Questions?
See the FAQ
or other info.

Polytope of Type {28,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,4,8}*1792a
Also Known As : {{28,4|2},{4,8|2}}. if this polytope has another name.
Group : SmallGroup(1792,200564)
Rank : 4
Schlafli Type : {28,4,8}
Number of vertices, edges, etc : 28, 56, 16, 8
Order of s0s1s2s3 : 56
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 : {28,4,4}*896, {28,2,8}*896, {14,4,8}*896a
   4-fold quotients : {28,4,2}*448, {28,2,4}*448, {14,4,4}*448, {14,2,8}*448
   7-fold quotients : {4,4,8}*256a
   8-fold quotients : {7,2,8}*224, {28,2,2}*224, {14,2,4}*224, {14,4,2}*224
   14-fold quotients : {4,4,4}*128, {2,4,8}*128a, {4,2,8}*128
   16-fold quotients : {7,2,4}*112, {14,2,2}*112
   28-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,2,8}*64
   32-fold quotients : {7,2,2}*56
   56-fold quotients : {2,2,4}*32, {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 := (  1,561)(  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)( 15,575)( 16,581)
( 17,580)( 18,579)( 19,578)( 20,577)( 21,576)( 22,582)( 23,588)( 24,587)
( 25,586)( 26,585)( 27,584)( 28,583)( 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)( 43,603)( 44,609)( 45,608)( 46,607)( 47,606)( 48,605)
( 49,604)( 50,610)( 51,616)( 52,615)( 53,614)( 54,613)( 55,612)( 56,611)
( 57,617)( 58,623)( 59,622)( 60,621)( 61,620)( 62,619)( 63,618)( 64,624)
( 65,630)( 66,629)( 67,628)( 68,627)( 69,626)( 70,625)( 71,631)( 72,637)
( 73,636)( 74,635)( 75,634)( 76,633)( 77,632)( 78,638)( 79,644)( 80,643)
( 81,642)( 82,641)( 83,640)( 84,639)( 85,645)( 86,651)( 87,650)( 88,649)
( 89,648)( 90,647)( 91,646)( 92,652)( 93,658)( 94,657)( 95,656)( 96,655)
( 97,654)( 98,653)( 99,659)(100,665)(101,664)(102,663)(103,662)(104,661)
(105,660)(106,666)(107,672)(108,671)(109,670)(110,669)(111,668)(112,667)
(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)(127,463)(128,469)
(129,468)(130,467)(131,466)(132,465)(133,464)(134,470)(135,476)(136,475)
(137,474)(138,473)(139,472)(140,471)(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)(155,491)(156,497)(157,496)(158,495)(159,494)(160,493)
(161,492)(162,498)(163,504)(164,503)(165,502)(166,501)(167,500)(168,499)
(169,505)(170,511)(171,510)(172,509)(173,508)(174,507)(175,506)(176,512)
(177,518)(178,517)(179,516)(180,515)(181,514)(182,513)(183,519)(184,525)
(185,524)(186,523)(187,522)(188,521)(189,520)(190,526)(191,532)(192,531)
(193,530)(194,529)(195,528)(196,527)(197,533)(198,539)(199,538)(200,537)
(201,536)(202,535)(203,534)(204,540)(205,546)(206,545)(207,544)(208,543)
(209,542)(210,541)(211,547)(212,553)(213,552)(214,551)(215,550)(216,549)
(217,548)(218,554)(219,560)(220,559)(221,558)(222,557)(223,556)(224,555)
(225,799)(226,805)(227,804)(228,803)(229,802)(230,801)(231,800)(232,806)
(233,812)(234,811)(235,810)(236,809)(237,808)(238,807)(239,785)(240,791)
(241,790)(242,789)(243,788)(244,787)(245,786)(246,792)(247,798)(248,797)
(249,796)(250,795)(251,794)(252,793)(253,827)(254,833)(255,832)(256,831)
(257,830)(258,829)(259,828)(260,834)(261,840)(262,839)(263,838)(264,837)
(265,836)(266,835)(267,813)(268,819)(269,818)(270,817)(271,816)(272,815)
(273,814)(274,820)(275,826)(276,825)(277,824)(278,823)(279,822)(280,821)
(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)
(337,687)(338,693)(339,692)(340,691)(341,690)(342,689)(343,688)(344,694)
(345,700)(346,699)(347,698)(348,697)(349,696)(350,695)(351,673)(352,679)
(353,678)(354,677)(355,676)(356,675)(357,674)(358,680)(359,686)(360,685)
(361,684)(362,683)(363,682)(364,681)(365,715)(366,721)(367,720)(368,719)
(369,718)(370,717)(371,716)(372,722)(373,728)(374,727)(375,726)(376,725)
(377,724)(378,723)(379,701)(380,707)(381,706)(382,705)(383,704)(384,703)
(385,702)(386,708)(387,714)(388,713)(389,712)(390,711)(391,710)(392,709)
(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);;
s1 := (  1,226)(  2,225)(  3,231)(  4,230)(  5,229)(  6,228)(  7,227)(  8,233)
(  9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)( 24,252)
( 25,251)( 26,250)( 27,249)( 28,248)( 29,254)( 30,253)( 31,259)( 32,258)
( 33,257)( 34,256)( 35,255)( 36,261)( 37,260)( 38,266)( 39,265)( 40,264)
( 41,263)( 42,262)( 43,268)( 44,267)( 45,273)( 46,272)( 47,271)( 48,270)
( 49,269)( 50,275)( 51,274)( 52,280)( 53,279)( 54,278)( 55,277)( 56,276)
( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)( 64,289)
( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,296)( 72,295)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)( 80,308)
( 81,307)( 82,306)( 83,305)( 84,304)( 85,310)( 86,309)( 87,315)( 88,314)
( 89,313)( 90,312)( 91,311)( 92,317)( 93,316)( 94,322)( 95,321)( 96,320)
( 97,319)( 98,318)( 99,324)(100,323)(101,329)(102,328)(103,327)(104,326)
(105,325)(106,331)(107,330)(108,336)(109,335)(110,334)(111,333)(112,332)
(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)(120,345)
(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)(128,351)
(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)(136,364)
(137,363)(138,362)(139,361)(140,360)(141,366)(142,365)(143,371)(144,370)
(145,369)(146,368)(147,367)(148,373)(149,372)(150,378)(151,377)(152,376)
(153,375)(154,374)(155,380)(156,379)(157,385)(158,384)(159,383)(160,382)
(161,381)(162,387)(163,386)(164,392)(165,391)(166,390)(167,389)(168,388)
(169,394)(170,393)(171,399)(172,398)(173,397)(174,396)(175,395)(176,401)
(177,400)(178,406)(179,405)(180,404)(181,403)(182,402)(183,408)(184,407)
(185,413)(186,412)(187,411)(188,410)(189,409)(190,415)(191,414)(192,420)
(193,419)(194,418)(195,417)(196,416)(197,422)(198,421)(199,427)(200,426)
(201,425)(202,424)(203,423)(204,429)(205,428)(206,434)(207,433)(208,432)
(209,431)(210,430)(211,436)(212,435)(213,441)(214,440)(215,439)(216,438)
(217,437)(218,443)(219,442)(220,448)(221,447)(222,446)(223,445)(224,444)
(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)(456,681)
(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,688)(464,687)
(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)(472,700)
(473,699)(474,698)(475,697)(476,696)(477,702)(478,701)(479,707)(480,706)
(481,705)(482,704)(483,703)(484,709)(485,708)(486,714)(487,713)(488,712)
(489,711)(490,710)(491,716)(492,715)(493,721)(494,720)(495,719)(496,718)
(497,717)(498,723)(499,722)(500,728)(501,727)(502,726)(503,725)(504,724)
(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)(512,737)
(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(519,744)(520,743)
(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)(528,756)
(529,755)(530,754)(531,753)(532,752)(533,758)(534,757)(535,763)(536,762)
(537,761)(538,760)(539,759)(540,765)(541,764)(542,770)(543,769)(544,768)
(545,767)(546,766)(547,772)(548,771)(549,777)(550,776)(551,775)(552,774)
(553,773)(554,779)(555,778)(556,784)(557,783)(558,782)(559,781)(560,780)
(561,786)(562,785)(563,791)(564,790)(565,789)(566,788)(567,787)(568,793)
(569,792)(570,798)(571,797)(572,796)(573,795)(574,794)(575,800)(576,799)
(577,805)(578,804)(579,803)(580,802)(581,801)(582,807)(583,806)(584,812)
(585,811)(586,810)(587,809)(588,808)(589,814)(590,813)(591,819)(592,818)
(593,817)(594,816)(595,815)(596,821)(597,820)(598,826)(599,825)(600,824)
(601,823)(602,822)(603,828)(604,827)(605,833)(606,832)(607,831)(608,830)
(609,829)(610,835)(611,834)(612,840)(613,839)(614,838)(615,837)(616,836)
(617,842)(618,841)(619,847)(620,846)(621,845)(622,844)(623,843)(624,849)
(625,848)(626,854)(627,853)(628,852)(629,851)(630,850)(631,856)(632,855)
(633,861)(634,860)(635,859)(636,858)(637,857)(638,863)(639,862)(640,868)
(641,867)(642,866)(643,865)(644,864)(645,870)(646,869)(647,875)(648,874)
(649,873)(650,872)(651,871)(652,877)(653,876)(654,882)(655,881)(656,880)
(657,879)(658,878)(659,884)(660,883)(661,889)(662,888)(663,887)(664,886)
(665,885)(666,891)(667,890)(668,896)(669,895)(670,894)(671,893)(672,892);;
s2 := ( 57, 64)( 58, 65)( 59, 66)( 60, 67)( 61, 68)( 62, 69)( 63, 70)( 71, 78)
( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 85, 92)( 86, 93)
( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 99,106)(100,107)(101,108)
(102,109)(103,110)(104,111)(105,112)(113,169)(114,170)(115,171)(116,172)
(117,173)(118,174)(119,175)(120,176)(121,177)(122,178)(123,179)(124,180)
(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)(131,187)(132,188)
(133,189)(134,190)(135,191)(136,192)(137,193)(138,194)(139,195)(140,196)
(141,197)(142,198)(143,199)(144,200)(145,201)(146,202)(147,203)(148,204)
(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)(155,211)(156,212)
(157,213)(158,214)(159,215)(160,216)(161,217)(162,218)(163,219)(164,220)
(165,221)(166,222)(167,223)(168,224)(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)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)
(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)
(281,316)(282,317)(283,318)(284,319)(285,320)(286,321)(287,322)(288,309)
(289,310)(290,311)(291,312)(292,313)(293,314)(294,315)(295,330)(296,331)
(297,332)(298,333)(299,334)(300,335)(301,336)(302,323)(303,324)(304,325)
(305,326)(306,327)(307,328)(308,329)(337,421)(338,422)(339,423)(340,424)
(341,425)(342,426)(343,427)(344,428)(345,429)(346,430)(347,431)(348,432)
(349,433)(350,434)(351,435)(352,436)(353,437)(354,438)(355,439)(356,440)
(357,441)(358,442)(359,443)(360,444)(361,445)(362,446)(363,447)(364,448)
(365,393)(366,394)(367,395)(368,396)(369,397)(370,398)(371,399)(372,400)
(373,401)(374,402)(375,403)(376,404)(377,405)(378,406)(379,407)(380,408)
(381,409)(382,410)(383,411)(384,412)(385,413)(386,414)(387,415)(388,416)
(389,417)(390,418)(391,419)(392,420)(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)(463,519)(464,520)(465,521)(466,522)(467,523)(468,524)
(469,525)(470,526)(471,527)(472,528)(473,529)(474,530)(475,531)(476,532)
(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)(491,547)(492,548)
(493,549)(494,550)(495,551)(496,552)(497,553)(498,554)(499,555)(500,556)
(501,557)(502,558)(503,559)(504,560)(617,624)(618,625)(619,626)(620,627)
(621,628)(622,629)(623,630)(631,638)(632,639)(633,640)(634,641)(635,642)
(636,643)(637,644)(645,652)(646,653)(647,654)(648,655)(649,656)(650,657)
(651,658)(659,666)(660,667)(661,668)(662,669)(663,670)(664,671)(665,672)
(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)(687,771)(688,772)
(689,773)(690,774)(691,775)(692,776)(693,777)(694,778)(695,779)(696,780)
(697,781)(698,782)(699,783)(700,784)(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)(715,743)(716,744)(717,745)(718,746)(719,747)(720,748)
(721,749)(722,750)(723,751)(724,752)(725,753)(726,754)(727,755)(728,756)
(785,813)(786,814)(787,815)(788,816)(789,817)(790,818)(791,819)(792,820)
(793,821)(794,822)(795,823)(796,824)(797,825)(798,826)(799,827)(800,828)
(801,829)(802,830)(803,831)(804,832)(805,833)(806,834)(807,835)(808,836)
(809,837)(810,838)(811,839)(812,840)(841,876)(842,877)(843,878)(844,879)
(845,880)(846,881)(847,882)(848,869)(849,870)(850,871)(851,872)(852,873)
(853,874)(854,875)(855,890)(856,891)(857,892)(858,893)(859,894)(860,895)
(861,896)(862,883)(863,884)(864,885)(865,886)(866,887)(867,888)(868,889);;
s3 := (  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)(  8,120)
(  9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)
( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)
( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)( 32,144)
( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)
( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)
( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)
( 57,176)( 58,177)( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)( 64,169)
( 65,170)( 66,171)( 67,172)( 68,173)( 69,174)( 70,175)( 71,190)( 72,191)
( 73,192)( 74,193)( 75,194)( 76,195)( 77,196)( 78,183)( 79,184)( 80,185)
( 81,186)( 82,187)( 83,188)( 84,189)( 85,204)( 86,205)( 87,206)( 88,207)
( 89,208)( 90,209)( 91,210)( 92,197)( 93,198)( 94,199)( 95,200)( 96,201)
( 97,202)( 98,203)( 99,218)(100,219)(101,220)(102,221)(103,222)(104,223)
(105,224)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)
(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)
(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)
(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)
(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)
(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)
(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)
(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)
(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)(288,393)
(289,394)(290,395)(291,396)(292,397)(293,398)(294,399)(295,414)(296,415)
(297,416)(298,417)(299,418)(300,419)(301,420)(302,407)(303,408)(304,409)
(305,410)(306,411)(307,412)(308,413)(309,428)(310,429)(311,430)(312,431)
(313,432)(314,433)(315,434)(316,421)(317,422)(318,423)(319,424)(320,425)
(321,426)(322,427)(323,442)(324,443)(325,444)(326,445)(327,446)(328,447)
(329,448)(330,435)(331,436)(332,437)(333,438)(334,439)(335,440)(336,441)
(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)(455,567)(456,568)
(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)(463,575)(464,576)
(465,577)(466,578)(467,579)(468,580)(469,581)(470,582)(471,583)(472,584)
(473,585)(474,586)(475,587)(476,588)(477,589)(478,590)(479,591)(480,592)
(481,593)(482,594)(483,595)(484,596)(485,597)(486,598)(487,599)(488,600)
(489,601)(490,602)(491,603)(492,604)(493,605)(494,606)(495,607)(496,608)
(497,609)(498,610)(499,611)(500,612)(501,613)(502,614)(503,615)(504,616)
(505,624)(506,625)(507,626)(508,627)(509,628)(510,629)(511,630)(512,617)
(513,618)(514,619)(515,620)(516,621)(517,622)(518,623)(519,638)(520,639)
(521,640)(522,641)(523,642)(524,643)(525,644)(526,631)(527,632)(528,633)
(529,634)(530,635)(531,636)(532,637)(533,652)(534,653)(535,654)(536,655)
(537,656)(538,657)(539,658)(540,645)(541,646)(542,647)(543,648)(544,649)
(545,650)(546,651)(547,666)(548,667)(549,668)(550,669)(551,670)(552,671)
(553,672)(554,659)(555,660)(556,661)(557,662)(558,663)(559,664)(560,665)
(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)(679,791)(680,792)
(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)(687,799)(688,800)
(689,801)(690,802)(691,803)(692,804)(693,805)(694,806)(695,807)(696,808)
(697,809)(698,810)(699,811)(700,812)(701,813)(702,814)(703,815)(704,816)
(705,817)(706,818)(707,819)(708,820)(709,821)(710,822)(711,823)(712,824)
(713,825)(714,826)(715,827)(716,828)(717,829)(718,830)(719,831)(720,832)
(721,833)(722,834)(723,835)(724,836)(725,837)(726,838)(727,839)(728,840)
(729,848)(730,849)(731,850)(732,851)(733,852)(734,853)(735,854)(736,841)
(737,842)(738,843)(739,844)(740,845)(741,846)(742,847)(743,862)(744,863)
(745,864)(746,865)(747,866)(748,867)(749,868)(750,855)(751,856)(752,857)
(753,858)(754,859)(755,860)(756,861)(757,876)(758,877)(759,878)(760,879)
(761,880)(762,881)(763,882)(764,869)(765,870)(766,871)(767,872)(768,873)
(769,874)(770,875)(771,890)(772,891)(773,892)(774,893)(775,894)(776,895)
(777,896)(778,883)(779,884)(780,885)(781,886)(782,887)(783,888)(784,889);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!(  1,561)(  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)( 15,575)
( 16,581)( 17,580)( 18,579)( 19,578)( 20,577)( 21,576)( 22,582)( 23,588)
( 24,587)( 25,586)( 26,585)( 27,584)( 28,583)( 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)( 43,603)( 44,609)( 45,608)( 46,607)( 47,606)
( 48,605)( 49,604)( 50,610)( 51,616)( 52,615)( 53,614)( 54,613)( 55,612)
( 56,611)( 57,617)( 58,623)( 59,622)( 60,621)( 61,620)( 62,619)( 63,618)
( 64,624)( 65,630)( 66,629)( 67,628)( 68,627)( 69,626)( 70,625)( 71,631)
( 72,637)( 73,636)( 74,635)( 75,634)( 76,633)( 77,632)( 78,638)( 79,644)
( 80,643)( 81,642)( 82,641)( 83,640)( 84,639)( 85,645)( 86,651)( 87,650)
( 88,649)( 89,648)( 90,647)( 91,646)( 92,652)( 93,658)( 94,657)( 95,656)
( 96,655)( 97,654)( 98,653)( 99,659)(100,665)(101,664)(102,663)(103,662)
(104,661)(105,660)(106,666)(107,672)(108,671)(109,670)(110,669)(111,668)
(112,667)(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)(127,463)
(128,469)(129,468)(130,467)(131,466)(132,465)(133,464)(134,470)(135,476)
(136,475)(137,474)(138,473)(139,472)(140,471)(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)(155,491)(156,497)(157,496)(158,495)(159,494)
(160,493)(161,492)(162,498)(163,504)(164,503)(165,502)(166,501)(167,500)
(168,499)(169,505)(170,511)(171,510)(172,509)(173,508)(174,507)(175,506)
(176,512)(177,518)(178,517)(179,516)(180,515)(181,514)(182,513)(183,519)
(184,525)(185,524)(186,523)(187,522)(188,521)(189,520)(190,526)(191,532)
(192,531)(193,530)(194,529)(195,528)(196,527)(197,533)(198,539)(199,538)
(200,537)(201,536)(202,535)(203,534)(204,540)(205,546)(206,545)(207,544)
(208,543)(209,542)(210,541)(211,547)(212,553)(213,552)(214,551)(215,550)
(216,549)(217,548)(218,554)(219,560)(220,559)(221,558)(222,557)(223,556)
(224,555)(225,799)(226,805)(227,804)(228,803)(229,802)(230,801)(231,800)
(232,806)(233,812)(234,811)(235,810)(236,809)(237,808)(238,807)(239,785)
(240,791)(241,790)(242,789)(243,788)(244,787)(245,786)(246,792)(247,798)
(248,797)(249,796)(250,795)(251,794)(252,793)(253,827)(254,833)(255,832)
(256,831)(257,830)(258,829)(259,828)(260,834)(261,840)(262,839)(263,838)
(264,837)(265,836)(266,835)(267,813)(268,819)(269,818)(270,817)(271,816)
(272,815)(273,814)(274,820)(275,826)(276,825)(277,824)(278,823)(279,822)
(280,821)(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)(337,687)(338,693)(339,692)(340,691)(341,690)(342,689)(343,688)
(344,694)(345,700)(346,699)(347,698)(348,697)(349,696)(350,695)(351,673)
(352,679)(353,678)(354,677)(355,676)(356,675)(357,674)(358,680)(359,686)
(360,685)(361,684)(362,683)(363,682)(364,681)(365,715)(366,721)(367,720)
(368,719)(369,718)(370,717)(371,716)(372,722)(373,728)(374,727)(375,726)
(376,725)(377,724)(378,723)(379,701)(380,707)(381,706)(382,705)(383,704)
(384,703)(385,702)(386,708)(387,714)(388,713)(389,712)(390,711)(391,710)
(392,709)(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);
s1 := Sym(896)!(  1,226)(  2,225)(  3,231)(  4,230)(  5,229)(  6,228)(  7,227)
(  8,233)(  9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)
( 16,239)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)
( 24,252)( 25,251)( 26,250)( 27,249)( 28,248)( 29,254)( 30,253)( 31,259)
( 32,258)( 33,257)( 34,256)( 35,255)( 36,261)( 37,260)( 38,266)( 39,265)
( 40,264)( 41,263)( 42,262)( 43,268)( 44,267)( 45,273)( 46,272)( 47,271)
( 48,270)( 49,269)( 50,275)( 51,274)( 52,280)( 53,279)( 54,278)( 55,277)
( 56,276)( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)
( 64,289)( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,296)
( 72,295)( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)
( 80,308)( 81,307)( 82,306)( 83,305)( 84,304)( 85,310)( 86,309)( 87,315)
( 88,314)( 89,313)( 90,312)( 91,311)( 92,317)( 93,316)( 94,322)( 95,321)
( 96,320)( 97,319)( 98,318)( 99,324)(100,323)(101,329)(102,328)(103,327)
(104,326)(105,325)(106,331)(107,330)(108,336)(109,335)(110,334)(111,333)
(112,332)(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)
(120,345)(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)
(128,351)(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)
(136,364)(137,363)(138,362)(139,361)(140,360)(141,366)(142,365)(143,371)
(144,370)(145,369)(146,368)(147,367)(148,373)(149,372)(150,378)(151,377)
(152,376)(153,375)(154,374)(155,380)(156,379)(157,385)(158,384)(159,383)
(160,382)(161,381)(162,387)(163,386)(164,392)(165,391)(166,390)(167,389)
(168,388)(169,394)(170,393)(171,399)(172,398)(173,397)(174,396)(175,395)
(176,401)(177,400)(178,406)(179,405)(180,404)(181,403)(182,402)(183,408)
(184,407)(185,413)(186,412)(187,411)(188,410)(189,409)(190,415)(191,414)
(192,420)(193,419)(194,418)(195,417)(196,416)(197,422)(198,421)(199,427)
(200,426)(201,425)(202,424)(203,423)(204,429)(205,428)(206,434)(207,433)
(208,432)(209,431)(210,430)(211,436)(212,435)(213,441)(214,440)(215,439)
(216,438)(217,437)(218,443)(219,442)(220,448)(221,447)(222,446)(223,445)
(224,444)(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)
(456,681)(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,688)
(464,687)(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)
(472,700)(473,699)(474,698)(475,697)(476,696)(477,702)(478,701)(479,707)
(480,706)(481,705)(482,704)(483,703)(484,709)(485,708)(486,714)(487,713)
(488,712)(489,711)(490,710)(491,716)(492,715)(493,721)(494,720)(495,719)
(496,718)(497,717)(498,723)(499,722)(500,728)(501,727)(502,726)(503,725)
(504,724)(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)
(512,737)(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(519,744)
(520,743)(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)
(528,756)(529,755)(530,754)(531,753)(532,752)(533,758)(534,757)(535,763)
(536,762)(537,761)(538,760)(539,759)(540,765)(541,764)(542,770)(543,769)
(544,768)(545,767)(546,766)(547,772)(548,771)(549,777)(550,776)(551,775)
(552,774)(553,773)(554,779)(555,778)(556,784)(557,783)(558,782)(559,781)
(560,780)(561,786)(562,785)(563,791)(564,790)(565,789)(566,788)(567,787)
(568,793)(569,792)(570,798)(571,797)(572,796)(573,795)(574,794)(575,800)
(576,799)(577,805)(578,804)(579,803)(580,802)(581,801)(582,807)(583,806)
(584,812)(585,811)(586,810)(587,809)(588,808)(589,814)(590,813)(591,819)
(592,818)(593,817)(594,816)(595,815)(596,821)(597,820)(598,826)(599,825)
(600,824)(601,823)(602,822)(603,828)(604,827)(605,833)(606,832)(607,831)
(608,830)(609,829)(610,835)(611,834)(612,840)(613,839)(614,838)(615,837)
(616,836)(617,842)(618,841)(619,847)(620,846)(621,845)(622,844)(623,843)
(624,849)(625,848)(626,854)(627,853)(628,852)(629,851)(630,850)(631,856)
(632,855)(633,861)(634,860)(635,859)(636,858)(637,857)(638,863)(639,862)
(640,868)(641,867)(642,866)(643,865)(644,864)(645,870)(646,869)(647,875)
(648,874)(649,873)(650,872)(651,871)(652,877)(653,876)(654,882)(655,881)
(656,880)(657,879)(658,878)(659,884)(660,883)(661,889)(662,888)(663,887)
(664,886)(665,885)(666,891)(667,890)(668,896)(669,895)(670,894)(671,893)
(672,892);
s2 := Sym(896)!( 57, 64)( 58, 65)( 59, 66)( 60, 67)( 61, 68)( 62, 69)( 63, 70)
( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 85, 92)
( 86, 93)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 99,106)(100,107)
(101,108)(102,109)(103,110)(104,111)(105,112)(113,169)(114,170)(115,171)
(116,172)(117,173)(118,174)(119,175)(120,176)(121,177)(122,178)(123,179)
(124,180)(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)(131,187)
(132,188)(133,189)(134,190)(135,191)(136,192)(137,193)(138,194)(139,195)
(140,196)(141,197)(142,198)(143,199)(144,200)(145,201)(146,202)(147,203)
(148,204)(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)(155,211)
(156,212)(157,213)(158,214)(159,215)(160,216)(161,217)(162,218)(163,219)
(164,220)(165,221)(166,222)(167,223)(168,224)(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)(239,267)(240,268)(241,269)(242,270)(243,271)
(244,272)(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)
(252,280)(281,316)(282,317)(283,318)(284,319)(285,320)(286,321)(287,322)
(288,309)(289,310)(290,311)(291,312)(292,313)(293,314)(294,315)(295,330)
(296,331)(297,332)(298,333)(299,334)(300,335)(301,336)(302,323)(303,324)
(304,325)(305,326)(306,327)(307,328)(308,329)(337,421)(338,422)(339,423)
(340,424)(341,425)(342,426)(343,427)(344,428)(345,429)(346,430)(347,431)
(348,432)(349,433)(350,434)(351,435)(352,436)(353,437)(354,438)(355,439)
(356,440)(357,441)(358,442)(359,443)(360,444)(361,445)(362,446)(363,447)
(364,448)(365,393)(366,394)(367,395)(368,396)(369,397)(370,398)(371,399)
(372,400)(373,401)(374,402)(375,403)(376,404)(377,405)(378,406)(379,407)
(380,408)(381,409)(382,410)(383,411)(384,412)(385,413)(386,414)(387,415)
(388,416)(389,417)(390,418)(391,419)(392,420)(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)(463,519)(464,520)(465,521)(466,522)(467,523)
(468,524)(469,525)(470,526)(471,527)(472,528)(473,529)(474,530)(475,531)
(476,532)(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)(491,547)
(492,548)(493,549)(494,550)(495,551)(496,552)(497,553)(498,554)(499,555)
(500,556)(501,557)(502,558)(503,559)(504,560)(617,624)(618,625)(619,626)
(620,627)(621,628)(622,629)(623,630)(631,638)(632,639)(633,640)(634,641)
(635,642)(636,643)(637,644)(645,652)(646,653)(647,654)(648,655)(649,656)
(650,657)(651,658)(659,666)(660,667)(661,668)(662,669)(663,670)(664,671)
(665,672)(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)(687,771)
(688,772)(689,773)(690,774)(691,775)(692,776)(693,777)(694,778)(695,779)
(696,780)(697,781)(698,782)(699,783)(700,784)(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)(715,743)(716,744)(717,745)(718,746)(719,747)
(720,748)(721,749)(722,750)(723,751)(724,752)(725,753)(726,754)(727,755)
(728,756)(785,813)(786,814)(787,815)(788,816)(789,817)(790,818)(791,819)
(792,820)(793,821)(794,822)(795,823)(796,824)(797,825)(798,826)(799,827)
(800,828)(801,829)(802,830)(803,831)(804,832)(805,833)(806,834)(807,835)
(808,836)(809,837)(810,838)(811,839)(812,840)(841,876)(842,877)(843,878)
(844,879)(845,880)(846,881)(847,882)(848,869)(849,870)(850,871)(851,872)
(852,873)(853,874)(854,875)(855,890)(856,891)(857,892)(858,893)(859,894)
(860,895)(861,896)(862,883)(863,884)(864,885)(865,886)(866,887)(867,888)
(868,889);
s3 := Sym(896)!(  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)
(  8,120)(  9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)
( 16,128)( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)
( 24,136)( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)
( 32,144)( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)
( 40,152)( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)
( 48,160)( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)
( 56,168)( 57,176)( 58,177)( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)
( 64,169)( 65,170)( 66,171)( 67,172)( 68,173)( 69,174)( 70,175)( 71,190)
( 72,191)( 73,192)( 74,193)( 75,194)( 76,195)( 77,196)( 78,183)( 79,184)
( 80,185)( 81,186)( 82,187)( 83,188)( 84,189)( 85,204)( 86,205)( 87,206)
( 88,207)( 89,208)( 90,209)( 91,210)( 92,197)( 93,198)( 94,199)( 95,200)
( 96,201)( 97,202)( 98,203)( 99,218)(100,219)(101,220)(102,221)(103,222)
(104,223)(105,224)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)
(112,217)(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)
(232,344)(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)
(240,352)(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)
(248,360)(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)
(256,368)(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)
(264,376)(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)
(272,384)(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)
(280,392)(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)
(288,393)(289,394)(290,395)(291,396)(292,397)(293,398)(294,399)(295,414)
(296,415)(297,416)(298,417)(299,418)(300,419)(301,420)(302,407)(303,408)
(304,409)(305,410)(306,411)(307,412)(308,413)(309,428)(310,429)(311,430)
(312,431)(313,432)(314,433)(315,434)(316,421)(317,422)(318,423)(319,424)
(320,425)(321,426)(322,427)(323,442)(324,443)(325,444)(326,445)(327,446)
(328,447)(329,448)(330,435)(331,436)(332,437)(333,438)(334,439)(335,440)
(336,441)(449,561)(450,562)(451,563)(452,564)(453,565)(454,566)(455,567)
(456,568)(457,569)(458,570)(459,571)(460,572)(461,573)(462,574)(463,575)
(464,576)(465,577)(466,578)(467,579)(468,580)(469,581)(470,582)(471,583)
(472,584)(473,585)(474,586)(475,587)(476,588)(477,589)(478,590)(479,591)
(480,592)(481,593)(482,594)(483,595)(484,596)(485,597)(486,598)(487,599)
(488,600)(489,601)(490,602)(491,603)(492,604)(493,605)(494,606)(495,607)
(496,608)(497,609)(498,610)(499,611)(500,612)(501,613)(502,614)(503,615)
(504,616)(505,624)(506,625)(507,626)(508,627)(509,628)(510,629)(511,630)
(512,617)(513,618)(514,619)(515,620)(516,621)(517,622)(518,623)(519,638)
(520,639)(521,640)(522,641)(523,642)(524,643)(525,644)(526,631)(527,632)
(528,633)(529,634)(530,635)(531,636)(532,637)(533,652)(534,653)(535,654)
(536,655)(537,656)(538,657)(539,658)(540,645)(541,646)(542,647)(543,648)
(544,649)(545,650)(546,651)(547,666)(548,667)(549,668)(550,669)(551,670)
(552,671)(553,672)(554,659)(555,660)(556,661)(557,662)(558,663)(559,664)
(560,665)(673,785)(674,786)(675,787)(676,788)(677,789)(678,790)(679,791)
(680,792)(681,793)(682,794)(683,795)(684,796)(685,797)(686,798)(687,799)
(688,800)(689,801)(690,802)(691,803)(692,804)(693,805)(694,806)(695,807)
(696,808)(697,809)(698,810)(699,811)(700,812)(701,813)(702,814)(703,815)
(704,816)(705,817)(706,818)(707,819)(708,820)(709,821)(710,822)(711,823)
(712,824)(713,825)(714,826)(715,827)(716,828)(717,829)(718,830)(719,831)
(720,832)(721,833)(722,834)(723,835)(724,836)(725,837)(726,838)(727,839)
(728,840)(729,848)(730,849)(731,850)(732,851)(733,852)(734,853)(735,854)
(736,841)(737,842)(738,843)(739,844)(740,845)(741,846)(742,847)(743,862)
(744,863)(745,864)(746,865)(747,866)(748,867)(749,868)(750,855)(751,856)
(752,857)(753,858)(754,859)(755,860)(756,861)(757,876)(758,877)(759,878)
(760,879)(761,880)(762,881)(763,882)(764,869)(765,870)(766,871)(767,872)
(768,873)(769,874)(770,875)(771,890)(772,891)(773,892)(774,893)(775,894)
(776,895)(777,896)(778,883)(779,884)(780,885)(781,886)(782,887)(783,888)
(784,889);
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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