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Polytope of Type {4,16,14}

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