Polytope of Type {4,232}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,232}*1856a
Also Known As : {4,232|2}. if this polytope has another name.
Group : SmallGroup(1856,685)
Rank : 3
Schlafli Type : {4,232}
Number of vertices, edges, etc : 4, 464, 232
Order of s₀s₁s₂ : 232
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 : {4,116}*928, {2,232}*928
   4-fold quotients : {2,116}*464, {4,58}*464
   8-fold quotients : {2,58}*232
   16-fold quotients : {2,29}*116
   29-fold quotients : {4,8}*64a
   58-fold quotients : {4,4}*32, {2,8}*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 := (  1,233)(  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);;
s1 := (  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)
( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 31, 58)( 32, 57)
( 33, 56)( 34, 55)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 50)( 40, 49)
( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 60, 87)( 61, 86)( 62, 85)( 63, 84)
( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 71, 76)
( 72, 75)( 73, 74)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)( 94,111)
( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)(102,103)
(117,146)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,168)
(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)
(133,159)(134,158)(135,157)(136,156)(137,155)(138,154)(139,153)(140,152)
(141,151)(142,150)(143,149)(144,148)(145,147)(175,204)(176,232)(177,231)
(178,230)(179,229)(180,228)(181,227)(182,226)(183,225)(184,224)(185,223)
(186,222)(187,221)(188,220)(189,219)(190,218)(191,217)(192,216)(193,215)
(194,214)(195,213)(196,212)(197,211)(198,210)(199,209)(200,208)(201,207)
(202,206)(203,205)(233,291)(234,319)(235,318)(236,317)(237,316)(238,315)
(239,314)(240,313)(241,312)(242,311)(243,310)(244,309)(245,308)(246,307)
(247,306)(248,305)(249,304)(250,303)(251,302)(252,301)(253,300)(254,299)
(255,298)(256,297)(257,296)(258,295)(259,294)(260,293)(261,292)(262,320)
(263,348)(264,347)(265,346)(266,345)(267,344)(268,343)(269,342)(270,341)
(271,340)(272,339)(273,338)(274,337)(275,336)(276,335)(277,334)(278,333)
(279,332)(280,331)(281,330)(282,329)(283,328)(284,327)(285,326)(286,325)
(287,324)(288,323)(289,322)(290,321)(349,436)(350,464)(351,463)(352,462)
(353,461)(354,460)(355,459)(356,458)(357,457)(358,456)(359,455)(360,454)
(361,453)(362,452)(363,451)(364,450)(365,449)(366,448)(367,447)(368,446)
(369,445)(370,444)(371,443)(372,442)(373,441)(374,440)(375,439)(376,438)
(377,437)(378,407)(379,435)(380,434)(381,433)(382,432)(383,431)(384,430)
(385,429)(386,428)(387,427)(388,426)(389,425)(390,424)(391,423)(392,422)
(393,421)(394,420)(395,419)(396,418)(397,417)(398,416)(399,415)(400,414)
(401,413)(402,412)(403,411)(404,410)(405,409)(406,408)(465,581)(466,609)
(467,608)(468,607)(469,606)(470,605)(471,604)(472,603)(473,602)(474,601)
(475,600)(476,599)(477,598)(478,597)(479,596)(480,595)(481,594)(482,593)
(483,592)(484,591)(485,590)(486,589)(487,588)(488,587)(489,586)(490,585)
(491,584)(492,583)(493,582)(494,610)(495,638)(496,637)(497,636)(498,635)
(499,634)(500,633)(501,632)(502,631)(503,630)(504,629)(505,628)(506,627)
(507,626)(508,625)(509,624)(510,623)(511,622)(512,621)(513,620)(514,619)
(515,618)(516,617)(517,616)(518,615)(519,614)(520,613)(521,612)(522,611)
(523,639)(524,667)(525,666)(526,665)(527,664)(528,663)(529,662)(530,661)
(531,660)(532,659)(533,658)(534,657)(535,656)(536,655)(537,654)(538,653)
(539,652)(540,651)(541,650)(542,649)(543,648)(544,647)(545,646)(546,645)
(547,644)(548,643)(549,642)(550,641)(551,640)(552,668)(553,696)(554,695)
(555,694)(556,693)(557,692)(558,691)(559,690)(560,689)(561,688)(562,687)
(563,686)(564,685)(565,684)(566,683)(567,682)(568,681)(569,680)(570,679)
(571,678)(572,677)(573,676)(574,675)(575,674)(576,673)(577,672)(578,671)
(579,670)(580,669)(697,871)(698,899)(699,898)(700,897)(701,896)(702,895)
(703,894)(704,893)(705,892)(706,891)(707,890)(708,889)(709,888)(710,887)
(711,886)(712,885)(713,884)(714,883)(715,882)(716,881)(717,880)(718,879)
(719,878)(720,877)(721,876)(722,875)(723,874)(724,873)(725,872)(726,900)
(727,928)(728,927)(729,926)(730,925)(731,924)(732,923)(733,922)(734,921)
(735,920)(736,919)(737,918)(738,917)(739,916)(740,915)(741,914)(742,913)
(743,912)(744,911)(745,910)(746,909)(747,908)(748,907)(749,906)(750,905)
(751,904)(752,903)(753,902)(754,901)(755,813)(756,841)(757,840)(758,839)
(759,838)(760,837)(761,836)(762,835)(763,834)(764,833)(765,832)(766,831)
(767,830)(768,829)(769,828)(770,827)(771,826)(772,825)(773,824)(774,823)
(775,822)(776,821)(777,820)(778,819)(779,818)(780,817)(781,816)(782,815)
(783,814)(784,842)(785,870)(786,869)(787,868)(788,867)(789,866)(790,865)
(791,864)(792,863)(793,862)(794,861)(795,860)(796,859)(797,858)(798,857)
(799,856)(800,855)(801,854)(802,853)(803,852)(804,851)(805,850)(806,849)
(807,848)(808,847)(809,846)(810,845)(811,844)(812,843);;
s2 := (  1,466)(  2,465)(  3,493)(  4,492)(  5,491)(  6,490)(  7,489)(  8,488)
(  9,487)( 10,486)( 11,485)( 12,484)( 13,483)( 14,482)( 15,481)( 16,480)
( 17,479)( 18,478)( 19,477)( 20,476)( 21,475)( 22,474)( 23,473)( 24,472)
( 25,471)( 26,470)( 27,469)( 28,468)( 29,467)( 30,495)( 31,494)( 32,522)
( 33,521)( 34,520)( 35,519)( 36,518)( 37,517)( 38,516)( 39,515)( 40,514)
( 41,513)( 42,512)( 43,511)( 44,510)( 45,509)( 46,508)( 47,507)( 48,506)
( 49,505)( 50,504)( 51,503)( 52,502)( 53,501)( 54,500)( 55,499)( 56,498)
( 57,497)( 58,496)( 59,524)( 60,523)( 61,551)( 62,550)( 63,549)( 64,548)
( 65,547)( 66,546)( 67,545)( 68,544)( 69,543)( 70,542)( 71,541)( 72,540)
( 73,539)( 74,538)( 75,537)( 76,536)( 77,535)( 78,534)( 79,533)( 80,532)
( 81,531)( 82,530)( 83,529)( 84,528)( 85,527)( 86,526)( 87,525)( 88,553)
( 89,552)( 90,580)( 91,579)( 92,578)( 93,577)( 94,576)( 95,575)( 96,574)
( 97,573)( 98,572)( 99,571)(100,570)(101,569)(102,568)(103,567)(104,566)
(105,565)(106,564)(107,563)(108,562)(109,561)(110,560)(111,559)(112,558)
(113,557)(114,556)(115,555)(116,554)(117,611)(118,610)(119,638)(120,637)
(121,636)(122,635)(123,634)(124,633)(125,632)(126,631)(127,630)(128,629)
(129,628)(130,627)(131,626)(132,625)(133,624)(134,623)(135,622)(136,621)
(137,620)(138,619)(139,618)(140,617)(141,616)(142,615)(143,614)(144,613)
(145,612)(146,582)(147,581)(148,609)(149,608)(150,607)(151,606)(152,605)
(153,604)(154,603)(155,602)(156,601)(157,600)(158,599)(159,598)(160,597)
(161,596)(162,595)(163,594)(164,593)(165,592)(166,591)(167,590)(168,589)
(169,588)(170,587)(171,586)(172,585)(173,584)(174,583)(175,669)(176,668)
(177,696)(178,695)(179,694)(180,693)(181,692)(182,691)(183,690)(184,689)
(185,688)(186,687)(187,686)(188,685)(189,684)(190,683)(191,682)(192,681)
(193,680)(194,679)(195,678)(196,677)(197,676)(198,675)(199,674)(200,673)
(201,672)(202,671)(203,670)(204,640)(205,639)(206,667)(207,666)(208,665)
(209,664)(210,663)(211,662)(212,661)(213,660)(214,659)(215,658)(216,657)
(217,656)(218,655)(219,654)(220,653)(221,652)(222,651)(223,650)(224,649)
(225,648)(226,647)(227,646)(228,645)(229,644)(230,643)(231,642)(232,641)
(233,698)(234,697)(235,725)(236,724)(237,723)(238,722)(239,721)(240,720)
(241,719)(242,718)(243,717)(244,716)(245,715)(246,714)(247,713)(248,712)
(249,711)(250,710)(251,709)(252,708)(253,707)(254,706)(255,705)(256,704)
(257,703)(258,702)(259,701)(260,700)(261,699)(262,727)(263,726)(264,754)
(265,753)(266,752)(267,751)(268,750)(269,749)(270,748)(271,747)(272,746)
(273,745)(274,744)(275,743)(276,742)(277,741)(278,740)(279,739)(280,738)
(281,737)(282,736)(283,735)(284,734)(285,733)(286,732)(287,731)(288,730)
(289,729)(290,728)(291,756)(292,755)(293,783)(294,782)(295,781)(296,780)
(297,779)(298,778)(299,777)(300,776)(301,775)(302,774)(303,773)(304,772)
(305,771)(306,770)(307,769)(308,768)(309,767)(310,766)(311,765)(312,764)
(313,763)(314,762)(315,761)(316,760)(317,759)(318,758)(319,757)(320,785)
(321,784)(322,812)(323,811)(324,810)(325,809)(326,808)(327,807)(328,806)
(329,805)(330,804)(331,803)(332,802)(333,801)(334,800)(335,799)(336,798)
(337,797)(338,796)(339,795)(340,794)(341,793)(342,792)(343,791)(344,790)
(345,789)(346,788)(347,787)(348,786)(349,843)(350,842)(351,870)(352,869)
(353,868)(354,867)(355,866)(356,865)(357,864)(358,863)(359,862)(360,861)
(361,860)(362,859)(363,858)(364,857)(365,856)(366,855)(367,854)(368,853)
(369,852)(370,851)(371,850)(372,849)(373,848)(374,847)(375,846)(376,845)
(377,844)(378,814)(379,813)(380,841)(381,840)(382,839)(383,838)(384,837)
(385,836)(386,835)(387,834)(388,833)(389,832)(390,831)(391,830)(392,829)
(393,828)(394,827)(395,826)(396,825)(397,824)(398,823)(399,822)(400,821)
(401,820)(402,819)(403,818)(404,817)(405,816)(406,815)(407,901)(408,900)
(409,928)(410,927)(411,926)(412,925)(413,924)(414,923)(415,922)(416,921)
(417,920)(418,919)(419,918)(420,917)(421,916)(422,915)(423,914)(424,913)
(425,912)(426,911)(427,910)(428,909)(429,908)(430,907)(431,906)(432,905)
(433,904)(434,903)(435,902)(436,872)(437,871)(438,899)(439,898)(440,897)
(441,896)(442,895)(443,894)(444,893)(445,892)(446,891)(447,890)(448,889)
(449,888)(450,887)(451,886)(452,885)(453,884)(454,883)(455,882)(456,881)
(457,880)(458,879)(459,878)(460,877)(461,876)(462,875)(463,874)(464,873);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(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);
s1 := Sym(928)!(  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)
(  9, 22)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 31, 58)
( 32, 57)( 33, 56)( 34, 55)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 50)
( 40, 49)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 60, 87)( 61, 86)( 62, 85)
( 63, 84)( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)( 70, 77)
( 71, 76)( 72, 75)( 73, 74)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)
( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)
(102,103)(117,146)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)
(124,168)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)
(132,160)(133,159)(134,158)(135,157)(136,156)(137,155)(138,154)(139,153)
(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)(175,204)(176,232)
(177,231)(178,230)(179,229)(180,228)(181,227)(182,226)(183,225)(184,224)
(185,223)(186,222)(187,221)(188,220)(189,219)(190,218)(191,217)(192,216)
(193,215)(194,214)(195,213)(196,212)(197,211)(198,210)(199,209)(200,208)
(201,207)(202,206)(203,205)(233,291)(234,319)(235,318)(236,317)(237,316)
(238,315)(239,314)(240,313)(241,312)(242,311)(243,310)(244,309)(245,308)
(246,307)(247,306)(248,305)(249,304)(250,303)(251,302)(252,301)(253,300)
(254,299)(255,298)(256,297)(257,296)(258,295)(259,294)(260,293)(261,292)
(262,320)(263,348)(264,347)(265,346)(266,345)(267,344)(268,343)(269,342)
(270,341)(271,340)(272,339)(273,338)(274,337)(275,336)(276,335)(277,334)
(278,333)(279,332)(280,331)(281,330)(282,329)(283,328)(284,327)(285,326)
(286,325)(287,324)(288,323)(289,322)(290,321)(349,436)(350,464)(351,463)
(352,462)(353,461)(354,460)(355,459)(356,458)(357,457)(358,456)(359,455)
(360,454)(361,453)(362,452)(363,451)(364,450)(365,449)(366,448)(367,447)
(368,446)(369,445)(370,444)(371,443)(372,442)(373,441)(374,440)(375,439)
(376,438)(377,437)(378,407)(379,435)(380,434)(381,433)(382,432)(383,431)
(384,430)(385,429)(386,428)(387,427)(388,426)(389,425)(390,424)(391,423)
(392,422)(393,421)(394,420)(395,419)(396,418)(397,417)(398,416)(399,415)
(400,414)(401,413)(402,412)(403,411)(404,410)(405,409)(406,408)(465,581)
(466,609)(467,608)(468,607)(469,606)(470,605)(471,604)(472,603)(473,602)
(474,601)(475,600)(476,599)(477,598)(478,597)(479,596)(480,595)(481,594)
(482,593)(483,592)(484,591)(485,590)(486,589)(487,588)(488,587)(489,586)
(490,585)(491,584)(492,583)(493,582)(494,610)(495,638)(496,637)(497,636)
(498,635)(499,634)(500,633)(501,632)(502,631)(503,630)(504,629)(505,628)
(506,627)(507,626)(508,625)(509,624)(510,623)(511,622)(512,621)(513,620)
(514,619)(515,618)(516,617)(517,616)(518,615)(519,614)(520,613)(521,612)
(522,611)(523,639)(524,667)(525,666)(526,665)(527,664)(528,663)(529,662)
(530,661)(531,660)(532,659)(533,658)(534,657)(535,656)(536,655)(537,654)
(538,653)(539,652)(540,651)(541,650)(542,649)(543,648)(544,647)(545,646)
(546,645)(547,644)(548,643)(549,642)(550,641)(551,640)(552,668)(553,696)
(554,695)(555,694)(556,693)(557,692)(558,691)(559,690)(560,689)(561,688)
(562,687)(563,686)(564,685)(565,684)(566,683)(567,682)(568,681)(569,680)
(570,679)(571,678)(572,677)(573,676)(574,675)(575,674)(576,673)(577,672)
(578,671)(579,670)(580,669)(697,871)(698,899)(699,898)(700,897)(701,896)
(702,895)(703,894)(704,893)(705,892)(706,891)(707,890)(708,889)(709,888)
(710,887)(711,886)(712,885)(713,884)(714,883)(715,882)(716,881)(717,880)
(718,879)(719,878)(720,877)(721,876)(722,875)(723,874)(724,873)(725,872)
(726,900)(727,928)(728,927)(729,926)(730,925)(731,924)(732,923)(733,922)
(734,921)(735,920)(736,919)(737,918)(738,917)(739,916)(740,915)(741,914)
(742,913)(743,912)(744,911)(745,910)(746,909)(747,908)(748,907)(749,906)
(750,905)(751,904)(752,903)(753,902)(754,901)(755,813)(756,841)(757,840)
(758,839)(759,838)(760,837)(761,836)(762,835)(763,834)(764,833)(765,832)
(766,831)(767,830)(768,829)(769,828)(770,827)(771,826)(772,825)(773,824)
(774,823)(775,822)(776,821)(777,820)(778,819)(779,818)(780,817)(781,816)
(782,815)(783,814)(784,842)(785,870)(786,869)(787,868)(788,867)(789,866)
(790,865)(791,864)(792,863)(793,862)(794,861)(795,860)(796,859)(797,858)
(798,857)(799,856)(800,855)(801,854)(802,853)(803,852)(804,851)(805,850)
(806,849)(807,848)(808,847)(809,846)(810,845)(811,844)(812,843);
s2 := Sym(928)!(  1,466)(  2,465)(  3,493)(  4,492)(  5,491)(  6,490)(  7,489)
(  8,488)(  9,487)( 10,486)( 11,485)( 12,484)( 13,483)( 14,482)( 15,481)
( 16,480)( 17,479)( 18,478)( 19,477)( 20,476)( 21,475)( 22,474)( 23,473)
( 24,472)( 25,471)( 26,470)( 27,469)( 28,468)( 29,467)( 30,495)( 31,494)
( 32,522)( 33,521)( 34,520)( 35,519)( 36,518)( 37,517)( 38,516)( 39,515)
( 40,514)( 41,513)( 42,512)( 43,511)( 44,510)( 45,509)( 46,508)( 47,507)
( 48,506)( 49,505)( 50,504)( 51,503)( 52,502)( 53,501)( 54,500)( 55,499)
( 56,498)( 57,497)( 58,496)( 59,524)( 60,523)( 61,551)( 62,550)( 63,549)
( 64,548)( 65,547)( 66,546)( 67,545)( 68,544)( 69,543)( 70,542)( 71,541)
( 72,540)( 73,539)( 74,538)( 75,537)( 76,536)( 77,535)( 78,534)( 79,533)
( 80,532)( 81,531)( 82,530)( 83,529)( 84,528)( 85,527)( 86,526)( 87,525)
( 88,553)( 89,552)( 90,580)( 91,579)( 92,578)( 93,577)( 94,576)( 95,575)
( 96,574)( 97,573)( 98,572)( 99,571)(100,570)(101,569)(102,568)(103,567)
(104,566)(105,565)(106,564)(107,563)(108,562)(109,561)(110,560)(111,559)
(112,558)(113,557)(114,556)(115,555)(116,554)(117,611)(118,610)(119,638)
(120,637)(121,636)(122,635)(123,634)(124,633)(125,632)(126,631)(127,630)
(128,629)(129,628)(130,627)(131,626)(132,625)(133,624)(134,623)(135,622)
(136,621)(137,620)(138,619)(139,618)(140,617)(141,616)(142,615)(143,614)
(144,613)(145,612)(146,582)(147,581)(148,609)(149,608)(150,607)(151,606)
(152,605)(153,604)(154,603)(155,602)(156,601)(157,600)(158,599)(159,598)
(160,597)(161,596)(162,595)(163,594)(164,593)(165,592)(166,591)(167,590)
(168,589)(169,588)(170,587)(171,586)(172,585)(173,584)(174,583)(175,669)
(176,668)(177,696)(178,695)(179,694)(180,693)(181,692)(182,691)(183,690)
(184,689)(185,688)(186,687)(187,686)(188,685)(189,684)(190,683)(191,682)
(192,681)(193,680)(194,679)(195,678)(196,677)(197,676)(198,675)(199,674)
(200,673)(201,672)(202,671)(203,670)(204,640)(205,639)(206,667)(207,666)
(208,665)(209,664)(210,663)(211,662)(212,661)(213,660)(214,659)(215,658)
(216,657)(217,656)(218,655)(219,654)(220,653)(221,652)(222,651)(223,650)
(224,649)(225,648)(226,647)(227,646)(228,645)(229,644)(230,643)(231,642)
(232,641)(233,698)(234,697)(235,725)(236,724)(237,723)(238,722)(239,721)
(240,720)(241,719)(242,718)(243,717)(244,716)(245,715)(246,714)(247,713)
(248,712)(249,711)(250,710)(251,709)(252,708)(253,707)(254,706)(255,705)
(256,704)(257,703)(258,702)(259,701)(260,700)(261,699)(262,727)(263,726)
(264,754)(265,753)(266,752)(267,751)(268,750)(269,749)(270,748)(271,747)
(272,746)(273,745)(274,744)(275,743)(276,742)(277,741)(278,740)(279,739)
(280,738)(281,737)(282,736)(283,735)(284,734)(285,733)(286,732)(287,731)
(288,730)(289,729)(290,728)(291,756)(292,755)(293,783)(294,782)(295,781)
(296,780)(297,779)(298,778)(299,777)(300,776)(301,775)(302,774)(303,773)
(304,772)(305,771)(306,770)(307,769)(308,768)(309,767)(310,766)(311,765)
(312,764)(313,763)(314,762)(315,761)(316,760)(317,759)(318,758)(319,757)
(320,785)(321,784)(322,812)(323,811)(324,810)(325,809)(326,808)(327,807)
(328,806)(329,805)(330,804)(331,803)(332,802)(333,801)(334,800)(335,799)
(336,798)(337,797)(338,796)(339,795)(340,794)(341,793)(342,792)(343,791)
(344,790)(345,789)(346,788)(347,787)(348,786)(349,843)(350,842)(351,870)
(352,869)(353,868)(354,867)(355,866)(356,865)(357,864)(358,863)(359,862)
(360,861)(361,860)(362,859)(363,858)(364,857)(365,856)(366,855)(367,854)
(368,853)(369,852)(370,851)(371,850)(372,849)(373,848)(374,847)(375,846)
(376,845)(377,844)(378,814)(379,813)(380,841)(381,840)(382,839)(383,838)
(384,837)(385,836)(386,835)(387,834)(388,833)(389,832)(390,831)(391,830)
(392,829)(393,828)(394,827)(395,826)(396,825)(397,824)(398,823)(399,822)
(400,821)(401,820)(402,819)(403,818)(404,817)(405,816)(406,815)(407,901)
(408,900)(409,928)(410,927)(411,926)(412,925)(413,924)(414,923)(415,922)
(416,921)(417,920)(418,919)(419,918)(420,917)(421,916)(422,915)(423,914)
(424,913)(425,912)(426,911)(427,910)(428,909)(429,908)(430,907)(431,906)
(432,905)(433,904)(434,903)(435,902)(436,872)(437,871)(438,899)(439,898)
(440,897)(441,896)(442,895)(443,894)(444,893)(445,892)(446,891)(447,890)
(448,889)(449,888)(450,887)(451,886)(452,885)(453,884)(454,883)(455,882)
(456,881)(457,880)(458,879)(459,878)(460,877)(461,876)(462,875)(463,874)
(464,873);
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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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