Polytope of Type {8,8,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8,14}*1792a
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 : {4,8,14}*896a, {8,4,14}*896b
4-fold quotients : {4,4,14}*448, {2,8,14}*448
7-fold quotients : {8,8,2}*256a
8-fold quotients : {2,4,14}*224, {4,2,14}*224
14-fold quotients : {4,8,2}*128a, {8,4,2}*128b
16-fold quotients : {4,2,7}*112, {2,2,14}*112
28-fold quotients : {4,4,2}*64, {2,8,2}*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 := ( 1,225)( 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 := ( 1,561)( 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,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 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)!( 1,561)( 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, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
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