Polytope of Type {28,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,4,8}*1792b
if this polytope has a name.
Group : SmallGroup(1792,200904)
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, {14,4,8}*896b
4-fold quotients : {28,4,2}*448, {28,2,4}*448, {14,4,4}*448
7-fold quotients : {4,4,8}*256b
8-fold quotients : {28,2,2}*224, {14,2,4}*224, {14,4,2}*224
14-fold quotients : {4,4,4}*128, {2,4,8}*128b
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
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 := ( 1,338)( 2,337)( 3,343)( 4,342)( 5,341)( 6,340)( 7,339)( 8,345)
( 9,344)( 10,350)( 11,349)( 12,348)( 13,347)( 14,346)( 15,352)( 16,351)
( 17,357)( 18,356)( 19,355)( 20,354)( 21,353)( 22,359)( 23,358)( 24,364)
( 25,363)( 26,362)( 27,361)( 28,360)( 29,373)( 30,372)( 31,378)( 32,377)
( 33,376)( 34,375)( 35,374)( 36,366)( 37,365)( 38,371)( 39,370)( 40,369)
( 41,368)( 42,367)( 43,387)( 44,386)( 45,392)( 46,391)( 47,390)( 48,389)
( 49,388)( 50,380)( 51,379)( 52,385)( 53,384)( 54,383)( 55,382)( 56,381)
( 57,401)( 58,400)( 59,406)( 60,405)( 61,404)( 62,403)( 63,402)( 64,394)
( 65,393)( 66,399)( 67,398)( 68,397)( 69,396)( 70,395)( 71,415)( 72,414)
( 73,420)( 74,419)( 75,418)( 76,417)( 77,416)( 78,408)( 79,407)( 80,413)
( 81,412)( 82,411)( 83,410)( 84,409)( 85,422)( 86,421)( 87,427)( 88,426)
( 89,425)( 90,424)( 91,423)( 92,429)( 93,428)( 94,434)( 95,433)( 96,432)
( 97,431)( 98,430)( 99,436)(100,435)(101,441)(102,440)(103,439)(104,438)
(105,437)(106,443)(107,442)(108,448)(109,447)(110,446)(111,445)(112,444)
(113,226)(114,225)(115,231)(116,230)(117,229)(118,228)(119,227)(120,233)
(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,240)(128,239)
(129,245)(130,244)(131,243)(132,242)(133,241)(134,247)(135,246)(136,252)
(137,251)(138,250)(139,249)(140,248)(141,261)(142,260)(143,266)(144,265)
(145,264)(146,263)(147,262)(148,254)(149,253)(150,259)(151,258)(152,257)
(153,256)(154,255)(155,275)(156,274)(157,280)(158,279)(159,278)(160,277)
(161,276)(162,268)(163,267)(164,273)(165,272)(166,271)(167,270)(168,269)
(169,289)(170,288)(171,294)(172,293)(173,292)(174,291)(175,290)(176,282)
(177,281)(178,287)(179,286)(180,285)(181,284)(182,283)(183,303)(184,302)
(185,308)(186,307)(187,306)(188,305)(189,304)(190,296)(191,295)(192,301)
(193,300)(194,299)(195,298)(196,297)(197,310)(198,309)(199,315)(200,314)
(201,313)(202,312)(203,311)(204,317)(205,316)(206,322)(207,321)(208,320)
(209,319)(210,318)(211,324)(212,323)(213,329)(214,328)(215,327)(216,326)
(217,325)(218,331)(219,330)(220,336)(221,335)(222,334)(223,333)(224,332)
(449,786)(450,785)(451,791)(452,790)(453,789)(454,788)(455,787)(456,793)
(457,792)(458,798)(459,797)(460,796)(461,795)(462,794)(463,800)(464,799)
(465,805)(466,804)(467,803)(468,802)(469,801)(470,807)(471,806)(472,812)
(473,811)(474,810)(475,809)(476,808)(477,821)(478,820)(479,826)(480,825)
(481,824)(482,823)(483,822)(484,814)(485,813)(486,819)(487,818)(488,817)
(489,816)(490,815)(491,835)(492,834)(493,840)(494,839)(495,838)(496,837)
(497,836)(498,828)(499,827)(500,833)(501,832)(502,831)(503,830)(504,829)
(505,849)(506,848)(507,854)(508,853)(509,852)(510,851)(511,850)(512,842)
(513,841)(514,847)(515,846)(516,845)(517,844)(518,843)(519,863)(520,862)
(521,868)(522,867)(523,866)(524,865)(525,864)(526,856)(527,855)(528,861)
(529,860)(530,859)(531,858)(532,857)(533,870)(534,869)(535,875)(536,874)
(537,873)(538,872)(539,871)(540,877)(541,876)(542,882)(543,881)(544,880)
(545,879)(546,878)(547,884)(548,883)(549,889)(550,888)(551,887)(552,886)
(553,885)(554,891)(555,890)(556,896)(557,895)(558,894)(559,893)(560,892)
(561,674)(562,673)(563,679)(564,678)(565,677)(566,676)(567,675)(568,681)
(569,680)(570,686)(571,685)(572,684)(573,683)(574,682)(575,688)(576,687)
(577,693)(578,692)(579,691)(580,690)(581,689)(582,695)(583,694)(584,700)
(585,699)(586,698)(587,697)(588,696)(589,709)(590,708)(591,714)(592,713)
(593,712)(594,711)(595,710)(596,702)(597,701)(598,707)(599,706)(600,705)
(601,704)(602,703)(603,723)(604,722)(605,728)(606,727)(607,726)(608,725)
(609,724)(610,716)(611,715)(612,721)(613,720)(614,719)(615,718)(616,717)
(617,737)(618,736)(619,742)(620,741)(621,740)(622,739)(623,738)(624,730)
(625,729)(626,735)(627,734)(628,733)(629,732)(630,731)(631,751)(632,750)
(633,756)(634,755)(635,754)(636,753)(637,752)(638,744)(639,743)(640,749)
(641,748)(642,747)(643,746)(644,745)(645,758)(646,757)(647,763)(648,762)
(649,761)(650,760)(651,759)(652,765)(653,764)(654,770)(655,769)(656,768)
(657,767)(658,766)(659,772)(660,771)(661,777)(662,776)(663,775)(664,774)
(665,773)(666,779)(667,778)(668,784)(669,783)(670,782)(671,781)(672,780);;
s2 := ( 29, 36)( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 43, 50)
( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 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)(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)
(141,204)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)(148,197)
(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,218)(156,219)
(157,220)(158,221)(159,222)(160,223)(161,224)(162,211)(163,212)(164,213)
(165,214)(166,215)(167,216)(168,217)(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)
(477,540)(478,541)(479,542)(480,543)(481,544)(482,545)(483,546)(484,533)
(485,534)(486,535)(487,536)(488,537)(489,538)(490,539)(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)(589,596)(590,597)(591,598)(592,599)
(593,600)(594,601)(595,602)(603,610)(604,611)(605,612)(606,613)(607,614)
(608,615)(609,616)(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)
(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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!( 1,338)( 2,337)( 3,343)( 4,342)( 5,341)( 6,340)( 7,339)
( 8,345)( 9,344)( 10,350)( 11,349)( 12,348)( 13,347)( 14,346)( 15,352)
( 16,351)( 17,357)( 18,356)( 19,355)( 20,354)( 21,353)( 22,359)( 23,358)
( 24,364)( 25,363)( 26,362)( 27,361)( 28,360)( 29,373)( 30,372)( 31,378)
( 32,377)( 33,376)( 34,375)( 35,374)( 36,366)( 37,365)( 38,371)( 39,370)
( 40,369)( 41,368)( 42,367)( 43,387)( 44,386)( 45,392)( 46,391)( 47,390)
( 48,389)( 49,388)( 50,380)( 51,379)( 52,385)( 53,384)( 54,383)( 55,382)
( 56,381)( 57,401)( 58,400)( 59,406)( 60,405)( 61,404)( 62,403)( 63,402)
( 64,394)( 65,393)( 66,399)( 67,398)( 68,397)( 69,396)( 70,395)( 71,415)
( 72,414)( 73,420)( 74,419)( 75,418)( 76,417)( 77,416)( 78,408)( 79,407)
( 80,413)( 81,412)( 82,411)( 83,410)( 84,409)( 85,422)( 86,421)( 87,427)
( 88,426)( 89,425)( 90,424)( 91,423)( 92,429)( 93,428)( 94,434)( 95,433)
( 96,432)( 97,431)( 98,430)( 99,436)(100,435)(101,441)(102,440)(103,439)
(104,438)(105,437)(106,443)(107,442)(108,448)(109,447)(110,446)(111,445)
(112,444)(113,226)(114,225)(115,231)(116,230)(117,229)(118,228)(119,227)
(120,233)(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,240)
(128,239)(129,245)(130,244)(131,243)(132,242)(133,241)(134,247)(135,246)
(136,252)(137,251)(138,250)(139,249)(140,248)(141,261)(142,260)(143,266)
(144,265)(145,264)(146,263)(147,262)(148,254)(149,253)(150,259)(151,258)
(152,257)(153,256)(154,255)(155,275)(156,274)(157,280)(158,279)(159,278)
(160,277)(161,276)(162,268)(163,267)(164,273)(165,272)(166,271)(167,270)
(168,269)(169,289)(170,288)(171,294)(172,293)(173,292)(174,291)(175,290)
(176,282)(177,281)(178,287)(179,286)(180,285)(181,284)(182,283)(183,303)
(184,302)(185,308)(186,307)(187,306)(188,305)(189,304)(190,296)(191,295)
(192,301)(193,300)(194,299)(195,298)(196,297)(197,310)(198,309)(199,315)
(200,314)(201,313)(202,312)(203,311)(204,317)(205,316)(206,322)(207,321)
(208,320)(209,319)(210,318)(211,324)(212,323)(213,329)(214,328)(215,327)
(216,326)(217,325)(218,331)(219,330)(220,336)(221,335)(222,334)(223,333)
(224,332)(449,786)(450,785)(451,791)(452,790)(453,789)(454,788)(455,787)
(456,793)(457,792)(458,798)(459,797)(460,796)(461,795)(462,794)(463,800)
(464,799)(465,805)(466,804)(467,803)(468,802)(469,801)(470,807)(471,806)
(472,812)(473,811)(474,810)(475,809)(476,808)(477,821)(478,820)(479,826)
(480,825)(481,824)(482,823)(483,822)(484,814)(485,813)(486,819)(487,818)
(488,817)(489,816)(490,815)(491,835)(492,834)(493,840)(494,839)(495,838)
(496,837)(497,836)(498,828)(499,827)(500,833)(501,832)(502,831)(503,830)
(504,829)(505,849)(506,848)(507,854)(508,853)(509,852)(510,851)(511,850)
(512,842)(513,841)(514,847)(515,846)(516,845)(517,844)(518,843)(519,863)
(520,862)(521,868)(522,867)(523,866)(524,865)(525,864)(526,856)(527,855)
(528,861)(529,860)(530,859)(531,858)(532,857)(533,870)(534,869)(535,875)
(536,874)(537,873)(538,872)(539,871)(540,877)(541,876)(542,882)(543,881)
(544,880)(545,879)(546,878)(547,884)(548,883)(549,889)(550,888)(551,887)
(552,886)(553,885)(554,891)(555,890)(556,896)(557,895)(558,894)(559,893)
(560,892)(561,674)(562,673)(563,679)(564,678)(565,677)(566,676)(567,675)
(568,681)(569,680)(570,686)(571,685)(572,684)(573,683)(574,682)(575,688)
(576,687)(577,693)(578,692)(579,691)(580,690)(581,689)(582,695)(583,694)
(584,700)(585,699)(586,698)(587,697)(588,696)(589,709)(590,708)(591,714)
(592,713)(593,712)(594,711)(595,710)(596,702)(597,701)(598,707)(599,706)
(600,705)(601,704)(602,703)(603,723)(604,722)(605,728)(606,727)(607,726)
(608,725)(609,724)(610,716)(611,715)(612,721)(613,720)(614,719)(615,718)
(616,717)(617,737)(618,736)(619,742)(620,741)(621,740)(622,739)(623,738)
(624,730)(625,729)(626,735)(627,734)(628,733)(629,732)(630,731)(631,751)
(632,750)(633,756)(634,755)(635,754)(636,753)(637,752)(638,744)(639,743)
(640,749)(641,748)(642,747)(643,746)(644,745)(645,758)(646,757)(647,763)
(648,762)(649,761)(650,760)(651,759)(652,765)(653,764)(654,770)(655,769)
(656,768)(657,767)(658,766)(659,772)(660,771)(661,777)(662,776)(663,775)
(664,774)(665,773)(666,779)(667,778)(668,784)(669,783)(670,782)(671,781)
(672,780);
s2 := Sym(896)!( 29, 36)( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)
( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 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)(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)(141,204)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)
(148,197)(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,218)
(156,219)(157,220)(158,221)(159,222)(160,223)(161,224)(162,211)(163,212)
(164,213)(165,214)(166,215)(167,216)(168,217)(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)(477,540)(478,541)(479,542)(480,543)(481,544)(482,545)(483,546)
(484,533)(485,534)(486,535)(487,536)(488,537)(489,538)(490,539)(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)(589,596)(590,597)(591,598)
(592,599)(593,600)(594,601)(595,602)(603,610)(604,611)(605,612)(606,613)
(607,614)(608,615)(609,616)(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)(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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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