Questions?
See the FAQ
or other info.

Polytope of Type {8,8,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8,14}*1792b
Also Known As : {{8,8|2},{8,14|2}}. if this polytope has another name.
Group : SmallGroup(1792,145169)
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}*896a, {8,4,14}*896a
   4-fold quotients : {4,4,14}*448, {2,8,14}*448, {8,2,14}*448
   7-fold quotients : {8,8,2}*256b
   8-fold quotients : {8,2,7}*224, {2,4,14}*224, {4,2,14}*224
   14-fold quotients : {4,8,2}*128a, {8,4,2}*128a
   16-fold quotients : {4,2,7}*112, {2,2,14}*112
   28-fold quotients : {4,4,2}*64, {2,8,2}*64, {8,2,2}*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)( 29,260)( 30,261)( 31,262)( 32,263)
( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)( 40,257)
( 41,258)( 42,259)( 43,274)( 44,275)( 45,276)( 46,277)( 47,278)( 48,279)
( 49,280)( 50,267)( 51,268)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)
( 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)( 85,309)( 86,310)( 87,311)( 88,312)
( 89,313)( 90,314)( 91,315)( 92,316)( 93,317)( 94,318)( 95,319)( 96,320)
( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)(104,328)
(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)
(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)(141,372)(142,373)(143,374)(144,375)
(145,376)(146,377)(147,378)(148,365)(149,366)(150,367)(151,368)(152,369)
(153,370)(154,371)(155,386)(156,387)(157,388)(158,389)(159,390)(160,391)
(161,392)(162,379)(163,380)(164,381)(165,382)(166,383)(167,384)(168,385)
(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)(197,421)(198,422)(199,423)(200,424)
(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)(208,432)
(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)(216,440)
(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)
(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)(477,708)(478,709)(479,710)(480,711)
(481,712)(482,713)(483,714)(484,701)(485,702)(486,703)(487,704)(488,705)
(489,706)(490,707)(491,722)(492,723)(493,724)(494,725)(495,726)(496,727)
(497,728)(498,715)(499,716)(500,717)(501,718)(502,719)(503,720)(504,721)
(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)(533,757)(534,758)(535,759)(536,760)
(537,761)(538,762)(539,763)(540,764)(541,765)(542,766)(543,767)(544,768)
(545,769)(546,770)(547,771)(548,772)(549,773)(550,774)(551,775)(552,776)
(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)(560,784)
(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)(589,820)(590,821)(591,822)(592,823)
(593,824)(594,825)(595,826)(596,813)(597,814)(598,815)(599,816)(600,817)
(601,818)(602,819)(603,834)(604,835)(605,836)(606,837)(607,838)(608,839)
(609,840)(610,827)(611,828)(612,829)(613,830)(614,831)(615,832)(616,833)
(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)(645,869)(646,870)(647,871)(648,872)
(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)(656,880)
(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)(664,888)
(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)(672,896);;
s1 := ( 29, 36)( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 43, 50)
( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57, 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);;
s2 := (  1,785)(  2,791)(  3,790)(  4,789)(  5,788)(  6,787)(  7,786)(  8,792)
(  9,798)( 10,797)( 11,796)( 12,795)( 13,794)( 14,793)( 15,799)( 16,805)
( 17,804)( 18,803)( 19,802)( 20,801)( 21,800)( 22,806)( 23,812)( 24,811)
( 25,810)( 26,809)( 27,808)( 28,807)( 29,813)( 30,819)( 31,818)( 32,817)
( 33,816)( 34,815)( 35,814)( 36,820)( 37,826)( 38,825)( 39,824)( 40,823)
( 41,822)( 42,821)( 43,827)( 44,833)( 45,832)( 46,831)( 47,830)( 48,829)
( 49,828)( 50,834)( 51,840)( 52,839)( 53,838)( 54,837)( 55,836)( 56,835)
( 57,862)( 58,868)( 59,867)( 60,866)( 61,865)( 62,864)( 63,863)( 64,855)
( 65,861)( 66,860)( 67,859)( 68,858)( 69,857)( 70,856)( 71,848)( 72,854)
( 73,853)( 74,852)( 75,851)( 76,850)( 77,849)( 78,841)( 79,847)( 80,846)
( 81,845)( 82,844)( 83,843)( 84,842)( 85,890)( 86,896)( 87,895)( 88,894)
( 89,893)( 90,892)( 91,891)( 92,883)( 93,889)( 94,888)( 95,887)( 96,886)
( 97,885)( 98,884)( 99,876)(100,882)(101,881)(102,880)(103,879)(104,878)
(105,877)(106,869)(107,875)(108,874)(109,873)(110,872)(111,871)(112,870)
(113,673)(114,679)(115,678)(116,677)(117,676)(118,675)(119,674)(120,680)
(121,686)(122,685)(123,684)(124,683)(125,682)(126,681)(127,687)(128,693)
(129,692)(130,691)(131,690)(132,689)(133,688)(134,694)(135,700)(136,699)
(137,698)(138,697)(139,696)(140,695)(141,701)(142,707)(143,706)(144,705)
(145,704)(146,703)(147,702)(148,708)(149,714)(150,713)(151,712)(152,711)
(153,710)(154,709)(155,715)(156,721)(157,720)(158,719)(159,718)(160,717)
(161,716)(162,722)(163,728)(164,727)(165,726)(166,725)(167,724)(168,723)
(169,750)(170,756)(171,755)(172,754)(173,753)(174,752)(175,751)(176,743)
(177,749)(178,748)(179,747)(180,746)(181,745)(182,744)(183,736)(184,742)
(185,741)(186,740)(187,739)(188,738)(189,737)(190,729)(191,735)(192,734)
(193,733)(194,732)(195,731)(196,730)(197,778)(198,784)(199,783)(200,782)
(201,781)(202,780)(203,779)(204,771)(205,777)(206,776)(207,775)(208,774)
(209,773)(210,772)(211,764)(212,770)(213,769)(214,768)(215,767)(216,766)
(217,765)(218,757)(219,763)(220,762)(221,761)(222,760)(223,759)(224,758)
(225,561)(226,567)(227,566)(228,565)(229,564)(230,563)(231,562)(232,568)
(233,574)(234,573)(235,572)(236,571)(237,570)(238,569)(239,575)(240,581)
(241,580)(242,579)(243,578)(244,577)(245,576)(246,582)(247,588)(248,587)
(249,586)(250,585)(251,584)(252,583)(253,589)(254,595)(255,594)(256,593)
(257,592)(258,591)(259,590)(260,596)(261,602)(262,601)(263,600)(264,599)
(265,598)(266,597)(267,603)(268,609)(269,608)(270,607)(271,606)(272,605)
(273,604)(274,610)(275,616)(276,615)(277,614)(278,613)(279,612)(280,611)
(281,638)(282,644)(283,643)(284,642)(285,641)(286,640)(287,639)(288,631)
(289,637)(290,636)(291,635)(292,634)(293,633)(294,632)(295,624)(296,630)
(297,629)(298,628)(299,627)(300,626)(301,625)(302,617)(303,623)(304,622)
(305,621)(306,620)(307,619)(308,618)(309,666)(310,672)(311,671)(312,670)
(313,669)(314,668)(315,667)(316,659)(317,665)(318,664)(319,663)(320,662)
(321,661)(322,660)(323,652)(324,658)(325,657)(326,656)(327,655)(328,654)
(329,653)(330,645)(331,651)(332,650)(333,649)(334,648)(335,647)(336,646)
(337,449)(338,455)(339,454)(340,453)(341,452)(342,451)(343,450)(344,456)
(345,462)(346,461)(347,460)(348,459)(349,458)(350,457)(351,463)(352,469)
(353,468)(354,467)(355,466)(356,465)(357,464)(358,470)(359,476)(360,475)
(361,474)(362,473)(363,472)(364,471)(365,477)(366,483)(367,482)(368,481)
(369,480)(370,479)(371,478)(372,484)(373,490)(374,489)(375,488)(376,487)
(377,486)(378,485)(379,491)(380,497)(381,496)(382,495)(383,494)(384,493)
(385,492)(386,498)(387,504)(388,503)(389,502)(390,501)(391,500)(392,499)
(393,526)(394,532)(395,531)(396,530)(397,529)(398,528)(399,527)(400,519)
(401,525)(402,524)(403,523)(404,522)(405,521)(406,520)(407,512)(408,518)
(409,517)(410,516)(411,515)(412,514)(413,513)(414,505)(415,511)(416,510)
(417,509)(418,508)(419,507)(420,506)(421,554)(422,560)(423,559)(424,558)
(425,557)(426,556)(427,555)(428,547)(429,553)(430,552)(431,551)(432,550)
(433,549)(434,548)(435,540)(436,546)(437,545)(438,544)(439,543)(440,542)
(441,541)(442,533)(443,539)(444,538)(445,537)(446,536)(447,535)(448,534);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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)( 29,260)( 30,261)( 31,262)
( 32,263)( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)
( 40,257)( 41,258)( 42,259)( 43,274)( 44,275)( 45,276)( 46,277)( 47,278)
( 48,279)( 49,280)( 50,267)( 51,268)( 52,269)( 53,270)( 54,271)( 55,272)
( 56,273)( 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)( 85,309)( 86,310)( 87,311)
( 88,312)( 89,313)( 90,314)( 91,315)( 92,316)( 93,317)( 94,318)( 95,319)
( 96,320)( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)
(104,328)(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)
(112,336)(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)(141,372)(142,373)(143,374)
(144,375)(145,376)(146,377)(147,378)(148,365)(149,366)(150,367)(151,368)
(152,369)(153,370)(154,371)(155,386)(156,387)(157,388)(158,389)(159,390)
(160,391)(161,392)(162,379)(163,380)(164,381)(165,382)(166,383)(167,384)
(168,385)(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)(197,421)(198,422)(199,423)
(200,424)(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)
(208,432)(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)
(216,440)(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)
(224,448)(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)(477,708)(478,709)(479,710)
(480,711)(481,712)(482,713)(483,714)(484,701)(485,702)(486,703)(487,704)
(488,705)(489,706)(490,707)(491,722)(492,723)(493,724)(494,725)(495,726)
(496,727)(497,728)(498,715)(499,716)(500,717)(501,718)(502,719)(503,720)
(504,721)(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)(533,757)(534,758)(535,759)
(536,760)(537,761)(538,762)(539,763)(540,764)(541,765)(542,766)(543,767)
(544,768)(545,769)(546,770)(547,771)(548,772)(549,773)(550,774)(551,775)
(552,776)(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)
(560,784)(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)(589,820)(590,821)(591,822)
(592,823)(593,824)(594,825)(595,826)(596,813)(597,814)(598,815)(599,816)
(600,817)(601,818)(602,819)(603,834)(604,835)(605,836)(606,837)(607,838)
(608,839)(609,840)(610,827)(611,828)(612,829)(613,830)(614,831)(615,832)
(616,833)(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)(645,869)(646,870)(647,871)
(648,872)(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)
(656,880)(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)
(664,888)(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)
(672,896);
s1 := Sym(896)!( 29, 36)( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)
( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57, 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);
s2 := Sym(896)!(  1,785)(  2,791)(  3,790)(  4,789)(  5,788)(  6,787)(  7,786)
(  8,792)(  9,798)( 10,797)( 11,796)( 12,795)( 13,794)( 14,793)( 15,799)
( 16,805)( 17,804)( 18,803)( 19,802)( 20,801)( 21,800)( 22,806)( 23,812)
( 24,811)( 25,810)( 26,809)( 27,808)( 28,807)( 29,813)( 30,819)( 31,818)
( 32,817)( 33,816)( 34,815)( 35,814)( 36,820)( 37,826)( 38,825)( 39,824)
( 40,823)( 41,822)( 42,821)( 43,827)( 44,833)( 45,832)( 46,831)( 47,830)
( 48,829)( 49,828)( 50,834)( 51,840)( 52,839)( 53,838)( 54,837)( 55,836)
( 56,835)( 57,862)( 58,868)( 59,867)( 60,866)( 61,865)( 62,864)( 63,863)
( 64,855)( 65,861)( 66,860)( 67,859)( 68,858)( 69,857)( 70,856)( 71,848)
( 72,854)( 73,853)( 74,852)( 75,851)( 76,850)( 77,849)( 78,841)( 79,847)
( 80,846)( 81,845)( 82,844)( 83,843)( 84,842)( 85,890)( 86,896)( 87,895)
( 88,894)( 89,893)( 90,892)( 91,891)( 92,883)( 93,889)( 94,888)( 95,887)
( 96,886)( 97,885)( 98,884)( 99,876)(100,882)(101,881)(102,880)(103,879)
(104,878)(105,877)(106,869)(107,875)(108,874)(109,873)(110,872)(111,871)
(112,870)(113,673)(114,679)(115,678)(116,677)(117,676)(118,675)(119,674)
(120,680)(121,686)(122,685)(123,684)(124,683)(125,682)(126,681)(127,687)
(128,693)(129,692)(130,691)(131,690)(132,689)(133,688)(134,694)(135,700)
(136,699)(137,698)(138,697)(139,696)(140,695)(141,701)(142,707)(143,706)
(144,705)(145,704)(146,703)(147,702)(148,708)(149,714)(150,713)(151,712)
(152,711)(153,710)(154,709)(155,715)(156,721)(157,720)(158,719)(159,718)
(160,717)(161,716)(162,722)(163,728)(164,727)(165,726)(166,725)(167,724)
(168,723)(169,750)(170,756)(171,755)(172,754)(173,753)(174,752)(175,751)
(176,743)(177,749)(178,748)(179,747)(180,746)(181,745)(182,744)(183,736)
(184,742)(185,741)(186,740)(187,739)(188,738)(189,737)(190,729)(191,735)
(192,734)(193,733)(194,732)(195,731)(196,730)(197,778)(198,784)(199,783)
(200,782)(201,781)(202,780)(203,779)(204,771)(205,777)(206,776)(207,775)
(208,774)(209,773)(210,772)(211,764)(212,770)(213,769)(214,768)(215,767)
(216,766)(217,765)(218,757)(219,763)(220,762)(221,761)(222,760)(223,759)
(224,758)(225,561)(226,567)(227,566)(228,565)(229,564)(230,563)(231,562)
(232,568)(233,574)(234,573)(235,572)(236,571)(237,570)(238,569)(239,575)
(240,581)(241,580)(242,579)(243,578)(244,577)(245,576)(246,582)(247,588)
(248,587)(249,586)(250,585)(251,584)(252,583)(253,589)(254,595)(255,594)
(256,593)(257,592)(258,591)(259,590)(260,596)(261,602)(262,601)(263,600)
(264,599)(265,598)(266,597)(267,603)(268,609)(269,608)(270,607)(271,606)
(272,605)(273,604)(274,610)(275,616)(276,615)(277,614)(278,613)(279,612)
(280,611)(281,638)(282,644)(283,643)(284,642)(285,641)(286,640)(287,639)
(288,631)(289,637)(290,636)(291,635)(292,634)(293,633)(294,632)(295,624)
(296,630)(297,629)(298,628)(299,627)(300,626)(301,625)(302,617)(303,623)
(304,622)(305,621)(306,620)(307,619)(308,618)(309,666)(310,672)(311,671)
(312,670)(313,669)(314,668)(315,667)(316,659)(317,665)(318,664)(319,663)
(320,662)(321,661)(322,660)(323,652)(324,658)(325,657)(326,656)(327,655)
(328,654)(329,653)(330,645)(331,651)(332,650)(333,649)(334,648)(335,647)
(336,646)(337,449)(338,455)(339,454)(340,453)(341,452)(342,451)(343,450)
(344,456)(345,462)(346,461)(347,460)(348,459)(349,458)(350,457)(351,463)
(352,469)(353,468)(354,467)(355,466)(356,465)(357,464)(358,470)(359,476)
(360,475)(361,474)(362,473)(363,472)(364,471)(365,477)(366,483)(367,482)
(368,481)(369,480)(370,479)(371,478)(372,484)(373,490)(374,489)(375,488)
(376,487)(377,486)(378,485)(379,491)(380,497)(381,496)(382,495)(383,494)
(384,493)(385,492)(386,498)(387,504)(388,503)(389,502)(390,501)(391,500)
(392,499)(393,526)(394,532)(395,531)(396,530)(397,529)(398,528)(399,527)
(400,519)(401,525)(402,524)(403,523)(404,522)(405,521)(406,520)(407,512)
(408,518)(409,517)(410,516)(411,515)(412,514)(413,513)(414,505)(415,511)
(416,510)(417,509)(418,508)(419,507)(420,506)(421,554)(422,560)(423,559)
(424,558)(425,557)(426,556)(427,555)(428,547)(429,553)(430,552)(431,551)
(432,550)(433,549)(434,548)(435,540)(436,546)(437,545)(438,544)(439,543)
(440,542)(441,541)(442,533)(443,539)(444,538)(445,537)(446,536)(447,535)
(448,534);
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope