Polytope of Type {116,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {116,8}*1856a
Also Known As : {116,8|2}. if this polytope has another name.
Group : SmallGroup(1856,684)
Rank : 3
Schlafli Type : {116,8}
Number of vertices, edges, etc : 116, 464, 8
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 : {116,4}*928, {58,8}*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 : {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)( 2,261)( 3,260)( 4,259)( 5,258)( 6,257)( 7,256)( 8,255)
( 9,254)( 10,253)( 11,252)( 12,251)( 13,250)( 14,249)( 15,248)( 16,247)
( 17,246)( 18,245)( 19,244)( 20,243)( 21,242)( 22,241)( 23,240)( 24,239)
( 25,238)( 26,237)( 27,236)( 28,235)( 29,234)( 30,262)( 31,290)( 32,289)
( 33,288)( 34,287)( 35,286)( 36,285)( 37,284)( 38,283)( 39,282)( 40,281)
( 41,280)( 42,279)( 43,278)( 44,277)( 45,276)( 46,275)( 47,274)( 48,273)
( 49,272)( 50,271)( 51,270)( 52,269)( 53,268)( 54,267)( 55,266)( 56,265)
( 57,264)( 58,263)( 59,291)( 60,319)( 61,318)( 62,317)( 63,316)( 64,315)
( 65,314)( 66,313)( 67,312)( 68,311)( 69,310)( 70,309)( 71,308)( 72,307)
( 73,306)( 74,305)( 75,304)( 76,303)( 77,302)( 78,301)( 79,300)( 80,299)
( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)( 88,320)
( 89,348)( 90,347)( 91,346)( 92,345)( 93,344)( 94,343)( 95,342)( 96,341)
( 97,340)( 98,339)( 99,338)(100,337)(101,336)(102,335)(103,334)(104,333)
(105,332)(106,331)(107,330)(108,329)(109,328)(110,327)(111,326)(112,325)
(113,324)(114,323)(115,322)(116,321)(117,349)(118,377)(119,376)(120,375)
(121,374)(122,373)(123,372)(124,371)(125,370)(126,369)(127,368)(128,367)
(129,366)(130,365)(131,364)(132,363)(133,362)(134,361)(135,360)(136,359)
(137,358)(138,357)(139,356)(140,355)(141,354)(142,353)(143,352)(144,351)
(145,350)(146,378)(147,406)(148,405)(149,404)(150,403)(151,402)(152,401)
(153,400)(154,399)(155,398)(156,397)(157,396)(158,395)(159,394)(160,393)
(161,392)(162,391)(163,390)(164,389)(165,388)(166,387)(167,386)(168,385)
(169,384)(170,383)(171,382)(172,381)(173,380)(174,379)(175,407)(176,435)
(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,428)(184,427)
(185,426)(186,425)(187,424)(188,423)(189,422)(190,421)(191,420)(192,419)
(193,418)(194,417)(195,416)(196,415)(197,414)(198,413)(199,412)(200,411)
(201,410)(202,409)(203,408)(204,436)(205,464)(206,463)(207,462)(208,461)
(209,460)(210,459)(211,458)(212,457)(213,456)(214,455)(215,454)(216,453)
(217,452)(218,451)(219,450)(220,449)(221,448)(222,447)(223,446)(224,445)
(225,444)(226,443)(227,442)(228,441)(229,440)(230,439)(231,438)(232,437)
(465,697)(466,725)(467,724)(468,723)(469,722)(470,721)(471,720)(472,719)
(473,718)(474,717)(475,716)(476,715)(477,714)(478,713)(479,712)(480,711)
(481,710)(482,709)(483,708)(484,707)(485,706)(486,705)(487,704)(488,703)
(489,702)(490,701)(491,700)(492,699)(493,698)(494,726)(495,754)(496,753)
(497,752)(498,751)(499,750)(500,749)(501,748)(502,747)(503,746)(504,745)
(505,744)(506,743)(507,742)(508,741)(509,740)(510,739)(511,738)(512,737)
(513,736)(514,735)(515,734)(516,733)(517,732)(518,731)(519,730)(520,729)
(521,728)(522,727)(523,755)(524,783)(525,782)(526,781)(527,780)(528,779)
(529,778)(530,777)(531,776)(532,775)(533,774)(534,773)(535,772)(536,771)
(537,770)(538,769)(539,768)(540,767)(541,766)(542,765)(543,764)(544,763)
(545,762)(546,761)(547,760)(548,759)(549,758)(550,757)(551,756)(552,784)
(553,812)(554,811)(555,810)(556,809)(557,808)(558,807)(559,806)(560,805)
(561,804)(562,803)(563,802)(564,801)(565,800)(566,799)(567,798)(568,797)
(569,796)(570,795)(571,794)(572,793)(573,792)(574,791)(575,790)(576,789)
(577,788)(578,787)(579,786)(580,785)(581,813)(582,841)(583,840)(584,839)
(585,838)(586,837)(587,836)(588,835)(589,834)(590,833)(591,832)(592,831)
(593,830)(594,829)(595,828)(596,827)(597,826)(598,825)(599,824)(600,823)
(601,822)(602,821)(603,820)(604,819)(605,818)(606,817)(607,816)(608,815)
(609,814)(610,842)(611,870)(612,869)(613,868)(614,867)(615,866)(616,865)
(617,864)(618,863)(619,862)(620,861)(621,860)(622,859)(623,858)(624,857)
(625,856)(626,855)(627,854)(628,853)(629,852)(630,851)(631,850)(632,849)
(633,848)(634,847)(635,846)(636,845)(637,844)(638,843)(639,871)(640,899)
(641,898)(642,897)(643,896)(644,895)(645,894)(646,893)(647,892)(648,891)
(649,890)(650,889)(651,888)(652,887)(653,886)(654,885)(655,884)(656,883)
(657,882)(658,881)(659,880)(660,879)(661,878)(662,877)(663,876)(664,875)
(665,874)(666,873)(667,872)(668,900)(669,928)(670,927)(671,926)(672,925)
(673,924)(674,923)(675,922)(676,921)(677,920)(678,919)(679,918)(680,917)
(681,916)(682,915)(683,914)(684,913)(685,912)(686,911)(687,910)(688,909)
(689,908)(690,907)(691,906)(692,905)(693,904)(694,903)(695,902)(696,901);;
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)(697,872)(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 := ( 1,465)( 2,466)( 3,467)( 4,468)( 5,469)( 6,470)( 7,471)( 8,472)
( 9,473)( 10,474)( 11,475)( 12,476)( 13,477)( 14,478)( 15,479)( 16,480)
( 17,481)( 18,482)( 19,483)( 20,484)( 21,485)( 22,486)( 23,487)( 24,488)
( 25,489)( 26,490)( 27,491)( 28,492)( 29,493)( 30,494)( 31,495)( 32,496)
( 33,497)( 34,498)( 35,499)( 36,500)( 37,501)( 38,502)( 39,503)( 40,504)
( 41,505)( 42,506)( 43,507)( 44,508)( 45,509)( 46,510)( 47,511)( 48,512)
( 49,513)( 50,514)( 51,515)( 52,516)( 53,517)( 54,518)( 55,519)( 56,520)
( 57,521)( 58,522)( 59,523)( 60,524)( 61,525)( 62,526)( 63,527)( 64,528)
( 65,529)( 66,530)( 67,531)( 68,532)( 69,533)( 70,534)( 71,535)( 72,536)
( 73,537)( 74,538)( 75,539)( 76,540)( 77,541)( 78,542)( 79,543)( 80,544)
( 81,545)( 82,546)( 83,547)( 84,548)( 85,549)( 86,550)( 87,551)( 88,552)
( 89,553)( 90,554)( 91,555)( 92,556)( 93,557)( 94,558)( 95,559)( 96,560)
( 97,561)( 98,562)( 99,563)(100,564)(101,565)(102,566)(103,567)(104,568)
(105,569)(106,570)(107,571)(108,572)(109,573)(110,574)(111,575)(112,576)
(113,577)(114,578)(115,579)(116,580)(117,610)(118,611)(119,612)(120,613)
(121,614)(122,615)(123,616)(124,617)(125,618)(126,619)(127,620)(128,621)
(129,622)(130,623)(131,624)(132,625)(133,626)(134,627)(135,628)(136,629)
(137,630)(138,631)(139,632)(140,633)(141,634)(142,635)(143,636)(144,637)
(145,638)(146,581)(147,582)(148,583)(149,584)(150,585)(151,586)(152,587)
(153,588)(154,589)(155,590)(156,591)(157,592)(158,593)(159,594)(160,595)
(161,596)(162,597)(163,598)(164,599)(165,600)(166,601)(167,602)(168,603)
(169,604)(170,605)(171,606)(172,607)(173,608)(174,609)(175,668)(176,669)
(177,670)(178,671)(179,672)(180,673)(181,674)(182,675)(183,676)(184,677)
(185,678)(186,679)(187,680)(188,681)(189,682)(190,683)(191,684)(192,685)
(193,686)(194,687)(195,688)(196,689)(197,690)(198,691)(199,692)(200,693)
(201,694)(202,695)(203,696)(204,639)(205,640)(206,641)(207,642)(208,643)
(209,644)(210,645)(211,646)(212,647)(213,648)(214,649)(215,650)(216,651)
(217,652)(218,653)(219,654)(220,655)(221,656)(222,657)(223,658)(224,659)
(225,660)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)(232,667)
(233,697)(234,698)(235,699)(236,700)(237,701)(238,702)(239,703)(240,704)
(241,705)(242,706)(243,707)(244,708)(245,709)(246,710)(247,711)(248,712)
(249,713)(250,714)(251,715)(252,716)(253,717)(254,718)(255,719)(256,720)
(257,721)(258,722)(259,723)(260,724)(261,725)(262,726)(263,727)(264,728)
(265,729)(266,730)(267,731)(268,732)(269,733)(270,734)(271,735)(272,736)
(273,737)(274,738)(275,739)(276,740)(277,741)(278,742)(279,743)(280,744)
(281,745)(282,746)(283,747)(284,748)(285,749)(286,750)(287,751)(288,752)
(289,753)(290,754)(291,755)(292,756)(293,757)(294,758)(295,759)(296,760)
(297,761)(298,762)(299,763)(300,764)(301,765)(302,766)(303,767)(304,768)
(305,769)(306,770)(307,771)(308,772)(309,773)(310,774)(311,775)(312,776)
(313,777)(314,778)(315,779)(316,780)(317,781)(318,782)(319,783)(320,784)
(321,785)(322,786)(323,787)(324,788)(325,789)(326,790)(327,791)(328,792)
(329,793)(330,794)(331,795)(332,796)(333,797)(334,798)(335,799)(336,800)
(337,801)(338,802)(339,803)(340,804)(341,805)(342,806)(343,807)(344,808)
(345,809)(346,810)(347,811)(348,812)(349,842)(350,843)(351,844)(352,845)
(353,846)(354,847)(355,848)(356,849)(357,850)(358,851)(359,852)(360,853)
(361,854)(362,855)(363,856)(364,857)(365,858)(366,859)(367,860)(368,861)
(369,862)(370,863)(371,864)(372,865)(373,866)(374,867)(375,868)(376,869)
(377,870)(378,813)(379,814)(380,815)(381,816)(382,817)(383,818)(384,819)
(385,820)(386,821)(387,822)(388,823)(389,824)(390,825)(391,826)(392,827)
(393,828)(394,829)(395,830)(396,831)(397,832)(398,833)(399,834)(400,835)
(401,836)(402,837)(403,838)(404,839)(405,840)(406,841)(407,900)(408,901)
(409,902)(410,903)(411,904)(412,905)(413,906)(414,907)(415,908)(416,909)
(417,910)(418,911)(419,912)(420,913)(421,914)(422,915)(423,916)(424,917)
(425,918)(426,919)(427,920)(428,921)(429,922)(430,923)(431,924)(432,925)
(433,926)(434,927)(435,928)(436,871)(437,872)(438,873)(439,874)(440,875)
(441,876)(442,877)(443,878)(444,879)(445,880)(446,881)(447,882)(448,883)
(449,884)(450,885)(451,886)(452,887)(453,888)(454,889)(455,890)(456,891)
(457,892)(458,893)(459,894)(460,895)(461,896)(462,897)(463,898)(464,899);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(928)!( 1,233)( 2,261)( 3,260)( 4,259)( 5,258)( 6,257)( 7,256)
( 8,255)( 9,254)( 10,253)( 11,252)( 12,251)( 13,250)( 14,249)( 15,248)
( 16,247)( 17,246)( 18,245)( 19,244)( 20,243)( 21,242)( 22,241)( 23,240)
( 24,239)( 25,238)( 26,237)( 27,236)( 28,235)( 29,234)( 30,262)( 31,290)
( 32,289)( 33,288)( 34,287)( 35,286)( 36,285)( 37,284)( 38,283)( 39,282)
( 40,281)( 41,280)( 42,279)( 43,278)( 44,277)( 45,276)( 46,275)( 47,274)
( 48,273)( 49,272)( 50,271)( 51,270)( 52,269)( 53,268)( 54,267)( 55,266)
( 56,265)( 57,264)( 58,263)( 59,291)( 60,319)( 61,318)( 62,317)( 63,316)
( 64,315)( 65,314)( 66,313)( 67,312)( 68,311)( 69,310)( 70,309)( 71,308)
( 72,307)( 73,306)( 74,305)( 75,304)( 76,303)( 77,302)( 78,301)( 79,300)
( 80,299)( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)
( 88,320)( 89,348)( 90,347)( 91,346)( 92,345)( 93,344)( 94,343)( 95,342)
( 96,341)( 97,340)( 98,339)( 99,338)(100,337)(101,336)(102,335)(103,334)
(104,333)(105,332)(106,331)(107,330)(108,329)(109,328)(110,327)(111,326)
(112,325)(113,324)(114,323)(115,322)(116,321)(117,349)(118,377)(119,376)
(120,375)(121,374)(122,373)(123,372)(124,371)(125,370)(126,369)(127,368)
(128,367)(129,366)(130,365)(131,364)(132,363)(133,362)(134,361)(135,360)
(136,359)(137,358)(138,357)(139,356)(140,355)(141,354)(142,353)(143,352)
(144,351)(145,350)(146,378)(147,406)(148,405)(149,404)(150,403)(151,402)
(152,401)(153,400)(154,399)(155,398)(156,397)(157,396)(158,395)(159,394)
(160,393)(161,392)(162,391)(163,390)(164,389)(165,388)(166,387)(167,386)
(168,385)(169,384)(170,383)(171,382)(172,381)(173,380)(174,379)(175,407)
(176,435)(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,428)
(184,427)(185,426)(186,425)(187,424)(188,423)(189,422)(190,421)(191,420)
(192,419)(193,418)(194,417)(195,416)(196,415)(197,414)(198,413)(199,412)
(200,411)(201,410)(202,409)(203,408)(204,436)(205,464)(206,463)(207,462)
(208,461)(209,460)(210,459)(211,458)(212,457)(213,456)(214,455)(215,454)
(216,453)(217,452)(218,451)(219,450)(220,449)(221,448)(222,447)(223,446)
(224,445)(225,444)(226,443)(227,442)(228,441)(229,440)(230,439)(231,438)
(232,437)(465,697)(466,725)(467,724)(468,723)(469,722)(470,721)(471,720)
(472,719)(473,718)(474,717)(475,716)(476,715)(477,714)(478,713)(479,712)
(480,711)(481,710)(482,709)(483,708)(484,707)(485,706)(486,705)(487,704)
(488,703)(489,702)(490,701)(491,700)(492,699)(493,698)(494,726)(495,754)
(496,753)(497,752)(498,751)(499,750)(500,749)(501,748)(502,747)(503,746)
(504,745)(505,744)(506,743)(507,742)(508,741)(509,740)(510,739)(511,738)
(512,737)(513,736)(514,735)(515,734)(516,733)(517,732)(518,731)(519,730)
(520,729)(521,728)(522,727)(523,755)(524,783)(525,782)(526,781)(527,780)
(528,779)(529,778)(530,777)(531,776)(532,775)(533,774)(534,773)(535,772)
(536,771)(537,770)(538,769)(539,768)(540,767)(541,766)(542,765)(543,764)
(544,763)(545,762)(546,761)(547,760)(548,759)(549,758)(550,757)(551,756)
(552,784)(553,812)(554,811)(555,810)(556,809)(557,808)(558,807)(559,806)
(560,805)(561,804)(562,803)(563,802)(564,801)(565,800)(566,799)(567,798)
(568,797)(569,796)(570,795)(571,794)(572,793)(573,792)(574,791)(575,790)
(576,789)(577,788)(578,787)(579,786)(580,785)(581,813)(582,841)(583,840)
(584,839)(585,838)(586,837)(587,836)(588,835)(589,834)(590,833)(591,832)
(592,831)(593,830)(594,829)(595,828)(596,827)(597,826)(598,825)(599,824)
(600,823)(601,822)(602,821)(603,820)(604,819)(605,818)(606,817)(607,816)
(608,815)(609,814)(610,842)(611,870)(612,869)(613,868)(614,867)(615,866)
(616,865)(617,864)(618,863)(619,862)(620,861)(621,860)(622,859)(623,858)
(624,857)(625,856)(626,855)(627,854)(628,853)(629,852)(630,851)(631,850)
(632,849)(633,848)(634,847)(635,846)(636,845)(637,844)(638,843)(639,871)
(640,899)(641,898)(642,897)(643,896)(644,895)(645,894)(646,893)(647,892)
(648,891)(649,890)(650,889)(651,888)(652,887)(653,886)(654,885)(655,884)
(656,883)(657,882)(658,881)(659,880)(660,879)(661,878)(662,877)(663,876)
(664,875)(665,874)(666,873)(667,872)(668,900)(669,928)(670,927)(671,926)
(672,925)(673,924)(674,923)(675,922)(676,921)(677,920)(678,919)(679,918)
(680,917)(681,916)(682,915)(683,914)(684,913)(685,912)(686,911)(687,910)
(688,909)(689,908)(690,907)(691,906)(692,905)(693,904)(694,903)(695,902)
(696,901);
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)(697,872)(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)!( 1,465)( 2,466)( 3,467)( 4,468)( 5,469)( 6,470)( 7,471)
( 8,472)( 9,473)( 10,474)( 11,475)( 12,476)( 13,477)( 14,478)( 15,479)
( 16,480)( 17,481)( 18,482)( 19,483)( 20,484)( 21,485)( 22,486)( 23,487)
( 24,488)( 25,489)( 26,490)( 27,491)( 28,492)( 29,493)( 30,494)( 31,495)
( 32,496)( 33,497)( 34,498)( 35,499)( 36,500)( 37,501)( 38,502)( 39,503)
( 40,504)( 41,505)( 42,506)( 43,507)( 44,508)( 45,509)( 46,510)( 47,511)
( 48,512)( 49,513)( 50,514)( 51,515)( 52,516)( 53,517)( 54,518)( 55,519)
( 56,520)( 57,521)( 58,522)( 59,523)( 60,524)( 61,525)( 62,526)( 63,527)
( 64,528)( 65,529)( 66,530)( 67,531)( 68,532)( 69,533)( 70,534)( 71,535)
( 72,536)( 73,537)( 74,538)( 75,539)( 76,540)( 77,541)( 78,542)( 79,543)
( 80,544)( 81,545)( 82,546)( 83,547)( 84,548)( 85,549)( 86,550)( 87,551)
( 88,552)( 89,553)( 90,554)( 91,555)( 92,556)( 93,557)( 94,558)( 95,559)
( 96,560)( 97,561)( 98,562)( 99,563)(100,564)(101,565)(102,566)(103,567)
(104,568)(105,569)(106,570)(107,571)(108,572)(109,573)(110,574)(111,575)
(112,576)(113,577)(114,578)(115,579)(116,580)(117,610)(118,611)(119,612)
(120,613)(121,614)(122,615)(123,616)(124,617)(125,618)(126,619)(127,620)
(128,621)(129,622)(130,623)(131,624)(132,625)(133,626)(134,627)(135,628)
(136,629)(137,630)(138,631)(139,632)(140,633)(141,634)(142,635)(143,636)
(144,637)(145,638)(146,581)(147,582)(148,583)(149,584)(150,585)(151,586)
(152,587)(153,588)(154,589)(155,590)(156,591)(157,592)(158,593)(159,594)
(160,595)(161,596)(162,597)(163,598)(164,599)(165,600)(166,601)(167,602)
(168,603)(169,604)(170,605)(171,606)(172,607)(173,608)(174,609)(175,668)
(176,669)(177,670)(178,671)(179,672)(180,673)(181,674)(182,675)(183,676)
(184,677)(185,678)(186,679)(187,680)(188,681)(189,682)(190,683)(191,684)
(192,685)(193,686)(194,687)(195,688)(196,689)(197,690)(198,691)(199,692)
(200,693)(201,694)(202,695)(203,696)(204,639)(205,640)(206,641)(207,642)
(208,643)(209,644)(210,645)(211,646)(212,647)(213,648)(214,649)(215,650)
(216,651)(217,652)(218,653)(219,654)(220,655)(221,656)(222,657)(223,658)
(224,659)(225,660)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)
(232,667)(233,697)(234,698)(235,699)(236,700)(237,701)(238,702)(239,703)
(240,704)(241,705)(242,706)(243,707)(244,708)(245,709)(246,710)(247,711)
(248,712)(249,713)(250,714)(251,715)(252,716)(253,717)(254,718)(255,719)
(256,720)(257,721)(258,722)(259,723)(260,724)(261,725)(262,726)(263,727)
(264,728)(265,729)(266,730)(267,731)(268,732)(269,733)(270,734)(271,735)
(272,736)(273,737)(274,738)(275,739)(276,740)(277,741)(278,742)(279,743)
(280,744)(281,745)(282,746)(283,747)(284,748)(285,749)(286,750)(287,751)
(288,752)(289,753)(290,754)(291,755)(292,756)(293,757)(294,758)(295,759)
(296,760)(297,761)(298,762)(299,763)(300,764)(301,765)(302,766)(303,767)
(304,768)(305,769)(306,770)(307,771)(308,772)(309,773)(310,774)(311,775)
(312,776)(313,777)(314,778)(315,779)(316,780)(317,781)(318,782)(319,783)
(320,784)(321,785)(322,786)(323,787)(324,788)(325,789)(326,790)(327,791)
(328,792)(329,793)(330,794)(331,795)(332,796)(333,797)(334,798)(335,799)
(336,800)(337,801)(338,802)(339,803)(340,804)(341,805)(342,806)(343,807)
(344,808)(345,809)(346,810)(347,811)(348,812)(349,842)(350,843)(351,844)
(352,845)(353,846)(354,847)(355,848)(356,849)(357,850)(358,851)(359,852)
(360,853)(361,854)(362,855)(363,856)(364,857)(365,858)(366,859)(367,860)
(368,861)(369,862)(370,863)(371,864)(372,865)(373,866)(374,867)(375,868)
(376,869)(377,870)(378,813)(379,814)(380,815)(381,816)(382,817)(383,818)
(384,819)(385,820)(386,821)(387,822)(388,823)(389,824)(390,825)(391,826)
(392,827)(393,828)(394,829)(395,830)(396,831)(397,832)(398,833)(399,834)
(400,835)(401,836)(402,837)(403,838)(404,839)(405,840)(406,841)(407,900)
(408,901)(409,902)(410,903)(411,904)(412,905)(413,906)(414,907)(415,908)
(416,909)(417,910)(418,911)(419,912)(420,913)(421,914)(422,915)(423,916)
(424,917)(425,918)(426,919)(427,920)(428,921)(429,922)(430,923)(431,924)
(432,925)(433,926)(434,927)(435,928)(436,871)(437,872)(438,873)(439,874)
(440,875)(441,876)(442,877)(443,878)(444,879)(445,880)(446,881)(447,882)
(448,883)(449,884)(450,885)(451,886)(452,887)(453,888)(454,889)(455,890)
(456,891)(457,892)(458,893)(459,894)(460,895)(461,896)(462,897)(463,898)
(464,899);
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope