Polytope of Type {4,178}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,178}*1424
Also Known As : {4,178|2}. if this polytope has another name.
Group : SmallGroup(1424,34)
Rank : 3
Schlafli Type : {4,178}
Number of vertices, edges, etc : 4, 356, 178
Order of s₀s₁s₂ : 356
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {2,178}*712
   4-fold quotients : {2,89}*356
   89-fold quotients : {4,2}*16
   178-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (357,446)(358,447)(359,448)(360,449)(361,450)(362,451)(363,452)(364,453)
(365,454)(366,455)(367,456)(368,457)(369,458)(370,459)(371,460)(372,461)
(373,462)(374,463)(375,464)(376,465)(377,466)(378,467)(379,468)(380,469)
(381,470)(382,471)(383,472)(384,473)(385,474)(386,475)(387,476)(388,477)
(389,478)(390,479)(391,480)(392,481)(393,482)(394,483)(395,484)(396,485)
(397,486)(398,487)(399,488)(400,489)(401,490)(402,491)(403,492)(404,493)
(405,494)(406,495)(407,496)(408,497)(409,498)(410,499)(411,500)(412,501)
(413,502)(414,503)(415,504)(416,505)(417,506)(418,507)(419,508)(420,509)
(421,510)(422,511)(423,512)(424,513)(425,514)(426,515)(427,516)(428,517)
(429,518)(430,519)(431,520)(432,521)(433,522)(434,523)(435,524)(436,525)
(437,526)(438,527)(439,528)(440,529)(441,530)(442,531)(443,532)(444,533)
(445,534)(535,624)(536,625)(537,626)(538,627)(539,628)(540,629)(541,630)
(542,631)(543,632)(544,633)(545,634)(546,635)(547,636)(548,637)(549,638)
(550,639)(551,640)(552,641)(553,642)(554,643)(555,644)(556,645)(557,646)
(558,647)(559,648)(560,649)(561,650)(562,651)(563,652)(564,653)(565,654)
(566,655)(567,656)(568,657)(569,658)(570,659)(571,660)(572,661)(573,662)
(574,663)(575,664)(576,665)(577,666)(578,667)(579,668)(580,669)(581,670)
(582,671)(583,672)(584,673)(585,674)(586,675)(587,676)(588,677)(589,678)
(590,679)(591,680)(592,681)(593,682)(594,683)(595,684)(596,685)(597,686)
(598,687)(599,688)(600,689)(601,690)(602,691)(603,692)(604,693)(605,694)
(606,695)(607,696)(608,697)(609,698)(610,699)(611,700)(612,701)(613,702)
(614,703)(615,704)(616,705)(617,706)(618,707)(619,708)(620,709)(621,710)
(622,711)(623,712);;
s1 := (  1,535)(  2,623)(  3,622)(  4,621)(  5,620)(  6,619)(  7,618)(  8,617)
(  9,616)( 10,615)( 11,614)( 12,613)( 13,612)( 14,611)( 15,610)( 16,609)
( 17,608)( 18,607)( 19,606)( 20,605)( 21,604)( 22,603)( 23,602)( 24,601)
( 25,600)( 26,599)( 27,598)( 28,597)( 29,596)( 30,595)( 31,594)( 32,593)
( 33,592)( 34,591)( 35,590)( 36,589)( 37,588)( 38,587)( 39,586)( 40,585)
( 41,584)( 42,583)( 43,582)( 44,581)( 45,580)( 46,579)( 47,578)( 48,577)
( 49,576)( 50,575)( 51,574)( 52,573)( 53,572)( 54,571)( 55,570)( 56,569)
( 57,568)( 58,567)( 59,566)( 60,565)( 61,564)( 62,563)( 63,562)( 64,561)
( 65,560)( 66,559)( 67,558)( 68,557)( 69,556)( 70,555)( 71,554)( 72,553)
( 73,552)( 74,551)( 75,550)( 76,549)( 77,548)( 78,547)( 79,546)( 80,545)
( 81,544)( 82,543)( 83,542)( 84,541)( 85,540)( 86,539)( 87,538)( 88,537)
( 89,536)( 90,624)( 91,712)( 92,711)( 93,710)( 94,709)( 95,708)( 96,707)
( 97,706)( 98,705)( 99,704)(100,703)(101,702)(102,701)(103,700)(104,699)
(105,698)(106,697)(107,696)(108,695)(109,694)(110,693)(111,692)(112,691)
(113,690)(114,689)(115,688)(116,687)(117,686)(118,685)(119,684)(120,683)
(121,682)(122,681)(123,680)(124,679)(125,678)(126,677)(127,676)(128,675)
(129,674)(130,673)(131,672)(132,671)(133,670)(134,669)(135,668)(136,667)
(137,666)(138,665)(139,664)(140,663)(141,662)(142,661)(143,660)(144,659)
(145,658)(146,657)(147,656)(148,655)(149,654)(150,653)(151,652)(152,651)
(153,650)(154,649)(155,648)(156,647)(157,646)(158,645)(159,644)(160,643)
(161,642)(162,641)(163,640)(164,639)(165,638)(166,637)(167,636)(168,635)
(169,634)(170,633)(171,632)(172,631)(173,630)(174,629)(175,628)(176,627)
(177,626)(178,625)(179,357)(180,445)(181,444)(182,443)(183,442)(184,441)
(185,440)(186,439)(187,438)(188,437)(189,436)(190,435)(191,434)(192,433)
(193,432)(194,431)(195,430)(196,429)(197,428)(198,427)(199,426)(200,425)
(201,424)(202,423)(203,422)(204,421)(205,420)(206,419)(207,418)(208,417)
(209,416)(210,415)(211,414)(212,413)(213,412)(214,411)(215,410)(216,409)
(217,408)(218,407)(219,406)(220,405)(221,404)(222,403)(223,402)(224,401)
(225,400)(226,399)(227,398)(228,397)(229,396)(230,395)(231,394)(232,393)
(233,392)(234,391)(235,390)(236,389)(237,388)(238,387)(239,386)(240,385)
(241,384)(242,383)(243,382)(244,381)(245,380)(246,379)(247,378)(248,377)
(249,376)(250,375)(251,374)(252,373)(253,372)(254,371)(255,370)(256,369)
(257,368)(258,367)(259,366)(260,365)(261,364)(262,363)(263,362)(264,361)
(265,360)(266,359)(267,358)(268,446)(269,534)(270,533)(271,532)(272,531)
(273,530)(274,529)(275,528)(276,527)(277,526)(278,525)(279,524)(280,523)
(281,522)(282,521)(283,520)(284,519)(285,518)(286,517)(287,516)(288,515)
(289,514)(290,513)(291,512)(292,511)(293,510)(294,509)(295,508)(296,507)
(297,506)(298,505)(299,504)(300,503)(301,502)(302,501)(303,500)(304,499)
(305,498)(306,497)(307,496)(308,495)(309,494)(310,493)(311,492)(312,491)
(313,490)(314,489)(315,488)(316,487)(317,486)(318,485)(319,484)(320,483)
(321,482)(322,481)(323,480)(324,479)(325,478)(326,477)(327,476)(328,475)
(329,474)(330,473)(331,472)(332,471)(333,470)(334,469)(335,468)(336,467)
(337,466)(338,465)(339,464)(340,463)(341,462)(342,461)(343,460)(344,459)
(345,458)(346,457)(347,456)(348,455)(349,454)(350,453)(351,452)(352,451)
(353,450)(354,449)(355,448)(356,447);;
s2 := (  1,180)(  2,179)(  3,267)(  4,266)(  5,265)(  6,264)(  7,263)(  8,262)
(  9,261)( 10,260)( 11,259)( 12,258)( 13,257)( 14,256)( 15,255)( 16,254)
( 17,253)( 18,252)( 19,251)( 20,250)( 21,249)( 22,248)( 23,247)( 24,246)
( 25,245)( 26,244)( 27,243)( 28,242)( 29,241)( 30,240)( 31,239)( 32,238)
( 33,237)( 34,236)( 35,235)( 36,234)( 37,233)( 38,232)( 39,231)( 40,230)
( 41,229)( 42,228)( 43,227)( 44,226)( 45,225)( 46,224)( 47,223)( 48,222)
( 49,221)( 50,220)( 51,219)( 52,218)( 53,217)( 54,216)( 55,215)( 56,214)
( 57,213)( 58,212)( 59,211)( 60,210)( 61,209)( 62,208)( 63,207)( 64,206)
( 65,205)( 66,204)( 67,203)( 68,202)( 69,201)( 70,200)( 71,199)( 72,198)
( 73,197)( 74,196)( 75,195)( 76,194)( 77,193)( 78,192)( 79,191)( 80,190)
( 81,189)( 82,188)( 83,187)( 84,186)( 85,185)( 86,184)( 87,183)( 88,182)
( 89,181)( 90,269)( 91,268)( 92,356)( 93,355)( 94,354)( 95,353)( 96,352)
( 97,351)( 98,350)( 99,349)(100,348)(101,347)(102,346)(103,345)(104,344)
(105,343)(106,342)(107,341)(108,340)(109,339)(110,338)(111,337)(112,336)
(113,335)(114,334)(115,333)(116,332)(117,331)(118,330)(119,329)(120,328)
(121,327)(122,326)(123,325)(124,324)(125,323)(126,322)(127,321)(128,320)
(129,319)(130,318)(131,317)(132,316)(133,315)(134,314)(135,313)(136,312)
(137,311)(138,310)(139,309)(140,308)(141,307)(142,306)(143,305)(144,304)
(145,303)(146,302)(147,301)(148,300)(149,299)(150,298)(151,297)(152,296)
(153,295)(154,294)(155,293)(156,292)(157,291)(158,290)(159,289)(160,288)
(161,287)(162,286)(163,285)(164,284)(165,283)(166,282)(167,281)(168,280)
(169,279)(170,278)(171,277)(172,276)(173,275)(174,274)(175,273)(176,272)
(177,271)(178,270)(357,536)(358,535)(359,623)(360,622)(361,621)(362,620)
(363,619)(364,618)(365,617)(366,616)(367,615)(368,614)(369,613)(370,612)
(371,611)(372,610)(373,609)(374,608)(375,607)(376,606)(377,605)(378,604)
(379,603)(380,602)(381,601)(382,600)(383,599)(384,598)(385,597)(386,596)
(387,595)(388,594)(389,593)(390,592)(391,591)(392,590)(393,589)(394,588)
(395,587)(396,586)(397,585)(398,584)(399,583)(400,582)(401,581)(402,580)
(403,579)(404,578)(405,577)(406,576)(407,575)(408,574)(409,573)(410,572)
(411,571)(412,570)(413,569)(414,568)(415,567)(416,566)(417,565)(418,564)
(419,563)(420,562)(421,561)(422,560)(423,559)(424,558)(425,557)(426,556)
(427,555)(428,554)(429,553)(430,552)(431,551)(432,550)(433,549)(434,548)
(435,547)(436,546)(437,545)(438,544)(439,543)(440,542)(441,541)(442,540)
(443,539)(444,538)(445,537)(446,625)(447,624)(448,712)(449,711)(450,710)
(451,709)(452,708)(453,707)(454,706)(455,705)(456,704)(457,703)(458,702)
(459,701)(460,700)(461,699)(462,698)(463,697)(464,696)(465,695)(466,694)
(467,693)(468,692)(469,691)(470,690)(471,689)(472,688)(473,687)(474,686)
(475,685)(476,684)(477,683)(478,682)(479,681)(480,680)(481,679)(482,678)
(483,677)(484,676)(485,675)(486,674)(487,673)(488,672)(489,671)(490,670)
(491,669)(492,668)(493,667)(494,666)(495,665)(496,664)(497,663)(498,662)
(499,661)(500,660)(501,659)(502,658)(503,657)(504,656)(505,655)(506,654)
(507,653)(508,652)(509,651)(510,650)(511,649)(512,648)(513,647)(514,646)
(515,645)(516,644)(517,643)(518,642)(519,641)(520,640)(521,639)(522,638)
(523,637)(524,636)(525,635)(526,634)(527,633)(528,632)(529,631)(530,630)
(531,629)(532,628)(533,627)(534,626);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(712)!(357,446)(358,447)(359,448)(360,449)(361,450)(362,451)(363,452)
(364,453)(365,454)(366,455)(367,456)(368,457)(369,458)(370,459)(371,460)
(372,461)(373,462)(374,463)(375,464)(376,465)(377,466)(378,467)(379,468)
(380,469)(381,470)(382,471)(383,472)(384,473)(385,474)(386,475)(387,476)
(388,477)(389,478)(390,479)(391,480)(392,481)(393,482)(394,483)(395,484)
(396,485)(397,486)(398,487)(399,488)(400,489)(401,490)(402,491)(403,492)
(404,493)(405,494)(406,495)(407,496)(408,497)(409,498)(410,499)(411,500)
(412,501)(413,502)(414,503)(415,504)(416,505)(417,506)(418,507)(419,508)
(420,509)(421,510)(422,511)(423,512)(424,513)(425,514)(426,515)(427,516)
(428,517)(429,518)(430,519)(431,520)(432,521)(433,522)(434,523)(435,524)
(436,525)(437,526)(438,527)(439,528)(440,529)(441,530)(442,531)(443,532)
(444,533)(445,534)(535,624)(536,625)(537,626)(538,627)(539,628)(540,629)
(541,630)(542,631)(543,632)(544,633)(545,634)(546,635)(547,636)(548,637)
(549,638)(550,639)(551,640)(552,641)(553,642)(554,643)(555,644)(556,645)
(557,646)(558,647)(559,648)(560,649)(561,650)(562,651)(563,652)(564,653)
(565,654)(566,655)(567,656)(568,657)(569,658)(570,659)(571,660)(572,661)
(573,662)(574,663)(575,664)(576,665)(577,666)(578,667)(579,668)(580,669)
(581,670)(582,671)(583,672)(584,673)(585,674)(586,675)(587,676)(588,677)
(589,678)(590,679)(591,680)(592,681)(593,682)(594,683)(595,684)(596,685)
(597,686)(598,687)(599,688)(600,689)(601,690)(602,691)(603,692)(604,693)
(605,694)(606,695)(607,696)(608,697)(609,698)(610,699)(611,700)(612,701)
(613,702)(614,703)(615,704)(616,705)(617,706)(618,707)(619,708)(620,709)
(621,710)(622,711)(623,712);
s1 := Sym(712)!(  1,535)(  2,623)(  3,622)(  4,621)(  5,620)(  6,619)(  7,618)
(  8,617)(  9,616)( 10,615)( 11,614)( 12,613)( 13,612)( 14,611)( 15,610)
( 16,609)( 17,608)( 18,607)( 19,606)( 20,605)( 21,604)( 22,603)( 23,602)
( 24,601)( 25,600)( 26,599)( 27,598)( 28,597)( 29,596)( 30,595)( 31,594)
( 32,593)( 33,592)( 34,591)( 35,590)( 36,589)( 37,588)( 38,587)( 39,586)
( 40,585)( 41,584)( 42,583)( 43,582)( 44,581)( 45,580)( 46,579)( 47,578)
( 48,577)( 49,576)( 50,575)( 51,574)( 52,573)( 53,572)( 54,571)( 55,570)
( 56,569)( 57,568)( 58,567)( 59,566)( 60,565)( 61,564)( 62,563)( 63,562)
( 64,561)( 65,560)( 66,559)( 67,558)( 68,557)( 69,556)( 70,555)( 71,554)
( 72,553)( 73,552)( 74,551)( 75,550)( 76,549)( 77,548)( 78,547)( 79,546)
( 80,545)( 81,544)( 82,543)( 83,542)( 84,541)( 85,540)( 86,539)( 87,538)
( 88,537)( 89,536)( 90,624)( 91,712)( 92,711)( 93,710)( 94,709)( 95,708)
( 96,707)( 97,706)( 98,705)( 99,704)(100,703)(101,702)(102,701)(103,700)
(104,699)(105,698)(106,697)(107,696)(108,695)(109,694)(110,693)(111,692)
(112,691)(113,690)(114,689)(115,688)(116,687)(117,686)(118,685)(119,684)
(120,683)(121,682)(122,681)(123,680)(124,679)(125,678)(126,677)(127,676)
(128,675)(129,674)(130,673)(131,672)(132,671)(133,670)(134,669)(135,668)
(136,667)(137,666)(138,665)(139,664)(140,663)(141,662)(142,661)(143,660)
(144,659)(145,658)(146,657)(147,656)(148,655)(149,654)(150,653)(151,652)
(152,651)(153,650)(154,649)(155,648)(156,647)(157,646)(158,645)(159,644)
(160,643)(161,642)(162,641)(163,640)(164,639)(165,638)(166,637)(167,636)
(168,635)(169,634)(170,633)(171,632)(172,631)(173,630)(174,629)(175,628)
(176,627)(177,626)(178,625)(179,357)(180,445)(181,444)(182,443)(183,442)
(184,441)(185,440)(186,439)(187,438)(188,437)(189,436)(190,435)(191,434)
(192,433)(193,432)(194,431)(195,430)(196,429)(197,428)(198,427)(199,426)
(200,425)(201,424)(202,423)(203,422)(204,421)(205,420)(206,419)(207,418)
(208,417)(209,416)(210,415)(211,414)(212,413)(213,412)(214,411)(215,410)
(216,409)(217,408)(218,407)(219,406)(220,405)(221,404)(222,403)(223,402)
(224,401)(225,400)(226,399)(227,398)(228,397)(229,396)(230,395)(231,394)
(232,393)(233,392)(234,391)(235,390)(236,389)(237,388)(238,387)(239,386)
(240,385)(241,384)(242,383)(243,382)(244,381)(245,380)(246,379)(247,378)
(248,377)(249,376)(250,375)(251,374)(252,373)(253,372)(254,371)(255,370)
(256,369)(257,368)(258,367)(259,366)(260,365)(261,364)(262,363)(263,362)
(264,361)(265,360)(266,359)(267,358)(268,446)(269,534)(270,533)(271,532)
(272,531)(273,530)(274,529)(275,528)(276,527)(277,526)(278,525)(279,524)
(280,523)(281,522)(282,521)(283,520)(284,519)(285,518)(286,517)(287,516)
(288,515)(289,514)(290,513)(291,512)(292,511)(293,510)(294,509)(295,508)
(296,507)(297,506)(298,505)(299,504)(300,503)(301,502)(302,501)(303,500)
(304,499)(305,498)(306,497)(307,496)(308,495)(309,494)(310,493)(311,492)
(312,491)(313,490)(314,489)(315,488)(316,487)(317,486)(318,485)(319,484)
(320,483)(321,482)(322,481)(323,480)(324,479)(325,478)(326,477)(327,476)
(328,475)(329,474)(330,473)(331,472)(332,471)(333,470)(334,469)(335,468)
(336,467)(337,466)(338,465)(339,464)(340,463)(341,462)(342,461)(343,460)
(344,459)(345,458)(346,457)(347,456)(348,455)(349,454)(350,453)(351,452)
(352,451)(353,450)(354,449)(355,448)(356,447);
s2 := Sym(712)!(  1,180)(  2,179)(  3,267)(  4,266)(  5,265)(  6,264)(  7,263)
(  8,262)(  9,261)( 10,260)( 11,259)( 12,258)( 13,257)( 14,256)( 15,255)
( 16,254)( 17,253)( 18,252)( 19,251)( 20,250)( 21,249)( 22,248)( 23,247)
( 24,246)( 25,245)( 26,244)( 27,243)( 28,242)( 29,241)( 30,240)( 31,239)
( 32,238)( 33,237)( 34,236)( 35,235)( 36,234)( 37,233)( 38,232)( 39,231)
( 40,230)( 41,229)( 42,228)( 43,227)( 44,226)( 45,225)( 46,224)( 47,223)
( 48,222)( 49,221)( 50,220)( 51,219)( 52,218)( 53,217)( 54,216)( 55,215)
( 56,214)( 57,213)( 58,212)( 59,211)( 60,210)( 61,209)( 62,208)( 63,207)
( 64,206)( 65,205)( 66,204)( 67,203)( 68,202)( 69,201)( 70,200)( 71,199)
( 72,198)( 73,197)( 74,196)( 75,195)( 76,194)( 77,193)( 78,192)( 79,191)
( 80,190)( 81,189)( 82,188)( 83,187)( 84,186)( 85,185)( 86,184)( 87,183)
( 88,182)( 89,181)( 90,269)( 91,268)( 92,356)( 93,355)( 94,354)( 95,353)
( 96,352)( 97,351)( 98,350)( 99,349)(100,348)(101,347)(102,346)(103,345)
(104,344)(105,343)(106,342)(107,341)(108,340)(109,339)(110,338)(111,337)
(112,336)(113,335)(114,334)(115,333)(116,332)(117,331)(118,330)(119,329)
(120,328)(121,327)(122,326)(123,325)(124,324)(125,323)(126,322)(127,321)
(128,320)(129,319)(130,318)(131,317)(132,316)(133,315)(134,314)(135,313)
(136,312)(137,311)(138,310)(139,309)(140,308)(141,307)(142,306)(143,305)
(144,304)(145,303)(146,302)(147,301)(148,300)(149,299)(150,298)(151,297)
(152,296)(153,295)(154,294)(155,293)(156,292)(157,291)(158,290)(159,289)
(160,288)(161,287)(162,286)(163,285)(164,284)(165,283)(166,282)(167,281)
(168,280)(169,279)(170,278)(171,277)(172,276)(173,275)(174,274)(175,273)
(176,272)(177,271)(178,270)(357,536)(358,535)(359,623)(360,622)(361,621)
(362,620)(363,619)(364,618)(365,617)(366,616)(367,615)(368,614)(369,613)
(370,612)(371,611)(372,610)(373,609)(374,608)(375,607)(376,606)(377,605)
(378,604)(379,603)(380,602)(381,601)(382,600)(383,599)(384,598)(385,597)
(386,596)(387,595)(388,594)(389,593)(390,592)(391,591)(392,590)(393,589)
(394,588)(395,587)(396,586)(397,585)(398,584)(399,583)(400,582)(401,581)
(402,580)(403,579)(404,578)(405,577)(406,576)(407,575)(408,574)(409,573)
(410,572)(411,571)(412,570)(413,569)(414,568)(415,567)(416,566)(417,565)
(418,564)(419,563)(420,562)(421,561)(422,560)(423,559)(424,558)(425,557)
(426,556)(427,555)(428,554)(429,553)(430,552)(431,551)(432,550)(433,549)
(434,548)(435,547)(436,546)(437,545)(438,544)(439,543)(440,542)(441,541)
(442,540)(443,539)(444,538)(445,537)(446,625)(447,624)(448,712)(449,711)
(450,710)(451,709)(452,708)(453,707)(454,706)(455,705)(456,704)(457,703)
(458,702)(459,701)(460,700)(461,699)(462,698)(463,697)(464,696)(465,695)
(466,694)(467,693)(468,692)(469,691)(470,690)(471,689)(472,688)(473,687)
(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)(480,680)(481,679)
(482,678)(483,677)(484,676)(485,675)(486,674)(487,673)(488,672)(489,671)
(490,670)(491,669)(492,668)(493,667)(494,666)(495,665)(496,664)(497,663)
(498,662)(499,661)(500,660)(501,659)(502,658)(503,657)(504,656)(505,655)
(506,654)(507,653)(508,652)(509,651)(510,650)(511,649)(512,648)(513,647)
(514,646)(515,645)(516,644)(517,643)(518,642)(519,641)(520,640)(521,639)
(522,638)(523,637)(524,636)(525,635)(526,634)(527,633)(528,632)(529,631)
(530,630)(531,629)(532,628)(533,627)(534,626);
poly := sub<Sym(712)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope