Polytope of Type {602}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {602}*1204
Also Known As : 602-gon, {602}. if this polytope has another name.
Group : SmallGroup(1204,12)
Rank : 2
Schlafli Type : {602}
Number of vertices, edges, etc : 602, 602
Order of s₀s₁ : 602
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
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 : {301}*602
   7-fold quotients : {86}*172
   14-fold quotients : {43}*86
   43-fold quotients : {14}*28
   86-fold quotients : {7}*14
   301-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 43)(  3, 42)(  4, 41)(  5, 40)(  6, 39)(  7, 38)(  8, 37)(  9, 36)
( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 30)( 16, 29)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 44,259)( 45,301)( 46,300)
( 47,299)( 48,298)( 49,297)( 50,296)( 51,295)( 52,294)( 53,293)( 54,292)
( 55,291)( 56,290)( 57,289)( 58,288)( 59,287)( 60,286)( 61,285)( 62,284)
( 63,283)( 64,282)( 65,281)( 66,280)( 67,279)( 68,278)( 69,277)( 70,276)
( 71,275)( 72,274)( 73,273)( 74,272)( 75,271)( 76,270)( 77,269)( 78,268)
( 79,267)( 80,266)( 81,265)( 82,264)( 83,263)( 84,262)( 85,261)( 86,260)
( 87,216)( 88,258)( 89,257)( 90,256)( 91,255)( 92,254)( 93,253)( 94,252)
( 95,251)( 96,250)( 97,249)( 98,248)( 99,247)(100,246)(101,245)(102,244)
(103,243)(104,242)(105,241)(106,240)(107,239)(108,238)(109,237)(110,236)
(111,235)(112,234)(113,233)(114,232)(115,231)(116,230)(117,229)(118,228)
(119,227)(120,226)(121,225)(122,224)(123,223)(124,222)(125,221)(126,220)
(127,219)(128,218)(129,217)(130,173)(131,215)(132,214)(133,213)(134,212)
(135,211)(136,210)(137,209)(138,208)(139,207)(140,206)(141,205)(142,204)
(143,203)(144,202)(145,201)(146,200)(147,199)(148,198)(149,197)(150,196)
(151,195)(152,194)(153,193)(154,192)(155,191)(156,190)(157,189)(158,188)
(159,187)(160,186)(161,185)(162,184)(163,183)(164,182)(165,181)(166,180)
(167,179)(168,178)(169,177)(170,176)(171,175)(172,174)(303,344)(304,343)
(305,342)(306,341)(307,340)(308,339)(309,338)(310,337)(311,336)(312,335)
(313,334)(314,333)(315,332)(316,331)(317,330)(318,329)(319,328)(320,327)
(321,326)(322,325)(323,324)(345,560)(346,602)(347,601)(348,600)(349,599)
(350,598)(351,597)(352,596)(353,595)(354,594)(355,593)(356,592)(357,591)
(358,590)(359,589)(360,588)(361,587)(362,586)(363,585)(364,584)(365,583)
(366,582)(367,581)(368,580)(369,579)(370,578)(371,577)(372,576)(373,575)
(374,574)(375,573)(376,572)(377,571)(378,570)(379,569)(380,568)(381,567)
(382,566)(383,565)(384,564)(385,563)(386,562)(387,561)(388,517)(389,559)
(390,558)(391,557)(392,556)(393,555)(394,554)(395,553)(396,552)(397,551)
(398,550)(399,549)(400,548)(401,547)(402,546)(403,545)(404,544)(405,543)
(406,542)(407,541)(408,540)(409,539)(410,538)(411,537)(412,536)(413,535)
(414,534)(415,533)(416,532)(417,531)(418,530)(419,529)(420,528)(421,527)
(422,526)(423,525)(424,524)(425,523)(426,522)(427,521)(428,520)(429,519)
(430,518)(431,474)(432,516)(433,515)(434,514)(435,513)(436,512)(437,511)
(438,510)(439,509)(440,508)(441,507)(442,506)(443,505)(444,504)(445,503)
(446,502)(447,501)(448,500)(449,499)(450,498)(451,497)(452,496)(453,495)
(454,494)(455,493)(456,492)(457,491)(458,490)(459,489)(460,488)(461,487)
(462,486)(463,485)(464,484)(465,483)(466,482)(467,481)(468,480)(469,479)
(470,478)(471,477)(472,476)(473,475);;
s1 := (  1,346)(  2,345)(  3,387)(  4,386)(  5,385)(  6,384)(  7,383)(  8,382)
(  9,381)( 10,380)( 11,379)( 12,378)( 13,377)( 14,376)( 15,375)( 16,374)
( 17,373)( 18,372)( 19,371)( 20,370)( 21,369)( 22,368)( 23,367)( 24,366)
( 25,365)( 26,364)( 27,363)( 28,362)( 29,361)( 30,360)( 31,359)( 32,358)
( 33,357)( 34,356)( 35,355)( 36,354)( 37,353)( 38,352)( 39,351)( 40,350)
( 41,349)( 42,348)( 43,347)( 44,303)( 45,302)( 46,344)( 47,343)( 48,342)
( 49,341)( 50,340)( 51,339)( 52,338)( 53,337)( 54,336)( 55,335)( 56,334)
( 57,333)( 58,332)( 59,331)( 60,330)( 61,329)( 62,328)( 63,327)( 64,326)
( 65,325)( 66,324)( 67,323)( 68,322)( 69,321)( 70,320)( 71,319)( 72,318)
( 73,317)( 74,316)( 75,315)( 76,314)( 77,313)( 78,312)( 79,311)( 80,310)
( 81,309)( 82,308)( 83,307)( 84,306)( 85,305)( 86,304)( 87,561)( 88,560)
( 89,602)( 90,601)( 91,600)( 92,599)( 93,598)( 94,597)( 95,596)( 96,595)
( 97,594)( 98,593)( 99,592)(100,591)(101,590)(102,589)(103,588)(104,587)
(105,586)(106,585)(107,584)(108,583)(109,582)(110,581)(111,580)(112,579)
(113,578)(114,577)(115,576)(116,575)(117,574)(118,573)(119,572)(120,571)
(121,570)(122,569)(123,568)(124,567)(125,566)(126,565)(127,564)(128,563)
(129,562)(130,518)(131,517)(132,559)(133,558)(134,557)(135,556)(136,555)
(137,554)(138,553)(139,552)(140,551)(141,550)(142,549)(143,548)(144,547)
(145,546)(146,545)(147,544)(148,543)(149,542)(150,541)(151,540)(152,539)
(153,538)(154,537)(155,536)(156,535)(157,534)(158,533)(159,532)(160,531)
(161,530)(162,529)(163,528)(164,527)(165,526)(166,525)(167,524)(168,523)
(169,522)(170,521)(171,520)(172,519)(173,475)(174,474)(175,516)(176,515)
(177,514)(178,513)(179,512)(180,511)(181,510)(182,509)(183,508)(184,507)
(185,506)(186,505)(187,504)(188,503)(189,502)(190,501)(191,500)(192,499)
(193,498)(194,497)(195,496)(196,495)(197,494)(198,493)(199,492)(200,491)
(201,490)(202,489)(203,488)(204,487)(205,486)(206,485)(207,484)(208,483)
(209,482)(210,481)(211,480)(212,479)(213,478)(214,477)(215,476)(216,432)
(217,431)(218,473)(219,472)(220,471)(221,470)(222,469)(223,468)(224,467)
(225,466)(226,465)(227,464)(228,463)(229,462)(230,461)(231,460)(232,459)
(233,458)(234,457)(235,456)(236,455)(237,454)(238,453)(239,452)(240,451)
(241,450)(242,449)(243,448)(244,447)(245,446)(246,445)(247,444)(248,443)
(249,442)(250,441)(251,440)(252,439)(253,438)(254,437)(255,436)(256,435)
(257,434)(258,433)(259,389)(260,388)(261,430)(262,429)(263,428)(264,427)
(265,426)(266,425)(267,424)(268,423)(269,422)(270,421)(271,420)(272,419)
(273,418)(274,417)(275,416)(276,415)(277,414)(278,413)(279,412)(280,411)
(281,410)(282,409)(283,408)(284,407)(285,406)(286,405)(287,404)(288,403)
(289,402)(290,401)(291,400)(292,399)(293,398)(294,397)(295,396)(296,395)
(297,394)(298,393)(299,392)(300,391)(301,390);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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*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*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(602)!(  2, 43)(  3, 42)(  4, 41)(  5, 40)(  6, 39)(  7, 38)(  8, 37)
(  9, 36)( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 30)( 16, 29)
( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 44,259)( 45,301)
( 46,300)( 47,299)( 48,298)( 49,297)( 50,296)( 51,295)( 52,294)( 53,293)
( 54,292)( 55,291)( 56,290)( 57,289)( 58,288)( 59,287)( 60,286)( 61,285)
( 62,284)( 63,283)( 64,282)( 65,281)( 66,280)( 67,279)( 68,278)( 69,277)
( 70,276)( 71,275)( 72,274)( 73,273)( 74,272)( 75,271)( 76,270)( 77,269)
( 78,268)( 79,267)( 80,266)( 81,265)( 82,264)( 83,263)( 84,262)( 85,261)
( 86,260)( 87,216)( 88,258)( 89,257)( 90,256)( 91,255)( 92,254)( 93,253)
( 94,252)( 95,251)( 96,250)( 97,249)( 98,248)( 99,247)(100,246)(101,245)
(102,244)(103,243)(104,242)(105,241)(106,240)(107,239)(108,238)(109,237)
(110,236)(111,235)(112,234)(113,233)(114,232)(115,231)(116,230)(117,229)
(118,228)(119,227)(120,226)(121,225)(122,224)(123,223)(124,222)(125,221)
(126,220)(127,219)(128,218)(129,217)(130,173)(131,215)(132,214)(133,213)
(134,212)(135,211)(136,210)(137,209)(138,208)(139,207)(140,206)(141,205)
(142,204)(143,203)(144,202)(145,201)(146,200)(147,199)(148,198)(149,197)
(150,196)(151,195)(152,194)(153,193)(154,192)(155,191)(156,190)(157,189)
(158,188)(159,187)(160,186)(161,185)(162,184)(163,183)(164,182)(165,181)
(166,180)(167,179)(168,178)(169,177)(170,176)(171,175)(172,174)(303,344)
(304,343)(305,342)(306,341)(307,340)(308,339)(309,338)(310,337)(311,336)
(312,335)(313,334)(314,333)(315,332)(316,331)(317,330)(318,329)(319,328)
(320,327)(321,326)(322,325)(323,324)(345,560)(346,602)(347,601)(348,600)
(349,599)(350,598)(351,597)(352,596)(353,595)(354,594)(355,593)(356,592)
(357,591)(358,590)(359,589)(360,588)(361,587)(362,586)(363,585)(364,584)
(365,583)(366,582)(367,581)(368,580)(369,579)(370,578)(371,577)(372,576)
(373,575)(374,574)(375,573)(376,572)(377,571)(378,570)(379,569)(380,568)
(381,567)(382,566)(383,565)(384,564)(385,563)(386,562)(387,561)(388,517)
(389,559)(390,558)(391,557)(392,556)(393,555)(394,554)(395,553)(396,552)
(397,551)(398,550)(399,549)(400,548)(401,547)(402,546)(403,545)(404,544)
(405,543)(406,542)(407,541)(408,540)(409,539)(410,538)(411,537)(412,536)
(413,535)(414,534)(415,533)(416,532)(417,531)(418,530)(419,529)(420,528)
(421,527)(422,526)(423,525)(424,524)(425,523)(426,522)(427,521)(428,520)
(429,519)(430,518)(431,474)(432,516)(433,515)(434,514)(435,513)(436,512)
(437,511)(438,510)(439,509)(440,508)(441,507)(442,506)(443,505)(444,504)
(445,503)(446,502)(447,501)(448,500)(449,499)(450,498)(451,497)(452,496)
(453,495)(454,494)(455,493)(456,492)(457,491)(458,490)(459,489)(460,488)
(461,487)(462,486)(463,485)(464,484)(465,483)(466,482)(467,481)(468,480)
(469,479)(470,478)(471,477)(472,476)(473,475);
s1 := Sym(602)!(  1,346)(  2,345)(  3,387)(  4,386)(  5,385)(  6,384)(  7,383)
(  8,382)(  9,381)( 10,380)( 11,379)( 12,378)( 13,377)( 14,376)( 15,375)
( 16,374)( 17,373)( 18,372)( 19,371)( 20,370)( 21,369)( 22,368)( 23,367)
( 24,366)( 25,365)( 26,364)( 27,363)( 28,362)( 29,361)( 30,360)( 31,359)
( 32,358)( 33,357)( 34,356)( 35,355)( 36,354)( 37,353)( 38,352)( 39,351)
( 40,350)( 41,349)( 42,348)( 43,347)( 44,303)( 45,302)( 46,344)( 47,343)
( 48,342)( 49,341)( 50,340)( 51,339)( 52,338)( 53,337)( 54,336)( 55,335)
( 56,334)( 57,333)( 58,332)( 59,331)( 60,330)( 61,329)( 62,328)( 63,327)
( 64,326)( 65,325)( 66,324)( 67,323)( 68,322)( 69,321)( 70,320)( 71,319)
( 72,318)( 73,317)( 74,316)( 75,315)( 76,314)( 77,313)( 78,312)( 79,311)
( 80,310)( 81,309)( 82,308)( 83,307)( 84,306)( 85,305)( 86,304)( 87,561)
( 88,560)( 89,602)( 90,601)( 91,600)( 92,599)( 93,598)( 94,597)( 95,596)
( 96,595)( 97,594)( 98,593)( 99,592)(100,591)(101,590)(102,589)(103,588)
(104,587)(105,586)(106,585)(107,584)(108,583)(109,582)(110,581)(111,580)
(112,579)(113,578)(114,577)(115,576)(116,575)(117,574)(118,573)(119,572)
(120,571)(121,570)(122,569)(123,568)(124,567)(125,566)(126,565)(127,564)
(128,563)(129,562)(130,518)(131,517)(132,559)(133,558)(134,557)(135,556)
(136,555)(137,554)(138,553)(139,552)(140,551)(141,550)(142,549)(143,548)
(144,547)(145,546)(146,545)(147,544)(148,543)(149,542)(150,541)(151,540)
(152,539)(153,538)(154,537)(155,536)(156,535)(157,534)(158,533)(159,532)
(160,531)(161,530)(162,529)(163,528)(164,527)(165,526)(166,525)(167,524)
(168,523)(169,522)(170,521)(171,520)(172,519)(173,475)(174,474)(175,516)
(176,515)(177,514)(178,513)(179,512)(180,511)(181,510)(182,509)(183,508)
(184,507)(185,506)(186,505)(187,504)(188,503)(189,502)(190,501)(191,500)
(192,499)(193,498)(194,497)(195,496)(196,495)(197,494)(198,493)(199,492)
(200,491)(201,490)(202,489)(203,488)(204,487)(205,486)(206,485)(207,484)
(208,483)(209,482)(210,481)(211,480)(212,479)(213,478)(214,477)(215,476)
(216,432)(217,431)(218,473)(219,472)(220,471)(221,470)(222,469)(223,468)
(224,467)(225,466)(226,465)(227,464)(228,463)(229,462)(230,461)(231,460)
(232,459)(233,458)(234,457)(235,456)(236,455)(237,454)(238,453)(239,452)
(240,451)(241,450)(242,449)(243,448)(244,447)(245,446)(246,445)(247,444)
(248,443)(249,442)(250,441)(251,440)(252,439)(253,438)(254,437)(255,436)
(256,435)(257,434)(258,433)(259,389)(260,388)(261,430)(262,429)(263,428)
(264,427)(265,426)(266,425)(267,424)(268,423)(269,422)(270,421)(271,420)
(272,419)(273,418)(274,417)(275,416)(276,415)(277,414)(278,413)(279,412)
(280,411)(281,410)(282,409)(283,408)(284,407)(285,406)(286,405)(287,404)
(288,403)(289,402)(290,401)(291,400)(292,399)(293,398)(294,397)(295,396)
(296,395)(297,394)(298,393)(299,392)(300,391)(301,390);
poly := sub<Sym(602)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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*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*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