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Polytope of Type {16,4,14}

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