452)(210,451)(211,450)(212,449)(213,456)(214,455)(215,454)(216,453)
(217,460)(218,459)(219,458)(220,457)(221,464)(222,463)(223,462)(224,461)
(225,468)(226,467)(227,466)(228,465)(229,472)(230,471)(231,470)(232,469)
(233,476)(234,475)(235,474)(236,473)(237,480)(238,479)(239,478)(240,477);;
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,
s0*s1*s2*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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(480)!(  2,  3)(  5, 17)(  6, 19)(  7, 18)(  8, 20)(  9, 13)( 10, 15)
( 11, 14)( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)
( 27, 58)( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)
( 35, 50)( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)
( 66, 79)( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)
( 90,115)( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)
( 98,107)( 99,106)(100,108)(121,181)(122,183)(123,182)(124,184)(125,197)
(126,199)(127,198)(128,200)(129,193)(130,195)(131,194)(132,196)(133,189)
(134,191)(135,190)(136,192)(137,185)(138,187)(139,186)(140,188)(141,221)
(142,223)(143,222)(144,224)(145,237)(146,239)(147,238)(148,240)(149,233)
(150,235)(151,234)(152,236)(153,229)(154,231)(155,230)(156,232)(157,225)
(158,227)(159,226)(160,228)(161,201)(162,203)(163,202)(164,204)(165,217)
(166,219)(167,218)(168,220)(169,213)(170,215)(171,214)(172,216)(173,209)
(174,211)(175,210)(176,212)(177,205)(178,207)(179,206)(180,208)(242,243)
(245,257)(246,259)(247,258)(248,260)(249,253)(250,255)(251,254)(252,256)
(261,281)(262,283)(263,282)(264,284)(265,297)(266,299)(267,298)(268,300)
(269,293)(270,295)(271,294)(272,296)(273,289)(274,291)(275,290)(276,292)
(277,285)(278,287)(279,286)(280,288)(302,303)(305,317)(306,319)(307,318)
(308,320)(309,313)(310,315)(311,314)(312,316)(321,341)(322,343)(323,342)
(324,344)(325,357)(326,359)(327,358)(328,360)(329,353)(330,355)(331,354)
(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)(338,347)(339,346)
(340,348)(361,421)(362,423)(363,422)(364,424)(365,437)(366,439)(367,438)
(368,440)(369,433)(370,435)(371,434)(372,436)(373,429)(374,431)(375,430)
(376,432)(377,425)(378,427)(379,426)(380,428)(381,461)(382,463)(383,462)
(384,464)(385,477)(386,479)(387,478)(388,480)(389,473)(390,475)(391,474)
(392,476)(393,469)(394,471)(395,470)(396,472)(397,465)(398,467)(399,466)
(400,468)(401,441)(402,443)(403,442)(404,444)(405,457)(406,459)(407,458)
(408,460)(409,453)(410,455)(411,454)(412,456)(413,449)(414,451)(415,450)
(416,452)(417,445)(418,447)(419,446)(420,448);
s1 := Sym(480)!(  1,145)(  2,146)(  3,148)(  4,147)(  5,141)(  6,142)(  7,144)
(  8,143)(  9,157)( 10,158)( 11,160)( 12,159)( 13,153)( 14,154)( 15,156)
( 16,155)( 17,149)( 18,150)( 19,152)( 20,151)( 21,125)( 22,126)( 23,128)
( 24,127)( 25,121)( 26,122)( 27,124)( 28,123)( 29,137)( 30,138)( 31,140)
( 32,139)( 33,133)( 34,134)( 35,136)( 36,135)( 37,129)( 38,130)( 39,132)
( 40,131)( 41,165)( 42,166)( 43,168)( 44,167)( 45,161)( 46,162)( 47,164)
( 48,163)( 49,177)( 50,178)( 51,180)( 52,179)( 53,173)( 54,174)( 55,176)
( 56,175)( 57,169)( 58,170)( 59,172)( 60,171)( 61,205)( 62,206)( 63,208)
( 64,207)( 65,201)( 66,202)( 67,204)( 68,203)( 69,217)( 70,218)( 71,220)
( 72,219)( 73,213)( 74,214)( 75,216)( 76,215)( 77,209)( 78,210)( 79,212)
( 80,211)( 81,185)( 82,186)( 83,188)( 84,187)( 85,181)( 86,182)( 87,184)
( 88,183)( 89,197)( 90,198)( 91,200)( 92,199)( 93,193)( 94,194)( 95,196)
( 96,195)( 97,189)( 98,190)( 99,192)(100,191)(101,225)(102,226)(103,228)
(104,227)(105,221)(106,222)(107,224)(108,223)(109,237)(110,238)(111,240)
(112,239)(113,233)(114,234)(115,236)(116,235)(117,229)(118,230)(119,232)
(120,231)(241,385)(242,386)(243,388)(244,387)(245,381)(246,382)(247,384)
(248,383)(249,397)(250,398)(251,400)(252,399)(253,393)(254,394)(255,396)
(256,395)(257,389)(258,390)(259,392)(260,391)(261,365)(262,366)(263,368)
(264,367)(265,361)(266,362)(267,364)(268,363)(269,377)(270,378)(271,380)
(272,379)(273,373)(274,374)(275,376)(276,375)(277,369)(278,370)(279,372)
(280,371)(281,405)(282,406)(283,408)(284,407)(285,401)(286,402)(287,404)
(288,403)(289,417)(290,418)(291,420)(292,419)(293,413)(294,414)(295,416)
(296,415)(297,409)(298,410)(299,412)(300,411)(301,445)(302,446)(303,448)
(304,447)(305,441)(306,442)(307,444)(308,443)(309,457)(310,458)(311,460)
(312,459)(313,453)(314,454)(315,456)(316,455)(317,449)(318,450)(319,452)
(320,451)(321,425)(322,426)(323,428)(324,427)(325,421)(326,422)(327,424)
(328,423)(329,437)(330,438)(331,440)(332,439)(333,433)(334,434)(335,436)
(336,435)(337,429)(338,430)(339,432)(340,431)(341,465)(342,466)(343,468)
(344,467)(345,461)(346,462)(347,464)(348,463)(349,477)(350,478)(351,480)
(352,479)(353,473)(354,474)(355,476)(356,475)(357,469)(358,470)(359,472)
(360,471);
s2 := Sym(480)!(  1,244)(  2,243)(  3,242)(  4,241)(  5,248)(  6,247)(  7,246)
(  8,245)(  9,252)( 10,251)( 11,250)( 12,249)( 13,256)( 14,255)( 15,254)
( 16,253)( 17,260)( 18,259)( 19,258)( 20,257)( 21,264)( 22,263)( 23,262)
( 24,261)( 25,268)( 26,267)( 27,266)( 28,265)( 29,272)( 30,271)( 31,270)
( 32,269)( 33,276)( 34,275)( 35,274)( 36,273)( 37,280)( 38,279)( 39,278)
( 40,277)( 41,284)( 42,283)( 43,282)( 44,281)( 45,288)( 46,287)( 47,286)
( 48,285)( 49,292)( 50,291)( 51,290)( 52,289)( 53,296)( 54,295)( 55,294)
( 56,293)( 57,300)( 58,299)( 59,298)( 60,297)( 61,304)( 62,303)( 63,302)
( 64,301)( 65,308)( 66,307)( 67,306)( 68,305)( 69,312)( 70,311)( 71,310)
( 72,309)( 73,316)( 74,315)( 75,314)( 76,313)( 77,320)( 78,319)( 79,318)
( 80,317)( 81,324)( 82,323)( 83,322)( 84,321)( 85,328)( 86,327)( 87,326)
( 88,325)( 89,332)( 90,331)( 91,330)( 92,329)( 93,336)( 94,335)( 95,334)
( 96,333)( 97,340)( 98,339)( 99,338)(100,337)(101,344)(102,343)(103,342)
(104,341)(105,348)(106,347)(107,346)(108,345)(109,352)(110,351)(111,350)
(112,349)(113,356)(114,355)(115,354)(116,353)(117,360)(118,359)(119,358)
(120,357)(121,364)(122,363)(123,362)(124,361)(125,368)(126,367)(127,366)
(128,365)(129,372)(130,371)(131,370)(132,369)(133,376)(134,375)(135,374)
(136,373)(137,380)(138,379)(139,378)(140,377)(141,384)(142,383)(143,382)
(144,381)(145,388)(146,387)(147,386)(148,385)(149,392)(150,391)(151,390)
(152,389)(153,396)(154,395)(155,394)(156,393)(157,400)(158,399)(159,398)
(160,397)(161,404)(162,403)(163,402)(164,401)(165,408)(166,407)(167,406)
(168,405)(169,412)(170,411)(171,410)(172,409)(173,416)(174,415)(175,414)
(176,413)(177,420)(178,419)(179,418)(180,417)(181,424)(182,423)(183,422)
(184,421)(185,428)(186,427)(187,426)(188,425)(189,432)(190,431)(191,430)
(192,429)(193,436)(194,435)(195,434)(196,433)(197,440)(198,439)(199,438)
(200,437)(201,444)(202,443)(203,442)(204,441)(205,448)(206,447)(207,446)
(208,445)(209,452)(210,451)(211,450)(212,449)(213,456)(214,455)(215,454)
(216,453)(217,460)(218,459)(219,458)(220,457)(221,464)(222,463)(223,462)
(224,461)(225,468)(226,467)(227,466)(228,465)(229,472)(230,471)(231,470)
(232,469)(233,476)(234,475)(235,474)(236,473)(237,480)(238,479)(239,478)
(240,477);
poly := sub<Sym(480)|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,
s0*s1*s2*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 >;

```
References : None.
to this polytope