Polytope of Type {14,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4,8}*1792a
if this polytope has a name.
Group : SmallGroup(1792,141629)
Rank : 4
Schlafli Type : {14,4,8}
Number of vertices, edges, etc : 14, 56, 32, 16
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 : {14,4,8}*896a, {14,4,8}*896b, {14,4,4}*896
4-fold quotients : {14,4,4}*448, {14,2,8}*448
7-fold quotients : {2,4,8}*256a
8-fold quotients : {7,2,8}*224, {14,2,4}*224, {14,4,2}*224
14-fold quotients : {2,4,8}*128a, {2,4,8}*128b, {2,4,4}*128
16-fold quotients : {7,2,4}*112, {14,2,2}*112
28-fold quotients : {2,4,4}*64, {2,2,8}*64
32-fold quotients : {7,2,2}*56
56-fold quotients : {2,2,4}*32, {2,4,2}*32
112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,113)( 2,119)( 3,118)( 4,117)( 5,116)( 6,115)( 7,114)( 8,120)
( 9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)( 16,133)
( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)( 24,139)
( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)( 32,145)
( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)( 40,151)
( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)
( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)
( 57,169)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,176)
( 65,182)( 66,181)( 67,180)( 68,179)( 69,178)( 70,177)( 71,183)( 72,189)
( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,190)( 79,196)( 80,195)
( 81,194)( 82,193)( 83,192)( 84,191)( 85,197)( 86,203)( 87,202)( 88,201)
( 89,200)( 90,199)( 91,198)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)
( 97,206)( 98,205)( 99,211)(100,217)(101,216)(102,215)(103,214)(104,213)
(105,212)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)(112,219)
(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)
(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)(240,357)
(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)(248,363)
(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)(256,369)
(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)(264,375)
(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)
(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)
(281,393)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)(288,400)
(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,407)(296,413)
(297,412)(298,411)(299,410)(300,409)(301,408)(302,414)(303,420)(304,419)
(305,418)(306,417)(307,416)(308,415)(309,421)(310,427)(311,426)(312,425)
(313,424)(314,423)(315,422)(316,428)(317,434)(318,433)(319,432)(320,431)
(321,430)(322,429)(323,435)(324,441)(325,440)(326,439)(327,438)(328,437)
(329,436)(330,442)(331,448)(332,447)(333,446)(334,445)(335,444)(336,443)
(449,561)(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)
(457,574)(458,573)(459,572)(460,571)(461,570)(462,569)(463,575)(464,581)
(465,580)(466,579)(467,578)(468,577)(469,576)(470,582)(471,588)(472,587)
(473,586)(474,585)(475,584)(476,583)(477,589)(478,595)(479,594)(480,593)
(481,592)(482,591)(483,590)(484,596)(485,602)(486,601)(487,600)(488,599)
(489,598)(490,597)(491,603)(492,609)(493,608)(494,607)(495,606)(496,605)
(497,604)(498,610)(499,616)(500,615)(501,614)(502,613)(503,612)(504,611)
(505,617)(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)(512,624)
(513,630)(514,629)(515,628)(516,627)(517,626)(518,625)(519,631)(520,637)
(521,636)(522,635)(523,634)(524,633)(525,632)(526,638)(527,644)(528,643)
(529,642)(530,641)(531,640)(532,639)(533,645)(534,651)(535,650)(536,649)
(537,648)(538,647)(539,646)(540,652)(541,658)(542,657)(543,656)(544,655)
(545,654)(546,653)(547,659)(548,665)(549,664)(550,663)(551,662)(552,661)
(553,660)(554,666)(555,672)(556,671)(557,670)(558,669)(559,668)(560,667)
(673,785)(674,791)(675,790)(676,789)(677,788)(678,787)(679,786)(680,792)
(681,798)(682,797)(683,796)(684,795)(685,794)(686,793)(687,799)(688,805)
(689,804)(690,803)(691,802)(692,801)(693,800)(694,806)(695,812)(696,811)
(697,810)(698,809)(699,808)(700,807)(701,813)(702,819)(703,818)(704,817)
(705,816)(706,815)(707,814)(708,820)(709,826)(710,825)(711,824)(712,823)
(713,822)(714,821)(715,827)(716,833)(717,832)(718,831)(719,830)(720,829)
(721,828)(722,834)(723,840)(724,839)(725,838)(726,837)(727,836)(728,835)
(729,841)(730,847)(731,846)(732,845)(733,844)(734,843)(735,842)(736,848)
(737,854)(738,853)(739,852)(740,851)(741,850)(742,849)(743,855)(744,861)
(745,860)(746,859)(747,858)(748,857)(749,856)(750,862)(751,868)(752,867)
(753,866)(754,865)(755,864)(756,863)(757,869)(758,875)(759,874)(760,873)
(761,872)(762,871)(763,870)(764,876)(765,882)(766,881)(767,880)(768,879)
(769,878)(770,877)(771,883)(772,889)(773,888)(774,887)(775,886)(776,885)
(777,884)(778,890)(779,896)(780,895)(781,894)(782,893)(783,892)(784,891);;
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)( 29,366)( 30,365)( 31,371)( 32,370)
( 33,369)( 34,368)( 35,367)( 36,373)( 37,372)( 38,378)( 39,377)( 40,376)
( 41,375)( 42,374)( 43,380)( 44,379)( 45,385)( 46,384)( 47,383)( 48,382)
( 49,381)( 50,387)( 51,386)( 52,392)( 53,391)( 54,390)( 55,389)( 56,388)
( 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)( 85,429)( 86,428)( 87,434)( 88,433)
( 89,432)( 90,431)( 91,430)( 92,422)( 93,421)( 94,427)( 95,426)( 96,425)
( 97,424)( 98,423)( 99,443)(100,442)(101,448)(102,447)(103,446)(104,445)
(105,444)(106,436)(107,435)(108,441)(109,440)(110,439)(111,438)(112,437)
(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)(141,254)(142,253)(143,259)(144,258)
(145,257)(146,256)(147,255)(148,261)(149,260)(150,266)(151,265)(152,264)
(153,263)(154,262)(155,268)(156,267)(157,273)(158,272)(159,271)(160,270)
(161,269)(162,275)(163,274)(164,280)(165,279)(166,278)(167,277)(168,276)
(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)(197,317)(198,316)(199,322)(200,321)
(201,320)(202,319)(203,318)(204,310)(205,309)(206,315)(207,314)(208,313)
(209,312)(210,311)(211,331)(212,330)(213,336)(214,335)(215,334)(216,333)
(217,332)(218,324)(219,323)(220,329)(221,328)(222,327)(223,326)(224,325)
(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)(477,814)(478,813)(479,819)(480,818)
(481,817)(482,816)(483,815)(484,821)(485,820)(486,826)(487,825)(488,824)
(489,823)(490,822)(491,828)(492,827)(493,833)(494,832)(495,831)(496,830)
(497,829)(498,835)(499,834)(500,840)(501,839)(502,838)(503,837)(504,836)
(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)(533,877)(534,876)(535,882)(536,881)
(537,880)(538,879)(539,878)(540,870)(541,869)(542,875)(543,874)(544,873)
(545,872)(546,871)(547,891)(548,890)(549,896)(550,895)(551,894)(552,893)
(553,892)(554,884)(555,883)(556,889)(557,888)(558,887)(559,886)(560,885)
(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)(589,702)(590,701)(591,707)(592,706)
(593,705)(594,704)(595,703)(596,709)(597,708)(598,714)(599,713)(600,712)
(601,711)(602,710)(603,716)(604,715)(605,721)(606,720)(607,719)(608,718)
(609,717)(610,723)(611,722)(612,728)(613,727)(614,726)(615,725)(616,724)
(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)(645,765)(646,764)(647,770)(648,769)
(649,768)(650,767)(651,766)(652,758)(653,757)(654,763)(655,762)(656,761)
(657,760)(658,759)(659,779)(660,778)(661,784)(662,783)(663,782)(664,781)
(665,780)(666,772)(667,771)(668,777)(669,776)(670,775)(671,774)(672,773);;
s2 := ( 57, 71)( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)
( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 99)( 86,100)
( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)
( 95,109)( 96,110)( 97,111)( 98,112)(169,183)(170,184)(171,185)(172,186)
(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)
(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)
(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)
(225,253)(226,254)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)
(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,267)(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)(281,323)(282,324)(283,325)(284,326)
(285,327)(286,328)(287,329)(288,330)(289,331)(290,332)(291,333)(292,334)
(293,335)(294,336)(295,309)(296,310)(297,311)(298,312)(299,313)(300,314)
(301,315)(302,316)(303,317)(304,318)(305,319)(306,320)(307,321)(308,322)
(337,365)(338,366)(339,367)(340,368)(341,369)(342,370)(343,371)(344,372)
(345,373)(346,374)(347,375)(348,376)(349,377)(350,378)(351,379)(352,380)
(353,381)(354,382)(355,383)(356,384)(357,385)(358,386)(359,387)(360,388)
(361,389)(362,390)(363,391)(364,392)(393,435)(394,436)(395,437)(396,438)
(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)(403,445)(404,446)
(405,447)(406,448)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)
(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434)
(449,505)(450,506)(451,507)(452,508)(453,509)(454,510)(455,511)(456,512)
(457,513)(458,514)(459,515)(460,516)(461,517)(462,518)(463,519)(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)
(561,617)(562,618)(563,619)(564,620)(565,621)(566,622)(567,623)(568,624)
(569,625)(570,626)(571,627)(572,628)(573,629)(574,630)(575,631)(576,632)
(577,633)(578,634)(579,635)(580,636)(581,637)(582,638)(583,639)(584,640)
(585,641)(586,642)(587,643)(588,644)(589,645)(590,646)(591,647)(592,648)
(593,649)(594,650)(595,651)(596,652)(597,653)(598,654)(599,655)(600,656)
(601,657)(602,658)(603,659)(604,660)(605,661)(606,662)(607,663)(608,664)
(609,665)(610,666)(611,667)(612,668)(613,669)(614,670)(615,671)(616,672)
(673,764)(674,765)(675,766)(676,767)(677,768)(678,769)(679,770)(680,757)
(681,758)(682,759)(683,760)(684,761)(685,762)(686,763)(687,778)(688,779)
(689,780)(690,781)(691,782)(692,783)(693,784)(694,771)(695,772)(696,773)
(697,774)(698,775)(699,776)(700,777)(701,736)(702,737)(703,738)(704,739)
(705,740)(706,741)(707,742)(708,729)(709,730)(710,731)(711,732)(712,733)
(713,734)(714,735)(715,750)(716,751)(717,752)(718,753)(719,754)(720,755)
(721,756)(722,743)(723,744)(724,745)(725,746)(726,747)(727,748)(728,749)
(785,876)(786,877)(787,878)(788,879)(789,880)(790,881)(791,882)(792,869)
(793,870)(794,871)(795,872)(796,873)(797,874)(798,875)(799,890)(800,891)
(801,892)(802,893)(803,894)(804,895)(805,896)(806,883)(807,884)(808,885)
(809,886)(810,887)(811,888)(812,889)(813,848)(814,849)(815,850)(816,851)
(817,852)(818,853)(819,854)(820,841)(821,842)(822,843)(823,844)(824,845)
(825,846)(826,847)(827,862)(828,863)(829,864)(830,865)(831,866)(832,867)
(833,868)(834,855)(835,856)(836,857)(837,858)(838,859)(839,860)(840,861);;
s3 := ( 1,449)( 2,450)( 3,451)( 4,452)( 5,453)( 6,454)( 7,455)( 8,456)
( 9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)( 16,464)
( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)
( 25,473)( 26,474)( 27,475)( 28,476)( 29,484)( 30,485)( 31,486)( 32,487)
( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)( 40,481)
( 41,482)( 42,483)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)( 48,503)
( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)( 56,497)
( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)( 64,526)
( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)( 72,506)
( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)( 80,514)
( 81,515)( 82,516)( 83,517)( 84,518)( 85,554)( 86,555)( 87,556)( 88,557)
( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)
( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)
(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)
(113,561)(114,562)(115,563)(116,564)(117,565)(118,566)(119,567)(120,568)
(121,569)(122,570)(123,571)(124,572)(125,573)(126,574)(127,575)(128,576)
(129,577)(130,578)(131,579)(132,580)(133,581)(134,582)(135,583)(136,584)
(137,585)(138,586)(139,587)(140,588)(141,596)(142,597)(143,598)(144,599)
(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)
(153,594)(154,595)(155,610)(156,611)(157,612)(158,613)(159,614)(160,615)
(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)(168,609)
(169,631)(170,632)(171,633)(172,634)(173,635)(174,636)(175,637)(176,638)
(177,639)(178,640)(179,641)(180,642)(181,643)(182,644)(183,617)(184,618)
(185,619)(186,620)(187,621)(188,622)(189,623)(190,624)(191,625)(192,626)
(193,627)(194,628)(195,629)(196,630)(197,666)(198,667)(199,668)(200,669)
(201,670)(202,671)(203,672)(204,659)(205,660)(206,661)(207,662)(208,663)
(209,664)(210,665)(211,652)(212,653)(213,654)(214,655)(215,656)(216,657)
(217,658)(218,645)(219,646)(220,647)(221,648)(222,649)(223,650)(224,651)
(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)
(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,687)(240,688)
(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)(248,696)
(249,697)(250,698)(251,699)(252,700)(253,708)(254,709)(255,710)(256,711)
(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)
(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)
(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)
(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)(288,750)
(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)(296,730)
(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)(304,738)
(305,739)(306,740)(307,741)(308,742)(309,778)(310,779)(311,780)(312,781)
(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)
(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)
(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)
(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)
(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,799)(352,800)
(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)(360,808)
(361,809)(362,810)(363,811)(364,812)(365,820)(366,821)(367,822)(368,823)
(369,824)(370,825)(371,826)(372,813)(373,814)(374,815)(375,816)(376,817)
(377,818)(378,819)(379,834)(380,835)(381,836)(382,837)(383,838)(384,839)
(385,840)(386,827)(387,828)(388,829)(389,830)(390,831)(391,832)(392,833)
(393,855)(394,856)(395,857)(396,858)(397,859)(398,860)(399,861)(400,862)
(401,863)(402,864)(403,865)(404,866)(405,867)(406,868)(407,841)(408,842)
(409,843)(410,844)(411,845)(412,846)(413,847)(414,848)(415,849)(416,850)
(417,851)(418,852)(419,853)(420,854)(421,890)(422,891)(423,892)(424,893)
(425,894)(426,895)(427,896)(428,883)(429,884)(430,885)(431,886)(432,887)
(433,888)(434,889)(435,876)(436,877)(437,878)(438,879)(439,880)(440,881)
(441,882)(442,869)(443,870)(444,871)(445,872)(446,873)(447,874)(448,875);;
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*s1*s2*s1*s3*s2*s3*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 1,113)( 2,119)( 3,118)( 4,117)( 5,116)( 6,115)( 7,114)
( 8,120)( 9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)
( 16,133)( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)
( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)
( 32,145)( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)
( 40,151)( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)
( 48,157)( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)
( 56,163)( 57,169)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)
( 64,176)( 65,182)( 66,181)( 67,180)( 68,179)( 69,178)( 70,177)( 71,183)
( 72,189)( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,190)( 79,196)
( 80,195)( 81,194)( 82,193)( 83,192)( 84,191)( 85,197)( 86,203)( 87,202)
( 88,201)( 89,200)( 90,199)( 91,198)( 92,204)( 93,210)( 94,209)( 95,208)
( 96,207)( 97,206)( 98,205)( 99,211)(100,217)(101,216)(102,215)(103,214)
(104,213)(105,212)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)
(112,219)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)
(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)
(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)
(248,363)(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)
(256,369)(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)
(264,375)(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)
(272,381)(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)
(280,387)(281,393)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)
(288,400)(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,407)
(296,413)(297,412)(298,411)(299,410)(300,409)(301,408)(302,414)(303,420)
(304,419)(305,418)(306,417)(307,416)(308,415)(309,421)(310,427)(311,426)
(312,425)(313,424)(314,423)(315,422)(316,428)(317,434)(318,433)(319,432)
(320,431)(321,430)(322,429)(323,435)(324,441)(325,440)(326,439)(327,438)
(328,437)(329,436)(330,442)(331,448)(332,447)(333,446)(334,445)(335,444)
(336,443)(449,561)(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)
(456,568)(457,574)(458,573)(459,572)(460,571)(461,570)(462,569)(463,575)
(464,581)(465,580)(466,579)(467,578)(468,577)(469,576)(470,582)(471,588)
(472,587)(473,586)(474,585)(475,584)(476,583)(477,589)(478,595)(479,594)
(480,593)(481,592)(482,591)(483,590)(484,596)(485,602)(486,601)(487,600)
(488,599)(489,598)(490,597)(491,603)(492,609)(493,608)(494,607)(495,606)
(496,605)(497,604)(498,610)(499,616)(500,615)(501,614)(502,613)(503,612)
(504,611)(505,617)(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)
(512,624)(513,630)(514,629)(515,628)(516,627)(517,626)(518,625)(519,631)
(520,637)(521,636)(522,635)(523,634)(524,633)(525,632)(526,638)(527,644)
(528,643)(529,642)(530,641)(531,640)(532,639)(533,645)(534,651)(535,650)
(536,649)(537,648)(538,647)(539,646)(540,652)(541,658)(542,657)(543,656)
(544,655)(545,654)(546,653)(547,659)(548,665)(549,664)(550,663)(551,662)
(552,661)(553,660)(554,666)(555,672)(556,671)(557,670)(558,669)(559,668)
(560,667)(673,785)(674,791)(675,790)(676,789)(677,788)(678,787)(679,786)
(680,792)(681,798)(682,797)(683,796)(684,795)(685,794)(686,793)(687,799)
(688,805)(689,804)(690,803)(691,802)(692,801)(693,800)(694,806)(695,812)
(696,811)(697,810)(698,809)(699,808)(700,807)(701,813)(702,819)(703,818)
(704,817)(705,816)(706,815)(707,814)(708,820)(709,826)(710,825)(711,824)
(712,823)(713,822)(714,821)(715,827)(716,833)(717,832)(718,831)(719,830)
(720,829)(721,828)(722,834)(723,840)(724,839)(725,838)(726,837)(727,836)
(728,835)(729,841)(730,847)(731,846)(732,845)(733,844)(734,843)(735,842)
(736,848)(737,854)(738,853)(739,852)(740,851)(741,850)(742,849)(743,855)
(744,861)(745,860)(746,859)(747,858)(748,857)(749,856)(750,862)(751,868)
(752,867)(753,866)(754,865)(755,864)(756,863)(757,869)(758,875)(759,874)
(760,873)(761,872)(762,871)(763,870)(764,876)(765,882)(766,881)(767,880)
(768,879)(769,878)(770,877)(771,883)(772,889)(773,888)(774,887)(775,886)
(776,885)(777,884)(778,890)(779,896)(780,895)(781,894)(782,893)(783,892)
(784,891);
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)( 29,366)( 30,365)( 31,371)
( 32,370)( 33,369)( 34,368)( 35,367)( 36,373)( 37,372)( 38,378)( 39,377)
( 40,376)( 41,375)( 42,374)( 43,380)( 44,379)( 45,385)( 46,384)( 47,383)
( 48,382)( 49,381)( 50,387)( 51,386)( 52,392)( 53,391)( 54,390)( 55,389)
( 56,388)( 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)( 85,429)( 86,428)( 87,434)
( 88,433)( 89,432)( 90,431)( 91,430)( 92,422)( 93,421)( 94,427)( 95,426)
( 96,425)( 97,424)( 98,423)( 99,443)(100,442)(101,448)(102,447)(103,446)
(104,445)(105,444)(106,436)(107,435)(108,441)(109,440)(110,439)(111,438)
(112,437)(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)(141,254)(142,253)(143,259)
(144,258)(145,257)(146,256)(147,255)(148,261)(149,260)(150,266)(151,265)
(152,264)(153,263)(154,262)(155,268)(156,267)(157,273)(158,272)(159,271)
(160,270)(161,269)(162,275)(163,274)(164,280)(165,279)(166,278)(167,277)
(168,276)(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)(197,317)(198,316)(199,322)
(200,321)(201,320)(202,319)(203,318)(204,310)(205,309)(206,315)(207,314)
(208,313)(209,312)(210,311)(211,331)(212,330)(213,336)(214,335)(215,334)
(216,333)(217,332)(218,324)(219,323)(220,329)(221,328)(222,327)(223,326)
(224,325)(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)(477,814)(478,813)(479,819)
(480,818)(481,817)(482,816)(483,815)(484,821)(485,820)(486,826)(487,825)
(488,824)(489,823)(490,822)(491,828)(492,827)(493,833)(494,832)(495,831)
(496,830)(497,829)(498,835)(499,834)(500,840)(501,839)(502,838)(503,837)
(504,836)(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)(533,877)(534,876)(535,882)
(536,881)(537,880)(538,879)(539,878)(540,870)(541,869)(542,875)(543,874)
(544,873)(545,872)(546,871)(547,891)(548,890)(549,896)(550,895)(551,894)
(552,893)(553,892)(554,884)(555,883)(556,889)(557,888)(558,887)(559,886)
(560,885)(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)(589,702)(590,701)(591,707)
(592,706)(593,705)(594,704)(595,703)(596,709)(597,708)(598,714)(599,713)
(600,712)(601,711)(602,710)(603,716)(604,715)(605,721)(606,720)(607,719)
(608,718)(609,717)(610,723)(611,722)(612,728)(613,727)(614,726)(615,725)
(616,724)(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)(645,765)(646,764)(647,770)
(648,769)(649,768)(650,767)(651,766)(652,758)(653,757)(654,763)(655,762)
(656,761)(657,760)(658,759)(659,779)(660,778)(661,784)(662,783)(663,782)
(664,781)(665,780)(666,772)(667,771)(668,777)(669,776)(670,775)(671,774)
(672,773);
s2 := Sym(896)!( 57, 71)( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)
( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 99)
( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)
( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)(169,183)(170,184)(171,185)
(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)
(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)
(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)
(210,224)(225,253)(226,254)(227,255)(228,256)(229,257)(230,258)(231,259)
(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,267)
(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)(281,323)(282,324)(283,325)
(284,326)(285,327)(286,328)(287,329)(288,330)(289,331)(290,332)(291,333)
(292,334)(293,335)(294,336)(295,309)(296,310)(297,311)(298,312)(299,313)
(300,314)(301,315)(302,316)(303,317)(304,318)(305,319)(306,320)(307,321)
(308,322)(337,365)(338,366)(339,367)(340,368)(341,369)(342,370)(343,371)
(344,372)(345,373)(346,374)(347,375)(348,376)(349,377)(350,378)(351,379)
(352,380)(353,381)(354,382)(355,383)(356,384)(357,385)(358,386)(359,387)
(360,388)(361,389)(362,390)(363,391)(364,392)(393,435)(394,436)(395,437)
(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)(403,445)
(404,446)(405,447)(406,448)(407,421)(408,422)(409,423)(410,424)(411,425)
(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)
(420,434)(449,505)(450,506)(451,507)(452,508)(453,509)(454,510)(455,511)
(456,512)(457,513)(458,514)(459,515)(460,516)(461,517)(462,518)(463,519)
(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)(561,617)(562,618)(563,619)(564,620)(565,621)(566,622)(567,623)
(568,624)(569,625)(570,626)(571,627)(572,628)(573,629)(574,630)(575,631)
(576,632)(577,633)(578,634)(579,635)(580,636)(581,637)(582,638)(583,639)
(584,640)(585,641)(586,642)(587,643)(588,644)(589,645)(590,646)(591,647)
(592,648)(593,649)(594,650)(595,651)(596,652)(597,653)(598,654)(599,655)
(600,656)(601,657)(602,658)(603,659)(604,660)(605,661)(606,662)(607,663)
(608,664)(609,665)(610,666)(611,667)(612,668)(613,669)(614,670)(615,671)
(616,672)(673,764)(674,765)(675,766)(676,767)(677,768)(678,769)(679,770)
(680,757)(681,758)(682,759)(683,760)(684,761)(685,762)(686,763)(687,778)
(688,779)(689,780)(690,781)(691,782)(692,783)(693,784)(694,771)(695,772)
(696,773)(697,774)(698,775)(699,776)(700,777)(701,736)(702,737)(703,738)
(704,739)(705,740)(706,741)(707,742)(708,729)(709,730)(710,731)(711,732)
(712,733)(713,734)(714,735)(715,750)(716,751)(717,752)(718,753)(719,754)
(720,755)(721,756)(722,743)(723,744)(724,745)(725,746)(726,747)(727,748)
(728,749)(785,876)(786,877)(787,878)(788,879)(789,880)(790,881)(791,882)
(792,869)(793,870)(794,871)(795,872)(796,873)(797,874)(798,875)(799,890)
(800,891)(801,892)(802,893)(803,894)(804,895)(805,896)(806,883)(807,884)
(808,885)(809,886)(810,887)(811,888)(812,889)(813,848)(814,849)(815,850)
(816,851)(817,852)(818,853)(819,854)(820,841)(821,842)(822,843)(823,844)
(824,845)(825,846)(826,847)(827,862)(828,863)(829,864)(830,865)(831,866)
(832,867)(833,868)(834,855)(835,856)(836,857)(837,858)(838,859)(839,860)
(840,861);
s3 := Sym(896)!( 1,449)( 2,450)( 3,451)( 4,452)( 5,453)( 6,454)( 7,455)
( 8,456)( 9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)
( 16,464)( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)
( 24,472)( 25,473)( 26,474)( 27,475)( 28,476)( 29,484)( 30,485)( 31,486)
( 32,487)( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)
( 40,481)( 41,482)( 42,483)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)
( 48,503)( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)
( 56,497)( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)
( 64,526)( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)
( 72,506)( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)
( 80,514)( 81,515)( 82,516)( 83,517)( 84,518)( 85,554)( 86,555)( 87,556)
( 88,557)( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)
( 96,551)( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)
(104,545)(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)
(112,539)(113,561)(114,562)(115,563)(116,564)(117,565)(118,566)(119,567)
(120,568)(121,569)(122,570)(123,571)(124,572)(125,573)(126,574)(127,575)
(128,576)(129,577)(130,578)(131,579)(132,580)(133,581)(134,582)(135,583)
(136,584)(137,585)(138,586)(139,587)(140,588)(141,596)(142,597)(143,598)
(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)
(152,593)(153,594)(154,595)(155,610)(156,611)(157,612)(158,613)(159,614)
(160,615)(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)
(168,609)(169,631)(170,632)(171,633)(172,634)(173,635)(174,636)(175,637)
(176,638)(177,639)(178,640)(179,641)(180,642)(181,643)(182,644)(183,617)
(184,618)(185,619)(186,620)(187,621)(188,622)(189,623)(190,624)(191,625)
(192,626)(193,627)(194,628)(195,629)(196,630)(197,666)(198,667)(199,668)
(200,669)(201,670)(202,671)(203,672)(204,659)(205,660)(206,661)(207,662)
(208,663)(209,664)(210,665)(211,652)(212,653)(213,654)(214,655)(215,656)
(216,657)(217,658)(218,645)(219,646)(220,647)(221,648)(222,649)(223,650)
(224,651)(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)
(232,680)(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,687)
(240,688)(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)
(248,696)(249,697)(250,698)(251,699)(252,700)(253,708)(254,709)(255,710)
(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)
(264,705)(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)
(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)
(280,721)(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)
(288,750)(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)
(296,730)(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)
(304,738)(305,739)(306,740)(307,741)(308,742)(309,778)(310,779)(311,780)
(312,781)(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)
(320,775)(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)
(328,769)(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)
(336,763)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)
(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,799)
(352,800)(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)
(360,808)(361,809)(362,810)(363,811)(364,812)(365,820)(366,821)(367,822)
(368,823)(369,824)(370,825)(371,826)(372,813)(373,814)(374,815)(375,816)
(376,817)(377,818)(378,819)(379,834)(380,835)(381,836)(382,837)(383,838)
(384,839)(385,840)(386,827)(387,828)(388,829)(389,830)(390,831)(391,832)
(392,833)(393,855)(394,856)(395,857)(396,858)(397,859)(398,860)(399,861)
(400,862)(401,863)(402,864)(403,865)(404,866)(405,867)(406,868)(407,841)
(408,842)(409,843)(410,844)(411,845)(412,846)(413,847)(414,848)(415,849)
(416,850)(417,851)(418,852)(419,853)(420,854)(421,890)(422,891)(423,892)
(424,893)(425,894)(426,895)(427,896)(428,883)(429,884)(430,885)(431,886)
(432,887)(433,888)(434,889)(435,876)(436,877)(437,878)(438,879)(439,880)
(440,881)(441,882)(442,869)(443,870)(444,871)(445,872)(446,873)(447,874)
(448,875);
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*s1*s2*s1*s3*s2*s3*s2*s1*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 >;
References : None.
to this polytope