Polytope of Type {4,232}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,232}*1856b
if this polytope has a name.
Group : SmallGroup(1856,719)
Rank : 3
Schlafli Type : {4,232}
Number of vertices, edges, etc : 4, 464, 232
Order of s0s1s2 : 232
Order of s0s1s2s1 : 4
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
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}*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 := ( 1,233)( 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);;
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)(697,900)(698,928)(699,927)(700,926)(701,925)(702,924)
(703,923)(704,922)(705,921)(706,920)(707,919)(708,918)(709,917)(710,916)
(711,915)(712,914)(713,913)(714,912)(715,911)(716,910)(717,909)(718,908)
(719,907)(720,906)(721,905)(722,904)(723,903)(724,902)(725,901)(726,871)
(727,899)(728,898)(729,897)(730,896)(731,895)(732,894)(733,893)(734,892)
(735,891)(736,890)(737,889)(738,888)(739,887)(740,886)(741,885)(742,884)
(743,883)(744,882)(745,881)(746,880)(747,879)(748,878)(749,877)(750,876)
(751,875)(752,874)(753,873)(754,872)(755,842)(756,870)(757,869)(758,868)
(759,867)(760,866)(761,865)(762,864)(763,863)(764,862)(765,861)(766,860)
(767,859)(768,858)(769,857)(770,856)(771,855)(772,854)(773,853)(774,852)
(775,851)(776,850)(777,849)(778,848)(779,847)(780,846)(781,845)(782,844)
(783,843)(784,813)(785,841)(786,840)(787,839)(788,838)(789,837)(790,836)
(791,835)(792,834)(793,833)(794,832)(795,831)(796,830)(797,829)(798,828)
(799,827)(800,826)(801,825)(802,824)(803,823)(804,822)(805,821)(806,820)
(807,819)(808,818)(809,817)(810,816)(811,815)(812,814);;
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)( 59,553)( 60,552)( 61,580)( 62,579)( 63,578)( 64,577)
( 65,576)( 66,575)( 67,574)( 68,573)( 69,572)( 70,571)( 71,570)( 72,569)
( 73,568)( 74,567)( 75,566)( 76,565)( 77,564)( 78,563)( 79,562)( 80,561)
( 81,560)( 82,559)( 83,558)( 84,557)( 85,556)( 86,555)( 87,554)( 88,524)
( 89,523)( 90,551)( 91,550)( 92,549)( 93,548)( 94,547)( 95,546)( 96,545)
( 97,544)( 98,543)( 99,542)(100,541)(101,540)(102,539)(103,538)(104,537)
(105,536)(106,535)(107,534)(108,533)(109,532)(110,531)(111,530)(112,529)
(113,528)(114,527)(115,526)(116,525)(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)(175,640)(176,639)
(177,667)(178,666)(179,665)(180,664)(181,663)(182,662)(183,661)(184,660)
(185,659)(186,658)(187,657)(188,656)(189,655)(190,654)(191,653)(192,652)
(193,651)(194,650)(195,649)(196,648)(197,647)(198,646)(199,645)(200,644)
(201,643)(202,642)(203,641)(204,669)(205,668)(206,696)(207,695)(208,694)
(209,693)(210,692)(211,691)(212,690)(213,689)(214,688)(215,687)(216,686)
(217,685)(218,684)(219,683)(220,682)(221,681)(222,680)(223,679)(224,678)
(225,677)(226,676)(227,675)(228,674)(229,673)(230,672)(231,671)(232,670)
(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)(291,785)(292,784)(293,812)(294,811)(295,810)(296,809)
(297,808)(298,807)(299,806)(300,805)(301,804)(302,803)(303,802)(304,801)
(305,800)(306,799)(307,798)(308,797)(309,796)(310,795)(311,794)(312,793)
(313,792)(314,791)(315,790)(316,789)(317,788)(318,787)(319,786)(320,756)
(321,755)(322,783)(323,782)(324,781)(325,780)(326,779)(327,778)(328,777)
(329,776)(330,775)(331,774)(332,773)(333,772)(334,771)(335,770)(336,769)
(337,768)(338,767)(339,766)(340,765)(341,764)(342,763)(343,762)(344,761)
(345,760)(346,759)(347,758)(348,757)(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)(407,872)(408,871)
(409,899)(410,898)(411,897)(412,896)(413,895)(414,894)(415,893)(416,892)
(417,891)(418,890)(419,889)(420,888)(421,887)(422,886)(423,885)(424,884)
(425,883)(426,882)(427,881)(428,880)(429,879)(430,878)(431,877)(432,876)
(433,875)(434,874)(435,873)(436,901)(437,900)(438,928)(439,927)(440,926)
(441,925)(442,924)(443,923)(444,922)(445,921)(446,920)(447,919)(448,918)
(449,917)(450,916)(451,915)(452,914)(453,913)(454,912)(455,911)(456,910)
(457,909)(458,908)(459,907)(460,906)(461,905)(462,904)(463,903)(464,902);;
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,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
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)(117,378)(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);
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)(697,900)(698,928)(699,927)(700,926)(701,925)
(702,924)(703,923)(704,922)(705,921)(706,920)(707,919)(708,918)(709,917)
(710,916)(711,915)(712,914)(713,913)(714,912)(715,911)(716,910)(717,909)
(718,908)(719,907)(720,906)(721,905)(722,904)(723,903)(724,902)(725,901)
(726,871)(727,899)(728,898)(729,897)(730,896)(731,895)(732,894)(733,893)
(734,892)(735,891)(736,890)(737,889)(738,888)(739,887)(740,886)(741,885)
(742,884)(743,883)(744,882)(745,881)(746,880)(747,879)(748,878)(749,877)
(750,876)(751,875)(752,874)(753,873)(754,872)(755,842)(756,870)(757,869)
(758,868)(759,867)(760,866)(761,865)(762,864)(763,863)(764,862)(765,861)
(766,860)(767,859)(768,858)(769,857)(770,856)(771,855)(772,854)(773,853)
(774,852)(775,851)(776,850)(777,849)(778,848)(779,847)(780,846)(781,845)
(782,844)(783,843)(784,813)(785,841)(786,840)(787,839)(788,838)(789,837)
(790,836)(791,835)(792,834)(793,833)(794,832)(795,831)(796,830)(797,829)
(798,828)(799,827)(800,826)(801,825)(802,824)(803,823)(804,822)(805,821)
(806,820)(807,819)(808,818)(809,817)(810,816)(811,815)(812,814);
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)( 59,553)( 60,552)( 61,580)( 62,579)( 63,578)
( 64,577)( 65,576)( 66,575)( 67,574)( 68,573)( 69,572)( 70,571)( 71,570)
( 72,569)( 73,568)( 74,567)( 75,566)( 76,565)( 77,564)( 78,563)( 79,562)
( 80,561)( 81,560)( 82,559)( 83,558)( 84,557)( 85,556)( 86,555)( 87,554)
( 88,524)( 89,523)( 90,551)( 91,550)( 92,549)( 93,548)( 94,547)( 95,546)
( 96,545)( 97,544)( 98,543)( 99,542)(100,541)(101,540)(102,539)(103,538)
(104,537)(105,536)(106,535)(107,534)(108,533)(109,532)(110,531)(111,530)
(112,529)(113,528)(114,527)(115,526)(116,525)(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)(175,640)
(176,639)(177,667)(178,666)(179,665)(180,664)(181,663)(182,662)(183,661)
(184,660)(185,659)(186,658)(187,657)(188,656)(189,655)(190,654)(191,653)
(192,652)(193,651)(194,650)(195,649)(196,648)(197,647)(198,646)(199,645)
(200,644)(201,643)(202,642)(203,641)(204,669)(205,668)(206,696)(207,695)
(208,694)(209,693)(210,692)(211,691)(212,690)(213,689)(214,688)(215,687)
(216,686)(217,685)(218,684)(219,683)(220,682)(221,681)(222,680)(223,679)
(224,678)(225,677)(226,676)(227,675)(228,674)(229,673)(230,672)(231,671)
(232,670)(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)(291,785)(292,784)(293,812)(294,811)(295,810)
(296,809)(297,808)(298,807)(299,806)(300,805)(301,804)(302,803)(303,802)
(304,801)(305,800)(306,799)(307,798)(308,797)(309,796)(310,795)(311,794)
(312,793)(313,792)(314,791)(315,790)(316,789)(317,788)(318,787)(319,786)
(320,756)(321,755)(322,783)(323,782)(324,781)(325,780)(326,779)(327,778)
(328,777)(329,776)(330,775)(331,774)(332,773)(333,772)(334,771)(335,770)
(336,769)(337,768)(338,767)(339,766)(340,765)(341,764)(342,763)(343,762)
(344,761)(345,760)(346,759)(347,758)(348,757)(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)(407,872)
(408,871)(409,899)(410,898)(411,897)(412,896)(413,895)(414,894)(415,893)
(416,892)(417,891)(418,890)(419,889)(420,888)(421,887)(422,886)(423,885)
(424,884)(425,883)(426,882)(427,881)(428,880)(429,879)(430,878)(431,877)
(432,876)(433,875)(434,874)(435,873)(436,901)(437,900)(438,928)(439,927)
(440,926)(441,925)(442,924)(443,923)(444,922)(445,921)(446,920)(447,919)
(448,918)(449,917)(450,916)(451,915)(452,914)(453,913)(454,912)(455,911)
(456,910)(457,909)(458,908)(459,907)(460,906)(461,905)(462,904)(463,903)
(464,902);
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,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope