Polytope of Type {8,8,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8,14}*1792d
if this polytope has a name.
Group : SmallGroup(1792,150681)
Rank : 4
Schlafli Type : {8,8,14}
Number of vertices, edges, etc : 8, 32, 56, 14
Order of s0s1s2s3 : 56
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,8,14}*896b, {8,4,14}*896b
4-fold quotients : {4,4,14}*448
7-fold quotients : {8,8,2}*256d
8-fold quotients : {2,4,14}*224, {4,2,14}*224
14-fold quotients : {4,8,2}*128b, {8,4,2}*128b
16-fold quotients : {4,2,7}*112, {2,2,14}*112
28-fold quotients : {4,4,2}*64
32-fold quotients : {2,2,7}*56
56-fold quotients : {2,4,2}*32, {4,2,2}*32
112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,225)( 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)( 29,274)( 30,275)( 31,276)( 32,277)
( 33,278)( 34,279)( 35,280)( 36,267)( 37,268)( 38,269)( 39,270)( 40,271)
( 41,272)( 42,273)( 43,260)( 44,261)( 45,262)( 46,263)( 47,264)( 48,265)
( 49,266)( 50,253)( 51,254)( 52,255)( 53,256)( 54,257)( 55,258)( 56,259)
( 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)( 85,323)( 86,324)( 87,325)( 88,326)
( 89,327)( 90,328)( 91,329)( 92,330)( 93,331)( 94,332)( 95,333)( 96,334)
( 97,335)( 98,336)( 99,309)(100,310)(101,311)(102,312)(103,313)(104,314)
(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)
(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)(141,386)(142,387)(143,388)(144,389)
(145,390)(146,391)(147,392)(148,379)(149,380)(150,381)(151,382)(152,383)
(153,384)(154,385)(155,372)(156,373)(157,374)(158,375)(159,376)(160,377)
(161,378)(162,365)(163,366)(164,367)(165,368)(166,369)(167,370)(168,371)
(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)(197,435)(198,436)(199,437)(200,438)
(201,439)(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)(208,446)
(209,447)(210,448)(211,421)(212,422)(213,423)(214,424)(215,425)(216,426)
(217,427)(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)(224,434)
(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)(477,722)(478,723)(479,724)(480,725)
(481,726)(482,727)(483,728)(484,715)(485,716)(486,717)(487,718)(488,719)
(489,720)(490,721)(491,708)(492,709)(493,710)(494,711)(495,712)(496,713)
(497,714)(498,701)(499,702)(500,703)(501,704)(502,705)(503,706)(504,707)
(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)(533,771)(534,772)(535,773)(536,774)
(537,775)(538,776)(539,777)(540,778)(541,779)(542,780)(543,781)(544,782)
(545,783)(546,784)(547,757)(548,758)(549,759)(550,760)(551,761)(552,762)
(553,763)(554,764)(555,765)(556,766)(557,767)(558,768)(559,769)(560,770)
(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)(589,834)(590,835)(591,836)(592,837)
(593,838)(594,839)(595,840)(596,827)(597,828)(598,829)(599,830)(600,831)
(601,832)(602,833)(603,820)(604,821)(605,822)(606,823)(607,824)(608,825)
(609,826)(610,813)(611,814)(612,815)(613,816)(614,817)(615,818)(616,819)
(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)(645,883)(646,884)(647,885)(648,886)
(649,887)(650,888)(651,889)(652,890)(653,891)(654,892)(655,893)(656,894)
(657,895)(658,896)(659,869)(660,870)(661,871)(662,872)(663,873)(664,874)
(665,875)(666,876)(667,877)(668,878)(669,879)(670,880)(671,881)(672,882);;
s1 := ( 29, 50)( 30, 51)( 31, 52)( 32, 53)( 33, 54)( 34, 55)( 35, 56)( 36, 43)
( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 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, 92)( 86, 93)( 87, 94)( 88, 95)
( 89, 96)( 90, 97)( 91, 98)( 99,106)(100,107)(101,108)(102,109)(103,110)
(104,111)(105,112)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)
(147,168)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161)
(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)(197,204)(198,205)
(199,206)(200,207)(201,208)(202,209)(203,210)(211,218)(212,219)(213,220)
(214,221)(215,222)(216,223)(217,224)(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)
(477,554)(478,555)(479,556)(480,557)(481,558)(482,559)(483,560)(484,547)
(485,548)(486,549)(487,550)(488,551)(489,552)(490,553)(491,540)(492,541)
(493,542)(494,543)(495,544)(496,545)(497,546)(498,533)(499,534)(500,535)
(501,536)(502,537)(503,538)(504,539)(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)
(589,666)(590,667)(591,668)(592,669)(593,670)(594,671)(595,672)(596,659)
(597,660)(598,661)(599,662)(600,663)(601,664)(602,665)(603,652)(604,653)
(605,654)(606,655)(607,656)(608,657)(609,658)(610,645)(611,646)(612,647)
(613,648)(614,649)(615,650)(616,651)(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);;
s2 := ( 1,561)( 2,567)( 3,566)( 4,565)( 5,564)( 6,563)( 7,562)( 8,568)
( 9,574)( 10,573)( 11,572)( 12,571)( 13,570)( 14,569)( 15,575)( 16,581)
( 17,580)( 18,579)( 19,578)( 20,577)( 21,576)( 22,582)( 23,588)( 24,587)
( 25,586)( 26,585)( 27,584)( 28,583)( 29,596)( 30,602)( 31,601)( 32,600)
( 33,599)( 34,598)( 35,597)( 36,589)( 37,595)( 38,594)( 39,593)( 40,592)
( 41,591)( 42,590)( 43,610)( 44,616)( 45,615)( 46,614)( 47,613)( 48,612)
( 49,611)( 50,603)( 51,609)( 52,608)( 53,607)( 54,606)( 55,605)( 56,604)
( 57,631)( 58,637)( 59,636)( 60,635)( 61,634)( 62,633)( 63,632)( 64,638)
( 65,644)( 66,643)( 67,642)( 68,641)( 69,640)( 70,639)( 71,617)( 72,623)
( 73,622)( 74,621)( 75,620)( 76,619)( 77,618)( 78,624)( 79,630)( 80,629)
( 81,628)( 82,627)( 83,626)( 84,625)( 85,666)( 86,672)( 87,671)( 88,670)
( 89,669)( 90,668)( 91,667)( 92,659)( 93,665)( 94,664)( 95,663)( 96,662)
( 97,661)( 98,660)( 99,652)(100,658)(101,657)(102,656)(103,655)(104,654)
(105,653)(106,645)(107,651)(108,650)(109,649)(110,648)(111,647)(112,646)
(113,449)(114,455)(115,454)(116,453)(117,452)(118,451)(119,450)(120,456)
(121,462)(122,461)(123,460)(124,459)(125,458)(126,457)(127,463)(128,469)
(129,468)(130,467)(131,466)(132,465)(133,464)(134,470)(135,476)(136,475)
(137,474)(138,473)(139,472)(140,471)(141,484)(142,490)(143,489)(144,488)
(145,487)(146,486)(147,485)(148,477)(149,483)(150,482)(151,481)(152,480)
(153,479)(154,478)(155,498)(156,504)(157,503)(158,502)(159,501)(160,500)
(161,499)(162,491)(163,497)(164,496)(165,495)(166,494)(167,493)(168,492)
(169,519)(170,525)(171,524)(172,523)(173,522)(174,521)(175,520)(176,526)
(177,532)(178,531)(179,530)(180,529)(181,528)(182,527)(183,505)(184,511)
(185,510)(186,509)(187,508)(188,507)(189,506)(190,512)(191,518)(192,517)
(193,516)(194,515)(195,514)(196,513)(197,554)(198,560)(199,559)(200,558)
(201,557)(202,556)(203,555)(204,547)(205,553)(206,552)(207,551)(208,550)
(209,549)(210,548)(211,540)(212,546)(213,545)(214,544)(215,543)(216,542)
(217,541)(218,533)(219,539)(220,538)(221,537)(222,536)(223,535)(224,534)
(225,785)(226,791)(227,790)(228,789)(229,788)(230,787)(231,786)(232,792)
(233,798)(234,797)(235,796)(236,795)(237,794)(238,793)(239,799)(240,805)
(241,804)(242,803)(243,802)(244,801)(245,800)(246,806)(247,812)(248,811)
(249,810)(250,809)(251,808)(252,807)(253,820)(254,826)(255,825)(256,824)
(257,823)(258,822)(259,821)(260,813)(261,819)(262,818)(263,817)(264,816)
(265,815)(266,814)(267,834)(268,840)(269,839)(270,838)(271,837)(272,836)
(273,835)(274,827)(275,833)(276,832)(277,831)(278,830)(279,829)(280,828)
(281,855)(282,861)(283,860)(284,859)(285,858)(286,857)(287,856)(288,862)
(289,868)(290,867)(291,866)(292,865)(293,864)(294,863)(295,841)(296,847)
(297,846)(298,845)(299,844)(300,843)(301,842)(302,848)(303,854)(304,853)
(305,852)(306,851)(307,850)(308,849)(309,890)(310,896)(311,895)(312,894)
(313,893)(314,892)(315,891)(316,883)(317,889)(318,888)(319,887)(320,886)
(321,885)(322,884)(323,876)(324,882)(325,881)(326,880)(327,879)(328,878)
(329,877)(330,869)(331,875)(332,874)(333,873)(334,872)(335,871)(336,870)
(337,673)(338,679)(339,678)(340,677)(341,676)(342,675)(343,674)(344,680)
(345,686)(346,685)(347,684)(348,683)(349,682)(350,681)(351,687)(352,693)
(353,692)(354,691)(355,690)(356,689)(357,688)(358,694)(359,700)(360,699)
(361,698)(362,697)(363,696)(364,695)(365,708)(366,714)(367,713)(368,712)
(369,711)(370,710)(371,709)(372,701)(373,707)(374,706)(375,705)(376,704)
(377,703)(378,702)(379,722)(380,728)(381,727)(382,726)(383,725)(384,724)
(385,723)(386,715)(387,721)(388,720)(389,719)(390,718)(391,717)(392,716)
(393,743)(394,749)(395,748)(396,747)(397,746)(398,745)(399,744)(400,750)
(401,756)(402,755)(403,754)(404,753)(405,752)(406,751)(407,729)(408,735)
(409,734)(410,733)(411,732)(412,731)(413,730)(414,736)(415,742)(416,741)
(417,740)(418,739)(419,738)(420,737)(421,778)(422,784)(423,783)(424,782)
(425,781)(426,780)(427,779)(428,771)(429,777)(430,776)(431,775)(432,774)
(433,773)(434,772)(435,764)(436,770)(437,769)(438,768)(439,767)(440,766)
(441,765)(442,757)(443,763)(444,762)(445,761)(446,760)(447,759)(448,758);;
s3 := ( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)( 8,121)
( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)( 16,127)
( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)( 24,140)
( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)( 32,146)
( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)
( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)
( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)
( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)
( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)( 72,183)
( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)( 80,196)
( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)( 88,202)
( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)
( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)
(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220)
(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)(232,345)
(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)(240,351)
(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)(248,364)
(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)(256,370)
(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)(264,376)
(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)(272,382)
(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)(280,388)
(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)(288,401)
(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)(296,407)
(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)(304,420)
(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)(312,426)
(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)(320,432)
(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)(328,438)
(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)(336,444)
(449,562)(450,561)(451,567)(452,566)(453,565)(454,564)(455,563)(456,569)
(457,568)(458,574)(459,573)(460,572)(461,571)(462,570)(463,576)(464,575)
(465,581)(466,580)(467,579)(468,578)(469,577)(470,583)(471,582)(472,588)
(473,587)(474,586)(475,585)(476,584)(477,590)(478,589)(479,595)(480,594)
(481,593)(482,592)(483,591)(484,597)(485,596)(486,602)(487,601)(488,600)
(489,599)(490,598)(491,604)(492,603)(493,609)(494,608)(495,607)(496,606)
(497,605)(498,611)(499,610)(500,616)(501,615)(502,614)(503,613)(504,612)
(505,618)(506,617)(507,623)(508,622)(509,621)(510,620)(511,619)(512,625)
(513,624)(514,630)(515,629)(516,628)(517,627)(518,626)(519,632)(520,631)
(521,637)(522,636)(523,635)(524,634)(525,633)(526,639)(527,638)(528,644)
(529,643)(530,642)(531,641)(532,640)(533,646)(534,645)(535,651)(536,650)
(537,649)(538,648)(539,647)(540,653)(541,652)(542,658)(543,657)(544,656)
(545,655)(546,654)(547,660)(548,659)(549,665)(550,664)(551,663)(552,662)
(553,661)(554,667)(555,666)(556,672)(557,671)(558,670)(559,669)(560,668)
(673,786)(674,785)(675,791)(676,790)(677,789)(678,788)(679,787)(680,793)
(681,792)(682,798)(683,797)(684,796)(685,795)(686,794)(687,800)(688,799)
(689,805)(690,804)(691,803)(692,802)(693,801)(694,807)(695,806)(696,812)
(697,811)(698,810)(699,809)(700,808)(701,814)(702,813)(703,819)(704,818)
(705,817)(706,816)(707,815)(708,821)(709,820)(710,826)(711,825)(712,824)
(713,823)(714,822)(715,828)(716,827)(717,833)(718,832)(719,831)(720,830)
(721,829)(722,835)(723,834)(724,840)(725,839)(726,838)(727,837)(728,836)
(729,842)(730,841)(731,847)(732,846)(733,845)(734,844)(735,843)(736,849)
(737,848)(738,854)(739,853)(740,852)(741,851)(742,850)(743,856)(744,855)
(745,861)(746,860)(747,859)(748,858)(749,857)(750,863)(751,862)(752,868)
(753,867)(754,866)(755,865)(756,864)(757,870)(758,869)(759,875)(760,874)
(761,873)(762,872)(763,871)(764,877)(765,876)(766,882)(767,881)(768,880)
(769,879)(770,878)(771,884)(772,883)(773,889)(774,888)(775,887)(776,886)
(777,885)(778,891)(779,890)(780,896)(781,895)(782,894)(783,893)(784,892);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 29,274)( 30,275)( 31,276)
( 32,277)( 33,278)( 34,279)( 35,280)( 36,267)( 37,268)( 38,269)( 39,270)
( 40,271)( 41,272)( 42,273)( 43,260)( 44,261)( 45,262)( 46,263)( 47,264)
( 48,265)( 49,266)( 50,253)( 51,254)( 52,255)( 53,256)( 54,257)( 55,258)
( 56,259)( 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)( 85,323)( 86,324)( 87,325)
( 88,326)( 89,327)( 90,328)( 91,329)( 92,330)( 93,331)( 94,332)( 95,333)
( 96,334)( 97,335)( 98,336)( 99,309)(100,310)(101,311)(102,312)(103,313)
(104,314)(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)
(112,322)(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)(141,386)(142,387)(143,388)
(144,389)(145,390)(146,391)(147,392)(148,379)(149,380)(150,381)(151,382)
(152,383)(153,384)(154,385)(155,372)(156,373)(157,374)(158,375)(159,376)
(160,377)(161,378)(162,365)(163,366)(164,367)(165,368)(166,369)(167,370)
(168,371)(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)(197,435)(198,436)(199,437)
(200,438)(201,439)(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)
(208,446)(209,447)(210,448)(211,421)(212,422)(213,423)(214,424)(215,425)
(216,426)(217,427)(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)
(224,434)(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)(477,722)(478,723)(479,724)
(480,725)(481,726)(482,727)(483,728)(484,715)(485,716)(486,717)(487,718)
(488,719)(489,720)(490,721)(491,708)(492,709)(493,710)(494,711)(495,712)
(496,713)(497,714)(498,701)(499,702)(500,703)(501,704)(502,705)(503,706)
(504,707)(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)(533,771)(534,772)(535,773)
(536,774)(537,775)(538,776)(539,777)(540,778)(541,779)(542,780)(543,781)
(544,782)(545,783)(546,784)(547,757)(548,758)(549,759)(550,760)(551,761)
(552,762)(553,763)(554,764)(555,765)(556,766)(557,767)(558,768)(559,769)
(560,770)(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)(589,834)(590,835)(591,836)
(592,837)(593,838)(594,839)(595,840)(596,827)(597,828)(598,829)(599,830)
(600,831)(601,832)(602,833)(603,820)(604,821)(605,822)(606,823)(607,824)
(608,825)(609,826)(610,813)(611,814)(612,815)(613,816)(614,817)(615,818)
(616,819)(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)(645,883)(646,884)(647,885)
(648,886)(649,887)(650,888)(651,889)(652,890)(653,891)(654,892)(655,893)
(656,894)(657,895)(658,896)(659,869)(660,870)(661,871)(662,872)(663,873)
(664,874)(665,875)(666,876)(667,877)(668,878)(669,879)(670,880)(671,881)
(672,882);
s1 := Sym(896)!( 29, 50)( 30, 51)( 31, 52)( 32, 53)( 33, 54)( 34, 55)( 35, 56)
( 36, 43)( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 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, 92)( 86, 93)( 87, 94)
( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 99,106)(100,107)(101,108)(102,109)
(103,110)(104,111)(105,112)(141,162)(142,163)(143,164)(144,165)(145,166)
(146,167)(147,168)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)
(154,161)(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)(197,204)
(198,205)(199,206)(200,207)(201,208)(202,209)(203,210)(211,218)(212,219)
(213,220)(214,221)(215,222)(216,223)(217,224)(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)(477,554)(478,555)(479,556)(480,557)(481,558)(482,559)(483,560)
(484,547)(485,548)(486,549)(487,550)(488,551)(489,552)(490,553)(491,540)
(492,541)(493,542)(494,543)(495,544)(496,545)(497,546)(498,533)(499,534)
(500,535)(501,536)(502,537)(503,538)(504,539)(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)(589,666)(590,667)(591,668)(592,669)(593,670)(594,671)(595,672)
(596,659)(597,660)(598,661)(599,662)(600,663)(601,664)(602,665)(603,652)
(604,653)(605,654)(606,655)(607,656)(608,657)(609,658)(610,645)(611,646)
(612,647)(613,648)(614,649)(615,650)(616,651)(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);
s2 := Sym(896)!( 1,561)( 2,567)( 3,566)( 4,565)( 5,564)( 6,563)( 7,562)
( 8,568)( 9,574)( 10,573)( 11,572)( 12,571)( 13,570)( 14,569)( 15,575)
( 16,581)( 17,580)( 18,579)( 19,578)( 20,577)( 21,576)( 22,582)( 23,588)
( 24,587)( 25,586)( 26,585)( 27,584)( 28,583)( 29,596)( 30,602)( 31,601)
( 32,600)( 33,599)( 34,598)( 35,597)( 36,589)( 37,595)( 38,594)( 39,593)
( 40,592)( 41,591)( 42,590)( 43,610)( 44,616)( 45,615)( 46,614)( 47,613)
( 48,612)( 49,611)( 50,603)( 51,609)( 52,608)( 53,607)( 54,606)( 55,605)
( 56,604)( 57,631)( 58,637)( 59,636)( 60,635)( 61,634)( 62,633)( 63,632)
( 64,638)( 65,644)( 66,643)( 67,642)( 68,641)( 69,640)( 70,639)( 71,617)
( 72,623)( 73,622)( 74,621)( 75,620)( 76,619)( 77,618)( 78,624)( 79,630)
( 80,629)( 81,628)( 82,627)( 83,626)( 84,625)( 85,666)( 86,672)( 87,671)
( 88,670)( 89,669)( 90,668)( 91,667)( 92,659)( 93,665)( 94,664)( 95,663)
( 96,662)( 97,661)( 98,660)( 99,652)(100,658)(101,657)(102,656)(103,655)
(104,654)(105,653)(106,645)(107,651)(108,650)(109,649)(110,648)(111,647)
(112,646)(113,449)(114,455)(115,454)(116,453)(117,452)(118,451)(119,450)
(120,456)(121,462)(122,461)(123,460)(124,459)(125,458)(126,457)(127,463)
(128,469)(129,468)(130,467)(131,466)(132,465)(133,464)(134,470)(135,476)
(136,475)(137,474)(138,473)(139,472)(140,471)(141,484)(142,490)(143,489)
(144,488)(145,487)(146,486)(147,485)(148,477)(149,483)(150,482)(151,481)
(152,480)(153,479)(154,478)(155,498)(156,504)(157,503)(158,502)(159,501)
(160,500)(161,499)(162,491)(163,497)(164,496)(165,495)(166,494)(167,493)
(168,492)(169,519)(170,525)(171,524)(172,523)(173,522)(174,521)(175,520)
(176,526)(177,532)(178,531)(179,530)(180,529)(181,528)(182,527)(183,505)
(184,511)(185,510)(186,509)(187,508)(188,507)(189,506)(190,512)(191,518)
(192,517)(193,516)(194,515)(195,514)(196,513)(197,554)(198,560)(199,559)
(200,558)(201,557)(202,556)(203,555)(204,547)(205,553)(206,552)(207,551)
(208,550)(209,549)(210,548)(211,540)(212,546)(213,545)(214,544)(215,543)
(216,542)(217,541)(218,533)(219,539)(220,538)(221,537)(222,536)(223,535)
(224,534)(225,785)(226,791)(227,790)(228,789)(229,788)(230,787)(231,786)
(232,792)(233,798)(234,797)(235,796)(236,795)(237,794)(238,793)(239,799)
(240,805)(241,804)(242,803)(243,802)(244,801)(245,800)(246,806)(247,812)
(248,811)(249,810)(250,809)(251,808)(252,807)(253,820)(254,826)(255,825)
(256,824)(257,823)(258,822)(259,821)(260,813)(261,819)(262,818)(263,817)
(264,816)(265,815)(266,814)(267,834)(268,840)(269,839)(270,838)(271,837)
(272,836)(273,835)(274,827)(275,833)(276,832)(277,831)(278,830)(279,829)
(280,828)(281,855)(282,861)(283,860)(284,859)(285,858)(286,857)(287,856)
(288,862)(289,868)(290,867)(291,866)(292,865)(293,864)(294,863)(295,841)
(296,847)(297,846)(298,845)(299,844)(300,843)(301,842)(302,848)(303,854)
(304,853)(305,852)(306,851)(307,850)(308,849)(309,890)(310,896)(311,895)
(312,894)(313,893)(314,892)(315,891)(316,883)(317,889)(318,888)(319,887)
(320,886)(321,885)(322,884)(323,876)(324,882)(325,881)(326,880)(327,879)
(328,878)(329,877)(330,869)(331,875)(332,874)(333,873)(334,872)(335,871)
(336,870)(337,673)(338,679)(339,678)(340,677)(341,676)(342,675)(343,674)
(344,680)(345,686)(346,685)(347,684)(348,683)(349,682)(350,681)(351,687)
(352,693)(353,692)(354,691)(355,690)(356,689)(357,688)(358,694)(359,700)
(360,699)(361,698)(362,697)(363,696)(364,695)(365,708)(366,714)(367,713)
(368,712)(369,711)(370,710)(371,709)(372,701)(373,707)(374,706)(375,705)
(376,704)(377,703)(378,702)(379,722)(380,728)(381,727)(382,726)(383,725)
(384,724)(385,723)(386,715)(387,721)(388,720)(389,719)(390,718)(391,717)
(392,716)(393,743)(394,749)(395,748)(396,747)(397,746)(398,745)(399,744)
(400,750)(401,756)(402,755)(403,754)(404,753)(405,752)(406,751)(407,729)
(408,735)(409,734)(410,733)(411,732)(412,731)(413,730)(414,736)(415,742)
(416,741)(417,740)(418,739)(419,738)(420,737)(421,778)(422,784)(423,783)
(424,782)(425,781)(426,780)(427,779)(428,771)(429,777)(430,776)(431,775)
(432,774)(433,773)(434,772)(435,764)(436,770)(437,769)(438,768)(439,767)
(440,766)(441,765)(442,757)(443,763)(444,762)(445,761)(446,760)(447,759)
(448,758);
s3 := Sym(896)!( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)
( 8,121)( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)
( 16,127)( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)
( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)
( 32,146)( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)
( 40,152)( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)
( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)
( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)
( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)
( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)
( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)
( 88,202)( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)
( 96,208)( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)
(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)
(112,220)(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)
(232,345)(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)
(240,351)(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)
(248,364)(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)
(256,370)(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)
(264,376)(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)
(272,382)(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)
(280,388)(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)
(288,401)(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)
(296,407)(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)
(304,420)(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)
(312,426)(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)
(320,432)(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)
(328,438)(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)
(336,444)(449,562)(450,561)(451,567)(452,566)(453,565)(454,564)(455,563)
(456,569)(457,568)(458,574)(459,573)(460,572)(461,571)(462,570)(463,576)
(464,575)(465,581)(466,580)(467,579)(468,578)(469,577)(470,583)(471,582)
(472,588)(473,587)(474,586)(475,585)(476,584)(477,590)(478,589)(479,595)
(480,594)(481,593)(482,592)(483,591)(484,597)(485,596)(486,602)(487,601)
(488,600)(489,599)(490,598)(491,604)(492,603)(493,609)(494,608)(495,607)
(496,606)(497,605)(498,611)(499,610)(500,616)(501,615)(502,614)(503,613)
(504,612)(505,618)(506,617)(507,623)(508,622)(509,621)(510,620)(511,619)
(512,625)(513,624)(514,630)(515,629)(516,628)(517,627)(518,626)(519,632)
(520,631)(521,637)(522,636)(523,635)(524,634)(525,633)(526,639)(527,638)
(528,644)(529,643)(530,642)(531,641)(532,640)(533,646)(534,645)(535,651)
(536,650)(537,649)(538,648)(539,647)(540,653)(541,652)(542,658)(543,657)
(544,656)(545,655)(546,654)(547,660)(548,659)(549,665)(550,664)(551,663)
(552,662)(553,661)(554,667)(555,666)(556,672)(557,671)(558,670)(559,669)
(560,668)(673,786)(674,785)(675,791)(676,790)(677,789)(678,788)(679,787)
(680,793)(681,792)(682,798)(683,797)(684,796)(685,795)(686,794)(687,800)
(688,799)(689,805)(690,804)(691,803)(692,802)(693,801)(694,807)(695,806)
(696,812)(697,811)(698,810)(699,809)(700,808)(701,814)(702,813)(703,819)
(704,818)(705,817)(706,816)(707,815)(708,821)(709,820)(710,826)(711,825)
(712,824)(713,823)(714,822)(715,828)(716,827)(717,833)(718,832)(719,831)
(720,830)(721,829)(722,835)(723,834)(724,840)(725,839)(726,838)(727,837)
(728,836)(729,842)(730,841)(731,847)(732,846)(733,845)(734,844)(735,843)
(736,849)(737,848)(738,854)(739,853)(740,852)(741,851)(742,850)(743,856)
(744,855)(745,861)(746,860)(747,859)(748,858)(749,857)(750,863)(751,862)
(752,868)(753,867)(754,866)(755,865)(756,864)(757,870)(758,869)(759,875)
(760,874)(761,873)(762,872)(763,871)(764,877)(765,876)(766,882)(767,881)
(768,880)(769,879)(770,878)(771,884)(772,883)(773,889)(774,888)(775,887)
(776,886)(777,885)(778,891)(779,890)(780,896)(781,895)(782,894)(783,893)
(784,892);
poly := sub<Sym(896)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope