Polytope of Type {232,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {232,4}*1856b
if this polytope has a name.
Group : SmallGroup(1856,719)
Rank : 3
Schlafli Type : {232,4}
Number of vertices, edges, etc : 232, 464, 4
Order of s₀s₁s₂ : 232
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {116,4}*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}*64b
   58-fold quotients : {4,4}*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)( 59,552)( 60,580)( 61,579)( 62,578)( 63,577)( 64,576)
( 65,575)( 66,574)( 67,573)( 68,572)( 69,571)( 70,570)( 71,569)( 72,568)
( 73,567)( 74,566)( 75,565)( 76,564)( 77,563)( 78,562)( 79,561)( 80,560)
( 81,559)( 82,558)( 83,557)( 84,556)( 85,555)( 86,554)( 87,553)( 88,523)
( 89,551)( 90,550)( 91,549)( 92,548)( 93,547)( 94,546)( 95,545)( 96,544)
( 97,543)( 98,542)( 99,541)(100,540)(101,539)(102,538)(103,537)(104,536)
(105,535)(106,534)(107,533)(108,532)(109,531)(110,530)(111,529)(112,528)
(113,527)(114,526)(115,525)(116,524)(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)(175,639)(176,667)
(177,666)(178,665)(179,664)(180,663)(181,662)(182,661)(183,660)(184,659)
(185,658)(186,657)(187,656)(188,655)(189,654)(190,653)(191,652)(192,651)
(193,650)(194,649)(195,648)(196,647)(197,646)(198,645)(199,644)(200,643)
(201,642)(202,641)(203,640)(204,668)(205,696)(206,695)(207,694)(208,693)
(209,692)(210,691)(211,690)(212,689)(213,688)(214,687)(215,686)(216,685)
(217,684)(218,683)(219,682)(220,681)(221,680)(222,679)(223,678)(224,677)
(225,676)(226,675)(227,674)(228,673)(229,672)(230,671)(231,670)(232,669)
(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)(291,784)(292,812)(293,811)(294,810)(295,809)(296,808)
(297,807)(298,806)(299,805)(300,804)(301,803)(302,802)(303,801)(304,800)
(305,799)(306,798)(307,797)(308,796)(309,795)(310,794)(311,793)(312,792)
(313,791)(314,790)(315,789)(316,788)(317,787)(318,786)(319,785)(320,755)
(321,783)(322,782)(323,781)(324,780)(325,779)(326,778)(327,777)(328,776)
(329,775)(330,774)(331,773)(332,772)(333,771)(334,770)(335,769)(336,768)
(337,767)(338,766)(339,765)(340,764)(341,763)(342,762)(343,761)(344,760)
(345,759)(346,758)(347,757)(348,756)(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)(407,871)(408,899)
(409,898)(410,897)(411,896)(412,895)(413,894)(414,893)(415,892)(416,891)
(417,890)(418,889)(419,888)(420,887)(421,886)(422,885)(423,884)(424,883)
(425,882)(426,881)(427,880)(428,879)(429,878)(430,877)(431,876)(432,875)
(433,874)(434,873)(435,872)(436,900)(437,928)(438,927)(439,926)(440,925)
(441,924)(442,923)(443,922)(444,921)(445,920)(446,919)(447,918)(448,917)
(449,916)(450,915)(451,914)(452,913)(453,912)(454,911)(455,910)(456,909)
(457,908)(458,907)(459,906)(460,905)(461,904)(462,903)(463,902)(464,901);;
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)(697,901)(698,900)(699,928)(700,927)(701,926)(702,925)
(703,924)(704,923)(705,922)(706,921)(707,920)(708,919)(709,918)(710,917)
(711,916)(712,915)(713,914)(714,913)(715,912)(716,911)(717,910)(718,909)
(719,908)(720,907)(721,906)(722,905)(723,904)(724,903)(725,902)(726,872)
(727,871)(728,899)(729,898)(730,897)(731,896)(732,895)(733,894)(734,893)
(735,892)(736,891)(737,890)(738,889)(739,888)(740,887)(741,886)(742,885)
(743,884)(744,883)(745,882)(746,881)(747,880)(748,879)(749,878)(750,877)
(751,876)(752,875)(753,874)(754,873)(755,843)(756,842)(757,870)(758,869)
(759,868)(760,867)(761,866)(762,865)(763,864)(764,863)(765,862)(766,861)
(767,860)(768,859)(769,858)(770,857)(771,856)(772,855)(773,854)(774,853)
(775,852)(776,851)(777,850)(778,849)(779,848)(780,847)(781,846)(782,845)
(783,844)(784,814)(785,813)(786,841)(787,840)(788,839)(789,838)(790,837)
(791,836)(792,835)(793,834)(794,833)(795,832)(796,831)(797,830)(798,829)
(799,828)(800,827)(801,826)(802,825)(803,824)(804,823)(805,822)(806,821)
(807,820)(808,819)(809,818)(810,817)(811,816)(812,815);;
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)(117,378)(118,379)(119,380)(120,381)
(121,382)(122,383)(123,384)(124,385)(125,386)(126,387)(127,388)(128,389)
(129,390)(130,391)(131,392)(132,393)(133,394)(134,395)(135,396)(136,397)
(137,398)(138,399)(139,400)(140,401)(141,402)(142,403)(143,404)(144,405)
(145,406)(146,349)(147,350)(148,351)(149,352)(150,353)(151,354)(152,355)
(153,356)(154,357)(155,358)(156,359)(157,360)(158,361)(159,362)(160,363)
(161,364)(162,365)(163,366)(164,367)(165,368)(166,369)(167,370)(168,371)
(169,372)(170,373)(171,374)(172,375)(173,376)(174,377)(175,436)(176,437)
(177,438)(178,439)(179,440)(180,441)(181,442)(182,443)(183,444)(184,445)
(185,446)(186,447)(187,448)(188,449)(189,450)(190,451)(191,452)(192,453)
(193,454)(194,455)(195,456)(196,457)(197,458)(198,459)(199,460)(200,461)
(201,462)(202,463)(203,464)(204,407)(205,408)(206,409)(207,410)(208,411)
(209,412)(210,413)(211,414)(212,415)(213,416)(214,417)(215,418)(216,419)
(217,420)(218,421)(219,422)(220,423)(221,424)(222,425)(223,426)(224,427)
(225,428)(226,429)(227,430)(228,431)(229,432)(230,433)(231,434)(232,435)
(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)(581,842)(582,843)(583,844)(584,845)
(585,846)(586,847)(587,848)(588,849)(589,850)(590,851)(591,852)(592,853)
(593,854)(594,855)(595,856)(596,857)(597,858)(598,859)(599,860)(600,861)
(601,862)(602,863)(603,864)(604,865)(605,866)(606,867)(607,868)(608,869)
(609,870)(610,813)(611,814)(612,815)(613,816)(614,817)(615,818)(616,819)
(617,820)(618,821)(619,822)(620,823)(621,824)(622,825)(623,826)(624,827)
(625,828)(626,829)(627,830)(628,831)(629,832)(630,833)(631,834)(632,835)
(633,836)(634,837)(635,838)(636,839)(637,840)(638,841)(639,900)(640,901)
(641,902)(642,903)(643,904)(644,905)(645,906)(646,907)(647,908)(648,909)
(649,910)(650,911)(651,912)(652,913)(653,914)(654,915)(655,916)(656,917)
(657,918)(658,919)(659,920)(660,921)(661,922)(662,923)(663,924)(664,925)
(665,926)(666,927)(667,928)(668,871)(669,872)(670,873)(671,874)(672,875)
(673,876)(674,877)(675,878)(676,879)(677,880)(678,881)(679,882)(680,883)
(681,884)(682,885)(683,886)(684,887)(685,888)(686,889)(687,890)(688,891)
(689,892)(690,893)(691,894)(692,895)(693,896)(694,897)(695,898)(696,899);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 59,552)( 60,580)( 61,579)( 62,578)( 63,577)
( 64,576)( 65,575)( 66,574)( 67,573)( 68,572)( 69,571)( 70,570)( 71,569)
( 72,568)( 73,567)( 74,566)( 75,565)( 76,564)( 77,563)( 78,562)( 79,561)
( 80,560)( 81,559)( 82,558)( 83,557)( 84,556)( 85,555)( 86,554)( 87,553)
( 88,523)( 89,551)( 90,550)( 91,549)( 92,548)( 93,547)( 94,546)( 95,545)
( 96,544)( 97,543)( 98,542)( 99,541)(100,540)(101,539)(102,538)(103,537)
(104,536)(105,535)(106,534)(107,533)(108,532)(109,531)(110,530)(111,529)
(112,528)(113,527)(114,526)(115,525)(116,524)(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)(175,639)
(176,667)(177,666)(178,665)(179,664)(180,663)(181,662)(182,661)(183,660)
(184,659)(185,658)(186,657)(187,656)(188,655)(189,654)(190,653)(191,652)
(192,651)(193,650)(194,649)(195,648)(196,647)(197,646)(198,645)(199,644)
(200,643)(201,642)(202,641)(203,640)(204,668)(205,696)(206,695)(207,694)
(208,693)(209,692)(210,691)(211,690)(212,689)(213,688)(214,687)(215,686)
(216,685)(217,684)(218,683)(219,682)(220,681)(221,680)(222,679)(223,678)
(224,677)(225,676)(226,675)(227,674)(228,673)(229,672)(230,671)(231,670)
(232,669)(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)(291,784)(292,812)(293,811)(294,810)(295,809)
(296,808)(297,807)(298,806)(299,805)(300,804)(301,803)(302,802)(303,801)
(304,800)(305,799)(306,798)(307,797)(308,796)(309,795)(310,794)(311,793)
(312,792)(313,791)(314,790)(315,789)(316,788)(317,787)(318,786)(319,785)
(320,755)(321,783)(322,782)(323,781)(324,780)(325,779)(326,778)(327,777)
(328,776)(329,775)(330,774)(331,773)(332,772)(333,771)(334,770)(335,769)
(336,768)(337,767)(338,766)(339,765)(340,764)(341,763)(342,762)(343,761)
(344,760)(345,759)(346,758)(347,757)(348,756)(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)(407,871)
(408,899)(409,898)(410,897)(411,896)(412,895)(413,894)(414,893)(415,892)
(416,891)(417,890)(418,889)(419,888)(420,887)(421,886)(422,885)(423,884)
(424,883)(425,882)(426,881)(427,880)(428,879)(429,878)(430,877)(431,876)
(432,875)(433,874)(434,873)(435,872)(436,900)(437,928)(438,927)(439,926)
(440,925)(441,924)(442,923)(443,922)(444,921)(445,920)(446,919)(447,918)
(448,917)(449,916)(450,915)(451,914)(452,913)(453,912)(454,911)(455,910)
(456,909)(457,908)(458,907)(459,906)(460,905)(461,904)(462,903)(463,902)
(464,901);
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)(697,901)(698,900)(699,928)(700,927)(701,926)
(702,925)(703,924)(704,923)(705,922)(706,921)(707,920)(708,919)(709,918)
(710,917)(711,916)(712,915)(713,914)(714,913)(715,912)(716,911)(717,910)
(718,909)(719,908)(720,907)(721,906)(722,905)(723,904)(724,903)(725,902)
(726,872)(727,871)(728,899)(729,898)(730,897)(731,896)(732,895)(733,894)
(734,893)(735,892)(736,891)(737,890)(738,889)(739,888)(740,887)(741,886)
(742,885)(743,884)(744,883)(745,882)(746,881)(747,880)(748,879)(749,878)
(750,877)(751,876)(752,875)(753,874)(754,873)(755,843)(756,842)(757,870)
(758,869)(759,868)(760,867)(761,866)(762,865)(763,864)(764,863)(765,862)
(766,861)(767,860)(768,859)(769,858)(770,857)(771,856)(772,855)(773,854)
(774,853)(775,852)(776,851)(777,850)(778,849)(779,848)(780,847)(781,846)
(782,845)(783,844)(784,814)(785,813)(786,841)(787,840)(788,839)(789,838)
(790,837)(791,836)(792,835)(793,834)(794,833)(795,832)(796,831)(797,830)
(798,829)(799,828)(800,827)(801,826)(802,825)(803,824)(804,823)(805,822)
(806,821)(807,820)(808,819)(809,818)(810,817)(811,816)(812,815);
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)(117,378)(118,379)(119,380)
(120,381)(121,382)(122,383)(123,384)(124,385)(125,386)(126,387)(127,388)
(128,389)(129,390)(130,391)(131,392)(132,393)(133,394)(134,395)(135,396)
(136,397)(137,398)(138,399)(139,400)(140,401)(141,402)(142,403)(143,404)
(144,405)(145,406)(146,349)(147,350)(148,351)(149,352)(150,353)(151,354)
(152,355)(153,356)(154,357)(155,358)(156,359)(157,360)(158,361)(159,362)
(160,363)(161,364)(162,365)(163,366)(164,367)(165,368)(166,369)(167,370)
(168,371)(169,372)(170,373)(171,374)(172,375)(173,376)(174,377)(175,436)
(176,437)(177,438)(178,439)(179,440)(180,441)(181,442)(182,443)(183,444)
(184,445)(185,446)(186,447)(187,448)(188,449)(189,450)(190,451)(191,452)
(192,453)(193,454)(194,455)(195,456)(196,457)(197,458)(198,459)(199,460)
(200,461)(201,462)(202,463)(203,464)(204,407)(205,408)(206,409)(207,410)
(208,411)(209,412)(210,413)(211,414)(212,415)(213,416)(214,417)(215,418)
(216,419)(217,420)(218,421)(219,422)(220,423)(221,424)(222,425)(223,426)
(224,427)(225,428)(226,429)(227,430)(228,431)(229,432)(230,433)(231,434)
(232,435)(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)(581,842)(582,843)(583,844)
(584,845)(585,846)(586,847)(587,848)(588,849)(589,850)(590,851)(591,852)
(592,853)(593,854)(594,855)(595,856)(596,857)(597,858)(598,859)(599,860)
(600,861)(601,862)(602,863)(603,864)(604,865)(605,866)(606,867)(607,868)
(608,869)(609,870)(610,813)(611,814)(612,815)(613,816)(614,817)(615,818)
(616,819)(617,820)(618,821)(619,822)(620,823)(621,824)(622,825)(623,826)
(624,827)(625,828)(626,829)(627,830)(628,831)(629,832)(630,833)(631,834)
(632,835)(633,836)(634,837)(635,838)(636,839)(637,840)(638,841)(639,900)
(640,901)(641,902)(642,903)(643,904)(644,905)(645,906)(646,907)(647,908)
(648,909)(649,910)(650,911)(651,912)(652,913)(653,914)(654,915)(655,916)
(656,917)(657,918)(658,919)(659,920)(660,921)(661,922)(662,923)(663,924)
(664,925)(665,926)(666,927)(667,928)(668,871)(669,872)(670,873)(671,874)
(672,875)(673,876)(674,877)(675,878)(676,879)(677,880)(678,881)(679,882)
(680,883)(681,884)(682,885)(683,886)(684,887)(685,888)(686,889)(687,890)
(688,891)(689,892)(690,893)(691,894)(692,895)(693,896)(694,897)(695,898)
(696,899);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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