Polytope of Type {756}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {756}*1512
Also Known As : 756-gon, {756}. if this polytope has another name.
Group : SmallGroup(1512,36)
Rank : 2
Schlafli Type : {756}
Number of vertices, edges, etc : 756, 756
Order of s₀s₁ : 756
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 : {378}*756
   3-fold quotients : {252}*504
   4-fold quotients : {189}*378
   6-fold quotients : {126}*252
   7-fold quotients : {108}*216
   9-fold quotients : {84}*168
   12-fold quotients : {63}*126
   14-fold quotients : {54}*108
   18-fold quotients : {42}*84
   21-fold quotients : {36}*72
   27-fold quotients : {28}*56
   28-fold quotients : {27}*54
   36-fold quotients : {21}*42
   42-fold quotients : {18}*36
   54-fold quotients : {14}*28
   63-fold quotients : {12}*24
   84-fold quotients : {9}*18
   108-fold quotients : {7}*14
   126-fold quotients : {6}*12
   189-fold quotients : {4}*8
   252-fold quotients : {3}*6
   378-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4,  9)(  5,  8)(  6,  7)( 10, 55)( 11, 57)( 12, 56)( 13, 63)
( 14, 62)( 15, 61)( 16, 60)( 17, 59)( 18, 58)( 19, 46)( 20, 48)( 21, 47)
( 22, 54)( 23, 53)( 24, 52)( 25, 51)( 26, 50)( 27, 49)( 28, 37)( 29, 39)
( 30, 38)( 31, 45)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 64,135)
( 65,134)( 66,133)( 67,132)( 68,131)( 69,130)( 70,129)( 71,128)( 72,127)
( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,184)( 79,183)( 80,182)
( 81,181)( 82,180)( 83,179)( 84,178)( 85,177)( 86,176)( 87,175)( 88,174)
( 89,173)( 90,172)( 91,171)( 92,170)( 93,169)( 94,168)( 95,167)( 96,166)
( 97,165)( 98,164)( 99,163)(100,162)(101,161)(102,160)(103,159)(104,158)
(105,157)(106,156)(107,155)(108,154)(109,153)(110,152)(111,151)(112,150)
(113,149)(114,148)(115,147)(116,146)(117,145)(118,144)(119,143)(120,142)
(121,141)(122,140)(123,139)(124,138)(125,137)(126,136)(191,192)(193,198)
(194,197)(195,196)(199,244)(200,246)(201,245)(202,252)(203,251)(204,250)
(205,249)(206,248)(207,247)(208,235)(209,237)(210,236)(211,243)(212,242)
(213,241)(214,240)(215,239)(216,238)(217,226)(218,228)(219,227)(220,234)
(221,233)(222,232)(223,231)(224,230)(225,229)(253,324)(254,323)(255,322)
(256,321)(257,320)(258,319)(259,318)(260,317)(261,316)(262,378)(263,377)
(264,376)(265,375)(266,374)(267,373)(268,372)(269,371)(270,370)(271,369)
(272,368)(273,367)(274,366)(275,365)(276,364)(277,363)(278,362)(279,361)
(280,360)(281,359)(282,358)(283,357)(284,356)(285,355)(286,354)(287,353)
(288,352)(289,351)(290,350)(291,349)(292,348)(293,347)(294,346)(295,345)
(296,344)(297,343)(298,342)(299,341)(300,340)(301,339)(302,338)(303,337)
(304,336)(305,335)(306,334)(307,333)(308,332)(309,331)(310,330)(311,329)
(312,328)(313,327)(314,326)(315,325)(379,568)(380,570)(381,569)(382,576)
(383,575)(384,574)(385,573)(386,572)(387,571)(388,622)(389,624)(390,623)
(391,630)(392,629)(393,628)(394,627)(395,626)(396,625)(397,613)(398,615)
(399,614)(400,621)(401,620)(402,619)(403,618)(404,617)(405,616)(406,604)
(407,606)(408,605)(409,612)(410,611)(411,610)(412,609)(413,608)(414,607)
(415,595)(416,597)(417,596)(418,603)(419,602)(420,601)(421,600)(422,599)
(423,598)(424,586)(425,588)(426,587)(427,594)(428,593)(429,592)(430,591)
(431,590)(432,589)(433,577)(434,579)(435,578)(436,585)(437,584)(438,583)
(439,582)(440,581)(441,580)(442,702)(443,701)(444,700)(445,699)(446,698)
(447,697)(448,696)(449,695)(450,694)(451,756)(452,755)(453,754)(454,753)
(455,752)(456,751)(457,750)(458,749)(459,748)(460,747)(461,746)(462,745)
(463,744)(464,743)(465,742)(466,741)(467,740)(468,739)(469,738)(470,737)
(471,736)(472,735)(473,734)(474,733)(475,732)(476,731)(477,730)(478,729)
(479,728)(480,727)(481,726)(482,725)(483,724)(484,723)(485,722)(486,721)
(487,720)(488,719)(489,718)(490,717)(491,716)(492,715)(493,714)(494,713)
(495,712)(496,711)(497,710)(498,709)(499,708)(500,707)(501,706)(502,705)
(503,704)(504,703)(505,639)(506,638)(507,637)(508,636)(509,635)(510,634)
(511,633)(512,632)(513,631)(514,693)(515,692)(516,691)(517,690)(518,689)
(519,688)(520,687)(521,686)(522,685)(523,684)(524,683)(525,682)(526,681)
(527,680)(528,679)(529,678)(530,677)(531,676)(532,675)(533,674)(534,673)
(535,672)(536,671)(537,670)(538,669)(539,668)(540,667)(541,666)(542,665)
(543,664)(544,663)(545,662)(546,661)(547,660)(548,659)(549,658)(550,657)
(551,656)(552,655)(553,654)(554,653)(555,652)(556,651)(557,650)(558,649)
(559,648)(560,647)(561,646)(562,645)(563,644)(564,643)(565,642)(566,641)
(567,640);;
s1 := (  1,451)(  2,453)(  3,452)(  4,459)(  5,458)(  6,457)(  7,456)(  8,455)
(  9,454)( 10,442)( 11,444)( 12,443)( 13,450)( 14,449)( 15,448)( 16,447)
( 17,446)( 18,445)( 19,496)( 20,498)( 21,497)( 22,504)( 23,503)( 24,502)
( 25,501)( 26,500)( 27,499)( 28,487)( 29,489)( 30,488)( 31,495)( 32,494)
( 33,493)( 34,492)( 35,491)( 36,490)( 37,478)( 38,480)( 39,479)( 40,486)
( 41,485)( 42,484)( 43,483)( 44,482)( 45,481)( 46,469)( 47,471)( 48,470)
( 49,477)( 50,476)( 51,475)( 52,474)( 53,473)( 54,472)( 55,460)( 56,462)
( 57,461)( 58,468)( 59,467)( 60,466)( 61,465)( 62,464)( 63,463)( 64,388)
( 65,390)( 66,389)( 67,396)( 68,395)( 69,394)( 70,393)( 71,392)( 72,391)
( 73,379)( 74,381)( 75,380)( 76,387)( 77,386)( 78,385)( 79,384)( 80,383)
( 81,382)( 82,433)( 83,435)( 84,434)( 85,441)( 86,440)( 87,439)( 88,438)
( 89,437)( 90,436)( 91,424)( 92,426)( 93,425)( 94,432)( 95,431)( 96,430)
( 97,429)( 98,428)( 99,427)(100,415)(101,417)(102,416)(103,423)(104,422)
(105,421)(106,420)(107,419)(108,418)(109,406)(110,408)(111,407)(112,414)
(113,413)(114,412)(115,411)(116,410)(117,409)(118,397)(119,399)(120,398)
(121,405)(122,404)(123,403)(124,402)(125,401)(126,400)(127,522)(128,521)
(129,520)(130,519)(131,518)(132,517)(133,516)(134,515)(135,514)(136,513)
(137,512)(138,511)(139,510)(140,509)(141,508)(142,507)(143,506)(144,505)
(145,567)(146,566)(147,565)(148,564)(149,563)(150,562)(151,561)(152,560)
(153,559)(154,558)(155,557)(156,556)(157,555)(158,554)(159,553)(160,552)
(161,551)(162,550)(163,549)(164,548)(165,547)(166,546)(167,545)(168,544)
(169,543)(170,542)(171,541)(172,540)(173,539)(174,538)(175,537)(176,536)
(177,535)(178,534)(179,533)(180,532)(181,531)(182,530)(183,529)(184,528)
(185,527)(186,526)(187,525)(188,524)(189,523)(190,640)(191,642)(192,641)
(193,648)(194,647)(195,646)(196,645)(197,644)(198,643)(199,631)(200,633)
(201,632)(202,639)(203,638)(204,637)(205,636)(206,635)(207,634)(208,685)
(209,687)(210,686)(211,693)(212,692)(213,691)(214,690)(215,689)(216,688)
(217,676)(218,678)(219,677)(220,684)(221,683)(222,682)(223,681)(224,680)
(225,679)(226,667)(227,669)(228,668)(229,675)(230,674)(231,673)(232,672)
(233,671)(234,670)(235,658)(236,660)(237,659)(238,666)(239,665)(240,664)
(241,663)(242,662)(243,661)(244,649)(245,651)(246,650)(247,657)(248,656)
(249,655)(250,654)(251,653)(252,652)(253,577)(254,579)(255,578)(256,585)
(257,584)(258,583)(259,582)(260,581)(261,580)(262,568)(263,570)(264,569)
(265,576)(266,575)(267,574)(268,573)(269,572)(270,571)(271,622)(272,624)
(273,623)(274,630)(275,629)(276,628)(277,627)(278,626)(279,625)(280,613)
(281,615)(282,614)(283,621)(284,620)(285,619)(286,618)(287,617)(288,616)
(289,604)(290,606)(291,605)(292,612)(293,611)(294,610)(295,609)(296,608)
(297,607)(298,595)(299,597)(300,596)(301,603)(302,602)(303,601)(304,600)
(305,599)(306,598)(307,586)(308,588)(309,587)(310,594)(311,593)(312,592)
(313,591)(314,590)(315,589)(316,711)(317,710)(318,709)(319,708)(320,707)
(321,706)(322,705)(323,704)(324,703)(325,702)(326,701)(327,700)(328,699)
(329,698)(330,697)(331,696)(332,695)(333,694)(334,756)(335,755)(336,754)
(337,753)(338,752)(339,751)(340,750)(341,749)(342,748)(343,747)(344,746)
(345,745)(346,744)(347,743)(348,742)(349,741)(350,740)(351,739)(352,738)
(353,737)(354,736)(355,735)(356,734)(357,733)(358,732)(359,731)(360,730)
(361,729)(362,728)(363,727)(364,726)(365,725)(366,724)(367,723)(368,722)
(369,721)(370,720)(371,719)(372,718)(373,717)(374,716)(375,715)(376,714)
(377,713)(378,712);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(756)!(  2,  3)(  4,  9)(  5,  8)(  6,  7)( 10, 55)( 11, 57)( 12, 56)
( 13, 63)( 14, 62)( 15, 61)( 16, 60)( 17, 59)( 18, 58)( 19, 46)( 20, 48)
( 21, 47)( 22, 54)( 23, 53)( 24, 52)( 25, 51)( 26, 50)( 27, 49)( 28, 37)
( 29, 39)( 30, 38)( 31, 45)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)
( 64,135)( 65,134)( 66,133)( 67,132)( 68,131)( 69,130)( 70,129)( 71,128)
( 72,127)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,184)( 79,183)
( 80,182)( 81,181)( 82,180)( 83,179)( 84,178)( 85,177)( 86,176)( 87,175)
( 88,174)( 89,173)( 90,172)( 91,171)( 92,170)( 93,169)( 94,168)( 95,167)
( 96,166)( 97,165)( 98,164)( 99,163)(100,162)(101,161)(102,160)(103,159)
(104,158)(105,157)(106,156)(107,155)(108,154)(109,153)(110,152)(111,151)
(112,150)(113,149)(114,148)(115,147)(116,146)(117,145)(118,144)(119,143)
(120,142)(121,141)(122,140)(123,139)(124,138)(125,137)(126,136)(191,192)
(193,198)(194,197)(195,196)(199,244)(200,246)(201,245)(202,252)(203,251)
(204,250)(205,249)(206,248)(207,247)(208,235)(209,237)(210,236)(211,243)
(212,242)(213,241)(214,240)(215,239)(216,238)(217,226)(218,228)(219,227)
(220,234)(221,233)(222,232)(223,231)(224,230)(225,229)(253,324)(254,323)
(255,322)(256,321)(257,320)(258,319)(259,318)(260,317)(261,316)(262,378)
(263,377)(264,376)(265,375)(266,374)(267,373)(268,372)(269,371)(270,370)
(271,369)(272,368)(273,367)(274,366)(275,365)(276,364)(277,363)(278,362)
(279,361)(280,360)(281,359)(282,358)(283,357)(284,356)(285,355)(286,354)
(287,353)(288,352)(289,351)(290,350)(291,349)(292,348)(293,347)(294,346)
(295,345)(296,344)(297,343)(298,342)(299,341)(300,340)(301,339)(302,338)
(303,337)(304,336)(305,335)(306,334)(307,333)(308,332)(309,331)(310,330)
(311,329)(312,328)(313,327)(314,326)(315,325)(379,568)(380,570)(381,569)
(382,576)(383,575)(384,574)(385,573)(386,572)(387,571)(388,622)(389,624)
(390,623)(391,630)(392,629)(393,628)(394,627)(395,626)(396,625)(397,613)
(398,615)(399,614)(400,621)(401,620)(402,619)(403,618)(404,617)(405,616)
(406,604)(407,606)(408,605)(409,612)(410,611)(411,610)(412,609)(413,608)
(414,607)(415,595)(416,597)(417,596)(418,603)(419,602)(420,601)(421,600)
(422,599)(423,598)(424,586)(425,588)(426,587)(427,594)(428,593)(429,592)
(430,591)(431,590)(432,589)(433,577)(434,579)(435,578)(436,585)(437,584)
(438,583)(439,582)(440,581)(441,580)(442,702)(443,701)(444,700)(445,699)
(446,698)(447,697)(448,696)(449,695)(450,694)(451,756)(452,755)(453,754)
(454,753)(455,752)(456,751)(457,750)(458,749)(459,748)(460,747)(461,746)
(462,745)(463,744)(464,743)(465,742)(466,741)(467,740)(468,739)(469,738)
(470,737)(471,736)(472,735)(473,734)(474,733)(475,732)(476,731)(477,730)
(478,729)(479,728)(480,727)(481,726)(482,725)(483,724)(484,723)(485,722)
(486,721)(487,720)(488,719)(489,718)(490,717)(491,716)(492,715)(493,714)
(494,713)(495,712)(496,711)(497,710)(498,709)(499,708)(500,707)(501,706)
(502,705)(503,704)(504,703)(505,639)(506,638)(507,637)(508,636)(509,635)
(510,634)(511,633)(512,632)(513,631)(514,693)(515,692)(516,691)(517,690)
(518,689)(519,688)(520,687)(521,686)(522,685)(523,684)(524,683)(525,682)
(526,681)(527,680)(528,679)(529,678)(530,677)(531,676)(532,675)(533,674)
(534,673)(535,672)(536,671)(537,670)(538,669)(539,668)(540,667)(541,666)
(542,665)(543,664)(544,663)(545,662)(546,661)(547,660)(548,659)(549,658)
(550,657)(551,656)(552,655)(553,654)(554,653)(555,652)(556,651)(557,650)
(558,649)(559,648)(560,647)(561,646)(562,645)(563,644)(564,643)(565,642)
(566,641)(567,640);
s1 := Sym(756)!(  1,451)(  2,453)(  3,452)(  4,459)(  5,458)(  6,457)(  7,456)
(  8,455)(  9,454)( 10,442)( 11,444)( 12,443)( 13,450)( 14,449)( 15,448)
( 16,447)( 17,446)( 18,445)( 19,496)( 20,498)( 21,497)( 22,504)( 23,503)
( 24,502)( 25,501)( 26,500)( 27,499)( 28,487)( 29,489)( 30,488)( 31,495)
( 32,494)( 33,493)( 34,492)( 35,491)( 36,490)( 37,478)( 38,480)( 39,479)
( 40,486)( 41,485)( 42,484)( 43,483)( 44,482)( 45,481)( 46,469)( 47,471)
( 48,470)( 49,477)( 50,476)( 51,475)( 52,474)( 53,473)( 54,472)( 55,460)
( 56,462)( 57,461)( 58,468)( 59,467)( 60,466)( 61,465)( 62,464)( 63,463)
( 64,388)( 65,390)( 66,389)( 67,396)( 68,395)( 69,394)( 70,393)( 71,392)
( 72,391)( 73,379)( 74,381)( 75,380)( 76,387)( 77,386)( 78,385)( 79,384)
( 80,383)( 81,382)( 82,433)( 83,435)( 84,434)( 85,441)( 86,440)( 87,439)
( 88,438)( 89,437)( 90,436)( 91,424)( 92,426)( 93,425)( 94,432)( 95,431)
( 96,430)( 97,429)( 98,428)( 99,427)(100,415)(101,417)(102,416)(103,423)
(104,422)(105,421)(106,420)(107,419)(108,418)(109,406)(110,408)(111,407)
(112,414)(113,413)(114,412)(115,411)(116,410)(117,409)(118,397)(119,399)
(120,398)(121,405)(122,404)(123,403)(124,402)(125,401)(126,400)(127,522)
(128,521)(129,520)(130,519)(131,518)(132,517)(133,516)(134,515)(135,514)
(136,513)(137,512)(138,511)(139,510)(140,509)(141,508)(142,507)(143,506)
(144,505)(145,567)(146,566)(147,565)(148,564)(149,563)(150,562)(151,561)
(152,560)(153,559)(154,558)(155,557)(156,556)(157,555)(158,554)(159,553)
(160,552)(161,551)(162,550)(163,549)(164,548)(165,547)(166,546)(167,545)
(168,544)(169,543)(170,542)(171,541)(172,540)(173,539)(174,538)(175,537)
(176,536)(177,535)(178,534)(179,533)(180,532)(181,531)(182,530)(183,529)
(184,528)(185,527)(186,526)(187,525)(188,524)(189,523)(190,640)(191,642)
(192,641)(193,648)(194,647)(195,646)(196,645)(197,644)(198,643)(199,631)
(200,633)(201,632)(202,639)(203,638)(204,637)(205,636)(206,635)(207,634)
(208,685)(209,687)(210,686)(211,693)(212,692)(213,691)(214,690)(215,689)
(216,688)(217,676)(218,678)(219,677)(220,684)(221,683)(222,682)(223,681)
(224,680)(225,679)(226,667)(227,669)(228,668)(229,675)(230,674)(231,673)
(232,672)(233,671)(234,670)(235,658)(236,660)(237,659)(238,666)(239,665)
(240,664)(241,663)(242,662)(243,661)(244,649)(245,651)(246,650)(247,657)
(248,656)(249,655)(250,654)(251,653)(252,652)(253,577)(254,579)(255,578)
(256,585)(257,584)(258,583)(259,582)(260,581)(261,580)(262,568)(263,570)
(264,569)(265,576)(266,575)(267,574)(268,573)(269,572)(270,571)(271,622)
(272,624)(273,623)(274,630)(275,629)(276,628)(277,627)(278,626)(279,625)
(280,613)(281,615)(282,614)(283,621)(284,620)(285,619)(286,618)(287,617)
(288,616)(289,604)(290,606)(291,605)(292,612)(293,611)(294,610)(295,609)
(296,608)(297,607)(298,595)(299,597)(300,596)(301,603)(302,602)(303,601)
(304,600)(305,599)(306,598)(307,586)(308,588)(309,587)(310,594)(311,593)
(312,592)(313,591)(314,590)(315,589)(316,711)(317,710)(318,709)(319,708)
(320,707)(321,706)(322,705)(323,704)(324,703)(325,702)(326,701)(327,700)
(328,699)(329,698)(330,697)(331,696)(332,695)(333,694)(334,756)(335,755)
(336,754)(337,753)(338,752)(339,751)(340,750)(341,749)(342,748)(343,747)
(344,746)(345,745)(346,744)(347,743)(348,742)(349,741)(350,740)(351,739)
(352,738)(353,737)(354,736)(355,735)(356,734)(357,733)(358,732)(359,731)
(360,730)(361,729)(362,728)(363,727)(364,726)(365,725)(366,724)(367,723)
(368,722)(369,721)(370,720)(371,719)(372,718)(373,717)(374,716)(375,715)
(376,714)(377,713)(378,712);
poly := sub<Sym(756)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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