Polytope of Type {14,8,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,8,8}*1792b
Also Known As : {{14,8|2},{8,8|2}}. if this polytope has another name.
Group : SmallGroup(1792,145169)
Rank : 4
Schlafli Type : {14,8,8}
Number of vertices, edges, etc : 14, 56, 32, 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 : {14,4,8}*896a, {14,8,4}*896a
4-fold quotients : {14,4,4}*448, {14,2,8}*448, {14,8,2}*448
7-fold quotients : {2,8,8}*256b
8-fold quotients : {7,2,8}*224, {14,2,4}*224, {14,4,2}*224
14-fold quotients : {2,4,8}*128a, {2,8,4}*128a
16-fold quotients : {7,2,4}*112, {14,2,2}*112
28-fold quotients : {2,4,4}*64, {2,2,8}*64, {2,8,2}*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)( 29,373)( 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, 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)( 85,106)( 86,107)( 87,108)( 88,109)
( 89,110)( 90,111)( 91,112)( 92, 99)( 93,100)( 94,101)( 95,102)( 96,103)
( 97,104)( 98,105)(141,148)(142,149)(143,150)(144,151)(145,152)(146,153)
(147,154)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)
(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)
(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,218)(198,219)
(199,220)(200,221)(201,222)(202,223)(203,224)(204,211)(205,212)(206,213)
(207,214)(208,215)(209,216)(210,217)(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)
(281,323)(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)
(477,540)(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)(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)
(589,652)(590,653)(591,654)(592,655)(593,656)(594,657)(595,658)(596,645)
(597,646)(598,647)(599,648)(600,649)(601,650)(602,651)(603,666)(604,667)
(605,668)(606,669)(607,670)(608,671)(609,672)(610,659)(611,660)(612,661)
(613,662)(614,663)(615,664)(616,665)(673,764)(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 := ( 1,673)( 2,674)( 3,675)( 4,676)( 5,677)( 6,678)( 7,679)( 8,680)
( 9,681)( 10,682)( 11,683)( 12,684)( 13,685)( 14,686)( 15,687)( 16,688)
( 17,689)( 18,690)( 19,691)( 20,692)( 21,693)( 22,694)( 23,695)( 24,696)
( 25,697)( 26,698)( 27,699)( 28,700)( 29,701)( 30,702)( 31,703)( 32,704)
( 33,705)( 34,706)( 35,707)( 36,708)( 37,709)( 38,710)( 39,711)( 40,712)
( 41,713)( 42,714)( 43,715)( 44,716)( 45,717)( 46,718)( 47,719)( 48,720)
( 49,721)( 50,722)( 51,723)( 52,724)( 53,725)( 54,726)( 55,727)( 56,728)
( 57,750)( 58,751)( 59,752)( 60,753)( 61,754)( 62,755)( 63,756)( 64,743)
( 65,744)( 66,745)( 67,746)( 68,747)( 69,748)( 70,749)( 71,736)( 72,737)
( 73,738)( 74,739)( 75,740)( 76,741)( 77,742)( 78,729)( 79,730)( 80,731)
( 81,732)( 82,733)( 83,734)( 84,735)( 85,778)( 86,779)( 87,780)( 88,781)
( 89,782)( 90,783)( 91,784)( 92,771)( 93,772)( 94,773)( 95,774)( 96,775)
( 97,776)( 98,777)( 99,764)(100,765)(101,766)(102,767)(103,768)(104,769)
(105,770)(106,757)(107,758)(108,759)(109,760)(110,761)(111,762)(112,763)
(113,785)(114,786)(115,787)(116,788)(117,789)(118,790)(119,791)(120,792)
(121,793)(122,794)(123,795)(124,796)(125,797)(126,798)(127,799)(128,800)
(129,801)(130,802)(131,803)(132,804)(133,805)(134,806)(135,807)(136,808)
(137,809)(138,810)(139,811)(140,812)(141,813)(142,814)(143,815)(144,816)
(145,817)(146,818)(147,819)(148,820)(149,821)(150,822)(151,823)(152,824)
(153,825)(154,826)(155,827)(156,828)(157,829)(158,830)(159,831)(160,832)
(161,833)(162,834)(163,835)(164,836)(165,837)(166,838)(167,839)(168,840)
(169,862)(170,863)(171,864)(172,865)(173,866)(174,867)(175,868)(176,855)
(177,856)(178,857)(179,858)(180,859)(181,860)(182,861)(183,848)(184,849)
(185,850)(186,851)(187,852)(188,853)(189,854)(190,841)(191,842)(192,843)
(193,844)(194,845)(195,846)(196,847)(197,890)(198,891)(199,892)(200,893)
(201,894)(202,895)(203,896)(204,883)(205,884)(206,885)(207,886)(208,887)
(209,888)(210,889)(211,876)(212,877)(213,878)(214,879)(215,880)(216,881)
(217,882)(218,869)(219,870)(220,871)(221,872)(222,873)(223,874)(224,875)
(225,449)(226,450)(227,451)(228,452)(229,453)(230,454)(231,455)(232,456)
(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)(240,464)
(241,465)(242,466)(243,467)(244,468)(245,469)(246,470)(247,471)(248,472)
(249,473)(250,474)(251,475)(252,476)(253,477)(254,478)(255,479)(256,480)
(257,481)(258,482)(259,483)(260,484)(261,485)(262,486)(263,487)(264,488)
(265,489)(266,490)(267,491)(268,492)(269,493)(270,494)(271,495)(272,496)
(273,497)(274,498)(275,499)(276,500)(277,501)(278,502)(279,503)(280,504)
(281,526)(282,527)(283,528)(284,529)(285,530)(286,531)(287,532)(288,519)
(289,520)(290,521)(291,522)(292,523)(293,524)(294,525)(295,512)(296,513)
(297,514)(298,515)(299,516)(300,517)(301,518)(302,505)(303,506)(304,507)
(305,508)(306,509)(307,510)(308,511)(309,554)(310,555)(311,556)(312,557)
(313,558)(314,559)(315,560)(316,547)(317,548)(318,549)(319,550)(320,551)
(321,552)(322,553)(323,540)(324,541)(325,542)(326,543)(327,544)(328,545)
(329,546)(330,533)(331,534)(332,535)(333,536)(334,537)(335,538)(336,539)
(337,561)(338,562)(339,563)(340,564)(341,565)(342,566)(343,567)(344,568)
(345,569)(346,570)(347,571)(348,572)(349,573)(350,574)(351,575)(352,576)
(353,577)(354,578)(355,579)(356,580)(357,581)(358,582)(359,583)(360,584)
(361,585)(362,586)(363,587)(364,588)(365,589)(366,590)(367,591)(368,592)
(369,593)(370,594)(371,595)(372,596)(373,597)(374,598)(375,599)(376,600)
(377,601)(378,602)(379,603)(380,604)(381,605)(382,606)(383,607)(384,608)
(385,609)(386,610)(387,611)(388,612)(389,613)(390,614)(391,615)(392,616)
(393,638)(394,639)(395,640)(396,641)(397,642)(398,643)(399,644)(400,631)
(401,632)(402,633)(403,634)(404,635)(405,636)(406,637)(407,624)(408,625)
(409,626)(410,627)(411,628)(412,629)(413,630)(414,617)(415,618)(416,619)
(417,620)(418,621)(419,622)(420,623)(421,666)(422,667)(423,668)(424,669)
(425,670)(426,671)(427,672)(428,659)(429,660)(430,661)(431,662)(432,663)
(433,664)(434,665)(435,652)(436,653)(437,654)(438,655)(439,656)(440,657)
(441,658)(442,645)(443,646)(444,647)(445,648)(446,649)(447,650)(448,651);;
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*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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)( 29,373)( 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, 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)( 85,106)( 86,107)( 87,108)
( 88,109)( 89,110)( 90,111)( 91,112)( 92, 99)( 93,100)( 94,101)( 95,102)
( 96,103)( 97,104)( 98,105)(141,148)(142,149)(143,150)(144,151)(145,152)
(146,153)(147,154)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)
(161,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)
(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,218)
(198,219)(199,220)(200,221)(201,222)(202,223)(203,224)(204,211)(205,212)
(206,213)(207,214)(208,215)(209,216)(210,217)(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)(281,323)(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)(477,540)(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)(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)(589,652)(590,653)(591,654)(592,655)(593,656)(594,657)(595,658)
(596,645)(597,646)(598,647)(599,648)(600,649)(601,650)(602,651)(603,666)
(604,667)(605,668)(606,669)(607,670)(608,671)(609,672)(610,659)(611,660)
(612,661)(613,662)(614,663)(615,664)(616,665)(673,764)(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)!( 1,673)( 2,674)( 3,675)( 4,676)( 5,677)( 6,678)( 7,679)
( 8,680)( 9,681)( 10,682)( 11,683)( 12,684)( 13,685)( 14,686)( 15,687)
( 16,688)( 17,689)( 18,690)( 19,691)( 20,692)( 21,693)( 22,694)( 23,695)
( 24,696)( 25,697)( 26,698)( 27,699)( 28,700)( 29,701)( 30,702)( 31,703)
( 32,704)( 33,705)( 34,706)( 35,707)( 36,708)( 37,709)( 38,710)( 39,711)
( 40,712)( 41,713)( 42,714)( 43,715)( 44,716)( 45,717)( 46,718)( 47,719)
( 48,720)( 49,721)( 50,722)( 51,723)( 52,724)( 53,725)( 54,726)( 55,727)
( 56,728)( 57,750)( 58,751)( 59,752)( 60,753)( 61,754)( 62,755)( 63,756)
( 64,743)( 65,744)( 66,745)( 67,746)( 68,747)( 69,748)( 70,749)( 71,736)
( 72,737)( 73,738)( 74,739)( 75,740)( 76,741)( 77,742)( 78,729)( 79,730)
( 80,731)( 81,732)( 82,733)( 83,734)( 84,735)( 85,778)( 86,779)( 87,780)
( 88,781)( 89,782)( 90,783)( 91,784)( 92,771)( 93,772)( 94,773)( 95,774)
( 96,775)( 97,776)( 98,777)( 99,764)(100,765)(101,766)(102,767)(103,768)
(104,769)(105,770)(106,757)(107,758)(108,759)(109,760)(110,761)(111,762)
(112,763)(113,785)(114,786)(115,787)(116,788)(117,789)(118,790)(119,791)
(120,792)(121,793)(122,794)(123,795)(124,796)(125,797)(126,798)(127,799)
(128,800)(129,801)(130,802)(131,803)(132,804)(133,805)(134,806)(135,807)
(136,808)(137,809)(138,810)(139,811)(140,812)(141,813)(142,814)(143,815)
(144,816)(145,817)(146,818)(147,819)(148,820)(149,821)(150,822)(151,823)
(152,824)(153,825)(154,826)(155,827)(156,828)(157,829)(158,830)(159,831)
(160,832)(161,833)(162,834)(163,835)(164,836)(165,837)(166,838)(167,839)
(168,840)(169,862)(170,863)(171,864)(172,865)(173,866)(174,867)(175,868)
(176,855)(177,856)(178,857)(179,858)(180,859)(181,860)(182,861)(183,848)
(184,849)(185,850)(186,851)(187,852)(188,853)(189,854)(190,841)(191,842)
(192,843)(193,844)(194,845)(195,846)(196,847)(197,890)(198,891)(199,892)
(200,893)(201,894)(202,895)(203,896)(204,883)(205,884)(206,885)(207,886)
(208,887)(209,888)(210,889)(211,876)(212,877)(213,878)(214,879)(215,880)
(216,881)(217,882)(218,869)(219,870)(220,871)(221,872)(222,873)(223,874)
(224,875)(225,449)(226,450)(227,451)(228,452)(229,453)(230,454)(231,455)
(232,456)(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)
(240,464)(241,465)(242,466)(243,467)(244,468)(245,469)(246,470)(247,471)
(248,472)(249,473)(250,474)(251,475)(252,476)(253,477)(254,478)(255,479)
(256,480)(257,481)(258,482)(259,483)(260,484)(261,485)(262,486)(263,487)
(264,488)(265,489)(266,490)(267,491)(268,492)(269,493)(270,494)(271,495)
(272,496)(273,497)(274,498)(275,499)(276,500)(277,501)(278,502)(279,503)
(280,504)(281,526)(282,527)(283,528)(284,529)(285,530)(286,531)(287,532)
(288,519)(289,520)(290,521)(291,522)(292,523)(293,524)(294,525)(295,512)
(296,513)(297,514)(298,515)(299,516)(300,517)(301,518)(302,505)(303,506)
(304,507)(305,508)(306,509)(307,510)(308,511)(309,554)(310,555)(311,556)
(312,557)(313,558)(314,559)(315,560)(316,547)(317,548)(318,549)(319,550)
(320,551)(321,552)(322,553)(323,540)(324,541)(325,542)(326,543)(327,544)
(328,545)(329,546)(330,533)(331,534)(332,535)(333,536)(334,537)(335,538)
(336,539)(337,561)(338,562)(339,563)(340,564)(341,565)(342,566)(343,567)
(344,568)(345,569)(346,570)(347,571)(348,572)(349,573)(350,574)(351,575)
(352,576)(353,577)(354,578)(355,579)(356,580)(357,581)(358,582)(359,583)
(360,584)(361,585)(362,586)(363,587)(364,588)(365,589)(366,590)(367,591)
(368,592)(369,593)(370,594)(371,595)(372,596)(373,597)(374,598)(375,599)
(376,600)(377,601)(378,602)(379,603)(380,604)(381,605)(382,606)(383,607)
(384,608)(385,609)(386,610)(387,611)(388,612)(389,613)(390,614)(391,615)
(392,616)(393,638)(394,639)(395,640)(396,641)(397,642)(398,643)(399,644)
(400,631)(401,632)(402,633)(403,634)(404,635)(405,636)(406,637)(407,624)
(408,625)(409,626)(410,627)(411,628)(412,629)(413,630)(414,617)(415,618)
(416,619)(417,620)(418,621)(419,622)(420,623)(421,666)(422,667)(423,668)
(424,669)(425,670)(426,671)(427,672)(428,659)(429,660)(430,661)(431,662)
(432,663)(433,664)(434,665)(435,652)(436,653)(437,654)(438,655)(439,656)
(440,657)(441,658)(442,645)(443,646)(444,647)(445,648)(446,649)(447,650)
(448,651);
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*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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