Polytope of Type {14,16,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,16,4}*1792b
if this polytope has a name.
Group : SmallGroup(1792,323449)
Rank : 4
Schlafli Type : {14,16,4}
Number of vertices, edges, etc : 14, 112, 32, 4
Order of s0s1s2s3 : 112
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 : {14,8,4}*896a
4-fold quotients : {14,4,4}*448, {14,8,2}*448
7-fold quotients : {2,16,4}*256b
8-fold quotients : {14,2,4}*224, {14,4,2}*224
14-fold quotients : {2,8,4}*128a
16-fold quotients : {7,2,4}*112, {14,2,2}*112
28-fold quotients : {2,4,4}*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 := ( 1,562)( 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)( 15,583)( 16,582)
( 17,588)( 18,587)( 19,586)( 20,585)( 21,584)( 22,576)( 23,575)( 24,581)
( 25,580)( 26,579)( 27,578)( 28,577)( 29,597)( 30,596)( 31,602)( 32,601)
( 33,600)( 34,599)( 35,598)( 36,590)( 37,589)( 38,595)( 39,594)( 40,593)
( 41,592)( 42,591)( 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)
( 57,632)( 58,631)( 59,637)( 60,636)( 61,635)( 62,634)( 63,633)( 64,639)
( 65,638)( 66,644)( 67,643)( 68,642)( 69,641)( 70,640)( 71,618)( 72,617)
( 73,623)( 74,622)( 75,621)( 76,620)( 77,619)( 78,625)( 79,624)( 80,630)
( 81,629)( 82,628)( 83,627)( 84,626)( 85,667)( 86,666)( 87,672)( 88,671)
( 89,670)( 90,669)( 91,668)( 92,660)( 93,659)( 94,665)( 95,664)( 96,663)
( 97,662)( 98,661)( 99,653)(100,652)(101,658)(102,657)(103,656)(104,655)
(105,654)(106,646)(107,645)(108,651)(109,650)(110,649)(111,648)(112,647)
(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)(127,471)(128,470)
(129,476)(130,475)(131,474)(132,473)(133,472)(134,464)(135,463)(136,469)
(137,468)(138,467)(139,466)(140,465)(141,485)(142,484)(143,490)(144,489)
(145,488)(146,487)(147,486)(148,478)(149,477)(150,483)(151,482)(152,481)
(153,480)(154,479)(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)
(169,520)(170,519)(171,525)(172,524)(173,523)(174,522)(175,521)(176,527)
(177,526)(178,532)(179,531)(180,530)(181,529)(182,528)(183,506)(184,505)
(185,511)(186,510)(187,509)(188,508)(189,507)(190,513)(191,512)(192,518)
(193,517)(194,516)(195,515)(196,514)(197,555)(198,554)(199,560)(200,559)
(201,558)(202,557)(203,556)(204,548)(205,547)(206,553)(207,552)(208,551)
(209,550)(210,549)(211,541)(212,540)(213,546)(214,545)(215,544)(216,543)
(217,542)(218,534)(219,533)(220,539)(221,538)(222,537)(223,536)(224,535)
(225,786)(226,785)(227,791)(228,790)(229,789)(230,788)(231,787)(232,793)
(233,792)(234,798)(235,797)(236,796)(237,795)(238,794)(239,807)(240,806)
(241,812)(242,811)(243,810)(244,809)(245,808)(246,800)(247,799)(248,805)
(249,804)(250,803)(251,802)(252,801)(253,821)(254,820)(255,826)(256,825)
(257,824)(258,823)(259,822)(260,814)(261,813)(262,819)(263,818)(264,817)
(265,816)(266,815)(267,828)(268,827)(269,833)(270,832)(271,831)(272,830)
(273,829)(274,835)(275,834)(276,840)(277,839)(278,838)(279,837)(280,836)
(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)(309,891)(310,890)(311,896)(312,895)
(313,894)(314,893)(315,892)(316,884)(317,883)(318,889)(319,888)(320,887)
(321,886)(322,885)(323,877)(324,876)(325,882)(326,881)(327,880)(328,879)
(329,878)(330,870)(331,869)(332,875)(333,874)(334,873)(335,872)(336,871)
(337,674)(338,673)(339,679)(340,678)(341,677)(342,676)(343,675)(344,681)
(345,680)(346,686)(347,685)(348,684)(349,683)(350,682)(351,695)(352,694)
(353,700)(354,699)(355,698)(356,697)(357,696)(358,688)(359,687)(360,693)
(361,692)(362,691)(363,690)(364,689)(365,709)(366,708)(367,714)(368,713)
(369,712)(370,711)(371,710)(372,702)(373,701)(374,707)(375,706)(376,705)
(377,704)(378,703)(379,716)(380,715)(381,721)(382,720)(383,719)(384,718)
(385,717)(386,723)(387,722)(388,728)(389,727)(390,726)(391,725)(392,724)
(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)(421,779)(422,778)(423,784)(424,783)
(425,782)(426,781)(427,780)(428,772)(429,771)(430,777)(431,776)(432,775)
(433,774)(434,773)(435,765)(436,764)(437,770)(438,769)(439,768)(440,767)
(441,766)(442,758)(443,757)(444,763)(445,762)(446,761)(447,760)(448,759);;
s2 := ( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 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, 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)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)
(133,140)(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)(197,211)(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)(239,274)(240,275)(241,276)(242,277)(243,278)(244,279)
(245,280)(246,267)(247,268)(248,269)(249,270)(250,271)(251,272)(252,273)
(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)(351,386)(352,387)(353,388)(354,389)(355,390)(356,391)
(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)(364,385)
(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)(463,526)(464,527)(465,528)(466,529)(467,530)(468,531)
(469,532)(470,519)(471,520)(472,521)(473,522)(474,523)(475,524)(476,525)
(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)(491,554)(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)(575,638)(576,639)(577,640)(578,641)(579,642)(580,643)
(581,644)(582,631)(583,632)(584,633)(585,634)(586,635)(587,636)(588,637)
(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)(603,666)(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)(687,771)(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)
(701,736)(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)(715,743)(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)(785,876)(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)(799,883)(800,884)(801,885)(802,886)(803,887)(804,888)
(805,889)(806,890)(807,891)(808,892)(809,893)(810,894)(811,895)(812,896)
(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)(827,855)(828,856)
(829,857)(830,858)(831,859)(832,860)(833,861)(834,862)(835,863)(836,864)
(837,865)(838,866)(839,867)(840,868);;
s3 := ( 1,225)( 2,226)( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)( 8,232)
( 9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)
( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)
( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)( 32,256)
( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)
( 41,265)( 42,266)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)( 48,272)
( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)
( 57,288)( 58,289)( 59,290)( 60,291)( 61,292)( 62,293)( 63,294)( 64,281)
( 65,282)( 66,283)( 67,284)( 68,285)( 69,286)( 70,287)( 71,302)( 72,303)
( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)( 80,297)
( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)( 88,319)
( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)( 96,313)
( 97,314)( 98,315)( 99,330)(100,331)(101,332)(102,333)(103,334)(104,335)
(105,336)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)(112,329)
(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)
(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)
(129,353)(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)
(137,361)(138,362)(139,363)(140,364)(141,365)(142,366)(143,367)(144,368)
(145,369)(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)(152,376)
(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)
(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)
(169,400)(170,401)(171,402)(172,403)(173,404)(174,405)(175,406)(176,393)
(177,394)(178,395)(179,396)(180,397)(181,398)(182,399)(183,414)(184,415)
(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)(192,409)
(193,410)(194,411)(195,412)(196,413)(197,428)(198,429)(199,430)(200,431)
(201,432)(202,433)(203,434)(204,421)(205,422)(206,423)(207,424)(208,425)
(209,426)(210,427)(211,442)(212,443)(213,444)(214,445)(215,446)(216,447)
(217,448)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)(224,441)
(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)(456,680)
(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,687)(464,688)
(465,689)(466,690)(467,691)(468,692)(469,693)(470,694)(471,695)(472,696)
(473,697)(474,698)(475,699)(476,700)(477,701)(478,702)(479,703)(480,704)
(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)(488,712)
(489,713)(490,714)(491,715)(492,716)(493,717)(494,718)(495,719)(496,720)
(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)(504,728)
(505,736)(506,737)(507,738)(508,739)(509,740)(510,741)(511,742)(512,729)
(513,730)(514,731)(515,732)(516,733)(517,734)(518,735)(519,750)(520,751)
(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)(528,745)
(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)(536,767)
(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)(544,761)
(545,762)(546,763)(547,778)(548,779)(549,780)(550,781)(551,782)(552,783)
(553,784)(554,771)(555,772)(556,773)(557,774)(558,775)(559,776)(560,777)
(561,785)(562,786)(563,787)(564,788)(565,789)(566,790)(567,791)(568,792)
(569,793)(570,794)(571,795)(572,796)(573,797)(574,798)(575,799)(576,800)
(577,801)(578,802)(579,803)(580,804)(581,805)(582,806)(583,807)(584,808)
(585,809)(586,810)(587,811)(588,812)(589,813)(590,814)(591,815)(592,816)
(593,817)(594,818)(595,819)(596,820)(597,821)(598,822)(599,823)(600,824)
(601,825)(602,826)(603,827)(604,828)(605,829)(606,830)(607,831)(608,832)
(609,833)(610,834)(611,835)(612,836)(613,837)(614,838)(615,839)(616,840)
(617,848)(618,849)(619,850)(620,851)(621,852)(622,853)(623,854)(624,841)
(625,842)(626,843)(627,844)(628,845)(629,846)(630,847)(631,862)(632,863)
(633,864)(634,865)(635,866)(636,867)(637,868)(638,855)(639,856)(640,857)
(641,858)(642,859)(643,860)(644,861)(645,876)(646,877)(647,878)(648,879)
(649,880)(650,881)(651,882)(652,869)(653,870)(654,871)(655,872)(656,873)
(657,874)(658,875)(659,890)(660,891)(661,892)(662,893)(663,894)(664,895)
(665,896)(666,883)(667,884)(668,885)(669,886)(670,887)(671,888)(672,889);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
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)!( 1,562)( 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)( 15,583)
( 16,582)( 17,588)( 18,587)( 19,586)( 20,585)( 21,584)( 22,576)( 23,575)
( 24,581)( 25,580)( 26,579)( 27,578)( 28,577)( 29,597)( 30,596)( 31,602)
( 32,601)( 33,600)( 34,599)( 35,598)( 36,590)( 37,589)( 38,595)( 39,594)
( 40,593)( 41,592)( 42,591)( 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)( 57,632)( 58,631)( 59,637)( 60,636)( 61,635)( 62,634)( 63,633)
( 64,639)( 65,638)( 66,644)( 67,643)( 68,642)( 69,641)( 70,640)( 71,618)
( 72,617)( 73,623)( 74,622)( 75,621)( 76,620)( 77,619)( 78,625)( 79,624)
( 80,630)( 81,629)( 82,628)( 83,627)( 84,626)( 85,667)( 86,666)( 87,672)
( 88,671)( 89,670)( 90,669)( 91,668)( 92,660)( 93,659)( 94,665)( 95,664)
( 96,663)( 97,662)( 98,661)( 99,653)(100,652)(101,658)(102,657)(103,656)
(104,655)(105,654)(106,646)(107,645)(108,651)(109,650)(110,649)(111,648)
(112,647)(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)(127,471)
(128,470)(129,476)(130,475)(131,474)(132,473)(133,472)(134,464)(135,463)
(136,469)(137,468)(138,467)(139,466)(140,465)(141,485)(142,484)(143,490)
(144,489)(145,488)(146,487)(147,486)(148,478)(149,477)(150,483)(151,482)
(152,481)(153,480)(154,479)(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)(169,520)(170,519)(171,525)(172,524)(173,523)(174,522)(175,521)
(176,527)(177,526)(178,532)(179,531)(180,530)(181,529)(182,528)(183,506)
(184,505)(185,511)(186,510)(187,509)(188,508)(189,507)(190,513)(191,512)
(192,518)(193,517)(194,516)(195,515)(196,514)(197,555)(198,554)(199,560)
(200,559)(201,558)(202,557)(203,556)(204,548)(205,547)(206,553)(207,552)
(208,551)(209,550)(210,549)(211,541)(212,540)(213,546)(214,545)(215,544)
(216,543)(217,542)(218,534)(219,533)(220,539)(221,538)(222,537)(223,536)
(224,535)(225,786)(226,785)(227,791)(228,790)(229,789)(230,788)(231,787)
(232,793)(233,792)(234,798)(235,797)(236,796)(237,795)(238,794)(239,807)
(240,806)(241,812)(242,811)(243,810)(244,809)(245,808)(246,800)(247,799)
(248,805)(249,804)(250,803)(251,802)(252,801)(253,821)(254,820)(255,826)
(256,825)(257,824)(258,823)(259,822)(260,814)(261,813)(262,819)(263,818)
(264,817)(265,816)(266,815)(267,828)(268,827)(269,833)(270,832)(271,831)
(272,830)(273,829)(274,835)(275,834)(276,840)(277,839)(278,838)(279,837)
(280,836)(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)(309,891)(310,890)(311,896)
(312,895)(313,894)(314,893)(315,892)(316,884)(317,883)(318,889)(319,888)
(320,887)(321,886)(322,885)(323,877)(324,876)(325,882)(326,881)(327,880)
(328,879)(329,878)(330,870)(331,869)(332,875)(333,874)(334,873)(335,872)
(336,871)(337,674)(338,673)(339,679)(340,678)(341,677)(342,676)(343,675)
(344,681)(345,680)(346,686)(347,685)(348,684)(349,683)(350,682)(351,695)
(352,694)(353,700)(354,699)(355,698)(356,697)(357,696)(358,688)(359,687)
(360,693)(361,692)(362,691)(363,690)(364,689)(365,709)(366,708)(367,714)
(368,713)(369,712)(370,711)(371,710)(372,702)(373,701)(374,707)(375,706)
(376,705)(377,704)(378,703)(379,716)(380,715)(381,721)(382,720)(383,719)
(384,718)(385,717)(386,723)(387,722)(388,728)(389,727)(390,726)(391,725)
(392,724)(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)(421,779)(422,778)(423,784)
(424,783)(425,782)(426,781)(427,780)(428,772)(429,771)(430,777)(431,776)
(432,775)(433,774)(434,773)(435,765)(436,764)(437,770)(438,769)(439,768)
(440,767)(441,766)(442,758)(443,757)(444,763)(445,762)(446,761)(447,760)
(448,759);
s2 := Sym(896)!( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)
( 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, 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)(127,134)(128,135)(129,136)(130,137)(131,138)
(132,139)(133,140)(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)(197,211)
(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)(239,274)(240,275)(241,276)(242,277)(243,278)
(244,279)(245,280)(246,267)(247,268)(248,269)(249,270)(250,271)(251,272)
(252,273)(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)(351,386)(352,387)(353,388)(354,389)(355,390)
(356,391)(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)
(364,385)(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)(463,526)(464,527)(465,528)(466,529)(467,530)
(468,531)(469,532)(470,519)(471,520)(472,521)(473,522)(474,523)(475,524)
(476,525)(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)(491,554)
(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)(575,638)(576,639)(577,640)(578,641)(579,642)
(580,643)(581,644)(582,631)(583,632)(584,633)(585,634)(586,635)(587,636)
(588,637)(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)(603,666)
(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)(687,771)(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)(701,736)(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)(715,743)
(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)(785,876)(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)(799,883)(800,884)(801,885)(802,886)(803,887)
(804,888)(805,889)(806,890)(807,891)(808,892)(809,893)(810,894)(811,895)
(812,896)(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)(827,855)
(828,856)(829,857)(830,858)(831,859)(832,860)(833,861)(834,862)(835,863)
(836,864)(837,865)(838,866)(839,867)(840,868);
s3 := Sym(896)!( 1,225)( 2,226)( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)
( 8,232)( 9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)
( 16,240)( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)
( 24,248)( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)
( 32,256)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)
( 40,264)( 41,265)( 42,266)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)
( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)
( 56,280)( 57,288)( 58,289)( 59,290)( 60,291)( 61,292)( 62,293)( 63,294)
( 64,281)( 65,282)( 66,283)( 67,284)( 68,285)( 69,286)( 70,287)( 71,302)
( 72,303)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)
( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)
( 88,319)( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)
( 96,313)( 97,314)( 98,315)( 99,330)(100,331)(101,332)(102,333)(103,334)
(104,335)(105,336)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)
(112,329)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)
(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)
(128,352)(129,353)(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)
(136,360)(137,361)(138,362)(139,363)(140,364)(141,365)(142,366)(143,367)
(144,368)(145,369)(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)
(152,376)(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)
(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)
(168,392)(169,400)(170,401)(171,402)(172,403)(173,404)(174,405)(175,406)
(176,393)(177,394)(178,395)(179,396)(180,397)(181,398)(182,399)(183,414)
(184,415)(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)
(192,409)(193,410)(194,411)(195,412)(196,413)(197,428)(198,429)(199,430)
(200,431)(201,432)(202,433)(203,434)(204,421)(205,422)(206,423)(207,424)
(208,425)(209,426)(210,427)(211,442)(212,443)(213,444)(214,445)(215,446)
(216,447)(217,448)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)
(224,441)(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)
(456,680)(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,687)
(464,688)(465,689)(466,690)(467,691)(468,692)(469,693)(470,694)(471,695)
(472,696)(473,697)(474,698)(475,699)(476,700)(477,701)(478,702)(479,703)
(480,704)(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)
(488,712)(489,713)(490,714)(491,715)(492,716)(493,717)(494,718)(495,719)
(496,720)(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)
(504,728)(505,736)(506,737)(507,738)(508,739)(509,740)(510,741)(511,742)
(512,729)(513,730)(514,731)(515,732)(516,733)(517,734)(518,735)(519,750)
(520,751)(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)
(528,745)(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)
(536,767)(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)
(544,761)(545,762)(546,763)(547,778)(548,779)(549,780)(550,781)(551,782)
(552,783)(553,784)(554,771)(555,772)(556,773)(557,774)(558,775)(559,776)
(560,777)(561,785)(562,786)(563,787)(564,788)(565,789)(566,790)(567,791)
(568,792)(569,793)(570,794)(571,795)(572,796)(573,797)(574,798)(575,799)
(576,800)(577,801)(578,802)(579,803)(580,804)(581,805)(582,806)(583,807)
(584,808)(585,809)(586,810)(587,811)(588,812)(589,813)(590,814)(591,815)
(592,816)(593,817)(594,818)(595,819)(596,820)(597,821)(598,822)(599,823)
(600,824)(601,825)(602,826)(603,827)(604,828)(605,829)(606,830)(607,831)
(608,832)(609,833)(610,834)(611,835)(612,836)(613,837)(614,838)(615,839)
(616,840)(617,848)(618,849)(619,850)(620,851)(621,852)(622,853)(623,854)
(624,841)(625,842)(626,843)(627,844)(628,845)(629,846)(630,847)(631,862)
(632,863)(633,864)(634,865)(635,866)(636,867)(637,868)(638,855)(639,856)
(640,857)(641,858)(642,859)(643,860)(644,861)(645,876)(646,877)(647,878)
(648,879)(649,880)(650,881)(651,882)(652,869)(653,870)(654,871)(655,872)
(656,873)(657,874)(658,875)(659,890)(660,891)(661,892)(662,893)(663,894)
(664,895)(665,896)(666,883)(667,884)(668,885)(669,886)(670,887)(671,888)
(672,889);
poly := sub<Sym(896)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope