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Polytope of Type {14,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4,16}*1792a
Also Known As : {{14,4|2},{4,16|2}}. if this polytope has another name.
Group : SmallGroup(1792,323301)
Rank : 4
Schlafli Type : {14,4,16}
Number of vertices, edges, etc : 14, 28, 32, 16
Order of s0s1s2s3 : 112
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 : {14,4,8}*896a, {14,2,16}*896
   4-fold quotients : {7,2,16}*448, {14,4,4}*448, {14,2,8}*448
   7-fold quotients : {2,4,16}*256a
   8-fold quotients : {7,2,8}*224, {14,2,4}*224, {14,4,2}*224
   14-fold quotients : {2,4,8}*128a, {2,2,16}*128
   16-fold quotients : {7,2,4}*112, {14,2,2}*112
   28-fold quotients : {2,4,4}*64, {2,2,8}*64
   32-fold quotients : {7,2,2}*56
   56-fold quotients : {2,2,4}*32, {2,4,2}*32
   112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,113)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)(  8,120)
(  9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)( 16,133)
( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)( 24,139)
( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)( 32,145)
( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)( 40,151)
( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)
( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)
( 57,169)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,176)
( 65,182)( 66,181)( 67,180)( 68,179)( 69,178)( 70,177)( 71,183)( 72,189)
( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,190)( 79,196)( 80,195)
( 81,194)( 82,193)( 83,192)( 84,191)( 85,197)( 86,203)( 87,202)( 88,201)
( 89,200)( 90,199)( 91,198)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)
( 97,206)( 98,205)( 99,211)(100,217)(101,216)(102,215)(103,214)(104,213)
(105,212)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)(112,219)
(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)
(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)(240,357)
(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)(248,363)
(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)(256,369)
(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)(264,375)
(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)
(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)
(281,393)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)(288,400)
(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,407)(296,413)
(297,412)(298,411)(299,410)(300,409)(301,408)(302,414)(303,420)(304,419)
(305,418)(306,417)(307,416)(308,415)(309,421)(310,427)(311,426)(312,425)
(313,424)(314,423)(315,422)(316,428)(317,434)(318,433)(319,432)(320,431)
(321,430)(322,429)(323,435)(324,441)(325,440)(326,439)(327,438)(328,437)
(329,436)(330,442)(331,448)(332,447)(333,446)(334,445)(335,444)(336,443)
(449,561)(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)
(457,574)(458,573)(459,572)(460,571)(461,570)(462,569)(463,575)(464,581)
(465,580)(466,579)(467,578)(468,577)(469,576)(470,582)(471,588)(472,587)
(473,586)(474,585)(475,584)(476,583)(477,589)(478,595)(479,594)(480,593)
(481,592)(482,591)(483,590)(484,596)(485,602)(486,601)(487,600)(488,599)
(489,598)(490,597)(491,603)(492,609)(493,608)(494,607)(495,606)(496,605)
(497,604)(498,610)(499,616)(500,615)(501,614)(502,613)(503,612)(504,611)
(505,617)(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)(512,624)
(513,630)(514,629)(515,628)(516,627)(517,626)(518,625)(519,631)(520,637)
(521,636)(522,635)(523,634)(524,633)(525,632)(526,638)(527,644)(528,643)
(529,642)(530,641)(531,640)(532,639)(533,645)(534,651)(535,650)(536,649)
(537,648)(538,647)(539,646)(540,652)(541,658)(542,657)(543,656)(544,655)
(545,654)(546,653)(547,659)(548,665)(549,664)(550,663)(551,662)(552,661)
(553,660)(554,666)(555,672)(556,671)(557,670)(558,669)(559,668)(560,667)
(673,785)(674,791)(675,790)(676,789)(677,788)(678,787)(679,786)(680,792)
(681,798)(682,797)(683,796)(684,795)(685,794)(686,793)(687,799)(688,805)
(689,804)(690,803)(691,802)(692,801)(693,800)(694,806)(695,812)(696,811)
(697,810)(698,809)(699,808)(700,807)(701,813)(702,819)(703,818)(704,817)
(705,816)(706,815)(707,814)(708,820)(709,826)(710,825)(711,824)(712,823)
(713,822)(714,821)(715,827)(716,833)(717,832)(718,831)(719,830)(720,829)
(721,828)(722,834)(723,840)(724,839)(725,838)(726,837)(727,836)(728,835)
(729,841)(730,847)(731,846)(732,845)(733,844)(734,843)(735,842)(736,848)
(737,854)(738,853)(739,852)(740,851)(741,850)(742,849)(743,855)(744,861)
(745,860)(746,859)(747,858)(748,857)(749,856)(750,862)(751,868)(752,867)
(753,866)(754,865)(755,864)(756,863)(757,869)(758,875)(759,874)(760,873)
(761,872)(762,871)(763,870)(764,876)(765,882)(766,881)(767,880)(768,879)
(769,878)(770,877)(771,883)(772,889)(773,888)(774,887)(775,886)(776,885)
(777,884)(778,890)(779,896)(780,895)(781,894)(782,893)(783,892)(784,891);;
s1 := (  1,338)(  2,337)(  3,343)(  4,342)(  5,341)(  6,340)(  7,339)(  8,345)
(  9,344)( 10,350)( 11,349)( 12,348)( 13,347)( 14,346)( 15,352)( 16,351)
( 17,357)( 18,356)( 19,355)( 20,354)( 21,353)( 22,359)( 23,358)( 24,364)
( 25,363)( 26,362)( 27,361)( 28,360)( 29,366)( 30,365)( 31,371)( 32,370)
( 33,369)( 34,368)( 35,367)( 36,373)( 37,372)( 38,378)( 39,377)( 40,376)
( 41,375)( 42,374)( 43,380)( 44,379)( 45,385)( 46,384)( 47,383)( 48,382)
( 49,381)( 50,387)( 51,386)( 52,392)( 53,391)( 54,390)( 55,389)( 56,388)
( 57,394)( 58,393)( 59,399)( 60,398)( 61,397)( 62,396)( 63,395)( 64,401)
( 65,400)( 66,406)( 67,405)( 68,404)( 69,403)( 70,402)( 71,408)( 72,407)
( 73,413)( 74,412)( 75,411)( 76,410)( 77,409)( 78,415)( 79,414)( 80,420)
( 81,419)( 82,418)( 83,417)( 84,416)( 85,422)( 86,421)( 87,427)( 88,426)
( 89,425)( 90,424)( 91,423)( 92,429)( 93,428)( 94,434)( 95,433)( 96,432)
( 97,431)( 98,430)( 99,436)(100,435)(101,441)(102,440)(103,439)(104,438)
(105,437)(106,443)(107,442)(108,448)(109,447)(110,446)(111,445)(112,444)
(113,226)(114,225)(115,231)(116,230)(117,229)(118,228)(119,227)(120,233)
(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,240)(128,239)
(129,245)(130,244)(131,243)(132,242)(133,241)(134,247)(135,246)(136,252)
(137,251)(138,250)(139,249)(140,248)(141,254)(142,253)(143,259)(144,258)
(145,257)(146,256)(147,255)(148,261)(149,260)(150,266)(151,265)(152,264)
(153,263)(154,262)(155,268)(156,267)(157,273)(158,272)(159,271)(160,270)
(161,269)(162,275)(163,274)(164,280)(165,279)(166,278)(167,277)(168,276)
(169,282)(170,281)(171,287)(172,286)(173,285)(174,284)(175,283)(176,289)
(177,288)(178,294)(179,293)(180,292)(181,291)(182,290)(183,296)(184,295)
(185,301)(186,300)(187,299)(188,298)(189,297)(190,303)(191,302)(192,308)
(193,307)(194,306)(195,305)(196,304)(197,310)(198,309)(199,315)(200,314)
(201,313)(202,312)(203,311)(204,317)(205,316)(206,322)(207,321)(208,320)
(209,319)(210,318)(211,324)(212,323)(213,329)(214,328)(215,327)(216,326)
(217,325)(218,331)(219,330)(220,336)(221,335)(222,334)(223,333)(224,332)
(449,786)(450,785)(451,791)(452,790)(453,789)(454,788)(455,787)(456,793)
(457,792)(458,798)(459,797)(460,796)(461,795)(462,794)(463,800)(464,799)
(465,805)(466,804)(467,803)(468,802)(469,801)(470,807)(471,806)(472,812)
(473,811)(474,810)(475,809)(476,808)(477,814)(478,813)(479,819)(480,818)
(481,817)(482,816)(483,815)(484,821)(485,820)(486,826)(487,825)(488,824)
(489,823)(490,822)(491,828)(492,827)(493,833)(494,832)(495,831)(496,830)
(497,829)(498,835)(499,834)(500,840)(501,839)(502,838)(503,837)(504,836)
(505,842)(506,841)(507,847)(508,846)(509,845)(510,844)(511,843)(512,849)
(513,848)(514,854)(515,853)(516,852)(517,851)(518,850)(519,856)(520,855)
(521,861)(522,860)(523,859)(524,858)(525,857)(526,863)(527,862)(528,868)
(529,867)(530,866)(531,865)(532,864)(533,870)(534,869)(535,875)(536,874)
(537,873)(538,872)(539,871)(540,877)(541,876)(542,882)(543,881)(544,880)
(545,879)(546,878)(547,884)(548,883)(549,889)(550,888)(551,887)(552,886)
(553,885)(554,891)(555,890)(556,896)(557,895)(558,894)(559,893)(560,892)
(561,674)(562,673)(563,679)(564,678)(565,677)(566,676)(567,675)(568,681)
(569,680)(570,686)(571,685)(572,684)(573,683)(574,682)(575,688)(576,687)
(577,693)(578,692)(579,691)(580,690)(581,689)(582,695)(583,694)(584,700)
(585,699)(586,698)(587,697)(588,696)(589,702)(590,701)(591,707)(592,706)
(593,705)(594,704)(595,703)(596,709)(597,708)(598,714)(599,713)(600,712)
(601,711)(602,710)(603,716)(604,715)(605,721)(606,720)(607,719)(608,718)
(609,717)(610,723)(611,722)(612,728)(613,727)(614,726)(615,725)(616,724)
(617,730)(618,729)(619,735)(620,734)(621,733)(622,732)(623,731)(624,737)
(625,736)(626,742)(627,741)(628,740)(629,739)(630,738)(631,744)(632,743)
(633,749)(634,748)(635,747)(636,746)(637,745)(638,751)(639,750)(640,756)
(641,755)(642,754)(643,753)(644,752)(645,758)(646,757)(647,763)(648,762)
(649,761)(650,760)(651,759)(652,765)(653,764)(654,770)(655,769)(656,768)
(657,767)(658,766)(659,772)(660,771)(661,777)(662,776)(663,775)(664,774)
(665,773)(666,779)(667,778)(668,784)(669,783)(670,782)(671,781)(672,780);;
s2 := ( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 50)
( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57, 71)( 58, 72)
( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)
( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 99)( 86,100)( 87,101)( 88,102)
( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)
( 97,111)( 98,112)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)
(133,140)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)
(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)
(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)
(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)
(207,221)(208,222)(209,223)(210,224)(225,253)(226,254)(227,255)(228,256)
(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)
(237,265)(238,266)(239,274)(240,275)(241,276)(242,277)(243,278)(244,279)
(245,280)(246,267)(247,268)(248,269)(249,270)(250,271)(251,272)(252,273)
(281,323)(282,324)(283,325)(284,326)(285,327)(286,328)(287,329)(288,330)
(289,331)(290,332)(291,333)(292,334)(293,335)(294,336)(295,309)(296,310)
(297,311)(298,312)(299,313)(300,314)(301,315)(302,316)(303,317)(304,318)
(305,319)(306,320)(307,321)(308,322)(337,365)(338,366)(339,367)(340,368)
(341,369)(342,370)(343,371)(344,372)(345,373)(346,374)(347,375)(348,376)
(349,377)(350,378)(351,386)(352,387)(353,388)(354,389)(355,390)(356,391)
(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)(364,385)
(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)
(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)(408,422)
(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)
(417,431)(418,432)(419,433)(420,434)(449,505)(450,506)(451,507)(452,508)
(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)(460,516)
(461,517)(462,518)(463,526)(464,527)(465,528)(466,529)(467,530)(468,531)
(469,532)(470,519)(471,520)(472,521)(473,522)(474,523)(475,524)(476,525)
(477,533)(478,534)(479,535)(480,536)(481,537)(482,538)(483,539)(484,540)
(485,541)(486,542)(487,543)(488,544)(489,545)(490,546)(491,554)(492,555)
(493,556)(494,557)(495,558)(496,559)(497,560)(498,547)(499,548)(500,549)
(501,550)(502,551)(503,552)(504,553)(561,617)(562,618)(563,619)(564,620)
(565,621)(566,622)(567,623)(568,624)(569,625)(570,626)(571,627)(572,628)
(573,629)(574,630)(575,638)(576,639)(577,640)(578,641)(579,642)(580,643)
(581,644)(582,631)(583,632)(584,633)(585,634)(586,635)(587,636)(588,637)
(589,645)(590,646)(591,647)(592,648)(593,649)(594,650)(595,651)(596,652)
(597,653)(598,654)(599,655)(600,656)(601,657)(602,658)(603,666)(604,667)
(605,668)(606,669)(607,670)(608,671)(609,672)(610,659)(611,660)(612,661)
(613,662)(614,663)(615,664)(616,665)(673,757)(674,758)(675,759)(676,760)
(677,761)(678,762)(679,763)(680,764)(681,765)(682,766)(683,767)(684,768)
(685,769)(686,770)(687,778)(688,779)(689,780)(690,781)(691,782)(692,783)
(693,784)(694,771)(695,772)(696,773)(697,774)(698,775)(699,776)(700,777)
(701,729)(702,730)(703,731)(704,732)(705,733)(706,734)(707,735)(708,736)
(709,737)(710,738)(711,739)(712,740)(713,741)(714,742)(715,750)(716,751)
(717,752)(718,753)(719,754)(720,755)(721,756)(722,743)(723,744)(724,745)
(725,746)(726,747)(727,748)(728,749)(785,869)(786,870)(787,871)(788,872)
(789,873)(790,874)(791,875)(792,876)(793,877)(794,878)(795,879)(796,880)
(797,881)(798,882)(799,890)(800,891)(801,892)(802,893)(803,894)(804,895)
(805,896)(806,883)(807,884)(808,885)(809,886)(810,887)(811,888)(812,889)
(813,841)(814,842)(815,843)(816,844)(817,845)(818,846)(819,847)(820,848)
(821,849)(822,850)(823,851)(824,852)(825,853)(826,854)(827,862)(828,863)
(829,864)(830,865)(831,866)(832,867)(833,868)(834,855)(835,856)(836,857)
(837,858)(838,859)(839,860)(840,861);;
s3 := (  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)(  8,456)
(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,470)( 16,471)
( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)( 24,465)
( 25,466)( 26,467)( 27,468)( 28,469)( 29,477)( 30,478)( 31,479)( 32,480)
( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)( 40,488)
( 41,489)( 42,490)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)( 48,503)
( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)( 56,497)
( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)( 64,526)
( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)( 72,506)
( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)( 80,514)
( 81,515)( 82,516)( 83,517)( 84,518)( 85,547)( 86,548)( 87,549)( 88,550)
( 89,551)( 90,552)( 91,553)( 92,554)( 93,555)( 94,556)( 95,557)( 96,558)
( 97,559)( 98,560)( 99,533)(100,534)(101,535)(102,536)(103,537)(104,538)
(105,539)(106,540)(107,541)(108,542)(109,543)(110,544)(111,545)(112,546)
(113,561)(114,562)(115,563)(116,564)(117,565)(118,566)(119,567)(120,568)
(121,569)(122,570)(123,571)(124,572)(125,573)(126,574)(127,582)(128,583)
(129,584)(130,585)(131,586)(132,587)(133,588)(134,575)(135,576)(136,577)
(137,578)(138,579)(139,580)(140,581)(141,589)(142,590)(143,591)(144,592)
(145,593)(146,594)(147,595)(148,596)(149,597)(150,598)(151,599)(152,600)
(153,601)(154,602)(155,610)(156,611)(157,612)(158,613)(159,614)(160,615)
(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)(168,609)
(169,631)(170,632)(171,633)(172,634)(173,635)(174,636)(175,637)(176,638)
(177,639)(178,640)(179,641)(180,642)(181,643)(182,644)(183,617)(184,618)
(185,619)(186,620)(187,621)(188,622)(189,623)(190,624)(191,625)(192,626)
(193,627)(194,628)(195,629)(196,630)(197,659)(198,660)(199,661)(200,662)
(201,663)(202,664)(203,665)(204,666)(205,667)(206,668)(207,669)(208,670)
(209,671)(210,672)(211,645)(212,646)(213,647)(214,648)(215,649)(216,650)
(217,651)(218,652)(219,653)(220,654)(221,655)(222,656)(223,657)(224,658)
(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)
(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,694)(240,695)
(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)
(249,690)(250,691)(251,692)(252,693)(253,701)(254,702)(255,703)(256,704)
(257,705)(258,706)(259,707)(260,708)(261,709)(262,710)(263,711)(264,712)
(265,713)(266,714)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)
(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)
(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)(288,750)
(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)(296,730)
(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)(304,738)
(305,739)(306,740)(307,741)(308,742)(309,771)(310,772)(311,773)(312,774)
(313,775)(314,776)(315,777)(316,778)(317,779)(318,780)(319,781)(320,782)
(321,783)(322,784)(323,757)(324,758)(325,759)(326,760)(327,761)(328,762)
(329,763)(330,764)(331,765)(332,766)(333,767)(334,768)(335,769)(336,770)
(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)
(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,806)(352,807)
(353,808)(354,809)(355,810)(356,811)(357,812)(358,799)(359,800)(360,801)
(361,802)(362,803)(363,804)(364,805)(365,813)(366,814)(367,815)(368,816)
(369,817)(370,818)(371,819)(372,820)(373,821)(374,822)(375,823)(376,824)
(377,825)(378,826)(379,834)(380,835)(381,836)(382,837)(383,838)(384,839)
(385,840)(386,827)(387,828)(388,829)(389,830)(390,831)(391,832)(392,833)
(393,855)(394,856)(395,857)(396,858)(397,859)(398,860)(399,861)(400,862)
(401,863)(402,864)(403,865)(404,866)(405,867)(406,868)(407,841)(408,842)
(409,843)(410,844)(411,845)(412,846)(413,847)(414,848)(415,849)(416,850)
(417,851)(418,852)(419,853)(420,854)(421,883)(422,884)(423,885)(424,886)
(425,887)(426,888)(427,889)(428,890)(429,891)(430,892)(431,893)(432,894)
(433,895)(434,896)(435,869)(436,870)(437,871)(438,872)(439,873)(440,874)
(441,875)(442,876)(443,877)(444,878)(445,879)(446,880)(447,881)(448,882);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(896)!(  1,113)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)
(  8,120)(  9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)
( 16,133)( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)
( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)
( 32,145)( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)
( 40,151)( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)
( 48,157)( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)
( 56,163)( 57,169)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)
( 64,176)( 65,182)( 66,181)( 67,180)( 68,179)( 69,178)( 70,177)( 71,183)
( 72,189)( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,190)( 79,196)
( 80,195)( 81,194)( 82,193)( 83,192)( 84,191)( 85,197)( 86,203)( 87,202)
( 88,201)( 89,200)( 90,199)( 91,198)( 92,204)( 93,210)( 94,209)( 95,208)
( 96,207)( 97,206)( 98,205)( 99,211)(100,217)(101,216)(102,215)(103,214)
(104,213)(105,212)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)
(112,219)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)
(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)
(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)
(248,363)(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)
(256,369)(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)
(264,375)(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)
(272,381)(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)
(280,387)(281,393)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)
(288,400)(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,407)
(296,413)(297,412)(298,411)(299,410)(300,409)(301,408)(302,414)(303,420)
(304,419)(305,418)(306,417)(307,416)(308,415)(309,421)(310,427)(311,426)
(312,425)(313,424)(314,423)(315,422)(316,428)(317,434)(318,433)(319,432)
(320,431)(321,430)(322,429)(323,435)(324,441)(325,440)(326,439)(327,438)
(328,437)(329,436)(330,442)(331,448)(332,447)(333,446)(334,445)(335,444)
(336,443)(449,561)(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)
(456,568)(457,574)(458,573)(459,572)(460,571)(461,570)(462,569)(463,575)
(464,581)(465,580)(466,579)(467,578)(468,577)(469,576)(470,582)(471,588)
(472,587)(473,586)(474,585)(475,584)(476,583)(477,589)(478,595)(479,594)
(480,593)(481,592)(482,591)(483,590)(484,596)(485,602)(486,601)(487,600)
(488,599)(489,598)(490,597)(491,603)(492,609)(493,608)(494,607)(495,606)
(496,605)(497,604)(498,610)(499,616)(500,615)(501,614)(502,613)(503,612)
(504,611)(505,617)(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)
(512,624)(513,630)(514,629)(515,628)(516,627)(517,626)(518,625)(519,631)
(520,637)(521,636)(522,635)(523,634)(524,633)(525,632)(526,638)(527,644)
(528,643)(529,642)(530,641)(531,640)(532,639)(533,645)(534,651)(535,650)
(536,649)(537,648)(538,647)(539,646)(540,652)(541,658)(542,657)(543,656)
(544,655)(545,654)(546,653)(547,659)(548,665)(549,664)(550,663)(551,662)
(552,661)(553,660)(554,666)(555,672)(556,671)(557,670)(558,669)(559,668)
(560,667)(673,785)(674,791)(675,790)(676,789)(677,788)(678,787)(679,786)
(680,792)(681,798)(682,797)(683,796)(684,795)(685,794)(686,793)(687,799)
(688,805)(689,804)(690,803)(691,802)(692,801)(693,800)(694,806)(695,812)
(696,811)(697,810)(698,809)(699,808)(700,807)(701,813)(702,819)(703,818)
(704,817)(705,816)(706,815)(707,814)(708,820)(709,826)(710,825)(711,824)
(712,823)(713,822)(714,821)(715,827)(716,833)(717,832)(718,831)(719,830)
(720,829)(721,828)(722,834)(723,840)(724,839)(725,838)(726,837)(727,836)
(728,835)(729,841)(730,847)(731,846)(732,845)(733,844)(734,843)(735,842)
(736,848)(737,854)(738,853)(739,852)(740,851)(741,850)(742,849)(743,855)
(744,861)(745,860)(746,859)(747,858)(748,857)(749,856)(750,862)(751,868)
(752,867)(753,866)(754,865)(755,864)(756,863)(757,869)(758,875)(759,874)
(760,873)(761,872)(762,871)(763,870)(764,876)(765,882)(766,881)(767,880)
(768,879)(769,878)(770,877)(771,883)(772,889)(773,888)(774,887)(775,886)
(776,885)(777,884)(778,890)(779,896)(780,895)(781,894)(782,893)(783,892)
(784,891);
s1 := Sym(896)!(  1,338)(  2,337)(  3,343)(  4,342)(  5,341)(  6,340)(  7,339)
(  8,345)(  9,344)( 10,350)( 11,349)( 12,348)( 13,347)( 14,346)( 15,352)
( 16,351)( 17,357)( 18,356)( 19,355)( 20,354)( 21,353)( 22,359)( 23,358)
( 24,364)( 25,363)( 26,362)( 27,361)( 28,360)( 29,366)( 30,365)( 31,371)
( 32,370)( 33,369)( 34,368)( 35,367)( 36,373)( 37,372)( 38,378)( 39,377)
( 40,376)( 41,375)( 42,374)( 43,380)( 44,379)( 45,385)( 46,384)( 47,383)
( 48,382)( 49,381)( 50,387)( 51,386)( 52,392)( 53,391)( 54,390)( 55,389)
( 56,388)( 57,394)( 58,393)( 59,399)( 60,398)( 61,397)( 62,396)( 63,395)
( 64,401)( 65,400)( 66,406)( 67,405)( 68,404)( 69,403)( 70,402)( 71,408)
( 72,407)( 73,413)( 74,412)( 75,411)( 76,410)( 77,409)( 78,415)( 79,414)
( 80,420)( 81,419)( 82,418)( 83,417)( 84,416)( 85,422)( 86,421)( 87,427)
( 88,426)( 89,425)( 90,424)( 91,423)( 92,429)( 93,428)( 94,434)( 95,433)
( 96,432)( 97,431)( 98,430)( 99,436)(100,435)(101,441)(102,440)(103,439)
(104,438)(105,437)(106,443)(107,442)(108,448)(109,447)(110,446)(111,445)
(112,444)(113,226)(114,225)(115,231)(116,230)(117,229)(118,228)(119,227)
(120,233)(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,240)
(128,239)(129,245)(130,244)(131,243)(132,242)(133,241)(134,247)(135,246)
(136,252)(137,251)(138,250)(139,249)(140,248)(141,254)(142,253)(143,259)
(144,258)(145,257)(146,256)(147,255)(148,261)(149,260)(150,266)(151,265)
(152,264)(153,263)(154,262)(155,268)(156,267)(157,273)(158,272)(159,271)
(160,270)(161,269)(162,275)(163,274)(164,280)(165,279)(166,278)(167,277)
(168,276)(169,282)(170,281)(171,287)(172,286)(173,285)(174,284)(175,283)
(176,289)(177,288)(178,294)(179,293)(180,292)(181,291)(182,290)(183,296)
(184,295)(185,301)(186,300)(187,299)(188,298)(189,297)(190,303)(191,302)
(192,308)(193,307)(194,306)(195,305)(196,304)(197,310)(198,309)(199,315)
(200,314)(201,313)(202,312)(203,311)(204,317)(205,316)(206,322)(207,321)
(208,320)(209,319)(210,318)(211,324)(212,323)(213,329)(214,328)(215,327)
(216,326)(217,325)(218,331)(219,330)(220,336)(221,335)(222,334)(223,333)
(224,332)(449,786)(450,785)(451,791)(452,790)(453,789)(454,788)(455,787)
(456,793)(457,792)(458,798)(459,797)(460,796)(461,795)(462,794)(463,800)
(464,799)(465,805)(466,804)(467,803)(468,802)(469,801)(470,807)(471,806)
(472,812)(473,811)(474,810)(475,809)(476,808)(477,814)(478,813)(479,819)
(480,818)(481,817)(482,816)(483,815)(484,821)(485,820)(486,826)(487,825)
(488,824)(489,823)(490,822)(491,828)(492,827)(493,833)(494,832)(495,831)
(496,830)(497,829)(498,835)(499,834)(500,840)(501,839)(502,838)(503,837)
(504,836)(505,842)(506,841)(507,847)(508,846)(509,845)(510,844)(511,843)
(512,849)(513,848)(514,854)(515,853)(516,852)(517,851)(518,850)(519,856)
(520,855)(521,861)(522,860)(523,859)(524,858)(525,857)(526,863)(527,862)
(528,868)(529,867)(530,866)(531,865)(532,864)(533,870)(534,869)(535,875)
(536,874)(537,873)(538,872)(539,871)(540,877)(541,876)(542,882)(543,881)
(544,880)(545,879)(546,878)(547,884)(548,883)(549,889)(550,888)(551,887)
(552,886)(553,885)(554,891)(555,890)(556,896)(557,895)(558,894)(559,893)
(560,892)(561,674)(562,673)(563,679)(564,678)(565,677)(566,676)(567,675)
(568,681)(569,680)(570,686)(571,685)(572,684)(573,683)(574,682)(575,688)
(576,687)(577,693)(578,692)(579,691)(580,690)(581,689)(582,695)(583,694)
(584,700)(585,699)(586,698)(587,697)(588,696)(589,702)(590,701)(591,707)
(592,706)(593,705)(594,704)(595,703)(596,709)(597,708)(598,714)(599,713)
(600,712)(601,711)(602,710)(603,716)(604,715)(605,721)(606,720)(607,719)
(608,718)(609,717)(610,723)(611,722)(612,728)(613,727)(614,726)(615,725)
(616,724)(617,730)(618,729)(619,735)(620,734)(621,733)(622,732)(623,731)
(624,737)(625,736)(626,742)(627,741)(628,740)(629,739)(630,738)(631,744)
(632,743)(633,749)(634,748)(635,747)(636,746)(637,745)(638,751)(639,750)
(640,756)(641,755)(642,754)(643,753)(644,752)(645,758)(646,757)(647,763)
(648,762)(649,761)(650,760)(651,759)(652,765)(653,764)(654,770)(655,769)
(656,768)(657,767)(658,766)(659,772)(660,771)(661,777)(662,776)(663,775)
(664,774)(665,773)(666,779)(667,778)(668,784)(669,783)(670,782)(671,781)
(672,780);
s2 := Sym(896)!( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)
( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57, 71)
( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)
( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 99)( 86,100)( 87,101)
( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)
( 96,110)( 97,111)( 98,112)(127,134)(128,135)(129,136)(130,137)(131,138)
(132,139)(133,140)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)
(161,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)
(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)
(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)
(206,220)(207,221)(208,222)(209,223)(210,224)(225,253)(226,254)(227,255)
(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)
(236,264)(237,265)(238,266)(239,274)(240,275)(241,276)(242,277)(243,278)
(244,279)(245,280)(246,267)(247,268)(248,269)(249,270)(250,271)(251,272)
(252,273)(281,323)(282,324)(283,325)(284,326)(285,327)(286,328)(287,329)
(288,330)(289,331)(290,332)(291,333)(292,334)(293,335)(294,336)(295,309)
(296,310)(297,311)(298,312)(299,313)(300,314)(301,315)(302,316)(303,317)
(304,318)(305,319)(306,320)(307,321)(308,322)(337,365)(338,366)(339,367)
(340,368)(341,369)(342,370)(343,371)(344,372)(345,373)(346,374)(347,375)
(348,376)(349,377)(350,378)(351,386)(352,387)(353,388)(354,389)(355,390)
(356,391)(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)
(364,385)(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)
(400,442)(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)
(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)
(416,430)(417,431)(418,432)(419,433)(420,434)(449,505)(450,506)(451,507)
(452,508)(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)
(460,516)(461,517)(462,518)(463,526)(464,527)(465,528)(466,529)(467,530)
(468,531)(469,532)(470,519)(471,520)(472,521)(473,522)(474,523)(475,524)
(476,525)(477,533)(478,534)(479,535)(480,536)(481,537)(482,538)(483,539)
(484,540)(485,541)(486,542)(487,543)(488,544)(489,545)(490,546)(491,554)
(492,555)(493,556)(494,557)(495,558)(496,559)(497,560)(498,547)(499,548)
(500,549)(501,550)(502,551)(503,552)(504,553)(561,617)(562,618)(563,619)
(564,620)(565,621)(566,622)(567,623)(568,624)(569,625)(570,626)(571,627)
(572,628)(573,629)(574,630)(575,638)(576,639)(577,640)(578,641)(579,642)
(580,643)(581,644)(582,631)(583,632)(584,633)(585,634)(586,635)(587,636)
(588,637)(589,645)(590,646)(591,647)(592,648)(593,649)(594,650)(595,651)
(596,652)(597,653)(598,654)(599,655)(600,656)(601,657)(602,658)(603,666)
(604,667)(605,668)(606,669)(607,670)(608,671)(609,672)(610,659)(611,660)
(612,661)(613,662)(614,663)(615,664)(616,665)(673,757)(674,758)(675,759)
(676,760)(677,761)(678,762)(679,763)(680,764)(681,765)(682,766)(683,767)
(684,768)(685,769)(686,770)(687,778)(688,779)(689,780)(690,781)(691,782)
(692,783)(693,784)(694,771)(695,772)(696,773)(697,774)(698,775)(699,776)
(700,777)(701,729)(702,730)(703,731)(704,732)(705,733)(706,734)(707,735)
(708,736)(709,737)(710,738)(711,739)(712,740)(713,741)(714,742)(715,750)
(716,751)(717,752)(718,753)(719,754)(720,755)(721,756)(722,743)(723,744)
(724,745)(725,746)(726,747)(727,748)(728,749)(785,869)(786,870)(787,871)
(788,872)(789,873)(790,874)(791,875)(792,876)(793,877)(794,878)(795,879)
(796,880)(797,881)(798,882)(799,890)(800,891)(801,892)(802,893)(803,894)
(804,895)(805,896)(806,883)(807,884)(808,885)(809,886)(810,887)(811,888)
(812,889)(813,841)(814,842)(815,843)(816,844)(817,845)(818,846)(819,847)
(820,848)(821,849)(822,850)(823,851)(824,852)(825,853)(826,854)(827,862)
(828,863)(829,864)(830,865)(831,866)(832,867)(833,868)(834,855)(835,856)
(836,857)(837,858)(838,859)(839,860)(840,861);
s3 := Sym(896)!(  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)
(  8,456)(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,470)
( 16,471)( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)
( 24,465)( 25,466)( 26,467)( 27,468)( 28,469)( 29,477)( 30,478)( 31,479)
( 32,480)( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)
( 40,488)( 41,489)( 42,490)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)
( 48,503)( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)
( 56,497)( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)
( 64,526)( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)
( 72,506)( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)
( 80,514)( 81,515)( 82,516)( 83,517)( 84,518)( 85,547)( 86,548)( 87,549)
( 88,550)( 89,551)( 90,552)( 91,553)( 92,554)( 93,555)( 94,556)( 95,557)
( 96,558)( 97,559)( 98,560)( 99,533)(100,534)(101,535)(102,536)(103,537)
(104,538)(105,539)(106,540)(107,541)(108,542)(109,543)(110,544)(111,545)
(112,546)(113,561)(114,562)(115,563)(116,564)(117,565)(118,566)(119,567)
(120,568)(121,569)(122,570)(123,571)(124,572)(125,573)(126,574)(127,582)
(128,583)(129,584)(130,585)(131,586)(132,587)(133,588)(134,575)(135,576)
(136,577)(137,578)(138,579)(139,580)(140,581)(141,589)(142,590)(143,591)
(144,592)(145,593)(146,594)(147,595)(148,596)(149,597)(150,598)(151,599)
(152,600)(153,601)(154,602)(155,610)(156,611)(157,612)(158,613)(159,614)
(160,615)(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)
(168,609)(169,631)(170,632)(171,633)(172,634)(173,635)(174,636)(175,637)
(176,638)(177,639)(178,640)(179,641)(180,642)(181,643)(182,644)(183,617)
(184,618)(185,619)(186,620)(187,621)(188,622)(189,623)(190,624)(191,625)
(192,626)(193,627)(194,628)(195,629)(196,630)(197,659)(198,660)(199,661)
(200,662)(201,663)(202,664)(203,665)(204,666)(205,667)(206,668)(207,669)
(208,670)(209,671)(210,672)(211,645)(212,646)(213,647)(214,648)(215,649)
(216,650)(217,651)(218,652)(219,653)(220,654)(221,655)(222,656)(223,657)
(224,658)(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)
(232,680)(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,694)
(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)
(248,689)(249,690)(250,691)(251,692)(252,693)(253,701)(254,702)(255,703)
(256,704)(257,705)(258,706)(259,707)(260,708)(261,709)(262,710)(263,711)
(264,712)(265,713)(266,714)(267,722)(268,723)(269,724)(270,725)(271,726)
(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)
(280,721)(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)
(288,750)(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)
(296,730)(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)
(304,738)(305,739)(306,740)(307,741)(308,742)(309,771)(310,772)(311,773)
(312,774)(313,775)(314,776)(315,777)(316,778)(317,779)(318,780)(319,781)
(320,782)(321,783)(322,784)(323,757)(324,758)(325,759)(326,760)(327,761)
(328,762)(329,763)(330,764)(331,765)(332,766)(333,767)(334,768)(335,769)
(336,770)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)
(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,806)
(352,807)(353,808)(354,809)(355,810)(356,811)(357,812)(358,799)(359,800)
(360,801)(361,802)(362,803)(363,804)(364,805)(365,813)(366,814)(367,815)
(368,816)(369,817)(370,818)(371,819)(372,820)(373,821)(374,822)(375,823)
(376,824)(377,825)(378,826)(379,834)(380,835)(381,836)(382,837)(383,838)
(384,839)(385,840)(386,827)(387,828)(388,829)(389,830)(390,831)(391,832)
(392,833)(393,855)(394,856)(395,857)(396,858)(397,859)(398,860)(399,861)
(400,862)(401,863)(402,864)(403,865)(404,866)(405,867)(406,868)(407,841)
(408,842)(409,843)(410,844)(411,845)(412,846)(413,847)(414,848)(415,849)
(416,850)(417,851)(418,852)(419,853)(420,854)(421,883)(422,884)(423,885)
(424,886)(425,887)(426,888)(427,889)(428,890)(429,891)(430,892)(431,893)
(432,894)(433,895)(434,896)(435,869)(436,870)(437,871)(438,872)(439,873)
(440,874)(441,875)(442,876)(443,877)(444,878)(445,879)(446,880)(447,881)
(448,882);
poly := sub<Sym(896)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope