Polytope of Type {232,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {232,4}*1856a
Also Known As : {232,4|2}. if this polytope has another name.
Group : SmallGroup(1856,685)
Rank : 3
Schlafli Type : {232,4}
Number of vertices, edges, etc : 232, 464, 4
Order of s₀s₁s₂ : 232
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {116,4}*928, {232,2}*928
   4-fold quotients : {116,2}*464, {58,4}*464
   8-fold quotients : {58,2}*232
   16-fold quotients : {29,2}*116
   29-fold quotients : {8,4}*64a
   58-fold quotients : {4,4}*32, {8,2}*32
   116-fold quotients : {2,4}*16, {4,2}*16
   232-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,465)(  2,493)(  3,492)(  4,491)(  5,490)(  6,489)(  7,488)(  8,487)
(  9,486)( 10,485)( 11,484)( 12,483)( 13,482)( 14,481)( 15,480)( 16,479)
( 17,478)( 18,477)( 19,476)( 20,475)( 21,474)( 22,473)( 23,472)( 24,471)
( 25,470)( 26,469)( 27,468)( 28,467)( 29,466)( 30,494)( 31,522)( 32,521)
( 33,520)( 34,519)( 35,518)( 36,517)( 37,516)( 38,515)( 39,514)( 40,513)
( 41,512)( 42,511)( 43,510)( 44,509)( 45,508)( 46,507)( 47,506)( 48,505)
( 49,504)( 50,503)( 51,502)( 52,501)( 53,500)( 54,499)( 55,498)( 56,497)
( 57,496)( 58,495)( 59,523)( 60,551)( 61,550)( 62,549)( 63,548)( 64,547)
( 65,546)( 66,545)( 67,544)( 68,543)( 69,542)( 70,541)( 71,540)( 72,539)
( 73,538)( 74,537)( 75,536)( 76,535)( 77,534)( 78,533)( 79,532)( 80,531)
( 81,530)( 82,529)( 83,528)( 84,527)( 85,526)( 86,525)( 87,524)( 88,552)
( 89,580)( 90,579)( 91,578)( 92,577)( 93,576)( 94,575)( 95,574)( 96,573)
( 97,572)( 98,571)( 99,570)(100,569)(101,568)(102,567)(103,566)(104,565)
(105,564)(106,563)(107,562)(108,561)(109,560)(110,559)(111,558)(112,557)
(113,556)(114,555)(115,554)(116,553)(117,610)(118,638)(119,637)(120,636)
(121,635)(122,634)(123,633)(124,632)(125,631)(126,630)(127,629)(128,628)
(129,627)(130,626)(131,625)(132,624)(133,623)(134,622)(135,621)(136,620)
(137,619)(138,618)(139,617)(140,616)(141,615)(142,614)(143,613)(144,612)
(145,611)(146,581)(147,609)(148,608)(149,607)(150,606)(151,605)(152,604)
(153,603)(154,602)(155,601)(156,600)(157,599)(158,598)(159,597)(160,596)
(161,595)(162,594)(163,593)(164,592)(165,591)(166,590)(167,589)(168,588)
(169,587)(170,586)(171,585)(172,584)(173,583)(174,582)(175,668)(176,696)
(177,695)(178,694)(179,693)(180,692)(181,691)(182,690)(183,689)(184,688)
(185,687)(186,686)(187,685)(188,684)(189,683)(190,682)(191,681)(192,680)
(193,679)(194,678)(195,677)(196,676)(197,675)(198,674)(199,673)(200,672)
(201,671)(202,670)(203,669)(204,639)(205,667)(206,666)(207,665)(208,664)
(209,663)(210,662)(211,661)(212,660)(213,659)(214,658)(215,657)(216,656)
(217,655)(218,654)(219,653)(220,652)(221,651)(222,650)(223,649)(224,648)
(225,647)(226,646)(227,645)(228,644)(229,643)(230,642)(231,641)(232,640)
(233,697)(234,725)(235,724)(236,723)(237,722)(238,721)(239,720)(240,719)
(241,718)(242,717)(243,716)(244,715)(245,714)(246,713)(247,712)(248,711)
(249,710)(250,709)(251,708)(252,707)(253,706)(254,705)(255,704)(256,703)
(257,702)(258,701)(259,700)(260,699)(261,698)(262,726)(263,754)(264,753)
(265,752)(266,751)(267,750)(268,749)(269,748)(270,747)(271,746)(272,745)
(273,744)(274,743)(275,742)(276,741)(277,740)(278,739)(279,738)(280,737)
(281,736)(282,735)(283,734)(284,733)(285,732)(286,731)(287,730)(288,729)
(289,728)(290,727)(291,755)(292,783)(293,782)(294,781)(295,780)(296,779)
(297,778)(298,777)(299,776)(300,775)(301,774)(302,773)(303,772)(304,771)
(305,770)(306,769)(307,768)(308,767)(309,766)(310,765)(311,764)(312,763)
(313,762)(314,761)(315,760)(316,759)(317,758)(318,757)(319,756)(320,784)
(321,812)(322,811)(323,810)(324,809)(325,808)(326,807)(327,806)(328,805)
(329,804)(330,803)(331,802)(332,801)(333,800)(334,799)(335,798)(336,797)
(337,796)(338,795)(339,794)(340,793)(341,792)(342,791)(343,790)(344,789)
(345,788)(346,787)(347,786)(348,785)(349,842)(350,870)(351,869)(352,868)
(353,867)(354,866)(355,865)(356,864)(357,863)(358,862)(359,861)(360,860)
(361,859)(362,858)(363,857)(364,856)(365,855)(366,854)(367,853)(368,852)
(369,851)(370,850)(371,849)(372,848)(373,847)(374,846)(375,845)(376,844)
(377,843)(378,813)(379,841)(380,840)(381,839)(382,838)(383,837)(384,836)
(385,835)(386,834)(387,833)(388,832)(389,831)(390,830)(391,829)(392,828)
(393,827)(394,826)(395,825)(396,824)(397,823)(398,822)(399,821)(400,820)
(401,819)(402,818)(403,817)(404,816)(405,815)(406,814)(407,900)(408,928)
(409,927)(410,926)(411,925)(412,924)(413,923)(414,922)(415,921)(416,920)
(417,919)(418,918)(419,917)(420,916)(421,915)(422,914)(423,913)(424,912)
(425,911)(426,910)(427,909)(428,908)(429,907)(430,906)(431,905)(432,904)
(433,903)(434,902)(435,901)(436,871)(437,899)(438,898)(439,897)(440,896)
(441,895)(442,894)(443,893)(444,892)(445,891)(446,890)(447,889)(448,888)
(449,887)(450,886)(451,885)(452,884)(453,883)(454,882)(455,881)(456,880)
(457,879)(458,878)(459,877)(460,876)(461,875)(462,874)(463,873)(464,872);;
s1 := (  1,  2)(  3, 29)(  4, 28)(  5, 27)(  6, 26)(  7, 25)(  8, 24)(  9, 23)
( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)( 32, 58)
( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)
( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)( 63, 85)
( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)
( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)(102,104)
(117,147)(118,146)(119,174)(120,173)(121,172)(122,171)(123,170)(124,169)
(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)
(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)(140,153)
(141,152)(142,151)(143,150)(144,149)(145,148)(175,205)(176,204)(177,232)
(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)
(186,223)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)(193,216)
(194,215)(195,214)(196,213)(197,212)(198,211)(199,210)(200,209)(201,208)
(202,207)(203,206)(233,292)(234,291)(235,319)(236,318)(237,317)(238,316)
(239,315)(240,314)(241,313)(242,312)(243,311)(244,310)(245,309)(246,308)
(247,307)(248,306)(249,305)(250,304)(251,303)(252,302)(253,301)(254,300)
(255,299)(256,298)(257,297)(258,296)(259,295)(260,294)(261,293)(262,321)
(263,320)(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)(349,437)(350,436)(351,464)(352,463)
(353,462)(354,461)(355,460)(356,459)(357,458)(358,457)(359,456)(360,455)
(361,454)(362,453)(363,452)(364,451)(365,450)(366,449)(367,448)(368,447)
(369,446)(370,445)(371,444)(372,443)(373,442)(374,441)(375,440)(376,439)
(377,438)(378,408)(379,407)(380,435)(381,434)(382,433)(383,432)(384,431)
(385,430)(386,429)(387,428)(388,427)(389,426)(390,425)(391,424)(392,423)
(393,422)(394,421)(395,420)(396,419)(397,418)(398,417)(399,416)(400,415)
(401,414)(402,413)(403,412)(404,411)(405,410)(406,409)(465,582)(466,581)
(467,609)(468,608)(469,607)(470,606)(471,605)(472,604)(473,603)(474,602)
(475,601)(476,600)(477,599)(478,598)(479,597)(480,596)(481,595)(482,594)
(483,593)(484,592)(485,591)(486,590)(487,589)(488,588)(489,587)(490,586)
(491,585)(492,584)(493,583)(494,611)(495,610)(496,638)(497,637)(498,636)
(499,635)(500,634)(501,633)(502,632)(503,631)(504,630)(505,629)(506,628)
(507,627)(508,626)(509,625)(510,624)(511,623)(512,622)(513,621)(514,620)
(515,619)(516,618)(517,617)(518,616)(519,615)(520,614)(521,613)(522,612)
(523,640)(524,639)(525,667)(526,666)(527,665)(528,664)(529,663)(530,662)
(531,661)(532,660)(533,659)(534,658)(535,657)(536,656)(537,655)(538,654)
(539,653)(540,652)(541,651)(542,650)(543,649)(544,648)(545,647)(546,646)
(547,645)(548,644)(549,643)(550,642)(551,641)(552,669)(553,668)(554,696)
(555,695)(556,694)(557,693)(558,692)(559,691)(560,690)(561,689)(562,688)
(563,687)(564,686)(565,685)(566,684)(567,683)(568,682)(569,681)(570,680)
(571,679)(572,678)(573,677)(574,676)(575,675)(576,674)(577,673)(578,672)
(579,671)(580,670)(697,872)(698,871)(699,899)(700,898)(701,897)(702,896)
(703,895)(704,894)(705,893)(706,892)(707,891)(708,890)(709,889)(710,888)
(711,887)(712,886)(713,885)(714,884)(715,883)(716,882)(717,881)(718,880)
(719,879)(720,878)(721,877)(722,876)(723,875)(724,874)(725,873)(726,901)
(727,900)(728,928)(729,927)(730,926)(731,925)(732,924)(733,923)(734,922)
(735,921)(736,920)(737,919)(738,918)(739,917)(740,916)(741,915)(742,914)
(743,913)(744,912)(745,911)(746,910)(747,909)(748,908)(749,907)(750,906)
(751,905)(752,904)(753,903)(754,902)(755,814)(756,813)(757,841)(758,840)
(759,839)(760,838)(761,837)(762,836)(763,835)(764,834)(765,833)(766,832)
(767,831)(768,830)(769,829)(770,828)(771,827)(772,826)(773,825)(774,824)
(775,823)(776,822)(777,821)(778,820)(779,819)(780,818)(781,817)(782,816)
(783,815)(784,843)(785,842)(786,870)(787,869)(788,868)(789,867)(790,866)
(791,865)(792,864)(793,863)(794,862)(795,861)(796,860)(797,859)(798,858)
(799,857)(800,856)(801,855)(802,854)(803,853)(804,852)(805,851)(806,850)
(807,849)(808,848)(809,847)(810,846)(811,845)(812,844);;
s2 := (  1,233)(  2,234)(  3,235)(  4,236)(  5,237)(  6,238)(  7,239)(  8,240)
(  9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)
( 17,249)( 18,250)( 19,251)( 20,252)( 21,253)( 22,254)( 23,255)( 24,256)
( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)
( 33,265)( 34,266)( 35,267)( 36,268)( 37,269)( 38,270)( 39,271)( 40,272)
( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)
( 49,281)( 50,282)( 51,283)( 52,284)( 53,285)( 54,286)( 55,287)( 56,288)
( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)
( 65,297)( 66,298)( 67,299)( 68,300)( 69,301)( 70,302)( 71,303)( 72,304)
( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)
( 81,313)( 82,314)( 83,315)( 84,316)( 85,317)( 86,318)( 87,319)( 88,320)
( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)
( 97,329)( 98,330)( 99,331)(100,332)(101,333)(102,334)(103,335)(104,336)
(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)
(113,345)(114,346)(115,347)(116,348)(117,349)(118,350)(119,351)(120,352)
(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)
(129,361)(130,362)(131,363)(132,364)(133,365)(134,366)(135,367)(136,368)
(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)
(145,377)(146,378)(147,379)(148,380)(149,381)(150,382)(151,383)(152,384)
(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)
(161,393)(162,394)(163,395)(164,396)(165,397)(166,398)(167,399)(168,400)
(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)
(177,409)(178,410)(179,411)(180,412)(181,413)(182,414)(183,415)(184,416)
(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)
(193,425)(194,426)(195,427)(196,428)(197,429)(198,430)(199,431)(200,432)
(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)
(209,441)(210,442)(211,443)(212,444)(213,445)(214,446)(215,447)(216,448)
(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)
(225,457)(226,458)(227,459)(228,460)(229,461)(230,462)(231,463)(232,464)
(465,697)(466,698)(467,699)(468,700)(469,701)(470,702)(471,703)(472,704)
(473,705)(474,706)(475,707)(476,708)(477,709)(478,710)(479,711)(480,712)
(481,713)(482,714)(483,715)(484,716)(485,717)(486,718)(487,719)(488,720)
(489,721)(490,722)(491,723)(492,724)(493,725)(494,726)(495,727)(496,728)
(497,729)(498,730)(499,731)(500,732)(501,733)(502,734)(503,735)(504,736)
(505,737)(506,738)(507,739)(508,740)(509,741)(510,742)(511,743)(512,744)
(513,745)(514,746)(515,747)(516,748)(517,749)(518,750)(519,751)(520,752)
(521,753)(522,754)(523,755)(524,756)(525,757)(526,758)(527,759)(528,760)
(529,761)(530,762)(531,763)(532,764)(533,765)(534,766)(535,767)(536,768)
(537,769)(538,770)(539,771)(540,772)(541,773)(542,774)(543,775)(544,776)
(545,777)(546,778)(547,779)(548,780)(549,781)(550,782)(551,783)(552,784)
(553,785)(554,786)(555,787)(556,788)(557,789)(558,790)(559,791)(560,792)
(561,793)(562,794)(563,795)(564,796)(565,797)(566,798)(567,799)(568,800)
(569,801)(570,802)(571,803)(572,804)(573,805)(574,806)(575,807)(576,808)
(577,809)(578,810)(579,811)(580,812)(581,813)(582,814)(583,815)(584,816)
(585,817)(586,818)(587,819)(588,820)(589,821)(590,822)(591,823)(592,824)
(593,825)(594,826)(595,827)(596,828)(597,829)(598,830)(599,831)(600,832)
(601,833)(602,834)(603,835)(604,836)(605,837)(606,838)(607,839)(608,840)
(609,841)(610,842)(611,843)(612,844)(613,845)(614,846)(615,847)(616,848)
(617,849)(618,850)(619,851)(620,852)(621,853)(622,854)(623,855)(624,856)
(625,857)(626,858)(627,859)(628,860)(629,861)(630,862)(631,863)(632,864)
(633,865)(634,866)(635,867)(636,868)(637,869)(638,870)(639,871)(640,872)
(641,873)(642,874)(643,875)(644,876)(645,877)(646,878)(647,879)(648,880)
(649,881)(650,882)(651,883)(652,884)(653,885)(654,886)(655,887)(656,888)
(657,889)(658,890)(659,891)(660,892)(661,893)(662,894)(663,895)(664,896)
(665,897)(666,898)(667,899)(668,900)(669,901)(670,902)(671,903)(672,904)
(673,905)(674,906)(675,907)(676,908)(677,909)(678,910)(679,911)(680,912)
(681,913)(682,914)(683,915)(684,916)(685,917)(686,918)(687,919)(688,920)
(689,921)(690,922)(691,923)(692,924)(693,925)(694,926)(695,927)(696,928);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(928)!(  1,465)(  2,493)(  3,492)(  4,491)(  5,490)(  6,489)(  7,488)
(  8,487)(  9,486)( 10,485)( 11,484)( 12,483)( 13,482)( 14,481)( 15,480)
( 16,479)( 17,478)( 18,477)( 19,476)( 20,475)( 21,474)( 22,473)( 23,472)
( 24,471)( 25,470)( 26,469)( 27,468)( 28,467)( 29,466)( 30,494)( 31,522)
( 32,521)( 33,520)( 34,519)( 35,518)( 36,517)( 37,516)( 38,515)( 39,514)
( 40,513)( 41,512)( 42,511)( 43,510)( 44,509)( 45,508)( 46,507)( 47,506)
( 48,505)( 49,504)( 50,503)( 51,502)( 52,501)( 53,500)( 54,499)( 55,498)
( 56,497)( 57,496)( 58,495)( 59,523)( 60,551)( 61,550)( 62,549)( 63,548)
( 64,547)( 65,546)( 66,545)( 67,544)( 68,543)( 69,542)( 70,541)( 71,540)
( 72,539)( 73,538)( 74,537)( 75,536)( 76,535)( 77,534)( 78,533)( 79,532)
( 80,531)( 81,530)( 82,529)( 83,528)( 84,527)( 85,526)( 86,525)( 87,524)
( 88,552)( 89,580)( 90,579)( 91,578)( 92,577)( 93,576)( 94,575)( 95,574)
( 96,573)( 97,572)( 98,571)( 99,570)(100,569)(101,568)(102,567)(103,566)
(104,565)(105,564)(106,563)(107,562)(108,561)(109,560)(110,559)(111,558)
(112,557)(113,556)(114,555)(115,554)(116,553)(117,610)(118,638)(119,637)
(120,636)(121,635)(122,634)(123,633)(124,632)(125,631)(126,630)(127,629)
(128,628)(129,627)(130,626)(131,625)(132,624)(133,623)(134,622)(135,621)
(136,620)(137,619)(138,618)(139,617)(140,616)(141,615)(142,614)(143,613)
(144,612)(145,611)(146,581)(147,609)(148,608)(149,607)(150,606)(151,605)
(152,604)(153,603)(154,602)(155,601)(156,600)(157,599)(158,598)(159,597)
(160,596)(161,595)(162,594)(163,593)(164,592)(165,591)(166,590)(167,589)
(168,588)(169,587)(170,586)(171,585)(172,584)(173,583)(174,582)(175,668)
(176,696)(177,695)(178,694)(179,693)(180,692)(181,691)(182,690)(183,689)
(184,688)(185,687)(186,686)(187,685)(188,684)(189,683)(190,682)(191,681)
(192,680)(193,679)(194,678)(195,677)(196,676)(197,675)(198,674)(199,673)
(200,672)(201,671)(202,670)(203,669)(204,639)(205,667)(206,666)(207,665)
(208,664)(209,663)(210,662)(211,661)(212,660)(213,659)(214,658)(215,657)
(216,656)(217,655)(218,654)(219,653)(220,652)(221,651)(222,650)(223,649)
(224,648)(225,647)(226,646)(227,645)(228,644)(229,643)(230,642)(231,641)
(232,640)(233,697)(234,725)(235,724)(236,723)(237,722)(238,721)(239,720)
(240,719)(241,718)(242,717)(243,716)(244,715)(245,714)(246,713)(247,712)
(248,711)(249,710)(250,709)(251,708)(252,707)(253,706)(254,705)(255,704)
(256,703)(257,702)(258,701)(259,700)(260,699)(261,698)(262,726)(263,754)
(264,753)(265,752)(266,751)(267,750)(268,749)(269,748)(270,747)(271,746)
(272,745)(273,744)(274,743)(275,742)(276,741)(277,740)(278,739)(279,738)
(280,737)(281,736)(282,735)(283,734)(284,733)(285,732)(286,731)(287,730)
(288,729)(289,728)(290,727)(291,755)(292,783)(293,782)(294,781)(295,780)
(296,779)(297,778)(298,777)(299,776)(300,775)(301,774)(302,773)(303,772)
(304,771)(305,770)(306,769)(307,768)(308,767)(309,766)(310,765)(311,764)
(312,763)(313,762)(314,761)(315,760)(316,759)(317,758)(318,757)(319,756)
(320,784)(321,812)(322,811)(323,810)(324,809)(325,808)(326,807)(327,806)
(328,805)(329,804)(330,803)(331,802)(332,801)(333,800)(334,799)(335,798)
(336,797)(337,796)(338,795)(339,794)(340,793)(341,792)(342,791)(343,790)
(344,789)(345,788)(346,787)(347,786)(348,785)(349,842)(350,870)(351,869)
(352,868)(353,867)(354,866)(355,865)(356,864)(357,863)(358,862)(359,861)
(360,860)(361,859)(362,858)(363,857)(364,856)(365,855)(366,854)(367,853)
(368,852)(369,851)(370,850)(371,849)(372,848)(373,847)(374,846)(375,845)
(376,844)(377,843)(378,813)(379,841)(380,840)(381,839)(382,838)(383,837)
(384,836)(385,835)(386,834)(387,833)(388,832)(389,831)(390,830)(391,829)
(392,828)(393,827)(394,826)(395,825)(396,824)(397,823)(398,822)(399,821)
(400,820)(401,819)(402,818)(403,817)(404,816)(405,815)(406,814)(407,900)
(408,928)(409,927)(410,926)(411,925)(412,924)(413,923)(414,922)(415,921)
(416,920)(417,919)(418,918)(419,917)(420,916)(421,915)(422,914)(423,913)
(424,912)(425,911)(426,910)(427,909)(428,908)(429,907)(430,906)(431,905)
(432,904)(433,903)(434,902)(435,901)(436,871)(437,899)(438,898)(439,897)
(440,896)(441,895)(442,894)(443,893)(444,892)(445,891)(446,890)(447,889)
(448,888)(449,887)(450,886)(451,885)(452,884)(453,883)(454,882)(455,881)
(456,880)(457,879)(458,878)(459,877)(460,876)(461,875)(462,874)(463,873)
(464,872);
s1 := Sym(928)!(  1,  2)(  3, 29)(  4, 28)(  5, 27)(  6, 26)(  7, 25)(  8, 24)
(  9, 23)( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)
( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)
( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)
( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)
( 71, 77)( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)
(102,104)(117,147)(118,146)(119,174)(120,173)(121,172)(122,171)(123,170)
(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)
(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)
(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(175,205)(176,204)
(177,232)(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)
(185,224)(186,223)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)
(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)(199,210)(200,209)
(201,208)(202,207)(203,206)(233,292)(234,291)(235,319)(236,318)(237,317)
(238,316)(239,315)(240,314)(241,313)(242,312)(243,311)(244,310)(245,309)
(246,308)(247,307)(248,306)(249,305)(250,304)(251,303)(252,302)(253,301)
(254,300)(255,299)(256,298)(257,297)(258,296)(259,295)(260,294)(261,293)
(262,321)(263,320)(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)(349,437)(350,436)(351,464)
(352,463)(353,462)(354,461)(355,460)(356,459)(357,458)(358,457)(359,456)
(360,455)(361,454)(362,453)(363,452)(364,451)(365,450)(366,449)(367,448)
(368,447)(369,446)(370,445)(371,444)(372,443)(373,442)(374,441)(375,440)
(376,439)(377,438)(378,408)(379,407)(380,435)(381,434)(382,433)(383,432)
(384,431)(385,430)(386,429)(387,428)(388,427)(389,426)(390,425)(391,424)
(392,423)(393,422)(394,421)(395,420)(396,419)(397,418)(398,417)(399,416)
(400,415)(401,414)(402,413)(403,412)(404,411)(405,410)(406,409)(465,582)
(466,581)(467,609)(468,608)(469,607)(470,606)(471,605)(472,604)(473,603)
(474,602)(475,601)(476,600)(477,599)(478,598)(479,597)(480,596)(481,595)
(482,594)(483,593)(484,592)(485,591)(486,590)(487,589)(488,588)(489,587)
(490,586)(491,585)(492,584)(493,583)(494,611)(495,610)(496,638)(497,637)
(498,636)(499,635)(500,634)(501,633)(502,632)(503,631)(504,630)(505,629)
(506,628)(507,627)(508,626)(509,625)(510,624)(511,623)(512,622)(513,621)
(514,620)(515,619)(516,618)(517,617)(518,616)(519,615)(520,614)(521,613)
(522,612)(523,640)(524,639)(525,667)(526,666)(527,665)(528,664)(529,663)
(530,662)(531,661)(532,660)(533,659)(534,658)(535,657)(536,656)(537,655)
(538,654)(539,653)(540,652)(541,651)(542,650)(543,649)(544,648)(545,647)
(546,646)(547,645)(548,644)(549,643)(550,642)(551,641)(552,669)(553,668)
(554,696)(555,695)(556,694)(557,693)(558,692)(559,691)(560,690)(561,689)
(562,688)(563,687)(564,686)(565,685)(566,684)(567,683)(568,682)(569,681)
(570,680)(571,679)(572,678)(573,677)(574,676)(575,675)(576,674)(577,673)
(578,672)(579,671)(580,670)(697,872)(698,871)(699,899)(700,898)(701,897)
(702,896)(703,895)(704,894)(705,893)(706,892)(707,891)(708,890)(709,889)
(710,888)(711,887)(712,886)(713,885)(714,884)(715,883)(716,882)(717,881)
(718,880)(719,879)(720,878)(721,877)(722,876)(723,875)(724,874)(725,873)
(726,901)(727,900)(728,928)(729,927)(730,926)(731,925)(732,924)(733,923)
(734,922)(735,921)(736,920)(737,919)(738,918)(739,917)(740,916)(741,915)
(742,914)(743,913)(744,912)(745,911)(746,910)(747,909)(748,908)(749,907)
(750,906)(751,905)(752,904)(753,903)(754,902)(755,814)(756,813)(757,841)
(758,840)(759,839)(760,838)(761,837)(762,836)(763,835)(764,834)(765,833)
(766,832)(767,831)(768,830)(769,829)(770,828)(771,827)(772,826)(773,825)
(774,824)(775,823)(776,822)(777,821)(778,820)(779,819)(780,818)(781,817)
(782,816)(783,815)(784,843)(785,842)(786,870)(787,869)(788,868)(789,867)
(790,866)(791,865)(792,864)(793,863)(794,862)(795,861)(796,860)(797,859)
(798,858)(799,857)(800,856)(801,855)(802,854)(803,853)(804,852)(805,851)
(806,850)(807,849)(808,848)(809,847)(810,846)(811,845)(812,844);
s2 := Sym(928)!(  1,233)(  2,234)(  3,235)(  4,236)(  5,237)(  6,238)(  7,239)
(  8,240)(  9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)
( 16,248)( 17,249)( 18,250)( 19,251)( 20,252)( 21,253)( 22,254)( 23,255)
( 24,256)( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)
( 32,264)( 33,265)( 34,266)( 35,267)( 36,268)( 37,269)( 38,270)( 39,271)
( 40,272)( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)
( 48,280)( 49,281)( 50,282)( 51,283)( 52,284)( 53,285)( 54,286)( 55,287)
( 56,288)( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)
( 64,296)( 65,297)( 66,298)( 67,299)( 68,300)( 69,301)( 70,302)( 71,303)
( 72,304)( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)
( 80,312)( 81,313)( 82,314)( 83,315)( 84,316)( 85,317)( 86,318)( 87,319)
( 88,320)( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)
( 96,328)( 97,329)( 98,330)( 99,331)(100,332)(101,333)(102,334)(103,335)
(104,336)(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)
(112,344)(113,345)(114,346)(115,347)(116,348)(117,349)(118,350)(119,351)
(120,352)(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)
(128,360)(129,361)(130,362)(131,363)(132,364)(133,365)(134,366)(135,367)
(136,368)(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)
(144,376)(145,377)(146,378)(147,379)(148,380)(149,381)(150,382)(151,383)
(152,384)(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)
(160,392)(161,393)(162,394)(163,395)(164,396)(165,397)(166,398)(167,399)
(168,400)(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)
(176,408)(177,409)(178,410)(179,411)(180,412)(181,413)(182,414)(183,415)
(184,416)(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)
(192,424)(193,425)(194,426)(195,427)(196,428)(197,429)(198,430)(199,431)
(200,432)(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)
(208,440)(209,441)(210,442)(211,443)(212,444)(213,445)(214,446)(215,447)
(216,448)(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)
(224,456)(225,457)(226,458)(227,459)(228,460)(229,461)(230,462)(231,463)
(232,464)(465,697)(466,698)(467,699)(468,700)(469,701)(470,702)(471,703)
(472,704)(473,705)(474,706)(475,707)(476,708)(477,709)(478,710)(479,711)
(480,712)(481,713)(482,714)(483,715)(484,716)(485,717)(486,718)(487,719)
(488,720)(489,721)(490,722)(491,723)(492,724)(493,725)(494,726)(495,727)
(496,728)(497,729)(498,730)(499,731)(500,732)(501,733)(502,734)(503,735)
(504,736)(505,737)(506,738)(507,739)(508,740)(509,741)(510,742)(511,743)
(512,744)(513,745)(514,746)(515,747)(516,748)(517,749)(518,750)(519,751)
(520,752)(521,753)(522,754)(523,755)(524,756)(525,757)(526,758)(527,759)
(528,760)(529,761)(530,762)(531,763)(532,764)(533,765)(534,766)(535,767)
(536,768)(537,769)(538,770)(539,771)(540,772)(541,773)(542,774)(543,775)
(544,776)(545,777)(546,778)(547,779)(548,780)(549,781)(550,782)(551,783)
(552,784)(553,785)(554,786)(555,787)(556,788)(557,789)(558,790)(559,791)
(560,792)(561,793)(562,794)(563,795)(564,796)(565,797)(566,798)(567,799)
(568,800)(569,801)(570,802)(571,803)(572,804)(573,805)(574,806)(575,807)
(576,808)(577,809)(578,810)(579,811)(580,812)(581,813)(582,814)(583,815)
(584,816)(585,817)(586,818)(587,819)(588,820)(589,821)(590,822)(591,823)
(592,824)(593,825)(594,826)(595,827)(596,828)(597,829)(598,830)(599,831)
(600,832)(601,833)(602,834)(603,835)(604,836)(605,837)(606,838)(607,839)
(608,840)(609,841)(610,842)(611,843)(612,844)(613,845)(614,846)(615,847)
(616,848)(617,849)(618,850)(619,851)(620,852)(621,853)(622,854)(623,855)
(624,856)(625,857)(626,858)(627,859)(628,860)(629,861)(630,862)(631,863)
(632,864)(633,865)(634,866)(635,867)(636,868)(637,869)(638,870)(639,871)
(640,872)(641,873)(642,874)(643,875)(644,876)(645,877)(646,878)(647,879)
(648,880)(649,881)(650,882)(651,883)(652,884)(653,885)(654,886)(655,887)
(656,888)(657,889)(658,890)(659,891)(660,892)(661,893)(662,894)(663,895)
(664,896)(665,897)(666,898)(667,899)(668,900)(669,901)(670,902)(671,903)
(672,904)(673,905)(674,906)(675,907)(676,908)(677,909)(678,910)(679,911)
(680,912)(681,913)(682,914)(683,915)(684,916)(685,917)(686,918)(687,919)
(688,920)(689,921)(690,922)(691,923)(692,924)(693,925)(694,926)(695,927)
(696,928);
poly := sub<Sym(928)|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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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