Polytope of Type {4,56}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,56}*1792c
if this polytope has a name.
Group : SmallGroup(1792,90302)
Rank : 3
Schlafli Type : {4,56}
Number of vertices, edges, etc : 16, 448, 224
Order of s0s1s2 : 56
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,28}*896
   4-fold quotients : {4,28}*448
   7-fold quotients : {4,8}*256c
   8-fold quotients : {4,28}*224
   14-fold quotients : {4,4}*128
   16-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {4,4}*64
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*32
   64-fold quotients : {2,7}*28
   112-fold quotients : {2,4}*16, {4,2}*16
   224-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 2.
      112 facets:
         112 of {4}*8
      8 vertex figures:
         8 of {56}*112

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

Twisty Puzzle