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}*1792a
if this polytope has a name.
Group : SmallGroup(1792,81599)
Rank : 3
Schlafli Type : {4,56}
Number of vertices, edges, etc : 16, 448, 224
Order of s0s1s2 : 56
Order of s0s1s2s1 : 4
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 : {4,56}*896a, {4,28}*896, {4,56}*896b
   4-fold quotients : {4,56}*448a, {4,28}*448, {4,56}*448b
   7-fold quotients : {4,8}*256a
   8-fold quotients : {4,28}*224, {2,56}*224
   14-fold quotients : {4,8}*128a, {4,4}*128, {4,8}*128b
   16-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*32, {2,8}*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*s0*s1> of order 2.
      140 facets:
         56 of {2}*4
         84 of {4}*8
      8 vertex figures:
         8 of {56}*112
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      112 facets:
         112 of {4}*8
      8 vertex figures:
         8 of {56}*112
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      112 facets:
         112 of {4}*8
      8 vertex figures:
         8 of {56}*112
   P/N, where N=<s0*s1*s2*s1*s0*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> of order 2.
      112 facets:
         112 of {4}*8
      8 vertex figures:
         8 of {56}*112
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*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> of order 2.
      112 facets:
         112 of {4}*8
      8 vertex figures:
         8 of {56}*112
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 2.
      112 facets:
         112 of {4}*8
      8 vertex figures:
         8 of {56}*112
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*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> of order 4.
      56 facets:
         56 of {4}*8
      4 vertex figures:
         4 of {56}*112
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      70 facets:
         28 of {2}*4
         42 of {4}*8
      4 vertex figures:
         4 of {56}*112
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      56 facets:
         56 of {4}*8
      4 vertex figures:
         4 of {56}*112
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*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> of order 4.
      56 facets:
         56 of {4}*8
      4 vertex figures:
         4 of {56}*112
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s2*s1*s0*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> of order 4.
      56 facets:
         56 of {4}*8
      4 vertex figures:
         4 of {56}*112
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      56 facets:
         56 of {4}*8
      4 vertex figures:
         4 of {56}*112
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      56 facets:
         56 of {4}*8
      4 vertex figures:
         4 of {56}*112
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      84 facets:
         56 of {2}*4
         28 of {4}*8
      4 vertex figures:
         4 of {56}*112
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s0*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> of order 4.
      70 facets:
         28 of {2}*4
         42 of {4}*8
      4 vertex figures:
         4 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)( 15,239)( 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)( 29,253)( 30,254)( 31,255)( 32,256)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)( 41,265)( 42,266)( 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)( 71,295)( 72,296)( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)( 81,305)( 82,306)( 83,307)( 84,308)( 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)(113,351)(114,352)(115,353)(116,354)(117,355)(118,356)(119,357)(120,358)(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,337)(128,338)(129,339)(130,340)(131,341)(132,342)(133,343)(134,344)(135,345)(136,346)(137,347)(138,348)(139,349)(140,350)(141,379)(142,380)(143,381)(144,382)(145,383)(146,384)(147,385)(148,386)(149,387)(150,388)(151,389)(152,390)(153,391)(154,392)(155,365)(156,366)(157,367)(158,368)(159,369)(160,370)(161,371)(162,372)(163,373)(164,374)(165,375)(166,376)(167,377)(168,378)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)(184,394)(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)(193,403)(194,404)(195,405)(196,406)(197,435)(198,436)(199,437)(200,438)(201,439)(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)(208,446)(209,447)(210,448)(211,421)(212,422)(213,423)(214,424)(215,425)(216,426)(217,427)(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)(224,434)(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)(477,701)(478,702)(479,703)(480,704)(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)(488,712)(489,713)(490,714)(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)(519,743)(520,744)(521,745)(522,746)(523,747)(524,748)(525,749)(526,750)(527,751)(528,752)(529,753)(530,754)(531,755)(532,756)(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)(561,799)(562,800)(563,801)(564,802)(565,803)(566,804)(567,805)(568,806)(569,807)(570,808)(571,809)(572,810)(573,811)(574,812)(575,785)(576,786)(577,787)(578,788)(579,789)(580,790)(581,791)(582,792)(583,793)(584,794)(585,795)(586,796)(587,797)(588,798)(589,827)(590,828)(591,829)(592,830)(593,831)(594,832)(595,833)(596,834)(597,835)(598,836)(599,837)(600,838)(601,839)(602,840)(603,813)(604,814)(605,815)(606,816)(607,817)(608,818)(609,819)(610,820)(611,821)(612,822)(613,823)(614,824)(615,825)(616,826)(617,855)(618,856)(619,857)(620,858)(621,859)(622,860)(623,861)(624,862)(625,863)(626,864)(627,865)(628,866)(629,867)(630,868)(631,841)(632,842)(633,843)(634,844)(635,845)(636,846)(637,847)(638,848)(639,849)(640,850)(641,851)(642,852)(643,853)(644,854)(645,883)(646,884)(647,885)(648,886)(649,887)(650,888)(651,889)(652,890)(653,891)(654,892)(655,893)(656,894)(657,895)(658,896)(659,869)(660,870)(661,871)(662,872)(663,873)(664,874)(665,875)(666,876)(667,877)(668,878)(669,879)(670,880)(671,881)(672,882);;
s1 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 30, 35)( 31, 34)( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 86, 91)( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)(127,162)(128,168)(129,167)(130,166)(131,165)(132,164)(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,218)(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)(192,216)(193,215)(194,214)(195,213)(196,212)(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)(239,302)(240,308)(241,307)(242,306)(243,305)(244,304)(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)(252,296)(253,309)(254,315)(255,314)(256,313)(257,312)(258,311)(259,310)(260,316)(261,322)(262,321)(263,320)(264,319)(265,318)(266,317)(267,330)(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)(276,328)(277,327)(278,326)(279,325)(280,324)(337,428)(338,434)(339,433)(340,432)(341,431)(342,430)(343,429)(344,421)(345,427)(346,426)(347,425)(348,424)(349,423)(350,422)(351,435)(352,441)(353,440)(354,439)(355,438)(356,437)(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)(363,444)(364,443)(365,400)(366,406)(367,405)(368,404)(369,403)(370,402)(371,401)(372,393)(373,399)(374,398)(375,397)(376,396)(377,395)(378,394)(379,407)(380,413)(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)(387,420)(388,419)(389,418)(390,417)(391,416)(392,415)(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)(463,582)(464,588)(465,587)(466,586)(467,585)(468,584)(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)(475,577)(476,576)(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)(484,596)(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(491,610)(492,616)(493,615)(494,614)(495,613)(496,612)(497,611)(498,603)(499,609)(500,608)(501,607)(502,606)(503,605)(504,604)(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)(519,638)(520,644)(521,643)(522,642)(523,641)(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)(531,633)(532,632)(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)(540,652)(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,666)(548,672)(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)(556,664)(557,663)(558,662)(559,661)(560,660)(673,855)(674,861)(675,860)(676,859)(677,858)(678,857)(679,856)(680,862)(681,868)(682,867)(683,866)(684,865)(685,864)(686,863)(687,848)(688,854)(689,853)(690,852)(691,851)(692,850)(693,849)(694,841)(695,847)(696,846)(697,845)(698,844)(699,843)(700,842)(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)(707,884)(708,890)(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)(715,876)(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)(722,869)(723,875)(724,874)(725,873)(726,872)(727,871)(728,870)(729,799)(730,805)(731,804)(732,803)(733,802)(734,801)(735,800)(736,806)(737,812)(738,811)(739,810)(740,809)(741,808)(742,807)(743,792)(744,798)(745,797)(746,796)(747,795)(748,794)(749,793)(750,785)(751,791)(752,790)(753,789)(754,788)(755,787)(756,786)(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)(763,828)(764,834)(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)(771,820)(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)(778,813)(779,819)(780,818)(781,817)(782,816)(783,815)(784,814);;
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)( 15,464)( 16,463)( 17,469)( 18,468)( 19,467)( 20,466)( 21,465)( 22,471)( 23,470)( 24,476)( 25,475)( 26,474)( 27,473)( 28,472)( 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)( 43,492)( 44,491)( 45,497)( 46,496)( 47,495)( 48,494)( 49,493)( 50,499)( 51,498)( 52,504)( 53,503)( 54,502)( 55,501)( 56,500)( 57,527)( 58,526)( 59,532)( 60,531)( 61,530)( 62,529)( 63,528)( 64,520)( 65,519)( 66,525)( 67,524)( 68,523)( 69,522)( 70,521)( 71,513)( 72,512)( 73,518)( 74,517)( 75,516)( 76,515)( 77,514)( 78,506)( 79,505)( 80,511)( 81,510)( 82,509)( 83,508)( 84,507)( 85,555)( 86,554)( 87,560)( 88,559)( 89,558)( 90,557)( 91,556)( 92,548)( 93,547)( 94,553)( 95,552)( 96,551)( 97,550)( 98,549)( 99,541)(100,540)(101,546)(102,545)(103,544)(104,543)(105,542)(106,534)(107,533)(108,539)(109,538)(110,537)(111,536)(112,535)(113,590)(114,589)(115,595)(116,594)(117,593)(118,592)(119,591)(120,597)(121,596)(122,602)(123,601)(124,600)(125,599)(126,598)(127,604)(128,603)(129,609)(130,608)(131,607)(132,606)(133,605)(134,611)(135,610)(136,616)(137,615)(138,614)(139,613)(140,612)(141,562)(142,561)(143,567)(144,566)(145,565)(146,564)(147,563)(148,569)(149,568)(150,574)(151,573)(152,572)(153,571)(154,570)(155,576)(156,575)(157,581)(158,580)(159,579)(160,578)(161,577)(162,583)(163,582)(164,588)(165,587)(166,586)(167,585)(168,584)(169,667)(170,666)(171,672)(172,671)(173,670)(174,669)(175,668)(176,660)(177,659)(178,665)(179,664)(180,663)(181,662)(182,661)(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)(211,625)(212,624)(213,630)(214,629)(215,628)(216,627)(217,626)(218,618)(219,617)(220,623)(221,622)(222,621)(223,620)(224,619)(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)(239,688)(240,687)(241,693)(242,692)(243,691)(244,690)(245,689)(246,695)(247,694)(248,700)(249,699)(250,698)(251,697)(252,696)(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)(267,716)(268,715)(269,721)(270,720)(271,719)(272,718)(273,717)(274,723)(275,722)(276,728)(277,727)(278,726)(279,725)(280,724)(281,751)(282,750)(283,756)(284,755)(285,754)(286,753)(287,752)(288,744)(289,743)(290,749)(291,748)(292,747)(293,746)(294,745)(295,737)(296,736)(297,742)(298,741)(299,740)(300,739)(301,738)(302,730)(303,729)(304,735)(305,734)(306,733)(307,732)(308,731)(309,779)(310,778)(311,784)(312,783)(313,782)(314,781)(315,780)(316,772)(317,771)(318,777)(319,776)(320,775)(321,774)(322,773)(323,765)(324,764)(325,770)(326,769)(327,768)(328,767)(329,766)(330,758)(331,757)(332,763)(333,762)(334,761)(335,760)(336,759)(337,814)(338,813)(339,819)(340,818)(341,817)(342,816)(343,815)(344,821)(345,820)(346,826)(347,825)(348,824)(349,823)(350,822)(351,828)(352,827)(353,833)(354,832)(355,831)(356,830)(357,829)(358,835)(359,834)(360,840)(361,839)(362,838)(363,837)(364,836)(365,786)(366,785)(367,791)(368,790)(369,789)(370,788)(371,787)(372,793)(373,792)(374,798)(375,797)(376,796)(377,795)(378,794)(379,800)(380,799)(381,805)(382,804)(383,803)(384,802)(385,801)(386,807)(387,806)(388,812)(389,811)(390,810)(391,809)(392,808)(393,891)(394,890)(395,896)(396,895)(397,894)(398,893)(399,892)(400,884)(401,883)(402,889)(403,888)(404,887)(405,886)(406,885)(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)(435,849)(436,848)(437,854)(438,853)(439,852)(440,851)(441,850)(442,842)(443,841)(444,847)(445,846)(446,845)(447,844)(448,843);;
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*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 ];;
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)( 29,253)( 30,254)( 31,255)( 32,256)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)( 41,265)( 42,266)( 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)( 71,295)( 72,296)( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)( 81,305)( 82,306)( 83,307)( 84,308)( 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)(113,351)(114,352)(115,353)(116,354)(117,355)(118,356)(119,357)(120,358)(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,337)(128,338)(129,339)(130,340)(131,341)(132,342)(133,343)(134,344)(135,345)(136,346)(137,347)(138,348)(139,349)(140,350)(141,379)(142,380)(143,381)(144,382)(145,383)(146,384)(147,385)(148,386)(149,387)(150,388)(151,389)(152,390)(153,391)(154,392)(155,365)(156,366)(157,367)(158,368)(159,369)(160,370)(161,371)(162,372)(163,373)(164,374)(165,375)(166,376)(167,377)(168,378)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)(184,394)(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)(193,403)(194,404)(195,405)(196,406)(197,435)(198,436)(199,437)(200,438)(201,439)(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)(208,446)(209,447)(210,448)(211,421)(212,422)(213,423)(214,424)(215,425)(216,426)(217,427)(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)(224,434)(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)(477,701)(478,702)(479,703)(480,704)(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)(488,712)(489,713)(490,714)(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)(519,743)(520,744)(521,745)(522,746)(523,747)(524,748)(525,749)(526,750)(527,751)(528,752)(529,753)(530,754)(531,755)(532,756)(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)(561,799)(562,800)(563,801)(564,802)(565,803)(566,804)(567,805)(568,806)(569,807)(570,808)(571,809)(572,810)(573,811)(574,812)(575,785)(576,786)(577,787)(578,788)(579,789)(580,790)(581,791)(582,792)(583,793)(584,794)(585,795)(586,796)(587,797)(588,798)(589,827)(590,828)(591,829)(592,830)(593,831)(594,832)(595,833)(596,834)(597,835)(598,836)(599,837)(600,838)(601,839)(602,840)(603,813)(604,814)(605,815)(606,816)(607,817)(608,818)(609,819)(610,820)(611,821)(612,822)(613,823)(614,824)(615,825)(616,826)(617,855)(618,856)(619,857)(620,858)(621,859)(622,860)(623,861)(624,862)(625,863)(626,864)(627,865)(628,866)(629,867)(630,868)(631,841)(632,842)(633,843)(634,844)(635,845)(636,846)(637,847)(638,848)(639,849)(640,850)(641,851)(642,852)(643,853)(644,854)(645,883)(646,884)(647,885)(648,886)(649,887)(650,888)(651,889)(652,890)(653,891)(654,892)(655,893)(656,894)(657,895)(658,896)(659,869)(660,870)(661,871)(662,872)(663,873)(664,874)(665,875)(666,876)(667,877)(668,878)(669,879)(670,880)(671,881)(672,882);
s1 := Sym(896)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 30, 35)( 31, 34)( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 86, 91)( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)(127,162)(128,168)(129,167)(130,166)(131,165)(132,164)(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,218)(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)(192,216)(193,215)(194,214)(195,213)(196,212)(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)(239,302)(240,308)(241,307)(242,306)(243,305)(244,304)(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)(252,296)(253,309)(254,315)(255,314)(256,313)(257,312)(258,311)(259,310)(260,316)(261,322)(262,321)(263,320)(264,319)(265,318)(266,317)(267,330)(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)(276,328)(277,327)(278,326)(279,325)(280,324)(337,428)(338,434)(339,433)(340,432)(341,431)(342,430)(343,429)(344,421)(345,427)(346,426)(347,425)(348,424)(349,423)(350,422)(351,435)(352,441)(353,440)(354,439)(355,438)(356,437)(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)(363,444)(364,443)(365,400)(366,406)(367,405)(368,404)(369,403)(370,402)(371,401)(372,393)(373,399)(374,398)(375,397)(376,396)(377,395)(378,394)(379,407)(380,413)(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)(387,420)(388,419)(389,418)(390,417)(391,416)(392,415)(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)(463,582)(464,588)(465,587)(466,586)(467,585)(468,584)(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)(475,577)(476,576)(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)(484,596)(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(491,610)(492,616)(493,615)(494,614)(495,613)(496,612)(497,611)(498,603)(499,609)(500,608)(501,607)(502,606)(503,605)(504,604)(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)(519,638)(520,644)(521,643)(522,642)(523,641)(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)(531,633)(532,632)(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)(540,652)(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,666)(548,672)(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)(556,664)(557,663)(558,662)(559,661)(560,660)(673,855)(674,861)(675,860)(676,859)(677,858)(678,857)(679,856)(680,862)(681,868)(682,867)(683,866)(684,865)(685,864)(686,863)(687,848)(688,854)(689,853)(690,852)(691,851)(692,850)(693,849)(694,841)(695,847)(696,846)(697,845)(698,844)(699,843)(700,842)(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)(707,884)(708,890)(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)(715,876)(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)(722,869)(723,875)(724,874)(725,873)(726,872)(727,871)(728,870)(729,799)(730,805)(731,804)(732,803)(733,802)(734,801)(735,800)(736,806)(737,812)(738,811)(739,810)(740,809)(741,808)(742,807)(743,792)(744,798)(745,797)(746,796)(747,795)(748,794)(749,793)(750,785)(751,791)(752,790)(753,789)(754,788)(755,787)(756,786)(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)(763,828)(764,834)(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)(771,820)(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)(778,813)(779,819)(780,818)(781,817)(782,816)(783,815)(784,814);
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)( 15,464)( 16,463)( 17,469)( 18,468)( 19,467)( 20,466)( 21,465)( 22,471)( 23,470)( 24,476)( 25,475)( 26,474)( 27,473)( 28,472)( 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)( 43,492)( 44,491)( 45,497)( 46,496)( 47,495)( 48,494)( 49,493)( 50,499)( 51,498)( 52,504)( 53,503)( 54,502)( 55,501)( 56,500)( 57,527)( 58,526)( 59,532)( 60,531)( 61,530)( 62,529)( 63,528)( 64,520)( 65,519)( 66,525)( 67,524)( 68,523)( 69,522)( 70,521)( 71,513)( 72,512)( 73,518)( 74,517)( 75,516)( 76,515)( 77,514)( 78,506)( 79,505)( 80,511)( 81,510)( 82,509)( 83,508)( 84,507)( 85,555)( 86,554)( 87,560)( 88,559)( 89,558)( 90,557)( 91,556)( 92,548)( 93,547)( 94,553)( 95,552)( 96,551)( 97,550)( 98,549)( 99,541)(100,540)(101,546)(102,545)(103,544)(104,543)(105,542)(106,534)(107,533)(108,539)(109,538)(110,537)(111,536)(112,535)(113,590)(114,589)(115,595)(116,594)(117,593)(118,592)(119,591)(120,597)(121,596)(122,602)(123,601)(124,600)(125,599)(126,598)(127,604)(128,603)(129,609)(130,608)(131,607)(132,606)(133,605)(134,611)(135,610)(136,616)(137,615)(138,614)(139,613)(140,612)(141,562)(142,561)(143,567)(144,566)(145,565)(146,564)(147,563)(148,569)(149,568)(150,574)(151,573)(152,572)(153,571)(154,570)(155,576)(156,575)(157,581)(158,580)(159,579)(160,578)(161,577)(162,583)(163,582)(164,588)(165,587)(166,586)(167,585)(168,584)(169,667)(170,666)(171,672)(172,671)(173,670)(174,669)(175,668)(176,660)(177,659)(178,665)(179,664)(180,663)(181,662)(182,661)(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)(211,625)(212,624)(213,630)(214,629)(215,628)(216,627)(217,626)(218,618)(219,617)(220,623)(221,622)(222,621)(223,620)(224,619)(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)(239,688)(240,687)(241,693)(242,692)(243,691)(244,690)(245,689)(246,695)(247,694)(248,700)(249,699)(250,698)(251,697)(252,696)(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)(267,716)(268,715)(269,721)(270,720)(271,719)(272,718)(273,717)(274,723)(275,722)(276,728)(277,727)(278,726)(279,725)(280,724)(281,751)(282,750)(283,756)(284,755)(285,754)(286,753)(287,752)(288,744)(289,743)(290,749)(291,748)(292,747)(293,746)(294,745)(295,737)(296,736)(297,742)(298,741)(299,740)(300,739)(301,738)(302,730)(303,729)(304,735)(305,734)(306,733)(307,732)(308,731)(309,779)(310,778)(311,784)(312,783)(313,782)(314,781)(315,780)(316,772)(317,771)(318,777)(319,776)(320,775)(321,774)(322,773)(323,765)(324,764)(325,770)(326,769)(327,768)(328,767)(329,766)(330,758)(331,757)(332,763)(333,762)(334,761)(335,760)(336,759)(337,814)(338,813)(339,819)(340,818)(341,817)(342,816)(343,815)(344,821)(345,820)(346,826)(347,825)(348,824)(349,823)(350,822)(351,828)(352,827)(353,833)(354,832)(355,831)(356,830)(357,829)(358,835)(359,834)(360,840)(361,839)(362,838)(363,837)(364,836)(365,786)(366,785)(367,791)(368,790)(369,789)(370,788)(371,787)(372,793)(373,792)(374,798)(375,797)(376,796)(377,795)(378,794)(379,800)(380,799)(381,805)(382,804)(383,803)(384,802)(385,801)(386,807)(387,806)(388,812)(389,811)(390,810)(391,809)(392,808)(393,891)(394,890)(395,896)(396,895)(397,894)(398,893)(399,892)(400,884)(401,883)(402,889)(403,888)(404,887)(405,886)(406,885)(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)(435,849)(436,848)(437,854)(438,853)(439,852)(440,851)(441,850)(442,842)(443,841)(444,847)(445,846)(446,845)(447,844)(448,843);
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope

Twisty Puzzle