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Polytope of Type {14,64}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,64}*1792
Also Known As : {14,64|2}. if this polytope has another name.
Group : SmallGroup(1792,90609)
Rank : 3
Schlafli Type : {14,64}
Number of vertices, edges, etc : 14, 448, 64
Order of s0s1s2 : 448
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {14,32}*896
   4-fold quotients : {14,16}*448
   7-fold quotients : {2,64}*256
   8-fold quotients : {14,8}*224
   14-fold quotients : {2,32}*128
   16-fold quotients : {14,4}*112
   28-fold quotients : {2,16}*64
   32-fold quotients : {14,2}*56
   56-fold quotients : {2,8}*32
   64-fold quotients : {7,2}*28
   112-fold quotients : {2,4}*16
   224-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,225)(  2,231)(  3,230)(  4,229)(  5,228)(  6,227)(  7,226)(  8,232)
(  9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)( 16,245)
( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)( 24,251)
( 25,250)( 26,249)( 27,248)( 28,247)( 29,253)( 30,259)( 31,258)( 32,257)
( 33,256)( 34,255)( 35,254)( 36,260)( 37,266)( 38,265)( 39,264)( 40,263)
( 41,262)( 42,261)( 43,267)( 44,273)( 45,272)( 46,271)( 47,270)( 48,269)
( 49,268)( 50,274)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)( 56,275)
( 57,281)( 58,287)( 59,286)( 60,285)( 61,284)( 62,283)( 63,282)( 64,288)
( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,295)( 72,301)
( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,302)( 79,308)( 80,307)
( 81,306)( 82,305)( 83,304)( 84,303)( 85,309)( 86,315)( 87,314)( 88,313)
( 89,312)( 90,311)( 91,310)( 92,316)( 93,322)( 94,321)( 95,320)( 96,319)
( 97,318)( 98,317)( 99,323)(100,329)(101,328)(102,327)(103,326)(104,325)
(105,324)(106,330)(107,336)(108,335)(109,334)(110,333)(111,332)(112,331)
(113,337)(114,343)(115,342)(116,341)(117,340)(118,339)(119,338)(120,344)
(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,351)(128,357)
(129,356)(130,355)(131,354)(132,353)(133,352)(134,358)(135,364)(136,363)
(137,362)(138,361)(139,360)(140,359)(141,365)(142,371)(143,370)(144,369)
(145,368)(146,367)(147,366)(148,372)(149,378)(150,377)(151,376)(152,375)
(153,374)(154,373)(155,379)(156,385)(157,384)(158,383)(159,382)(160,381)
(161,380)(162,386)(163,392)(164,391)(165,390)(166,389)(167,388)(168,387)
(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)(176,400)
(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)(184,413)
(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)(192,419)
(193,418)(194,417)(195,416)(196,415)(197,421)(198,427)(199,426)(200,425)
(201,424)(202,423)(203,422)(204,428)(205,434)(206,433)(207,432)(208,431)
(209,430)(210,429)(211,435)(212,441)(213,440)(214,439)(215,438)(216,437)
(217,436)(218,442)(219,448)(220,447)(221,446)(222,445)(223,444)(224,443)
(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)(456,680)
(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,687)(464,693)
(465,692)(466,691)(467,690)(468,689)(469,688)(470,694)(471,700)(472,699)
(473,698)(474,697)(475,696)(476,695)(477,701)(478,707)(479,706)(480,705)
(481,704)(482,703)(483,702)(484,708)(485,714)(486,713)(487,712)(488,711)
(489,710)(490,709)(491,715)(492,721)(493,720)(494,719)(495,718)(496,717)
(497,716)(498,722)(499,728)(500,727)(501,726)(502,725)(503,724)(504,723)
(505,729)(506,735)(507,734)(508,733)(509,732)(510,731)(511,730)(512,736)
(513,742)(514,741)(515,740)(516,739)(517,738)(518,737)(519,743)(520,749)
(521,748)(522,747)(523,746)(524,745)(525,744)(526,750)(527,756)(528,755)
(529,754)(530,753)(531,752)(532,751)(533,757)(534,763)(535,762)(536,761)
(537,760)(538,759)(539,758)(540,764)(541,770)(542,769)(543,768)(544,767)
(545,766)(546,765)(547,771)(548,777)(549,776)(550,775)(551,774)(552,773)
(553,772)(554,778)(555,784)(556,783)(557,782)(558,781)(559,780)(560,779)
(561,785)(562,791)(563,790)(564,789)(565,788)(566,787)(567,786)(568,792)
(569,798)(570,797)(571,796)(572,795)(573,794)(574,793)(575,799)(576,805)
(577,804)(578,803)(579,802)(580,801)(581,800)(582,806)(583,812)(584,811)
(585,810)(586,809)(587,808)(588,807)(589,813)(590,819)(591,818)(592,817)
(593,816)(594,815)(595,814)(596,820)(597,826)(598,825)(599,824)(600,823)
(601,822)(602,821)(603,827)(604,833)(605,832)(606,831)(607,830)(608,829)
(609,828)(610,834)(611,840)(612,839)(613,838)(614,837)(615,836)(616,835)
(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)(624,848)
(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)(632,861)
(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)(640,867)
(641,866)(642,865)(643,864)(644,863)(645,869)(646,875)(647,874)(648,873)
(649,872)(650,871)(651,870)(652,876)(653,882)(654,881)(655,880)(656,879)
(657,878)(658,877)(659,883)(660,889)(661,888)(662,887)(663,886)(664,885)
(665,884)(666,890)(667,896)(668,895)(669,894)(670,893)(671,892)(672,891);;
s1 := (  1,226)(  2,225)(  3,231)(  4,230)(  5,229)(  6,228)(  7,227)(  8,233)
(  9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,247)( 16,246)
( 17,252)( 18,251)( 19,250)( 20,249)( 21,248)( 22,240)( 23,239)( 24,245)
( 25,244)( 26,243)( 27,242)( 28,241)( 29,268)( 30,267)( 31,273)( 32,272)
( 33,271)( 34,270)( 35,269)( 36,275)( 37,274)( 38,280)( 39,279)( 40,278)
( 41,277)( 42,276)( 43,254)( 44,253)( 45,259)( 46,258)( 47,257)( 48,256)
( 49,255)( 50,261)( 51,260)( 52,266)( 53,265)( 54,264)( 55,263)( 56,262)
( 57,310)( 58,309)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)( 64,317)
( 65,316)( 66,322)( 67,321)( 68,320)( 69,319)( 70,318)( 71,331)( 72,330)
( 73,336)( 74,335)( 75,334)( 76,333)( 77,332)( 78,324)( 79,323)( 80,329)
( 81,328)( 82,327)( 83,326)( 84,325)( 85,282)( 86,281)( 87,287)( 88,286)
( 89,285)( 90,284)( 91,283)( 92,289)( 93,288)( 94,294)( 95,293)( 96,292)
( 97,291)( 98,290)( 99,303)(100,302)(101,308)(102,307)(103,306)(104,305)
(105,304)(106,296)(107,295)(108,301)(109,300)(110,299)(111,298)(112,297)
(113,394)(114,393)(115,399)(116,398)(117,397)(118,396)(119,395)(120,401)
(121,400)(122,406)(123,405)(124,404)(125,403)(126,402)(127,415)(128,414)
(129,420)(130,419)(131,418)(132,417)(133,416)(134,408)(135,407)(136,413)
(137,412)(138,411)(139,410)(140,409)(141,436)(142,435)(143,441)(144,440)
(145,439)(146,438)(147,437)(148,443)(149,442)(150,448)(151,447)(152,446)
(153,445)(154,444)(155,422)(156,421)(157,427)(158,426)(159,425)(160,424)
(161,423)(162,429)(163,428)(164,434)(165,433)(166,432)(167,431)(168,430)
(169,338)(170,337)(171,343)(172,342)(173,341)(174,340)(175,339)(176,345)
(177,344)(178,350)(179,349)(180,348)(181,347)(182,346)(183,359)(184,358)
(185,364)(186,363)(187,362)(188,361)(189,360)(190,352)(191,351)(192,357)
(193,356)(194,355)(195,354)(196,353)(197,380)(198,379)(199,385)(200,384)
(201,383)(202,382)(203,381)(204,387)(205,386)(206,392)(207,391)(208,390)
(209,389)(210,388)(211,366)(212,365)(213,371)(214,370)(215,369)(216,368)
(217,367)(218,373)(219,372)(220,378)(221,377)(222,376)(223,375)(224,374)
(449,786)(450,785)(451,791)(452,790)(453,789)(454,788)(455,787)(456,793)
(457,792)(458,798)(459,797)(460,796)(461,795)(462,794)(463,807)(464,806)
(465,812)(466,811)(467,810)(468,809)(469,808)(470,800)(471,799)(472,805)
(473,804)(474,803)(475,802)(476,801)(477,828)(478,827)(479,833)(480,832)
(481,831)(482,830)(483,829)(484,835)(485,834)(486,840)(487,839)(488,838)
(489,837)(490,836)(491,814)(492,813)(493,819)(494,818)(495,817)(496,816)
(497,815)(498,821)(499,820)(500,826)(501,825)(502,824)(503,823)(504,822)
(505,870)(506,869)(507,875)(508,874)(509,873)(510,872)(511,871)(512,877)
(513,876)(514,882)(515,881)(516,880)(517,879)(518,878)(519,891)(520,890)
(521,896)(522,895)(523,894)(524,893)(525,892)(526,884)(527,883)(528,889)
(529,888)(530,887)(531,886)(532,885)(533,842)(534,841)(535,847)(536,846)
(537,845)(538,844)(539,843)(540,849)(541,848)(542,854)(543,853)(544,852)
(545,851)(546,850)(547,863)(548,862)(549,868)(550,867)(551,866)(552,865)
(553,864)(554,856)(555,855)(556,861)(557,860)(558,859)(559,858)(560,857)
(561,674)(562,673)(563,679)(564,678)(565,677)(566,676)(567,675)(568,681)
(569,680)(570,686)(571,685)(572,684)(573,683)(574,682)(575,695)(576,694)
(577,700)(578,699)(579,698)(580,697)(581,696)(582,688)(583,687)(584,693)
(585,692)(586,691)(587,690)(588,689)(589,716)(590,715)(591,721)(592,720)
(593,719)(594,718)(595,717)(596,723)(597,722)(598,728)(599,727)(600,726)
(601,725)(602,724)(603,702)(604,701)(605,707)(606,706)(607,705)(608,704)
(609,703)(610,709)(611,708)(612,714)(613,713)(614,712)(615,711)(616,710)
(617,758)(618,757)(619,763)(620,762)(621,761)(622,760)(623,759)(624,765)
(625,764)(626,770)(627,769)(628,768)(629,767)(630,766)(631,779)(632,778)
(633,784)(634,783)(635,782)(636,781)(637,780)(638,772)(639,771)(640,777)
(641,776)(642,775)(643,774)(644,773)(645,730)(646,729)(647,735)(648,734)
(649,733)(650,732)(651,731)(652,737)(653,736)(654,742)(655,741)(656,740)
(657,739)(658,738)(659,751)(660,750)(661,756)(662,755)(663,754)(664,753)
(665,752)(666,744)(667,743)(668,749)(669,748)(670,747)(671,746)(672,745);;
s2 := (  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)( 15,470)( 16,471)
( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)( 24,465)
( 25,466)( 26,467)( 27,468)( 28,469)( 29,491)( 30,492)( 31,493)( 32,494)
( 33,495)( 34,496)( 35,497)( 36,498)( 37,499)( 38,500)( 39,501)( 40,502)
( 41,503)( 42,504)( 43,477)( 44,478)( 45,479)( 46,480)( 47,481)( 48,482)
( 49,483)( 50,484)( 51,485)( 52,486)( 53,487)( 54,488)( 55,489)( 56,490)
( 57,533)( 58,534)( 59,535)( 60,536)( 61,537)( 62,538)( 63,539)( 64,540)
( 65,541)( 66,542)( 67,543)( 68,544)( 69,545)( 70,546)( 71,554)( 72,555)
( 73,556)( 74,557)( 75,558)( 76,559)( 77,560)( 78,547)( 79,548)( 80,549)
( 81,550)( 82,551)( 83,552)( 84,553)( 85,505)( 86,506)( 87,507)( 88,508)
( 89,509)( 90,510)( 91,511)( 92,512)( 93,513)( 94,514)( 95,515)( 96,516)
( 97,517)( 98,518)( 99,526)(100,527)(101,528)(102,529)(103,530)(104,531)
(105,532)(106,519)(107,520)(108,521)(109,522)(110,523)(111,524)(112,525)
(113,617)(114,618)(115,619)(116,620)(117,621)(118,622)(119,623)(120,624)
(121,625)(122,626)(123,627)(124,628)(125,629)(126,630)(127,638)(128,639)
(129,640)(130,641)(131,642)(132,643)(133,644)(134,631)(135,632)(136,633)
(137,634)(138,635)(139,636)(140,637)(141,659)(142,660)(143,661)(144,662)
(145,663)(146,664)(147,665)(148,666)(149,667)(150,668)(151,669)(152,670)
(153,671)(154,672)(155,645)(156,646)(157,647)(158,648)(159,649)(160,650)
(161,651)(162,652)(163,653)(164,654)(165,655)(166,656)(167,657)(168,658)
(169,561)(170,562)(171,563)(172,564)(173,565)(174,566)(175,567)(176,568)
(177,569)(178,570)(179,571)(180,572)(181,573)(182,574)(183,582)(184,583)
(185,584)(186,585)(187,586)(188,587)(189,588)(190,575)(191,576)(192,577)
(193,578)(194,579)(195,580)(196,581)(197,603)(198,604)(199,605)(200,606)
(201,607)(202,608)(203,609)(204,610)(205,611)(206,612)(207,613)(208,614)
(209,615)(210,616)(211,589)(212,590)(213,591)(214,592)(215,593)(216,594)
(217,595)(218,596)(219,597)(220,598)(221,599)(222,600)(223,601)(224,602)
(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)(239,694)(240,695)
(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)
(249,690)(250,691)(251,692)(252,693)(253,715)(254,716)(255,717)(256,718)
(257,719)(258,720)(259,721)(260,722)(261,723)(262,724)(263,725)(264,726)
(265,727)(266,728)(267,701)(268,702)(269,703)(270,704)(271,705)(272,706)
(273,707)(274,708)(275,709)(276,710)(277,711)(278,712)(279,713)(280,714)
(281,757)(282,758)(283,759)(284,760)(285,761)(286,762)(287,763)(288,764)
(289,765)(290,766)(291,767)(292,768)(293,769)(294,770)(295,778)(296,779)
(297,780)(298,781)(299,782)(300,783)(301,784)(302,771)(303,772)(304,773)
(305,774)(306,775)(307,776)(308,777)(309,729)(310,730)(311,731)(312,732)
(313,733)(314,734)(315,735)(316,736)(317,737)(318,738)(319,739)(320,740)
(321,741)(322,742)(323,750)(324,751)(325,752)(326,753)(327,754)(328,755)
(329,756)(330,743)(331,744)(332,745)(333,746)(334,747)(335,748)(336,749)
(337,841)(338,842)(339,843)(340,844)(341,845)(342,846)(343,847)(344,848)
(345,849)(346,850)(347,851)(348,852)(349,853)(350,854)(351,862)(352,863)
(353,864)(354,865)(355,866)(356,867)(357,868)(358,855)(359,856)(360,857)
(361,858)(362,859)(363,860)(364,861)(365,883)(366,884)(367,885)(368,886)
(369,887)(370,888)(371,889)(372,890)(373,891)(374,892)(375,893)(376,894)
(377,895)(378,896)(379,869)(380,870)(381,871)(382,872)(383,873)(384,874)
(385,875)(386,876)(387,877)(388,878)(389,879)(390,880)(391,881)(392,882)
(393,785)(394,786)(395,787)(396,788)(397,789)(398,790)(399,791)(400,792)
(401,793)(402,794)(403,795)(404,796)(405,797)(406,798)(407,806)(408,807)
(409,808)(410,809)(411,810)(412,811)(413,812)(414,799)(415,800)(416,801)
(417,802)(418,803)(419,804)(420,805)(421,827)(422,828)(423,829)(424,830)
(425,831)(426,832)(427,833)(428,834)(429,835)(430,836)(431,837)(432,838)
(433,839)(434,840)(435,813)(436,814)(437,815)(438,816)(439,817)(440,818)
(441,819)(442,820)(443,821)(444,822)(445,823)(446,824)(447,825)(448,826);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*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*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(896)!(  1,225)(  2,231)(  3,230)(  4,229)(  5,228)(  6,227)(  7,226)
(  8,232)(  9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)
( 16,245)( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)
( 24,251)( 25,250)( 26,249)( 27,248)( 28,247)( 29,253)( 30,259)( 31,258)
( 32,257)( 33,256)( 34,255)( 35,254)( 36,260)( 37,266)( 38,265)( 39,264)
( 40,263)( 41,262)( 42,261)( 43,267)( 44,273)( 45,272)( 46,271)( 47,270)
( 48,269)( 49,268)( 50,274)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)
( 56,275)( 57,281)( 58,287)( 59,286)( 60,285)( 61,284)( 62,283)( 63,282)
( 64,288)( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,295)
( 72,301)( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,302)( 79,308)
( 80,307)( 81,306)( 82,305)( 83,304)( 84,303)( 85,309)( 86,315)( 87,314)
( 88,313)( 89,312)( 90,311)( 91,310)( 92,316)( 93,322)( 94,321)( 95,320)
( 96,319)( 97,318)( 98,317)( 99,323)(100,329)(101,328)(102,327)(103,326)
(104,325)(105,324)(106,330)(107,336)(108,335)(109,334)(110,333)(111,332)
(112,331)(113,337)(114,343)(115,342)(116,341)(117,340)(118,339)(119,338)
(120,344)(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,351)
(128,357)(129,356)(130,355)(131,354)(132,353)(133,352)(134,358)(135,364)
(136,363)(137,362)(138,361)(139,360)(140,359)(141,365)(142,371)(143,370)
(144,369)(145,368)(146,367)(147,366)(148,372)(149,378)(150,377)(151,376)
(152,375)(153,374)(154,373)(155,379)(156,385)(157,384)(158,383)(159,382)
(160,381)(161,380)(162,386)(163,392)(164,391)(165,390)(166,389)(167,388)
(168,387)(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)
(176,400)(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)
(184,413)(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)
(192,419)(193,418)(194,417)(195,416)(196,415)(197,421)(198,427)(199,426)
(200,425)(201,424)(202,423)(203,422)(204,428)(205,434)(206,433)(207,432)
(208,431)(209,430)(210,429)(211,435)(212,441)(213,440)(214,439)(215,438)
(216,437)(217,436)(218,442)(219,448)(220,447)(221,446)(222,445)(223,444)
(224,443)(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)
(456,680)(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,687)
(464,693)(465,692)(466,691)(467,690)(468,689)(469,688)(470,694)(471,700)
(472,699)(473,698)(474,697)(475,696)(476,695)(477,701)(478,707)(479,706)
(480,705)(481,704)(482,703)(483,702)(484,708)(485,714)(486,713)(487,712)
(488,711)(489,710)(490,709)(491,715)(492,721)(493,720)(494,719)(495,718)
(496,717)(497,716)(498,722)(499,728)(500,727)(501,726)(502,725)(503,724)
(504,723)(505,729)(506,735)(507,734)(508,733)(509,732)(510,731)(511,730)
(512,736)(513,742)(514,741)(515,740)(516,739)(517,738)(518,737)(519,743)
(520,749)(521,748)(522,747)(523,746)(524,745)(525,744)(526,750)(527,756)
(528,755)(529,754)(530,753)(531,752)(532,751)(533,757)(534,763)(535,762)
(536,761)(537,760)(538,759)(539,758)(540,764)(541,770)(542,769)(543,768)
(544,767)(545,766)(546,765)(547,771)(548,777)(549,776)(550,775)(551,774)
(552,773)(553,772)(554,778)(555,784)(556,783)(557,782)(558,781)(559,780)
(560,779)(561,785)(562,791)(563,790)(564,789)(565,788)(566,787)(567,786)
(568,792)(569,798)(570,797)(571,796)(572,795)(573,794)(574,793)(575,799)
(576,805)(577,804)(578,803)(579,802)(580,801)(581,800)(582,806)(583,812)
(584,811)(585,810)(586,809)(587,808)(588,807)(589,813)(590,819)(591,818)
(592,817)(593,816)(594,815)(595,814)(596,820)(597,826)(598,825)(599,824)
(600,823)(601,822)(602,821)(603,827)(604,833)(605,832)(606,831)(607,830)
(608,829)(609,828)(610,834)(611,840)(612,839)(613,838)(614,837)(615,836)
(616,835)(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)
(624,848)(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)
(632,861)(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)
(640,867)(641,866)(642,865)(643,864)(644,863)(645,869)(646,875)(647,874)
(648,873)(649,872)(650,871)(651,870)(652,876)(653,882)(654,881)(655,880)
(656,879)(657,878)(658,877)(659,883)(660,889)(661,888)(662,887)(663,886)
(664,885)(665,884)(666,890)(667,896)(668,895)(669,894)(670,893)(671,892)
(672,891);
s1 := Sym(896)!(  1,226)(  2,225)(  3,231)(  4,230)(  5,229)(  6,228)(  7,227)
(  8,233)(  9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,247)
( 16,246)( 17,252)( 18,251)( 19,250)( 20,249)( 21,248)( 22,240)( 23,239)
( 24,245)( 25,244)( 26,243)( 27,242)( 28,241)( 29,268)( 30,267)( 31,273)
( 32,272)( 33,271)( 34,270)( 35,269)( 36,275)( 37,274)( 38,280)( 39,279)
( 40,278)( 41,277)( 42,276)( 43,254)( 44,253)( 45,259)( 46,258)( 47,257)
( 48,256)( 49,255)( 50,261)( 51,260)( 52,266)( 53,265)( 54,264)( 55,263)
( 56,262)( 57,310)( 58,309)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)
( 64,317)( 65,316)( 66,322)( 67,321)( 68,320)( 69,319)( 70,318)( 71,331)
( 72,330)( 73,336)( 74,335)( 75,334)( 76,333)( 77,332)( 78,324)( 79,323)
( 80,329)( 81,328)( 82,327)( 83,326)( 84,325)( 85,282)( 86,281)( 87,287)
( 88,286)( 89,285)( 90,284)( 91,283)( 92,289)( 93,288)( 94,294)( 95,293)
( 96,292)( 97,291)( 98,290)( 99,303)(100,302)(101,308)(102,307)(103,306)
(104,305)(105,304)(106,296)(107,295)(108,301)(109,300)(110,299)(111,298)
(112,297)(113,394)(114,393)(115,399)(116,398)(117,397)(118,396)(119,395)
(120,401)(121,400)(122,406)(123,405)(124,404)(125,403)(126,402)(127,415)
(128,414)(129,420)(130,419)(131,418)(132,417)(133,416)(134,408)(135,407)
(136,413)(137,412)(138,411)(139,410)(140,409)(141,436)(142,435)(143,441)
(144,440)(145,439)(146,438)(147,437)(148,443)(149,442)(150,448)(151,447)
(152,446)(153,445)(154,444)(155,422)(156,421)(157,427)(158,426)(159,425)
(160,424)(161,423)(162,429)(163,428)(164,434)(165,433)(166,432)(167,431)
(168,430)(169,338)(170,337)(171,343)(172,342)(173,341)(174,340)(175,339)
(176,345)(177,344)(178,350)(179,349)(180,348)(181,347)(182,346)(183,359)
(184,358)(185,364)(186,363)(187,362)(188,361)(189,360)(190,352)(191,351)
(192,357)(193,356)(194,355)(195,354)(196,353)(197,380)(198,379)(199,385)
(200,384)(201,383)(202,382)(203,381)(204,387)(205,386)(206,392)(207,391)
(208,390)(209,389)(210,388)(211,366)(212,365)(213,371)(214,370)(215,369)
(216,368)(217,367)(218,373)(219,372)(220,378)(221,377)(222,376)(223,375)
(224,374)(449,786)(450,785)(451,791)(452,790)(453,789)(454,788)(455,787)
(456,793)(457,792)(458,798)(459,797)(460,796)(461,795)(462,794)(463,807)
(464,806)(465,812)(466,811)(467,810)(468,809)(469,808)(470,800)(471,799)
(472,805)(473,804)(474,803)(475,802)(476,801)(477,828)(478,827)(479,833)
(480,832)(481,831)(482,830)(483,829)(484,835)(485,834)(486,840)(487,839)
(488,838)(489,837)(490,836)(491,814)(492,813)(493,819)(494,818)(495,817)
(496,816)(497,815)(498,821)(499,820)(500,826)(501,825)(502,824)(503,823)
(504,822)(505,870)(506,869)(507,875)(508,874)(509,873)(510,872)(511,871)
(512,877)(513,876)(514,882)(515,881)(516,880)(517,879)(518,878)(519,891)
(520,890)(521,896)(522,895)(523,894)(524,893)(525,892)(526,884)(527,883)
(528,889)(529,888)(530,887)(531,886)(532,885)(533,842)(534,841)(535,847)
(536,846)(537,845)(538,844)(539,843)(540,849)(541,848)(542,854)(543,853)
(544,852)(545,851)(546,850)(547,863)(548,862)(549,868)(550,867)(551,866)
(552,865)(553,864)(554,856)(555,855)(556,861)(557,860)(558,859)(559,858)
(560,857)(561,674)(562,673)(563,679)(564,678)(565,677)(566,676)(567,675)
(568,681)(569,680)(570,686)(571,685)(572,684)(573,683)(574,682)(575,695)
(576,694)(577,700)(578,699)(579,698)(580,697)(581,696)(582,688)(583,687)
(584,693)(585,692)(586,691)(587,690)(588,689)(589,716)(590,715)(591,721)
(592,720)(593,719)(594,718)(595,717)(596,723)(597,722)(598,728)(599,727)
(600,726)(601,725)(602,724)(603,702)(604,701)(605,707)(606,706)(607,705)
(608,704)(609,703)(610,709)(611,708)(612,714)(613,713)(614,712)(615,711)
(616,710)(617,758)(618,757)(619,763)(620,762)(621,761)(622,760)(623,759)
(624,765)(625,764)(626,770)(627,769)(628,768)(629,767)(630,766)(631,779)
(632,778)(633,784)(634,783)(635,782)(636,781)(637,780)(638,772)(639,771)
(640,777)(641,776)(642,775)(643,774)(644,773)(645,730)(646,729)(647,735)
(648,734)(649,733)(650,732)(651,731)(652,737)(653,736)(654,742)(655,741)
(656,740)(657,739)(658,738)(659,751)(660,750)(661,756)(662,755)(663,754)
(664,753)(665,752)(666,744)(667,743)(668,749)(669,748)(670,747)(671,746)
(672,745);
s2 := 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)( 15,470)
( 16,471)( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)
( 24,465)( 25,466)( 26,467)( 27,468)( 28,469)( 29,491)( 30,492)( 31,493)
( 32,494)( 33,495)( 34,496)( 35,497)( 36,498)( 37,499)( 38,500)( 39,501)
( 40,502)( 41,503)( 42,504)( 43,477)( 44,478)( 45,479)( 46,480)( 47,481)
( 48,482)( 49,483)( 50,484)( 51,485)( 52,486)( 53,487)( 54,488)( 55,489)
( 56,490)( 57,533)( 58,534)( 59,535)( 60,536)( 61,537)( 62,538)( 63,539)
( 64,540)( 65,541)( 66,542)( 67,543)( 68,544)( 69,545)( 70,546)( 71,554)
( 72,555)( 73,556)( 74,557)( 75,558)( 76,559)( 77,560)( 78,547)( 79,548)
( 80,549)( 81,550)( 82,551)( 83,552)( 84,553)( 85,505)( 86,506)( 87,507)
( 88,508)( 89,509)( 90,510)( 91,511)( 92,512)( 93,513)( 94,514)( 95,515)
( 96,516)( 97,517)( 98,518)( 99,526)(100,527)(101,528)(102,529)(103,530)
(104,531)(105,532)(106,519)(107,520)(108,521)(109,522)(110,523)(111,524)
(112,525)(113,617)(114,618)(115,619)(116,620)(117,621)(118,622)(119,623)
(120,624)(121,625)(122,626)(123,627)(124,628)(125,629)(126,630)(127,638)
(128,639)(129,640)(130,641)(131,642)(132,643)(133,644)(134,631)(135,632)
(136,633)(137,634)(138,635)(139,636)(140,637)(141,659)(142,660)(143,661)
(144,662)(145,663)(146,664)(147,665)(148,666)(149,667)(150,668)(151,669)
(152,670)(153,671)(154,672)(155,645)(156,646)(157,647)(158,648)(159,649)
(160,650)(161,651)(162,652)(163,653)(164,654)(165,655)(166,656)(167,657)
(168,658)(169,561)(170,562)(171,563)(172,564)(173,565)(174,566)(175,567)
(176,568)(177,569)(178,570)(179,571)(180,572)(181,573)(182,574)(183,582)
(184,583)(185,584)(186,585)(187,586)(188,587)(189,588)(190,575)(191,576)
(192,577)(193,578)(194,579)(195,580)(196,581)(197,603)(198,604)(199,605)
(200,606)(201,607)(202,608)(203,609)(204,610)(205,611)(206,612)(207,613)
(208,614)(209,615)(210,616)(211,589)(212,590)(213,591)(214,592)(215,593)
(216,594)(217,595)(218,596)(219,597)(220,598)(221,599)(222,600)(223,601)
(224,602)(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)(239,694)
(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)
(248,689)(249,690)(250,691)(251,692)(252,693)(253,715)(254,716)(255,717)
(256,718)(257,719)(258,720)(259,721)(260,722)(261,723)(262,724)(263,725)
(264,726)(265,727)(266,728)(267,701)(268,702)(269,703)(270,704)(271,705)
(272,706)(273,707)(274,708)(275,709)(276,710)(277,711)(278,712)(279,713)
(280,714)(281,757)(282,758)(283,759)(284,760)(285,761)(286,762)(287,763)
(288,764)(289,765)(290,766)(291,767)(292,768)(293,769)(294,770)(295,778)
(296,779)(297,780)(298,781)(299,782)(300,783)(301,784)(302,771)(303,772)
(304,773)(305,774)(306,775)(307,776)(308,777)(309,729)(310,730)(311,731)
(312,732)(313,733)(314,734)(315,735)(316,736)(317,737)(318,738)(319,739)
(320,740)(321,741)(322,742)(323,750)(324,751)(325,752)(326,753)(327,754)
(328,755)(329,756)(330,743)(331,744)(332,745)(333,746)(334,747)(335,748)
(336,749)(337,841)(338,842)(339,843)(340,844)(341,845)(342,846)(343,847)
(344,848)(345,849)(346,850)(347,851)(348,852)(349,853)(350,854)(351,862)
(352,863)(353,864)(354,865)(355,866)(356,867)(357,868)(358,855)(359,856)
(360,857)(361,858)(362,859)(363,860)(364,861)(365,883)(366,884)(367,885)
(368,886)(369,887)(370,888)(371,889)(372,890)(373,891)(374,892)(375,893)
(376,894)(377,895)(378,896)(379,869)(380,870)(381,871)(382,872)(383,873)
(384,874)(385,875)(386,876)(387,877)(388,878)(389,879)(390,880)(391,881)
(392,882)(393,785)(394,786)(395,787)(396,788)(397,789)(398,790)(399,791)
(400,792)(401,793)(402,794)(403,795)(404,796)(405,797)(406,798)(407,806)
(408,807)(409,808)(410,809)(411,810)(412,811)(413,812)(414,799)(415,800)
(416,801)(417,802)(418,803)(419,804)(420,805)(421,827)(422,828)(423,829)
(424,830)(425,831)(426,832)(427,833)(428,834)(429,835)(430,836)(431,837)
(432,838)(433,839)(434,840)(435,813)(436,814)(437,815)(438,816)(439,817)
(440,818)(441,819)(442,820)(443,821)(444,822)(445,823)(446,824)(447,825)
(448,826);
poly := sub<Sym(896)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*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*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope