Polytope of Type {646}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {646}*1292
Also Known As : 646-gon, {646}. if this polytope has another name.
Group : SmallGroup(1292,10)
Rank : 2
Schlafli Type : {646}
Number of vertices, edges, etc : 646, 646
Order of s₀s₁ : 646
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 : {323}*646
   17-fold quotients : {38}*76
   19-fold quotients : {34}*68
   34-fold quotients : {19}*38
   38-fold quotients : {17}*34
   323-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 20,305)( 21,323)( 22,322)( 23,321)( 24,320)( 25,319)( 26,318)
( 27,317)( 28,316)( 29,315)( 30,314)( 31,313)( 32,312)( 33,311)( 34,310)
( 35,309)( 36,308)( 37,307)( 38,306)( 39,286)( 40,304)( 41,303)( 42,302)
( 43,301)( 44,300)( 45,299)( 46,298)( 47,297)( 48,296)( 49,295)( 50,294)
( 51,293)( 52,292)( 53,291)( 54,290)( 55,289)( 56,288)( 57,287)( 58,267)
( 59,285)( 60,284)( 61,283)( 62,282)( 63,281)( 64,280)( 65,279)( 66,278)
( 67,277)( 68,276)( 69,275)( 70,274)( 71,273)( 72,272)( 73,271)( 74,270)
( 75,269)( 76,268)( 77,248)( 78,266)( 79,265)( 80,264)( 81,263)( 82,262)
( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)( 88,256)( 89,255)( 90,254)
( 91,253)( 92,252)( 93,251)( 94,250)( 95,249)( 96,229)( 97,247)( 98,246)
( 99,245)(100,244)(101,243)(102,242)(103,241)(104,240)(105,239)(106,238)
(107,237)(108,236)(109,235)(110,234)(111,233)(112,232)(113,231)(114,230)
(115,210)(116,228)(117,227)(118,226)(119,225)(120,224)(121,223)(122,222)
(123,221)(124,220)(125,219)(126,218)(127,217)(128,216)(129,215)(130,214)
(131,213)(132,212)(133,211)(134,191)(135,209)(136,208)(137,207)(138,206)
(139,205)(140,204)(141,203)(142,202)(143,201)(144,200)(145,199)(146,198)
(147,197)(148,196)(149,195)(150,194)(151,193)(152,192)(153,172)(154,190)
(155,189)(156,188)(157,187)(158,186)(159,185)(160,184)(161,183)(162,182)
(163,181)(164,180)(165,179)(166,178)(167,177)(168,176)(169,175)(170,174)
(171,173)(325,342)(326,341)(327,340)(328,339)(329,338)(330,337)(331,336)
(332,335)(333,334)(343,628)(344,646)(345,645)(346,644)(347,643)(348,642)
(349,641)(350,640)(351,639)(352,638)(353,637)(354,636)(355,635)(356,634)
(357,633)(358,632)(359,631)(360,630)(361,629)(362,609)(363,627)(364,626)
(365,625)(366,624)(367,623)(368,622)(369,621)(370,620)(371,619)(372,618)
(373,617)(374,616)(375,615)(376,614)(377,613)(378,612)(379,611)(380,610)
(381,590)(382,608)(383,607)(384,606)(385,605)(386,604)(387,603)(388,602)
(389,601)(390,600)(391,599)(392,598)(393,597)(394,596)(395,595)(396,594)
(397,593)(398,592)(399,591)(400,571)(401,589)(402,588)(403,587)(404,586)
(405,585)(406,584)(407,583)(408,582)(409,581)(410,580)(411,579)(412,578)
(413,577)(414,576)(415,575)(416,574)(417,573)(418,572)(419,552)(420,570)
(421,569)(422,568)(423,567)(424,566)(425,565)(426,564)(427,563)(428,562)
(429,561)(430,560)(431,559)(432,558)(433,557)(434,556)(435,555)(436,554)
(437,553)(438,533)(439,551)(440,550)(441,549)(442,548)(443,547)(444,546)
(445,545)(446,544)(447,543)(448,542)(449,541)(450,540)(451,539)(452,538)
(453,537)(454,536)(455,535)(456,534)(457,514)(458,532)(459,531)(460,530)
(461,529)(462,528)(463,527)(464,526)(465,525)(466,524)(467,523)(468,522)
(469,521)(470,520)(471,519)(472,518)(473,517)(474,516)(475,515)(476,495)
(477,513)(478,512)(479,511)(480,510)(481,509)(482,508)(483,507)(484,506)
(485,505)(486,504)(487,503)(488,502)(489,501)(490,500)(491,499)(492,498)
(493,497)(494,496);;
s1 := (  1,344)(  2,343)(  3,361)(  4,360)(  5,359)(  6,358)(  7,357)(  8,356)
(  9,355)( 10,354)( 11,353)( 12,352)( 13,351)( 14,350)( 15,349)( 16,348)
( 17,347)( 18,346)( 19,345)( 20,325)( 21,324)( 22,342)( 23,341)( 24,340)
( 25,339)( 26,338)( 27,337)( 28,336)( 29,335)( 30,334)( 31,333)( 32,332)
( 33,331)( 34,330)( 35,329)( 36,328)( 37,327)( 38,326)( 39,629)( 40,628)
( 41,646)( 42,645)( 43,644)( 44,643)( 45,642)( 46,641)( 47,640)( 48,639)
( 49,638)( 50,637)( 51,636)( 52,635)( 53,634)( 54,633)( 55,632)( 56,631)
( 57,630)( 58,610)( 59,609)( 60,627)( 61,626)( 62,625)( 63,624)( 64,623)
( 65,622)( 66,621)( 67,620)( 68,619)( 69,618)( 70,617)( 71,616)( 72,615)
( 73,614)( 74,613)( 75,612)( 76,611)( 77,591)( 78,590)( 79,608)( 80,607)
( 81,606)( 82,605)( 83,604)( 84,603)( 85,602)( 86,601)( 87,600)( 88,599)
( 89,598)( 90,597)( 91,596)( 92,595)( 93,594)( 94,593)( 95,592)( 96,572)
( 97,571)( 98,589)( 99,588)(100,587)(101,586)(102,585)(103,584)(104,583)
(105,582)(106,581)(107,580)(108,579)(109,578)(110,577)(111,576)(112,575)
(113,574)(114,573)(115,553)(116,552)(117,570)(118,569)(119,568)(120,567)
(121,566)(122,565)(123,564)(124,563)(125,562)(126,561)(127,560)(128,559)
(129,558)(130,557)(131,556)(132,555)(133,554)(134,534)(135,533)(136,551)
(137,550)(138,549)(139,548)(140,547)(141,546)(142,545)(143,544)(144,543)
(145,542)(146,541)(147,540)(148,539)(149,538)(150,537)(151,536)(152,535)
(153,515)(154,514)(155,532)(156,531)(157,530)(158,529)(159,528)(160,527)
(161,526)(162,525)(163,524)(164,523)(165,522)(166,521)(167,520)(168,519)
(169,518)(170,517)(171,516)(172,496)(173,495)(174,513)(175,512)(176,511)
(177,510)(178,509)(179,508)(180,507)(181,506)(182,505)(183,504)(184,503)
(185,502)(186,501)(187,500)(188,499)(189,498)(190,497)(191,477)(192,476)
(193,494)(194,493)(195,492)(196,491)(197,490)(198,489)(199,488)(200,487)
(201,486)(202,485)(203,484)(204,483)(205,482)(206,481)(207,480)(208,479)
(209,478)(210,458)(211,457)(212,475)(213,474)(214,473)(215,472)(216,471)
(217,470)(218,469)(219,468)(220,467)(221,466)(222,465)(223,464)(224,463)
(225,462)(226,461)(227,460)(228,459)(229,439)(230,438)(231,456)(232,455)
(233,454)(234,453)(235,452)(236,451)(237,450)(238,449)(239,448)(240,447)
(241,446)(242,445)(243,444)(244,443)(245,442)(246,441)(247,440)(248,420)
(249,419)(250,437)(251,436)(252,435)(253,434)(254,433)(255,432)(256,431)
(257,430)(258,429)(259,428)(260,427)(261,426)(262,425)(263,424)(264,423)
(265,422)(266,421)(267,401)(268,400)(269,418)(270,417)(271,416)(272,415)
(273,414)(274,413)(275,412)(276,411)(277,410)(278,409)(279,408)(280,407)
(281,406)(282,405)(283,404)(284,403)(285,402)(286,382)(287,381)(288,399)
(289,398)(290,397)(291,396)(292,395)(293,394)(294,393)(295,392)(296,391)
(297,390)(298,389)(299,388)(300,387)(301,386)(302,385)(303,384)(304,383)
(305,363)(306,362)(307,380)(308,379)(309,378)(310,377)(311,376)(312,375)
(313,374)(314,373)(315,372)(316,371)(317,370)(318,369)(319,368)(320,367)
(321,366)(322,365)(323,364);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(646)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 20,305)( 21,323)( 22,322)( 23,321)( 24,320)( 25,319)
( 26,318)( 27,317)( 28,316)( 29,315)( 30,314)( 31,313)( 32,312)( 33,311)
( 34,310)( 35,309)( 36,308)( 37,307)( 38,306)( 39,286)( 40,304)( 41,303)
( 42,302)( 43,301)( 44,300)( 45,299)( 46,298)( 47,297)( 48,296)( 49,295)
( 50,294)( 51,293)( 52,292)( 53,291)( 54,290)( 55,289)( 56,288)( 57,287)
( 58,267)( 59,285)( 60,284)( 61,283)( 62,282)( 63,281)( 64,280)( 65,279)
( 66,278)( 67,277)( 68,276)( 69,275)( 70,274)( 71,273)( 72,272)( 73,271)
( 74,270)( 75,269)( 76,268)( 77,248)( 78,266)( 79,265)( 80,264)( 81,263)
( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)( 88,256)( 89,255)
( 90,254)( 91,253)( 92,252)( 93,251)( 94,250)( 95,249)( 96,229)( 97,247)
( 98,246)( 99,245)(100,244)(101,243)(102,242)(103,241)(104,240)(105,239)
(106,238)(107,237)(108,236)(109,235)(110,234)(111,233)(112,232)(113,231)
(114,230)(115,210)(116,228)(117,227)(118,226)(119,225)(120,224)(121,223)
(122,222)(123,221)(124,220)(125,219)(126,218)(127,217)(128,216)(129,215)
(130,214)(131,213)(132,212)(133,211)(134,191)(135,209)(136,208)(137,207)
(138,206)(139,205)(140,204)(141,203)(142,202)(143,201)(144,200)(145,199)
(146,198)(147,197)(148,196)(149,195)(150,194)(151,193)(152,192)(153,172)
(154,190)(155,189)(156,188)(157,187)(158,186)(159,185)(160,184)(161,183)
(162,182)(163,181)(164,180)(165,179)(166,178)(167,177)(168,176)(169,175)
(170,174)(171,173)(325,342)(326,341)(327,340)(328,339)(329,338)(330,337)
(331,336)(332,335)(333,334)(343,628)(344,646)(345,645)(346,644)(347,643)
(348,642)(349,641)(350,640)(351,639)(352,638)(353,637)(354,636)(355,635)
(356,634)(357,633)(358,632)(359,631)(360,630)(361,629)(362,609)(363,627)
(364,626)(365,625)(366,624)(367,623)(368,622)(369,621)(370,620)(371,619)
(372,618)(373,617)(374,616)(375,615)(376,614)(377,613)(378,612)(379,611)
(380,610)(381,590)(382,608)(383,607)(384,606)(385,605)(386,604)(387,603)
(388,602)(389,601)(390,600)(391,599)(392,598)(393,597)(394,596)(395,595)
(396,594)(397,593)(398,592)(399,591)(400,571)(401,589)(402,588)(403,587)
(404,586)(405,585)(406,584)(407,583)(408,582)(409,581)(410,580)(411,579)
(412,578)(413,577)(414,576)(415,575)(416,574)(417,573)(418,572)(419,552)
(420,570)(421,569)(422,568)(423,567)(424,566)(425,565)(426,564)(427,563)
(428,562)(429,561)(430,560)(431,559)(432,558)(433,557)(434,556)(435,555)
(436,554)(437,553)(438,533)(439,551)(440,550)(441,549)(442,548)(443,547)
(444,546)(445,545)(446,544)(447,543)(448,542)(449,541)(450,540)(451,539)
(452,538)(453,537)(454,536)(455,535)(456,534)(457,514)(458,532)(459,531)
(460,530)(461,529)(462,528)(463,527)(464,526)(465,525)(466,524)(467,523)
(468,522)(469,521)(470,520)(471,519)(472,518)(473,517)(474,516)(475,515)
(476,495)(477,513)(478,512)(479,511)(480,510)(481,509)(482,508)(483,507)
(484,506)(485,505)(486,504)(487,503)(488,502)(489,501)(490,500)(491,499)
(492,498)(493,497)(494,496);
s1 := Sym(646)!(  1,344)(  2,343)(  3,361)(  4,360)(  5,359)(  6,358)(  7,357)
(  8,356)(  9,355)( 10,354)( 11,353)( 12,352)( 13,351)( 14,350)( 15,349)
( 16,348)( 17,347)( 18,346)( 19,345)( 20,325)( 21,324)( 22,342)( 23,341)
( 24,340)( 25,339)( 26,338)( 27,337)( 28,336)( 29,335)( 30,334)( 31,333)
( 32,332)( 33,331)( 34,330)( 35,329)( 36,328)( 37,327)( 38,326)( 39,629)
( 40,628)( 41,646)( 42,645)( 43,644)( 44,643)( 45,642)( 46,641)( 47,640)
( 48,639)( 49,638)( 50,637)( 51,636)( 52,635)( 53,634)( 54,633)( 55,632)
( 56,631)( 57,630)( 58,610)( 59,609)( 60,627)( 61,626)( 62,625)( 63,624)
( 64,623)( 65,622)( 66,621)( 67,620)( 68,619)( 69,618)( 70,617)( 71,616)
( 72,615)( 73,614)( 74,613)( 75,612)( 76,611)( 77,591)( 78,590)( 79,608)
( 80,607)( 81,606)( 82,605)( 83,604)( 84,603)( 85,602)( 86,601)( 87,600)
( 88,599)( 89,598)( 90,597)( 91,596)( 92,595)( 93,594)( 94,593)( 95,592)
( 96,572)( 97,571)( 98,589)( 99,588)(100,587)(101,586)(102,585)(103,584)
(104,583)(105,582)(106,581)(107,580)(108,579)(109,578)(110,577)(111,576)
(112,575)(113,574)(114,573)(115,553)(116,552)(117,570)(118,569)(119,568)
(120,567)(121,566)(122,565)(123,564)(124,563)(125,562)(126,561)(127,560)
(128,559)(129,558)(130,557)(131,556)(132,555)(133,554)(134,534)(135,533)
(136,551)(137,550)(138,549)(139,548)(140,547)(141,546)(142,545)(143,544)
(144,543)(145,542)(146,541)(147,540)(148,539)(149,538)(150,537)(151,536)
(152,535)(153,515)(154,514)(155,532)(156,531)(157,530)(158,529)(159,528)
(160,527)(161,526)(162,525)(163,524)(164,523)(165,522)(166,521)(167,520)
(168,519)(169,518)(170,517)(171,516)(172,496)(173,495)(174,513)(175,512)
(176,511)(177,510)(178,509)(179,508)(180,507)(181,506)(182,505)(183,504)
(184,503)(185,502)(186,501)(187,500)(188,499)(189,498)(190,497)(191,477)
(192,476)(193,494)(194,493)(195,492)(196,491)(197,490)(198,489)(199,488)
(200,487)(201,486)(202,485)(203,484)(204,483)(205,482)(206,481)(207,480)
(208,479)(209,478)(210,458)(211,457)(212,475)(213,474)(214,473)(215,472)
(216,471)(217,470)(218,469)(219,468)(220,467)(221,466)(222,465)(223,464)
(224,463)(225,462)(226,461)(227,460)(228,459)(229,439)(230,438)(231,456)
(232,455)(233,454)(234,453)(235,452)(236,451)(237,450)(238,449)(239,448)
(240,447)(241,446)(242,445)(243,444)(244,443)(245,442)(246,441)(247,440)
(248,420)(249,419)(250,437)(251,436)(252,435)(253,434)(254,433)(255,432)
(256,431)(257,430)(258,429)(259,428)(260,427)(261,426)(262,425)(263,424)
(264,423)(265,422)(266,421)(267,401)(268,400)(269,418)(270,417)(271,416)
(272,415)(273,414)(274,413)(275,412)(276,411)(277,410)(278,409)(279,408)
(280,407)(281,406)(282,405)(283,404)(284,403)(285,402)(286,382)(287,381)
(288,399)(289,398)(290,397)(291,396)(292,395)(293,394)(294,393)(295,392)
(296,391)(297,390)(298,389)(299,388)(300,387)(301,386)(302,385)(303,384)
(304,383)(305,363)(306,362)(307,380)(308,379)(309,378)(310,377)(311,376)
(312,375)(313,374)(314,373)(315,372)(316,371)(317,370)(318,369)(319,368)
(320,367)(321,366)(322,365)(323,364);
poly := sub<Sym(646)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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