Polytope of Type {666}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {666}*1332
Also Known As : 666-gon, {666}. if this polytope has another name.
Group : SmallGroup(1332,17)
Rank : 2
Schlafli Type : {666}
Number of vertices, edges, etc : 666, 666
Order of s₀s₁ : 666
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 : {333}*666
   3-fold quotients : {222}*444
   6-fold quotients : {111}*222
   9-fold quotients : {74}*148
   18-fold quotients : {37}*74
   37-fold quotients : {18}*36
   74-fold quotients : {9}*18
   111-fold quotients : {6}*12
   222-fold quotients : {3}*6
   333-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4,109)(  5,111)(  6,110)(  7,106)(  8,108)(  9,107)( 10,103)
( 11,105)( 12,104)( 13,100)( 14,102)( 15,101)( 16, 97)( 17, 99)( 18, 98)
( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)( 25, 88)( 26, 90)
( 27, 89)( 28, 85)( 29, 87)( 30, 86)( 31, 82)( 32, 84)( 33, 83)( 34, 79)
( 35, 81)( 36, 80)( 37, 76)( 38, 78)( 39, 77)( 40, 73)( 41, 75)( 42, 74)
( 43, 70)( 44, 72)( 45, 71)( 46, 67)( 47, 69)( 48, 68)( 49, 64)( 50, 66)
( 51, 65)( 52, 61)( 53, 63)( 54, 62)( 55, 58)( 56, 60)( 57, 59)(112,224)
(113,223)(114,225)(115,332)(116,331)(117,333)(118,329)(119,328)(120,330)
(121,326)(122,325)(123,327)(124,323)(125,322)(126,324)(127,320)(128,319)
(129,321)(130,317)(131,316)(132,318)(133,314)(134,313)(135,315)(136,311)
(137,310)(138,312)(139,308)(140,307)(141,309)(142,305)(143,304)(144,306)
(145,302)(146,301)(147,303)(148,299)(149,298)(150,300)(151,296)(152,295)
(153,297)(154,293)(155,292)(156,294)(157,290)(158,289)(159,291)(160,287)
(161,286)(162,288)(163,284)(164,283)(165,285)(166,281)(167,280)(168,282)
(169,278)(170,277)(171,279)(172,275)(173,274)(174,276)(175,272)(176,271)
(177,273)(178,269)(179,268)(180,270)(181,266)(182,265)(183,267)(184,263)
(185,262)(186,264)(187,260)(188,259)(189,261)(190,257)(191,256)(192,258)
(193,254)(194,253)(195,255)(196,251)(197,250)(198,252)(199,248)(200,247)
(201,249)(202,245)(203,244)(204,246)(205,242)(206,241)(207,243)(208,239)
(209,238)(210,240)(211,236)(212,235)(213,237)(214,233)(215,232)(216,234)
(217,230)(218,229)(219,231)(220,227)(221,226)(222,228)(335,336)(337,442)
(338,444)(339,443)(340,439)(341,441)(342,440)(343,436)(344,438)(345,437)
(346,433)(347,435)(348,434)(349,430)(350,432)(351,431)(352,427)(353,429)
(354,428)(355,424)(356,426)(357,425)(358,421)(359,423)(360,422)(361,418)
(362,420)(363,419)(364,415)(365,417)(366,416)(367,412)(368,414)(369,413)
(370,409)(371,411)(372,410)(373,406)(374,408)(375,407)(376,403)(377,405)
(378,404)(379,400)(380,402)(381,401)(382,397)(383,399)(384,398)(385,394)
(386,396)(387,395)(388,391)(389,393)(390,392)(445,557)(446,556)(447,558)
(448,665)(449,664)(450,666)(451,662)(452,661)(453,663)(454,659)(455,658)
(456,660)(457,656)(458,655)(459,657)(460,653)(461,652)(462,654)(463,650)
(464,649)(465,651)(466,647)(467,646)(468,648)(469,644)(470,643)(471,645)
(472,641)(473,640)(474,642)(475,638)(476,637)(477,639)(478,635)(479,634)
(480,636)(481,632)(482,631)(483,633)(484,629)(485,628)(486,630)(487,626)
(488,625)(489,627)(490,623)(491,622)(492,624)(493,620)(494,619)(495,621)
(496,617)(497,616)(498,618)(499,614)(500,613)(501,615)(502,611)(503,610)
(504,612)(505,608)(506,607)(507,609)(508,605)(509,604)(510,606)(511,602)
(512,601)(513,603)(514,599)(515,598)(516,600)(517,596)(518,595)(519,597)
(520,593)(521,592)(522,594)(523,590)(524,589)(525,591)(526,587)(527,586)
(528,588)(529,584)(530,583)(531,585)(532,581)(533,580)(534,582)(535,578)
(536,577)(537,579)(538,575)(539,574)(540,576)(541,572)(542,571)(543,573)
(544,569)(545,568)(546,570)(547,566)(548,565)(549,567)(550,563)(551,562)
(552,564)(553,560)(554,559)(555,561);;
s1 := (  1,448)(  2,450)(  3,449)(  4,445)(  5,447)(  6,446)(  7,553)(  8,555)
(  9,554)( 10,550)( 11,552)( 12,551)( 13,547)( 14,549)( 15,548)( 16,544)
( 17,546)( 18,545)( 19,541)( 20,543)( 21,542)( 22,538)( 23,540)( 24,539)
( 25,535)( 26,537)( 27,536)( 28,532)( 29,534)( 30,533)( 31,529)( 32,531)
( 33,530)( 34,526)( 35,528)( 36,527)( 37,523)( 38,525)( 39,524)( 40,520)
( 41,522)( 42,521)( 43,517)( 44,519)( 45,518)( 46,514)( 47,516)( 48,515)
( 49,511)( 50,513)( 51,512)( 52,508)( 53,510)( 54,509)( 55,505)( 56,507)
( 57,506)( 58,502)( 59,504)( 60,503)( 61,499)( 62,501)( 63,500)( 64,496)
( 65,498)( 66,497)( 67,493)( 68,495)( 69,494)( 70,490)( 71,492)( 72,491)
( 73,487)( 74,489)( 75,488)( 76,484)( 77,486)( 78,485)( 79,481)( 80,483)
( 81,482)( 82,478)( 83,480)( 84,479)( 85,475)( 86,477)( 87,476)( 88,472)
( 89,474)( 90,473)( 91,469)( 92,471)( 93,470)( 94,466)( 95,468)( 96,467)
( 97,463)( 98,465)( 99,464)(100,460)(101,462)(102,461)(103,457)(104,459)
(105,458)(106,454)(107,456)(108,455)(109,451)(110,453)(111,452)(112,337)
(113,339)(114,338)(115,334)(116,336)(117,335)(118,442)(119,444)(120,443)
(121,439)(122,441)(123,440)(124,436)(125,438)(126,437)(127,433)(128,435)
(129,434)(130,430)(131,432)(132,431)(133,427)(134,429)(135,428)(136,424)
(137,426)(138,425)(139,421)(140,423)(141,422)(142,418)(143,420)(144,419)
(145,415)(146,417)(147,416)(148,412)(149,414)(150,413)(151,409)(152,411)
(153,410)(154,406)(155,408)(156,407)(157,403)(158,405)(159,404)(160,400)
(161,402)(162,401)(163,397)(164,399)(165,398)(166,394)(167,396)(168,395)
(169,391)(170,393)(171,392)(172,388)(173,390)(174,389)(175,385)(176,387)
(177,386)(178,382)(179,384)(180,383)(181,379)(182,381)(183,380)(184,376)
(185,378)(186,377)(187,373)(188,375)(189,374)(190,370)(191,372)(192,371)
(193,367)(194,369)(195,368)(196,364)(197,366)(198,365)(199,361)(200,363)
(201,362)(202,358)(203,360)(204,359)(205,355)(206,357)(207,356)(208,352)
(209,354)(210,353)(211,349)(212,351)(213,350)(214,346)(215,348)(216,347)
(217,343)(218,345)(219,344)(220,340)(221,342)(222,341)(223,560)(224,559)
(225,561)(226,557)(227,556)(228,558)(229,665)(230,664)(231,666)(232,662)
(233,661)(234,663)(235,659)(236,658)(237,660)(238,656)(239,655)(240,657)
(241,653)(242,652)(243,654)(244,650)(245,649)(246,651)(247,647)(248,646)
(249,648)(250,644)(251,643)(252,645)(253,641)(254,640)(255,642)(256,638)
(257,637)(258,639)(259,635)(260,634)(261,636)(262,632)(263,631)(264,633)
(265,629)(266,628)(267,630)(268,626)(269,625)(270,627)(271,623)(272,622)
(273,624)(274,620)(275,619)(276,621)(277,617)(278,616)(279,618)(280,614)
(281,613)(282,615)(283,611)(284,610)(285,612)(286,608)(287,607)(288,609)
(289,605)(290,604)(291,606)(292,602)(293,601)(294,603)(295,599)(296,598)
(297,600)(298,596)(299,595)(300,597)(301,593)(302,592)(303,594)(304,590)
(305,589)(306,591)(307,587)(308,586)(309,588)(310,584)(311,583)(312,585)
(313,581)(314,580)(315,582)(316,578)(317,577)(318,579)(319,575)(320,574)
(321,576)(322,572)(323,571)(324,573)(325,569)(326,568)(327,570)(328,566)
(329,565)(330,567)(331,563)(332,562)(333,564);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(666)!(  2,  3)(  4,109)(  5,111)(  6,110)(  7,106)(  8,108)(  9,107)
( 10,103)( 11,105)( 12,104)( 13,100)( 14,102)( 15,101)( 16, 97)( 17, 99)
( 18, 98)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)( 25, 88)
( 26, 90)( 27, 89)( 28, 85)( 29, 87)( 30, 86)( 31, 82)( 32, 84)( 33, 83)
( 34, 79)( 35, 81)( 36, 80)( 37, 76)( 38, 78)( 39, 77)( 40, 73)( 41, 75)
( 42, 74)( 43, 70)( 44, 72)( 45, 71)( 46, 67)( 47, 69)( 48, 68)( 49, 64)
( 50, 66)( 51, 65)( 52, 61)( 53, 63)( 54, 62)( 55, 58)( 56, 60)( 57, 59)
(112,224)(113,223)(114,225)(115,332)(116,331)(117,333)(118,329)(119,328)
(120,330)(121,326)(122,325)(123,327)(124,323)(125,322)(126,324)(127,320)
(128,319)(129,321)(130,317)(131,316)(132,318)(133,314)(134,313)(135,315)
(136,311)(137,310)(138,312)(139,308)(140,307)(141,309)(142,305)(143,304)
(144,306)(145,302)(146,301)(147,303)(148,299)(149,298)(150,300)(151,296)
(152,295)(153,297)(154,293)(155,292)(156,294)(157,290)(158,289)(159,291)
(160,287)(161,286)(162,288)(163,284)(164,283)(165,285)(166,281)(167,280)
(168,282)(169,278)(170,277)(171,279)(172,275)(173,274)(174,276)(175,272)
(176,271)(177,273)(178,269)(179,268)(180,270)(181,266)(182,265)(183,267)
(184,263)(185,262)(186,264)(187,260)(188,259)(189,261)(190,257)(191,256)
(192,258)(193,254)(194,253)(195,255)(196,251)(197,250)(198,252)(199,248)
(200,247)(201,249)(202,245)(203,244)(204,246)(205,242)(206,241)(207,243)
(208,239)(209,238)(210,240)(211,236)(212,235)(213,237)(214,233)(215,232)
(216,234)(217,230)(218,229)(219,231)(220,227)(221,226)(222,228)(335,336)
(337,442)(338,444)(339,443)(340,439)(341,441)(342,440)(343,436)(344,438)
(345,437)(346,433)(347,435)(348,434)(349,430)(350,432)(351,431)(352,427)
(353,429)(354,428)(355,424)(356,426)(357,425)(358,421)(359,423)(360,422)
(361,418)(362,420)(363,419)(364,415)(365,417)(366,416)(367,412)(368,414)
(369,413)(370,409)(371,411)(372,410)(373,406)(374,408)(375,407)(376,403)
(377,405)(378,404)(379,400)(380,402)(381,401)(382,397)(383,399)(384,398)
(385,394)(386,396)(387,395)(388,391)(389,393)(390,392)(445,557)(446,556)
(447,558)(448,665)(449,664)(450,666)(451,662)(452,661)(453,663)(454,659)
(455,658)(456,660)(457,656)(458,655)(459,657)(460,653)(461,652)(462,654)
(463,650)(464,649)(465,651)(466,647)(467,646)(468,648)(469,644)(470,643)
(471,645)(472,641)(473,640)(474,642)(475,638)(476,637)(477,639)(478,635)
(479,634)(480,636)(481,632)(482,631)(483,633)(484,629)(485,628)(486,630)
(487,626)(488,625)(489,627)(490,623)(491,622)(492,624)(493,620)(494,619)
(495,621)(496,617)(497,616)(498,618)(499,614)(500,613)(501,615)(502,611)
(503,610)(504,612)(505,608)(506,607)(507,609)(508,605)(509,604)(510,606)
(511,602)(512,601)(513,603)(514,599)(515,598)(516,600)(517,596)(518,595)
(519,597)(520,593)(521,592)(522,594)(523,590)(524,589)(525,591)(526,587)
(527,586)(528,588)(529,584)(530,583)(531,585)(532,581)(533,580)(534,582)
(535,578)(536,577)(537,579)(538,575)(539,574)(540,576)(541,572)(542,571)
(543,573)(544,569)(545,568)(546,570)(547,566)(548,565)(549,567)(550,563)
(551,562)(552,564)(553,560)(554,559)(555,561);
s1 := Sym(666)!(  1,448)(  2,450)(  3,449)(  4,445)(  5,447)(  6,446)(  7,553)
(  8,555)(  9,554)( 10,550)( 11,552)( 12,551)( 13,547)( 14,549)( 15,548)
( 16,544)( 17,546)( 18,545)( 19,541)( 20,543)( 21,542)( 22,538)( 23,540)
( 24,539)( 25,535)( 26,537)( 27,536)( 28,532)( 29,534)( 30,533)( 31,529)
( 32,531)( 33,530)( 34,526)( 35,528)( 36,527)( 37,523)( 38,525)( 39,524)
( 40,520)( 41,522)( 42,521)( 43,517)( 44,519)( 45,518)( 46,514)( 47,516)
( 48,515)( 49,511)( 50,513)( 51,512)( 52,508)( 53,510)( 54,509)( 55,505)
( 56,507)( 57,506)( 58,502)( 59,504)( 60,503)( 61,499)( 62,501)( 63,500)
( 64,496)( 65,498)( 66,497)( 67,493)( 68,495)( 69,494)( 70,490)( 71,492)
( 72,491)( 73,487)( 74,489)( 75,488)( 76,484)( 77,486)( 78,485)( 79,481)
( 80,483)( 81,482)( 82,478)( 83,480)( 84,479)( 85,475)( 86,477)( 87,476)
( 88,472)( 89,474)( 90,473)( 91,469)( 92,471)( 93,470)( 94,466)( 95,468)
( 96,467)( 97,463)( 98,465)( 99,464)(100,460)(101,462)(102,461)(103,457)
(104,459)(105,458)(106,454)(107,456)(108,455)(109,451)(110,453)(111,452)
(112,337)(113,339)(114,338)(115,334)(116,336)(117,335)(118,442)(119,444)
(120,443)(121,439)(122,441)(123,440)(124,436)(125,438)(126,437)(127,433)
(128,435)(129,434)(130,430)(131,432)(132,431)(133,427)(134,429)(135,428)
(136,424)(137,426)(138,425)(139,421)(140,423)(141,422)(142,418)(143,420)
(144,419)(145,415)(146,417)(147,416)(148,412)(149,414)(150,413)(151,409)
(152,411)(153,410)(154,406)(155,408)(156,407)(157,403)(158,405)(159,404)
(160,400)(161,402)(162,401)(163,397)(164,399)(165,398)(166,394)(167,396)
(168,395)(169,391)(170,393)(171,392)(172,388)(173,390)(174,389)(175,385)
(176,387)(177,386)(178,382)(179,384)(180,383)(181,379)(182,381)(183,380)
(184,376)(185,378)(186,377)(187,373)(188,375)(189,374)(190,370)(191,372)
(192,371)(193,367)(194,369)(195,368)(196,364)(197,366)(198,365)(199,361)
(200,363)(201,362)(202,358)(203,360)(204,359)(205,355)(206,357)(207,356)
(208,352)(209,354)(210,353)(211,349)(212,351)(213,350)(214,346)(215,348)
(216,347)(217,343)(218,345)(219,344)(220,340)(221,342)(222,341)(223,560)
(224,559)(225,561)(226,557)(227,556)(228,558)(229,665)(230,664)(231,666)
(232,662)(233,661)(234,663)(235,659)(236,658)(237,660)(238,656)(239,655)
(240,657)(241,653)(242,652)(243,654)(244,650)(245,649)(246,651)(247,647)
(248,646)(249,648)(250,644)(251,643)(252,645)(253,641)(254,640)(255,642)
(256,638)(257,637)(258,639)(259,635)(260,634)(261,636)(262,632)(263,631)
(264,633)(265,629)(266,628)(267,630)(268,626)(269,625)(270,627)(271,623)
(272,622)(273,624)(274,620)(275,619)(276,621)(277,617)(278,616)(279,618)
(280,614)(281,613)(282,615)(283,611)(284,610)(285,612)(286,608)(287,607)
(288,609)(289,605)(290,604)(291,606)(292,602)(293,601)(294,603)(295,599)
(296,598)(297,600)(298,596)(299,595)(300,597)(301,593)(302,592)(303,594)
(304,590)(305,589)(306,591)(307,587)(308,586)(309,588)(310,584)(311,583)
(312,585)(313,581)(314,580)(315,582)(316,578)(317,577)(318,579)(319,575)
(320,574)(321,576)(322,572)(323,571)(324,573)(325,569)(326,568)(327,570)
(328,566)(329,565)(330,567)(331,563)(332,562)(333,564);
poly := sub<Sym(666)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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