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