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