Polytope of Type {732}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {732}*1464
Also Known As : 732-gon, {732}. if this polytope has another name.
Group : SmallGroup(1464,39)
Rank : 2
Schlafli Type : {732}
Number of vertices, edges, etc : 732, 732
Order of s₀s₁ : 732
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 : {366}*732
   3-fold quotients : {244}*488
   4-fold quotients : {183}*366
   6-fold quotients : {122}*244
   12-fold quotients : {61}*122
   61-fold quotients : {12}*24
   122-fold quotients : {6}*12
   183-fold quotients : {4}*8
   244-fold quotients : {3}*6
   366-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)(  9, 54)
( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)( 17, 46)
( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)( 25, 38)
( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 62,123)( 63,183)
( 64,182)( 65,181)( 66,180)( 67,179)( 68,178)( 69,177)( 70,176)( 71,175)
( 72,174)( 73,173)( 74,172)( 75,171)( 76,170)( 77,169)( 78,168)( 79,167)
( 80,166)( 81,165)( 82,164)( 83,163)( 84,162)( 85,161)( 86,160)( 87,159)
( 88,158)( 89,157)( 90,156)( 91,155)( 92,154)( 93,153)( 94,152)( 95,151)
( 96,150)( 97,149)( 98,148)( 99,147)(100,146)(101,145)(102,144)(103,143)
(104,142)(105,141)(106,140)(107,139)(108,138)(109,137)(110,136)(111,135)
(112,134)(113,133)(114,132)(115,131)(116,130)(117,129)(118,128)(119,127)
(120,126)(121,125)(122,124)(185,244)(186,243)(187,242)(188,241)(189,240)
(190,239)(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)(197,232)
(198,231)(199,230)(200,229)(201,228)(202,227)(203,226)(204,225)(205,224)
(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,216)
(214,215)(245,306)(246,366)(247,365)(248,364)(249,363)(250,362)(251,361)
(252,360)(253,359)(254,358)(255,357)(256,356)(257,355)(258,354)(259,353)
(260,352)(261,351)(262,350)(263,349)(264,348)(265,347)(266,346)(267,345)
(268,344)(269,343)(270,342)(271,341)(272,340)(273,339)(274,338)(275,337)
(276,336)(277,335)(278,334)(279,333)(280,332)(281,331)(282,330)(283,329)
(284,328)(285,327)(286,326)(287,325)(288,324)(289,323)(290,322)(291,321)
(292,320)(293,319)(294,318)(295,317)(296,316)(297,315)(298,314)(299,313)
(300,312)(301,311)(302,310)(303,309)(304,308)(305,307)(367,550)(368,610)
(369,609)(370,608)(371,607)(372,606)(373,605)(374,604)(375,603)(376,602)
(377,601)(378,600)(379,599)(380,598)(381,597)(382,596)(383,595)(384,594)
(385,593)(386,592)(387,591)(388,590)(389,589)(390,588)(391,587)(392,586)
(393,585)(394,584)(395,583)(396,582)(397,581)(398,580)(399,579)(400,578)
(401,577)(402,576)(403,575)(404,574)(405,573)(406,572)(407,571)(408,570)
(409,569)(410,568)(411,567)(412,566)(413,565)(414,564)(415,563)(416,562)
(417,561)(418,560)(419,559)(420,558)(421,557)(422,556)(423,555)(424,554)
(425,553)(426,552)(427,551)(428,672)(429,732)(430,731)(431,730)(432,729)
(433,728)(434,727)(435,726)(436,725)(437,724)(438,723)(439,722)(440,721)
(441,720)(442,719)(443,718)(444,717)(445,716)(446,715)(447,714)(448,713)
(449,712)(450,711)(451,710)(452,709)(453,708)(454,707)(455,706)(456,705)
(457,704)(458,703)(459,702)(460,701)(461,700)(462,699)(463,698)(464,697)
(465,696)(466,695)(467,694)(468,693)(469,692)(470,691)(471,690)(472,689)
(473,688)(474,687)(475,686)(476,685)(477,684)(478,683)(479,682)(480,681)
(481,680)(482,679)(483,678)(484,677)(485,676)(486,675)(487,674)(488,673)
(489,611)(490,671)(491,670)(492,669)(493,668)(494,667)(495,666)(496,665)
(497,664)(498,663)(499,662)(500,661)(501,660)(502,659)(503,658)(504,657)
(505,656)(506,655)(507,654)(508,653)(509,652)(510,651)(511,650)(512,649)
(513,648)(514,647)(515,646)(516,645)(517,644)(518,643)(519,642)(520,641)
(521,640)(522,639)(523,638)(524,637)(525,636)(526,635)(527,634)(528,633)
(529,632)(530,631)(531,630)(532,629)(533,628)(534,627)(535,626)(536,625)
(537,624)(538,623)(539,622)(540,621)(541,620)(542,619)(543,618)(544,617)
(545,616)(546,615)(547,614)(548,613)(549,612);;
s1 := (  1,429)(  2,428)(  3,488)(  4,487)(  5,486)(  6,485)(  7,484)(  8,483)
(  9,482)( 10,481)( 11,480)( 12,479)( 13,478)( 14,477)( 15,476)( 16,475)
( 17,474)( 18,473)( 19,472)( 20,471)( 21,470)( 22,469)( 23,468)( 24,467)
( 25,466)( 26,465)( 27,464)( 28,463)( 29,462)( 30,461)( 31,460)( 32,459)
( 33,458)( 34,457)( 35,456)( 36,455)( 37,454)( 38,453)( 39,452)( 40,451)
( 41,450)( 42,449)( 43,448)( 44,447)( 45,446)( 46,445)( 47,444)( 48,443)
( 49,442)( 50,441)( 51,440)( 52,439)( 53,438)( 54,437)( 55,436)( 56,435)
( 57,434)( 58,433)( 59,432)( 60,431)( 61,430)( 62,368)( 63,367)( 64,427)
( 65,426)( 66,425)( 67,424)( 68,423)( 69,422)( 70,421)( 71,420)( 72,419)
( 73,418)( 74,417)( 75,416)( 76,415)( 77,414)( 78,413)( 79,412)( 80,411)
( 81,410)( 82,409)( 83,408)( 84,407)( 85,406)( 86,405)( 87,404)( 88,403)
( 89,402)( 90,401)( 91,400)( 92,399)( 93,398)( 94,397)( 95,396)( 96,395)
( 97,394)( 98,393)( 99,392)(100,391)(101,390)(102,389)(103,388)(104,387)
(105,386)(106,385)(107,384)(108,383)(109,382)(110,381)(111,380)(112,379)
(113,378)(114,377)(115,376)(116,375)(117,374)(118,373)(119,372)(120,371)
(121,370)(122,369)(123,490)(124,489)(125,549)(126,548)(127,547)(128,546)
(129,545)(130,544)(131,543)(132,542)(133,541)(134,540)(135,539)(136,538)
(137,537)(138,536)(139,535)(140,534)(141,533)(142,532)(143,531)(144,530)
(145,529)(146,528)(147,527)(148,526)(149,525)(150,524)(151,523)(152,522)
(153,521)(154,520)(155,519)(156,518)(157,517)(158,516)(159,515)(160,514)
(161,513)(162,512)(163,511)(164,510)(165,509)(166,508)(167,507)(168,506)
(169,505)(170,504)(171,503)(172,502)(173,501)(174,500)(175,499)(176,498)
(177,497)(178,496)(179,495)(180,494)(181,493)(182,492)(183,491)(184,612)
(185,611)(186,671)(187,670)(188,669)(189,668)(190,667)(191,666)(192,665)
(193,664)(194,663)(195,662)(196,661)(197,660)(198,659)(199,658)(200,657)
(201,656)(202,655)(203,654)(204,653)(205,652)(206,651)(207,650)(208,649)
(209,648)(210,647)(211,646)(212,645)(213,644)(214,643)(215,642)(216,641)
(217,640)(218,639)(219,638)(220,637)(221,636)(222,635)(223,634)(224,633)
(225,632)(226,631)(227,630)(228,629)(229,628)(230,627)(231,626)(232,625)
(233,624)(234,623)(235,622)(236,621)(237,620)(238,619)(239,618)(240,617)
(241,616)(242,615)(243,614)(244,613)(245,551)(246,550)(247,610)(248,609)
(249,608)(250,607)(251,606)(252,605)(253,604)(254,603)(255,602)(256,601)
(257,600)(258,599)(259,598)(260,597)(261,596)(262,595)(263,594)(264,593)
(265,592)(266,591)(267,590)(268,589)(269,588)(270,587)(271,586)(272,585)
(273,584)(274,583)(275,582)(276,581)(277,580)(278,579)(279,578)(280,577)
(281,576)(282,575)(283,574)(284,573)(285,572)(286,571)(287,570)(288,569)
(289,568)(290,567)(291,566)(292,565)(293,564)(294,563)(295,562)(296,561)
(297,560)(298,559)(299,558)(300,557)(301,556)(302,555)(303,554)(304,553)
(305,552)(306,673)(307,672)(308,732)(309,731)(310,730)(311,729)(312,728)
(313,727)(314,726)(315,725)(316,724)(317,723)(318,722)(319,721)(320,720)
(321,719)(322,718)(323,717)(324,716)(325,715)(326,714)(327,713)(328,712)
(329,711)(330,710)(331,709)(332,708)(333,707)(334,706)(335,705)(336,704)
(337,703)(338,702)(339,701)(340,700)(341,699)(342,698)(343,697)(344,696)
(345,695)(346,694)(347,693)(348,692)(349,691)(350,690)(351,689)(352,688)
(353,687)(354,686)(355,685)(356,684)(357,683)(358,682)(359,681)(360,680)
(361,679)(362,678)(363,677)(364,676)(365,675)(366,674);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(732)!(  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)
(  9, 54)( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)
( 17, 46)( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)
( 25, 38)( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 62,123)
( 63,183)( 64,182)( 65,181)( 66,180)( 67,179)( 68,178)( 69,177)( 70,176)
( 71,175)( 72,174)( 73,173)( 74,172)( 75,171)( 76,170)( 77,169)( 78,168)
( 79,167)( 80,166)( 81,165)( 82,164)( 83,163)( 84,162)( 85,161)( 86,160)
( 87,159)( 88,158)( 89,157)( 90,156)( 91,155)( 92,154)( 93,153)( 94,152)
( 95,151)( 96,150)( 97,149)( 98,148)( 99,147)(100,146)(101,145)(102,144)
(103,143)(104,142)(105,141)(106,140)(107,139)(108,138)(109,137)(110,136)
(111,135)(112,134)(113,133)(114,132)(115,131)(116,130)(117,129)(118,128)
(119,127)(120,126)(121,125)(122,124)(185,244)(186,243)(187,242)(188,241)
(189,240)(190,239)(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)
(197,232)(198,231)(199,230)(200,229)(201,228)(202,227)(203,226)(204,225)
(205,224)(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)
(213,216)(214,215)(245,306)(246,366)(247,365)(248,364)(249,363)(250,362)
(251,361)(252,360)(253,359)(254,358)(255,357)(256,356)(257,355)(258,354)
(259,353)(260,352)(261,351)(262,350)(263,349)(264,348)(265,347)(266,346)
(267,345)(268,344)(269,343)(270,342)(271,341)(272,340)(273,339)(274,338)
(275,337)(276,336)(277,335)(278,334)(279,333)(280,332)(281,331)(282,330)
(283,329)(284,328)(285,327)(286,326)(287,325)(288,324)(289,323)(290,322)
(291,321)(292,320)(293,319)(294,318)(295,317)(296,316)(297,315)(298,314)
(299,313)(300,312)(301,311)(302,310)(303,309)(304,308)(305,307)(367,550)
(368,610)(369,609)(370,608)(371,607)(372,606)(373,605)(374,604)(375,603)
(376,602)(377,601)(378,600)(379,599)(380,598)(381,597)(382,596)(383,595)
(384,594)(385,593)(386,592)(387,591)(388,590)(389,589)(390,588)(391,587)
(392,586)(393,585)(394,584)(395,583)(396,582)(397,581)(398,580)(399,579)
(400,578)(401,577)(402,576)(403,575)(404,574)(405,573)(406,572)(407,571)
(408,570)(409,569)(410,568)(411,567)(412,566)(413,565)(414,564)(415,563)
(416,562)(417,561)(418,560)(419,559)(420,558)(421,557)(422,556)(423,555)
(424,554)(425,553)(426,552)(427,551)(428,672)(429,732)(430,731)(431,730)
(432,729)(433,728)(434,727)(435,726)(436,725)(437,724)(438,723)(439,722)
(440,721)(441,720)(442,719)(443,718)(444,717)(445,716)(446,715)(447,714)
(448,713)(449,712)(450,711)(451,710)(452,709)(453,708)(454,707)(455,706)
(456,705)(457,704)(458,703)(459,702)(460,701)(461,700)(462,699)(463,698)
(464,697)(465,696)(466,695)(467,694)(468,693)(469,692)(470,691)(471,690)
(472,689)(473,688)(474,687)(475,686)(476,685)(477,684)(478,683)(479,682)
(480,681)(481,680)(482,679)(483,678)(484,677)(485,676)(486,675)(487,674)
(488,673)(489,611)(490,671)(491,670)(492,669)(493,668)(494,667)(495,666)
(496,665)(497,664)(498,663)(499,662)(500,661)(501,660)(502,659)(503,658)
(504,657)(505,656)(506,655)(507,654)(508,653)(509,652)(510,651)(511,650)
(512,649)(513,648)(514,647)(515,646)(516,645)(517,644)(518,643)(519,642)
(520,641)(521,640)(522,639)(523,638)(524,637)(525,636)(526,635)(527,634)
(528,633)(529,632)(530,631)(531,630)(532,629)(533,628)(534,627)(535,626)
(536,625)(537,624)(538,623)(539,622)(540,621)(541,620)(542,619)(543,618)
(544,617)(545,616)(546,615)(547,614)(548,613)(549,612);
s1 := Sym(732)!(  1,429)(  2,428)(  3,488)(  4,487)(  5,486)(  6,485)(  7,484)
(  8,483)(  9,482)( 10,481)( 11,480)( 12,479)( 13,478)( 14,477)( 15,476)
( 16,475)( 17,474)( 18,473)( 19,472)( 20,471)( 21,470)( 22,469)( 23,468)
( 24,467)( 25,466)( 26,465)( 27,464)( 28,463)( 29,462)( 30,461)( 31,460)
( 32,459)( 33,458)( 34,457)( 35,456)( 36,455)( 37,454)( 38,453)( 39,452)
( 40,451)( 41,450)( 42,449)( 43,448)( 44,447)( 45,446)( 46,445)( 47,444)
( 48,443)( 49,442)( 50,441)( 51,440)( 52,439)( 53,438)( 54,437)( 55,436)
( 56,435)( 57,434)( 58,433)( 59,432)( 60,431)( 61,430)( 62,368)( 63,367)
( 64,427)( 65,426)( 66,425)( 67,424)( 68,423)( 69,422)( 70,421)( 71,420)
( 72,419)( 73,418)( 74,417)( 75,416)( 76,415)( 77,414)( 78,413)( 79,412)
( 80,411)( 81,410)( 82,409)( 83,408)( 84,407)( 85,406)( 86,405)( 87,404)
( 88,403)( 89,402)( 90,401)( 91,400)( 92,399)( 93,398)( 94,397)( 95,396)
( 96,395)( 97,394)( 98,393)( 99,392)(100,391)(101,390)(102,389)(103,388)
(104,387)(105,386)(106,385)(107,384)(108,383)(109,382)(110,381)(111,380)
(112,379)(113,378)(114,377)(115,376)(116,375)(117,374)(118,373)(119,372)
(120,371)(121,370)(122,369)(123,490)(124,489)(125,549)(126,548)(127,547)
(128,546)(129,545)(130,544)(131,543)(132,542)(133,541)(134,540)(135,539)
(136,538)(137,537)(138,536)(139,535)(140,534)(141,533)(142,532)(143,531)
(144,530)(145,529)(146,528)(147,527)(148,526)(149,525)(150,524)(151,523)
(152,522)(153,521)(154,520)(155,519)(156,518)(157,517)(158,516)(159,515)
(160,514)(161,513)(162,512)(163,511)(164,510)(165,509)(166,508)(167,507)
(168,506)(169,505)(170,504)(171,503)(172,502)(173,501)(174,500)(175,499)
(176,498)(177,497)(178,496)(179,495)(180,494)(181,493)(182,492)(183,491)
(184,612)(185,611)(186,671)(187,670)(188,669)(189,668)(190,667)(191,666)
(192,665)(193,664)(194,663)(195,662)(196,661)(197,660)(198,659)(199,658)
(200,657)(201,656)(202,655)(203,654)(204,653)(205,652)(206,651)(207,650)
(208,649)(209,648)(210,647)(211,646)(212,645)(213,644)(214,643)(215,642)
(216,641)(217,640)(218,639)(219,638)(220,637)(221,636)(222,635)(223,634)
(224,633)(225,632)(226,631)(227,630)(228,629)(229,628)(230,627)(231,626)
(232,625)(233,624)(234,623)(235,622)(236,621)(237,620)(238,619)(239,618)
(240,617)(241,616)(242,615)(243,614)(244,613)(245,551)(246,550)(247,610)
(248,609)(249,608)(250,607)(251,606)(252,605)(253,604)(254,603)(255,602)
(256,601)(257,600)(258,599)(259,598)(260,597)(261,596)(262,595)(263,594)
(264,593)(265,592)(266,591)(267,590)(268,589)(269,588)(270,587)(271,586)
(272,585)(273,584)(274,583)(275,582)(276,581)(277,580)(278,579)(279,578)
(280,577)(281,576)(282,575)(283,574)(284,573)(285,572)(286,571)(287,570)
(288,569)(289,568)(290,567)(291,566)(292,565)(293,564)(294,563)(295,562)
(296,561)(297,560)(298,559)(299,558)(300,557)(301,556)(302,555)(303,554)
(304,553)(305,552)(306,673)(307,672)(308,732)(309,731)(310,730)(311,729)
(312,728)(313,727)(314,726)(315,725)(316,724)(317,723)(318,722)(319,721)
(320,720)(321,719)(322,718)(323,717)(324,716)(325,715)(326,714)(327,713)
(328,712)(329,711)(330,710)(331,709)(332,708)(333,707)(334,706)(335,705)
(336,704)(337,703)(338,702)(339,701)(340,700)(341,699)(342,698)(343,697)
(344,696)(345,695)(346,694)(347,693)(348,692)(349,691)(350,690)(351,689)
(352,688)(353,687)(354,686)(355,685)(356,684)(357,683)(358,682)(359,681)
(360,680)(361,679)(362,678)(363,677)(364,676)(365,675)(366,674);
poly := sub<Sym(732)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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