Polytope of Type {58,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {58,4,4}*1856
Also Known As : {{58,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1856,1033)
Rank : 4
Schlafli Type : {58,4,4}
Number of vertices, edges, etc : 58, 116, 8, 4
Order of s0s1s2s3 : 116
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {58,2,4}*928, {58,4,2}*928
4-fold quotients : {29,2,4}*464, {58,2,2}*464
8-fold quotients : {29,2,2}*232
29-fold quotients : {2,4,4}*64
58-fold quotients : {2,2,4}*32, {2,4,2}*32
116-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,117)( 2,145)( 3,144)( 4,143)( 5,142)( 6,141)( 7,140)( 8,139)
( 9,138)( 10,137)( 11,136)( 12,135)( 13,134)( 14,133)( 15,132)( 16,131)
( 17,130)( 18,129)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)( 24,123)
( 25,122)( 26,121)( 27,120)( 28,119)( 29,118)( 30,146)( 31,174)( 32,173)
( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)( 40,165)
( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)
( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)
( 57,148)( 58,147)( 59,175)( 60,203)( 61,202)( 62,201)( 63,200)( 64,199)
( 65,198)( 66,197)( 67,196)( 68,195)( 69,194)( 70,193)( 71,192)( 72,191)
( 73,190)( 74,189)( 75,188)( 76,187)( 77,186)( 78,185)( 79,184)( 80,183)
( 81,182)( 82,181)( 83,180)( 84,179)( 85,178)( 86,177)( 87,176)( 88,204)
( 89,232)( 90,231)( 91,230)( 92,229)( 93,228)( 94,227)( 95,226)( 96,225)
( 97,224)( 98,223)( 99,222)(100,221)(101,220)(102,219)(103,218)(104,217)
(105,216)(106,215)(107,214)(108,213)(109,212)(110,211)(111,210)(112,209)
(113,208)(114,207)(115,206)(116,205)(233,349)(234,377)(235,376)(236,375)
(237,374)(238,373)(239,372)(240,371)(241,370)(242,369)(243,368)(244,367)
(245,366)(246,365)(247,364)(248,363)(249,362)(250,361)(251,360)(252,359)
(253,358)(254,357)(255,356)(256,355)(257,354)(258,353)(259,352)(260,351)
(261,350)(262,378)(263,406)(264,405)(265,404)(266,403)(267,402)(268,401)
(269,400)(270,399)(271,398)(272,397)(273,396)(274,395)(275,394)(276,393)
(277,392)(278,391)(279,390)(280,389)(281,388)(282,387)(283,386)(284,385)
(285,384)(286,383)(287,382)(288,381)(289,380)(290,379)(291,407)(292,435)
(293,434)(294,433)(295,432)(296,431)(297,430)(298,429)(299,428)(300,427)
(301,426)(302,425)(303,424)(304,423)(305,422)(306,421)(307,420)(308,419)
(309,418)(310,417)(311,416)(312,415)(313,414)(314,413)(315,412)(316,411)
(317,410)(318,409)(319,408)(320,436)(321,464)(322,463)(323,462)(324,461)
(325,460)(326,459)(327,458)(328,457)(329,456)(330,455)(331,454)(332,453)
(333,452)(334,451)(335,450)(336,449)(337,448)(338,447)(339,446)(340,445)
(341,444)(342,443)(343,442)(344,441)(345,440)(346,439)(347,438)(348,437)
(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)(697,813)(698,841)(699,840)(700,839)
(701,838)(702,837)(703,836)(704,835)(705,834)(706,833)(707,832)(708,831)
(709,830)(710,829)(711,828)(712,827)(713,826)(714,825)(715,824)(716,823)
(717,822)(718,821)(719,820)(720,819)(721,818)(722,817)(723,816)(724,815)
(725,814)(726,842)(727,870)(728,869)(729,868)(730,867)(731,866)(732,865)
(733,864)(734,863)(735,862)(736,861)(737,860)(738,859)(739,858)(740,857)
(741,856)(742,855)(743,854)(744,853)(745,852)(746,851)(747,850)(748,849)
(749,848)(750,847)(751,846)(752,845)(753,844)(754,843)(755,871)(756,899)
(757,898)(758,897)(759,896)(760,895)(761,894)(762,893)(763,892)(764,891)
(765,890)(766,889)(767,888)(768,887)(769,886)(770,885)(771,884)(772,883)
(773,882)(774,881)(775,880)(776,879)(777,878)(778,877)(779,876)(780,875)
(781,874)(782,873)(783,872)(784,900)(785,928)(786,927)(787,926)(788,925)
(789,924)(790,923)(791,922)(792,921)(793,920)(794,919)(795,918)(796,917)
(797,916)(798,915)(799,914)(800,913)(801,912)(802,911)(803,910)(804,909)
(805,908)(806,907)(807,906)(808,905)(809,904)(810,903)(811,902)(812,901);;
s1 := ( 1,582)( 2,581)( 3,609)( 4,608)( 5,607)( 6,606)( 7,605)( 8,604)
( 9,603)( 10,602)( 11,601)( 12,600)( 13,599)( 14,598)( 15,597)( 16,596)
( 17,595)( 18,594)( 19,593)( 20,592)( 21,591)( 22,590)( 23,589)( 24,588)
( 25,587)( 26,586)( 27,585)( 28,584)( 29,583)( 30,611)( 31,610)( 32,638)
( 33,637)( 34,636)( 35,635)( 36,634)( 37,633)( 38,632)( 39,631)( 40,630)
( 41,629)( 42,628)( 43,627)( 44,626)( 45,625)( 46,624)( 47,623)( 48,622)
( 49,621)( 50,620)( 51,619)( 52,618)( 53,617)( 54,616)( 55,615)( 56,614)
( 57,613)( 58,612)( 59,640)( 60,639)( 61,667)( 62,666)( 63,665)( 64,664)
( 65,663)( 66,662)( 67,661)( 68,660)( 69,659)( 70,658)( 71,657)( 72,656)
( 73,655)( 74,654)( 75,653)( 76,652)( 77,651)( 78,650)( 79,649)( 80,648)
( 81,647)( 82,646)( 83,645)( 84,644)( 85,643)( 86,642)( 87,641)( 88,669)
( 89,668)( 90,696)( 91,695)( 92,694)( 93,693)( 94,692)( 95,691)( 96,690)
( 97,689)( 98,688)( 99,687)(100,686)(101,685)(102,684)(103,683)(104,682)
(105,681)(106,680)(107,679)(108,678)(109,677)(110,676)(111,675)(112,674)
(113,673)(114,672)(115,671)(116,670)(117,466)(118,465)(119,493)(120,492)
(121,491)(122,490)(123,489)(124,488)(125,487)(126,486)(127,485)(128,484)
(129,483)(130,482)(131,481)(132,480)(133,479)(134,478)(135,477)(136,476)
(137,475)(138,474)(139,473)(140,472)(141,471)(142,470)(143,469)(144,468)
(145,467)(146,495)(147,494)(148,522)(149,521)(150,520)(151,519)(152,518)
(153,517)(154,516)(155,515)(156,514)(157,513)(158,512)(159,511)(160,510)
(161,509)(162,508)(163,507)(164,506)(165,505)(166,504)(167,503)(168,502)
(169,501)(170,500)(171,499)(172,498)(173,497)(174,496)(175,524)(176,523)
(177,551)(178,550)(179,549)(180,548)(181,547)(182,546)(183,545)(184,544)
(185,543)(186,542)(187,541)(188,540)(189,539)(190,538)(191,537)(192,536)
(193,535)(194,534)(195,533)(196,532)(197,531)(198,530)(199,529)(200,528)
(201,527)(202,526)(203,525)(204,553)(205,552)(206,580)(207,579)(208,578)
(209,577)(210,576)(211,575)(212,574)(213,573)(214,572)(215,571)(216,570)
(217,569)(218,568)(219,567)(220,566)(221,565)(222,564)(223,563)(224,562)
(225,561)(226,560)(227,559)(228,558)(229,557)(230,556)(231,555)(232,554)
(233,814)(234,813)(235,841)(236,840)(237,839)(238,838)(239,837)(240,836)
(241,835)(242,834)(243,833)(244,832)(245,831)(246,830)(247,829)(248,828)
(249,827)(250,826)(251,825)(252,824)(253,823)(254,822)(255,821)(256,820)
(257,819)(258,818)(259,817)(260,816)(261,815)(262,843)(263,842)(264,870)
(265,869)(266,868)(267,867)(268,866)(269,865)(270,864)(271,863)(272,862)
(273,861)(274,860)(275,859)(276,858)(277,857)(278,856)(279,855)(280,854)
(281,853)(282,852)(283,851)(284,850)(285,849)(286,848)(287,847)(288,846)
(289,845)(290,844)(291,872)(292,871)(293,899)(294,898)(295,897)(296,896)
(297,895)(298,894)(299,893)(300,892)(301,891)(302,890)(303,889)(304,888)
(305,887)(306,886)(307,885)(308,884)(309,883)(310,882)(311,881)(312,880)
(313,879)(314,878)(315,877)(316,876)(317,875)(318,874)(319,873)(320,901)
(321,900)(322,928)(323,927)(324,926)(325,925)(326,924)(327,923)(328,922)
(329,921)(330,920)(331,919)(332,918)(333,917)(334,916)(335,915)(336,914)
(337,913)(338,912)(339,911)(340,910)(341,909)(342,908)(343,907)(344,906)
(345,905)(346,904)(347,903)(348,902)(349,698)(350,697)(351,725)(352,724)
(353,723)(354,722)(355,721)(356,720)(357,719)(358,718)(359,717)(360,716)
(361,715)(362,714)(363,713)(364,712)(365,711)(366,710)(367,709)(368,708)
(369,707)(370,706)(371,705)(372,704)(373,703)(374,702)(375,701)(376,700)
(377,699)(378,727)(379,726)(380,754)(381,753)(382,752)(383,751)(384,750)
(385,749)(386,748)(387,747)(388,746)(389,745)(390,744)(391,743)(392,742)
(393,741)(394,740)(395,739)(396,738)(397,737)(398,736)(399,735)(400,734)
(401,733)(402,732)(403,731)(404,730)(405,729)(406,728)(407,756)(408,755)
(409,783)(410,782)(411,781)(412,780)(413,779)(414,778)(415,777)(416,776)
(417,775)(418,774)(419,773)(420,772)(421,771)(422,770)(423,769)(424,768)
(425,767)(426,766)(427,765)(428,764)(429,763)(430,762)(431,761)(432,760)
(433,759)(434,758)(435,757)(436,785)(437,784)(438,812)(439,811)(440,810)
(441,809)(442,808)(443,807)(444,806)(445,805)(446,804)(447,803)(448,802)
(449,801)(450,800)(451,799)(452,798)(453,797)(454,796)(455,795)(456,794)
(457,793)(458,792)(459,791)(460,790)(461,789)(462,788)(463,787)(464,786);;
s2 := (233,262)(234,263)(235,264)(236,265)(237,266)(238,267)(239,268)(240,269)
(241,270)(242,271)(243,272)(244,273)(245,274)(246,275)(247,276)(248,277)
(249,278)(250,279)(251,280)(252,281)(253,282)(254,283)(255,284)(256,285)
(257,286)(258,287)(259,288)(260,289)(261,290)(291,320)(292,321)(293,322)
(294,323)(295,324)(296,325)(297,326)(298,327)(299,328)(300,329)(301,330)
(302,331)(303,332)(304,333)(305,334)(306,335)(307,336)(308,337)(309,338)
(310,339)(311,340)(312,341)(313,342)(314,343)(315,344)(316,345)(317,346)
(318,347)(319,348)(349,378)(350,379)(351,380)(352,381)(353,382)(354,383)
(355,384)(356,385)(357,386)(358,387)(359,388)(360,389)(361,390)(362,391)
(363,392)(364,393)(365,394)(366,395)(367,396)(368,397)(369,398)(370,399)
(371,400)(372,401)(373,402)(374,403)(375,404)(376,405)(377,406)(407,436)
(408,437)(409,438)(410,439)(411,440)(412,441)(413,442)(414,443)(415,444)
(416,445)(417,446)(418,447)(419,448)(420,449)(421,450)(422,451)(423,452)
(424,453)(425,454)(426,455)(427,456)(428,457)(429,458)(430,459)(431,460)
(432,461)(433,462)(434,463)(435,464)(465,523)(466,524)(467,525)(468,526)
(469,527)(470,528)(471,529)(472,530)(473,531)(474,532)(475,533)(476,534)
(477,535)(478,536)(479,537)(480,538)(481,539)(482,540)(483,541)(484,542)
(485,543)(486,544)(487,545)(488,546)(489,547)(490,548)(491,549)(492,550)
(493,551)(494,552)(495,553)(496,554)(497,555)(498,556)(499,557)(500,558)
(501,559)(502,560)(503,561)(504,562)(505,563)(506,564)(507,565)(508,566)
(509,567)(510,568)(511,569)(512,570)(513,571)(514,572)(515,573)(516,574)
(517,575)(518,576)(519,577)(520,578)(521,579)(522,580)(581,639)(582,640)
(583,641)(584,642)(585,643)(586,644)(587,645)(588,646)(589,647)(590,648)
(591,649)(592,650)(593,651)(594,652)(595,653)(596,654)(597,655)(598,656)
(599,657)(600,658)(601,659)(602,660)(603,661)(604,662)(605,663)(606,664)
(607,665)(608,666)(609,667)(610,668)(611,669)(612,670)(613,671)(614,672)
(615,673)(616,674)(617,675)(618,676)(619,677)(620,678)(621,679)(622,680)
(623,681)(624,682)(625,683)(626,684)(627,685)(628,686)(629,687)(630,688)
(631,689)(632,690)(633,691)(634,692)(635,693)(636,694)(637,695)(638,696)
(697,784)(698,785)(699,786)(700,787)(701,788)(702,789)(703,790)(704,791)
(705,792)(706,793)(707,794)(708,795)(709,796)(710,797)(711,798)(712,799)
(713,800)(714,801)(715,802)(716,803)(717,804)(718,805)(719,806)(720,807)
(721,808)(722,809)(723,810)(724,811)(725,812)(726,755)(727,756)(728,757)
(729,758)(730,759)(731,760)(732,761)(733,762)(734,763)(735,764)(736,765)
(737,766)(738,767)(739,768)(740,769)(741,770)(742,771)(743,772)(744,773)
(745,774)(746,775)(747,776)(748,777)(749,778)(750,779)(751,780)(752,781)
(753,782)(754,783)(813,900)(814,901)(815,902)(816,903)(817,904)(818,905)
(819,906)(820,907)(821,908)(822,909)(823,910)(824,911)(825,912)(826,913)
(827,914)(828,915)(829,916)(830,917)(831,918)(832,919)(833,920)(834,921)
(835,922)(836,923)(837,924)(838,925)(839,926)(840,927)(841,928)(842,871)
(843,872)(844,873)(845,874)(846,875)(847,876)(848,877)(849,878)(850,879)
(851,880)(852,881)(853,882)(854,883)(855,884)(856,885)(857,886)(858,887)
(859,888)(860,889)(861,890)(862,891)(863,892)(864,893)(865,894)(866,895)
(867,896)(868,897)(869,898)(870,899);;
s3 := ( 1,233)( 2,234)( 3,235)( 4,236)( 5,237)( 6,238)( 7,239)( 8,240)
( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)
( 17,249)( 18,250)( 19,251)( 20,252)( 21,253)( 22,254)( 23,255)( 24,256)
( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)
( 33,265)( 34,266)( 35,267)( 36,268)( 37,269)( 38,270)( 39,271)( 40,272)
( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)
( 49,281)( 50,282)( 51,283)( 52,284)( 53,285)( 54,286)( 55,287)( 56,288)
( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)
( 65,297)( 66,298)( 67,299)( 68,300)( 69,301)( 70,302)( 71,303)( 72,304)
( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)
( 81,313)( 82,314)( 83,315)( 84,316)( 85,317)( 86,318)( 87,319)( 88,320)
( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)
( 97,329)( 98,330)( 99,331)(100,332)(101,333)(102,334)(103,335)(104,336)
(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)
(113,345)(114,346)(115,347)(116,348)(117,349)(118,350)(119,351)(120,352)
(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)
(129,361)(130,362)(131,363)(132,364)(133,365)(134,366)(135,367)(136,368)
(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)
(145,377)(146,378)(147,379)(148,380)(149,381)(150,382)(151,383)(152,384)
(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)
(161,393)(162,394)(163,395)(164,396)(165,397)(166,398)(167,399)(168,400)
(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)
(177,409)(178,410)(179,411)(180,412)(181,413)(182,414)(183,415)(184,416)
(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)
(193,425)(194,426)(195,427)(196,428)(197,429)(198,430)(199,431)(200,432)
(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)
(209,441)(210,442)(211,443)(212,444)(213,445)(214,446)(215,447)(216,448)
(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)
(225,457)(226,458)(227,459)(228,460)(229,461)(230,462)(231,463)(232,464)
(465,697)(466,698)(467,699)(468,700)(469,701)(470,702)(471,703)(472,704)
(473,705)(474,706)(475,707)(476,708)(477,709)(478,710)(479,711)(480,712)
(481,713)(482,714)(483,715)(484,716)(485,717)(486,718)(487,719)(488,720)
(489,721)(490,722)(491,723)(492,724)(493,725)(494,726)(495,727)(496,728)
(497,729)(498,730)(499,731)(500,732)(501,733)(502,734)(503,735)(504,736)
(505,737)(506,738)(507,739)(508,740)(509,741)(510,742)(511,743)(512,744)
(513,745)(514,746)(515,747)(516,748)(517,749)(518,750)(519,751)(520,752)
(521,753)(522,754)(523,755)(524,756)(525,757)(526,758)(527,759)(528,760)
(529,761)(530,762)(531,763)(532,764)(533,765)(534,766)(535,767)(536,768)
(537,769)(538,770)(539,771)(540,772)(541,773)(542,774)(543,775)(544,776)
(545,777)(546,778)(547,779)(548,780)(549,781)(550,782)(551,783)(552,784)
(553,785)(554,786)(555,787)(556,788)(557,789)(558,790)(559,791)(560,792)
(561,793)(562,794)(563,795)(564,796)(565,797)(566,798)(567,799)(568,800)
(569,801)(570,802)(571,803)(572,804)(573,805)(574,806)(575,807)(576,808)
(577,809)(578,810)(579,811)(580,812)(581,813)(582,814)(583,815)(584,816)
(585,817)(586,818)(587,819)(588,820)(589,821)(590,822)(591,823)(592,824)
(593,825)(594,826)(595,827)(596,828)(597,829)(598,830)(599,831)(600,832)
(601,833)(602,834)(603,835)(604,836)(605,837)(606,838)(607,839)(608,840)
(609,841)(610,842)(611,843)(612,844)(613,845)(614,846)(615,847)(616,848)
(617,849)(618,850)(619,851)(620,852)(621,853)(622,854)(623,855)(624,856)
(625,857)(626,858)(627,859)(628,860)(629,861)(630,862)(631,863)(632,864)
(633,865)(634,866)(635,867)(636,868)(637,869)(638,870)(639,871)(640,872)
(641,873)(642,874)(643,875)(644,876)(645,877)(646,878)(647,879)(648,880)
(649,881)(650,882)(651,883)(652,884)(653,885)(654,886)(655,887)(656,888)
(657,889)(658,890)(659,891)(660,892)(661,893)(662,894)(663,895)(664,896)
(665,897)(666,898)(667,899)(668,900)(669,901)(670,902)(671,903)(672,904)
(673,905)(674,906)(675,907)(676,908)(677,909)(678,910)(679,911)(680,912)
(681,913)(682,914)(683,915)(684,916)(685,917)(686,918)(687,919)(688,920)
(689,921)(690,922)(691,923)(692,924)(693,925)(694,926)(695,927)(696,928);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!( 1,117)( 2,145)( 3,144)( 4,143)( 5,142)( 6,141)( 7,140)
( 8,139)( 9,138)( 10,137)( 11,136)( 12,135)( 13,134)( 14,133)( 15,132)
( 16,131)( 17,130)( 18,129)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)
( 24,123)( 25,122)( 26,121)( 27,120)( 28,119)( 29,118)( 30,146)( 31,174)
( 32,173)( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)
( 40,165)( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)
( 48,157)( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)
( 56,149)( 57,148)( 58,147)( 59,175)( 60,203)( 61,202)( 62,201)( 63,200)
( 64,199)( 65,198)( 66,197)( 67,196)( 68,195)( 69,194)( 70,193)( 71,192)
( 72,191)( 73,190)( 74,189)( 75,188)( 76,187)( 77,186)( 78,185)( 79,184)
( 80,183)( 81,182)( 82,181)( 83,180)( 84,179)( 85,178)( 86,177)( 87,176)
( 88,204)( 89,232)( 90,231)( 91,230)( 92,229)( 93,228)( 94,227)( 95,226)
( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,220)(102,219)(103,218)
(104,217)(105,216)(106,215)(107,214)(108,213)(109,212)(110,211)(111,210)
(112,209)(113,208)(114,207)(115,206)(116,205)(233,349)(234,377)(235,376)
(236,375)(237,374)(238,373)(239,372)(240,371)(241,370)(242,369)(243,368)
(244,367)(245,366)(246,365)(247,364)(248,363)(249,362)(250,361)(251,360)
(252,359)(253,358)(254,357)(255,356)(256,355)(257,354)(258,353)(259,352)
(260,351)(261,350)(262,378)(263,406)(264,405)(265,404)(266,403)(267,402)
(268,401)(269,400)(270,399)(271,398)(272,397)(273,396)(274,395)(275,394)
(276,393)(277,392)(278,391)(279,390)(280,389)(281,388)(282,387)(283,386)
(284,385)(285,384)(286,383)(287,382)(288,381)(289,380)(290,379)(291,407)
(292,435)(293,434)(294,433)(295,432)(296,431)(297,430)(298,429)(299,428)
(300,427)(301,426)(302,425)(303,424)(304,423)(305,422)(306,421)(307,420)
(308,419)(309,418)(310,417)(311,416)(312,415)(313,414)(314,413)(315,412)
(316,411)(317,410)(318,409)(319,408)(320,436)(321,464)(322,463)(323,462)
(324,461)(325,460)(326,459)(327,458)(328,457)(329,456)(330,455)(331,454)
(332,453)(333,452)(334,451)(335,450)(336,449)(337,448)(338,447)(339,446)
(340,445)(341,444)(342,443)(343,442)(344,441)(345,440)(346,439)(347,438)
(348,437)(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)(697,813)(698,841)(699,840)
(700,839)(701,838)(702,837)(703,836)(704,835)(705,834)(706,833)(707,832)
(708,831)(709,830)(710,829)(711,828)(712,827)(713,826)(714,825)(715,824)
(716,823)(717,822)(718,821)(719,820)(720,819)(721,818)(722,817)(723,816)
(724,815)(725,814)(726,842)(727,870)(728,869)(729,868)(730,867)(731,866)
(732,865)(733,864)(734,863)(735,862)(736,861)(737,860)(738,859)(739,858)
(740,857)(741,856)(742,855)(743,854)(744,853)(745,852)(746,851)(747,850)
(748,849)(749,848)(750,847)(751,846)(752,845)(753,844)(754,843)(755,871)
(756,899)(757,898)(758,897)(759,896)(760,895)(761,894)(762,893)(763,892)
(764,891)(765,890)(766,889)(767,888)(768,887)(769,886)(770,885)(771,884)
(772,883)(773,882)(774,881)(775,880)(776,879)(777,878)(778,877)(779,876)
(780,875)(781,874)(782,873)(783,872)(784,900)(785,928)(786,927)(787,926)
(788,925)(789,924)(790,923)(791,922)(792,921)(793,920)(794,919)(795,918)
(796,917)(797,916)(798,915)(799,914)(800,913)(801,912)(802,911)(803,910)
(804,909)(805,908)(806,907)(807,906)(808,905)(809,904)(810,903)(811,902)
(812,901);
s1 := Sym(928)!( 1,582)( 2,581)( 3,609)( 4,608)( 5,607)( 6,606)( 7,605)
( 8,604)( 9,603)( 10,602)( 11,601)( 12,600)( 13,599)( 14,598)( 15,597)
( 16,596)( 17,595)( 18,594)( 19,593)( 20,592)( 21,591)( 22,590)( 23,589)
( 24,588)( 25,587)( 26,586)( 27,585)( 28,584)( 29,583)( 30,611)( 31,610)
( 32,638)( 33,637)( 34,636)( 35,635)( 36,634)( 37,633)( 38,632)( 39,631)
( 40,630)( 41,629)( 42,628)( 43,627)( 44,626)( 45,625)( 46,624)( 47,623)
( 48,622)( 49,621)( 50,620)( 51,619)( 52,618)( 53,617)( 54,616)( 55,615)
( 56,614)( 57,613)( 58,612)( 59,640)( 60,639)( 61,667)( 62,666)( 63,665)
( 64,664)( 65,663)( 66,662)( 67,661)( 68,660)( 69,659)( 70,658)( 71,657)
( 72,656)( 73,655)( 74,654)( 75,653)( 76,652)( 77,651)( 78,650)( 79,649)
( 80,648)( 81,647)( 82,646)( 83,645)( 84,644)( 85,643)( 86,642)( 87,641)
( 88,669)( 89,668)( 90,696)( 91,695)( 92,694)( 93,693)( 94,692)( 95,691)
( 96,690)( 97,689)( 98,688)( 99,687)(100,686)(101,685)(102,684)(103,683)
(104,682)(105,681)(106,680)(107,679)(108,678)(109,677)(110,676)(111,675)
(112,674)(113,673)(114,672)(115,671)(116,670)(117,466)(118,465)(119,493)
(120,492)(121,491)(122,490)(123,489)(124,488)(125,487)(126,486)(127,485)
(128,484)(129,483)(130,482)(131,481)(132,480)(133,479)(134,478)(135,477)
(136,476)(137,475)(138,474)(139,473)(140,472)(141,471)(142,470)(143,469)
(144,468)(145,467)(146,495)(147,494)(148,522)(149,521)(150,520)(151,519)
(152,518)(153,517)(154,516)(155,515)(156,514)(157,513)(158,512)(159,511)
(160,510)(161,509)(162,508)(163,507)(164,506)(165,505)(166,504)(167,503)
(168,502)(169,501)(170,500)(171,499)(172,498)(173,497)(174,496)(175,524)
(176,523)(177,551)(178,550)(179,549)(180,548)(181,547)(182,546)(183,545)
(184,544)(185,543)(186,542)(187,541)(188,540)(189,539)(190,538)(191,537)
(192,536)(193,535)(194,534)(195,533)(196,532)(197,531)(198,530)(199,529)
(200,528)(201,527)(202,526)(203,525)(204,553)(205,552)(206,580)(207,579)
(208,578)(209,577)(210,576)(211,575)(212,574)(213,573)(214,572)(215,571)
(216,570)(217,569)(218,568)(219,567)(220,566)(221,565)(222,564)(223,563)
(224,562)(225,561)(226,560)(227,559)(228,558)(229,557)(230,556)(231,555)
(232,554)(233,814)(234,813)(235,841)(236,840)(237,839)(238,838)(239,837)
(240,836)(241,835)(242,834)(243,833)(244,832)(245,831)(246,830)(247,829)
(248,828)(249,827)(250,826)(251,825)(252,824)(253,823)(254,822)(255,821)
(256,820)(257,819)(258,818)(259,817)(260,816)(261,815)(262,843)(263,842)
(264,870)(265,869)(266,868)(267,867)(268,866)(269,865)(270,864)(271,863)
(272,862)(273,861)(274,860)(275,859)(276,858)(277,857)(278,856)(279,855)
(280,854)(281,853)(282,852)(283,851)(284,850)(285,849)(286,848)(287,847)
(288,846)(289,845)(290,844)(291,872)(292,871)(293,899)(294,898)(295,897)
(296,896)(297,895)(298,894)(299,893)(300,892)(301,891)(302,890)(303,889)
(304,888)(305,887)(306,886)(307,885)(308,884)(309,883)(310,882)(311,881)
(312,880)(313,879)(314,878)(315,877)(316,876)(317,875)(318,874)(319,873)
(320,901)(321,900)(322,928)(323,927)(324,926)(325,925)(326,924)(327,923)
(328,922)(329,921)(330,920)(331,919)(332,918)(333,917)(334,916)(335,915)
(336,914)(337,913)(338,912)(339,911)(340,910)(341,909)(342,908)(343,907)
(344,906)(345,905)(346,904)(347,903)(348,902)(349,698)(350,697)(351,725)
(352,724)(353,723)(354,722)(355,721)(356,720)(357,719)(358,718)(359,717)
(360,716)(361,715)(362,714)(363,713)(364,712)(365,711)(366,710)(367,709)
(368,708)(369,707)(370,706)(371,705)(372,704)(373,703)(374,702)(375,701)
(376,700)(377,699)(378,727)(379,726)(380,754)(381,753)(382,752)(383,751)
(384,750)(385,749)(386,748)(387,747)(388,746)(389,745)(390,744)(391,743)
(392,742)(393,741)(394,740)(395,739)(396,738)(397,737)(398,736)(399,735)
(400,734)(401,733)(402,732)(403,731)(404,730)(405,729)(406,728)(407,756)
(408,755)(409,783)(410,782)(411,781)(412,780)(413,779)(414,778)(415,777)
(416,776)(417,775)(418,774)(419,773)(420,772)(421,771)(422,770)(423,769)
(424,768)(425,767)(426,766)(427,765)(428,764)(429,763)(430,762)(431,761)
(432,760)(433,759)(434,758)(435,757)(436,785)(437,784)(438,812)(439,811)
(440,810)(441,809)(442,808)(443,807)(444,806)(445,805)(446,804)(447,803)
(448,802)(449,801)(450,800)(451,799)(452,798)(453,797)(454,796)(455,795)
(456,794)(457,793)(458,792)(459,791)(460,790)(461,789)(462,788)(463,787)
(464,786);
s2 := Sym(928)!(233,262)(234,263)(235,264)(236,265)(237,266)(238,267)(239,268)
(240,269)(241,270)(242,271)(243,272)(244,273)(245,274)(246,275)(247,276)
(248,277)(249,278)(250,279)(251,280)(252,281)(253,282)(254,283)(255,284)
(256,285)(257,286)(258,287)(259,288)(260,289)(261,290)(291,320)(292,321)
(293,322)(294,323)(295,324)(296,325)(297,326)(298,327)(299,328)(300,329)
(301,330)(302,331)(303,332)(304,333)(305,334)(306,335)(307,336)(308,337)
(309,338)(310,339)(311,340)(312,341)(313,342)(314,343)(315,344)(316,345)
(317,346)(318,347)(319,348)(349,378)(350,379)(351,380)(352,381)(353,382)
(354,383)(355,384)(356,385)(357,386)(358,387)(359,388)(360,389)(361,390)
(362,391)(363,392)(364,393)(365,394)(366,395)(367,396)(368,397)(369,398)
(370,399)(371,400)(372,401)(373,402)(374,403)(375,404)(376,405)(377,406)
(407,436)(408,437)(409,438)(410,439)(411,440)(412,441)(413,442)(414,443)
(415,444)(416,445)(417,446)(418,447)(419,448)(420,449)(421,450)(422,451)
(423,452)(424,453)(425,454)(426,455)(427,456)(428,457)(429,458)(430,459)
(431,460)(432,461)(433,462)(434,463)(435,464)(465,523)(466,524)(467,525)
(468,526)(469,527)(470,528)(471,529)(472,530)(473,531)(474,532)(475,533)
(476,534)(477,535)(478,536)(479,537)(480,538)(481,539)(482,540)(483,541)
(484,542)(485,543)(486,544)(487,545)(488,546)(489,547)(490,548)(491,549)
(492,550)(493,551)(494,552)(495,553)(496,554)(497,555)(498,556)(499,557)
(500,558)(501,559)(502,560)(503,561)(504,562)(505,563)(506,564)(507,565)
(508,566)(509,567)(510,568)(511,569)(512,570)(513,571)(514,572)(515,573)
(516,574)(517,575)(518,576)(519,577)(520,578)(521,579)(522,580)(581,639)
(582,640)(583,641)(584,642)(585,643)(586,644)(587,645)(588,646)(589,647)
(590,648)(591,649)(592,650)(593,651)(594,652)(595,653)(596,654)(597,655)
(598,656)(599,657)(600,658)(601,659)(602,660)(603,661)(604,662)(605,663)
(606,664)(607,665)(608,666)(609,667)(610,668)(611,669)(612,670)(613,671)
(614,672)(615,673)(616,674)(617,675)(618,676)(619,677)(620,678)(621,679)
(622,680)(623,681)(624,682)(625,683)(626,684)(627,685)(628,686)(629,687)
(630,688)(631,689)(632,690)(633,691)(634,692)(635,693)(636,694)(637,695)
(638,696)(697,784)(698,785)(699,786)(700,787)(701,788)(702,789)(703,790)
(704,791)(705,792)(706,793)(707,794)(708,795)(709,796)(710,797)(711,798)
(712,799)(713,800)(714,801)(715,802)(716,803)(717,804)(718,805)(719,806)
(720,807)(721,808)(722,809)(723,810)(724,811)(725,812)(726,755)(727,756)
(728,757)(729,758)(730,759)(731,760)(732,761)(733,762)(734,763)(735,764)
(736,765)(737,766)(738,767)(739,768)(740,769)(741,770)(742,771)(743,772)
(744,773)(745,774)(746,775)(747,776)(748,777)(749,778)(750,779)(751,780)
(752,781)(753,782)(754,783)(813,900)(814,901)(815,902)(816,903)(817,904)
(818,905)(819,906)(820,907)(821,908)(822,909)(823,910)(824,911)(825,912)
(826,913)(827,914)(828,915)(829,916)(830,917)(831,918)(832,919)(833,920)
(834,921)(835,922)(836,923)(837,924)(838,925)(839,926)(840,927)(841,928)
(842,871)(843,872)(844,873)(845,874)(846,875)(847,876)(848,877)(849,878)
(850,879)(851,880)(852,881)(853,882)(854,883)(855,884)(856,885)(857,886)
(858,887)(859,888)(860,889)(861,890)(862,891)(863,892)(864,893)(865,894)
(866,895)(867,896)(868,897)(869,898)(870,899);
s3 := Sym(928)!( 1,233)( 2,234)( 3,235)( 4,236)( 5,237)( 6,238)( 7,239)
( 8,240)( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)
( 16,248)( 17,249)( 18,250)( 19,251)( 20,252)( 21,253)( 22,254)( 23,255)
( 24,256)( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)
( 32,264)( 33,265)( 34,266)( 35,267)( 36,268)( 37,269)( 38,270)( 39,271)
( 40,272)( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)
( 48,280)( 49,281)( 50,282)( 51,283)( 52,284)( 53,285)( 54,286)( 55,287)
( 56,288)( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)
( 64,296)( 65,297)( 66,298)( 67,299)( 68,300)( 69,301)( 70,302)( 71,303)
( 72,304)( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)
( 80,312)( 81,313)( 82,314)( 83,315)( 84,316)( 85,317)( 86,318)( 87,319)
( 88,320)( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)
( 96,328)( 97,329)( 98,330)( 99,331)(100,332)(101,333)(102,334)(103,335)
(104,336)(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)
(112,344)(113,345)(114,346)(115,347)(116,348)(117,349)(118,350)(119,351)
(120,352)(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)
(128,360)(129,361)(130,362)(131,363)(132,364)(133,365)(134,366)(135,367)
(136,368)(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)
(144,376)(145,377)(146,378)(147,379)(148,380)(149,381)(150,382)(151,383)
(152,384)(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)
(160,392)(161,393)(162,394)(163,395)(164,396)(165,397)(166,398)(167,399)
(168,400)(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)
(176,408)(177,409)(178,410)(179,411)(180,412)(181,413)(182,414)(183,415)
(184,416)(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)
(192,424)(193,425)(194,426)(195,427)(196,428)(197,429)(198,430)(199,431)
(200,432)(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)
(208,440)(209,441)(210,442)(211,443)(212,444)(213,445)(214,446)(215,447)
(216,448)(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)
(224,456)(225,457)(226,458)(227,459)(228,460)(229,461)(230,462)(231,463)
(232,464)(465,697)(466,698)(467,699)(468,700)(469,701)(470,702)(471,703)
(472,704)(473,705)(474,706)(475,707)(476,708)(477,709)(478,710)(479,711)
(480,712)(481,713)(482,714)(483,715)(484,716)(485,717)(486,718)(487,719)
(488,720)(489,721)(490,722)(491,723)(492,724)(493,725)(494,726)(495,727)
(496,728)(497,729)(498,730)(499,731)(500,732)(501,733)(502,734)(503,735)
(504,736)(505,737)(506,738)(507,739)(508,740)(509,741)(510,742)(511,743)
(512,744)(513,745)(514,746)(515,747)(516,748)(517,749)(518,750)(519,751)
(520,752)(521,753)(522,754)(523,755)(524,756)(525,757)(526,758)(527,759)
(528,760)(529,761)(530,762)(531,763)(532,764)(533,765)(534,766)(535,767)
(536,768)(537,769)(538,770)(539,771)(540,772)(541,773)(542,774)(543,775)
(544,776)(545,777)(546,778)(547,779)(548,780)(549,781)(550,782)(551,783)
(552,784)(553,785)(554,786)(555,787)(556,788)(557,789)(558,790)(559,791)
(560,792)(561,793)(562,794)(563,795)(564,796)(565,797)(566,798)(567,799)
(568,800)(569,801)(570,802)(571,803)(572,804)(573,805)(574,806)(575,807)
(576,808)(577,809)(578,810)(579,811)(580,812)(581,813)(582,814)(583,815)
(584,816)(585,817)(586,818)(587,819)(588,820)(589,821)(590,822)(591,823)
(592,824)(593,825)(594,826)(595,827)(596,828)(597,829)(598,830)(599,831)
(600,832)(601,833)(602,834)(603,835)(604,836)(605,837)(606,838)(607,839)
(608,840)(609,841)(610,842)(611,843)(612,844)(613,845)(614,846)(615,847)
(616,848)(617,849)(618,850)(619,851)(620,852)(621,853)(622,854)(623,855)
(624,856)(625,857)(626,858)(627,859)(628,860)(629,861)(630,862)(631,863)
(632,864)(633,865)(634,866)(635,867)(636,868)(637,869)(638,870)(639,871)
(640,872)(641,873)(642,874)(643,875)(644,876)(645,877)(646,878)(647,879)
(648,880)(649,881)(650,882)(651,883)(652,884)(653,885)(654,886)(655,887)
(656,888)(657,889)(658,890)(659,891)(660,892)(661,893)(662,894)(663,895)
(664,896)(665,897)(666,898)(667,899)(668,900)(669,901)(670,902)(671,903)
(672,904)(673,905)(674,906)(675,907)(676,908)(677,909)(678,910)(679,911)
(680,912)(681,913)(682,914)(683,915)(684,916)(685,917)(686,918)(687,919)
(688,920)(689,921)(690,922)(691,923)(692,924)(693,925)(694,926)(695,927)
(696,928);
poly := sub<Sym(928)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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