Polytope of Type {8,28}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,28}*1792a
if this polytope has a name.
Group : SmallGroup(1792,81598)
Rank : 3
Schlafli Type : {8,28}
Number of vertices, edges, etc : 32, 448, 112
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 : {8,28}*896a, {4,28}*896, {8,28}*896b
   4-fold quotients : {4,28}*448, {8,28}*448a, {8,28}*448b
   7-fold quotients : {8,4}*256a
   8-fold quotients : {4,28}*224, {8,14}*224
   14-fold quotients : {8,4}*128a, {4,4}*128, {8,4}*128b
   16-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*32, {8,2}*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*s0*s2*s1*s0*s1*s2> of order 2.
      56 facets:
         56 of {8}*16
      16 vertex figures:
         16 of {28}*56
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      56 facets:
         56 of {8}*16
      16 vertex figures:
         16 of {28}*56
   P/N, where N=<s1*s2*s1*s2*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.
      56 facets:
         56 of {8}*16
      20 vertex figures:
         8 of {14}*28
         12 of {28}*56
   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.
      56 facets:
         56 of {8}*16
      16 vertex figures:
         16 of {28}*56
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1> of order 2.
      56 facets:
         56 of {8}*16
      16 vertex figures:
         16 of {28}*56
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      56 facets:
         56 of {8}*16
      16 vertex figures:
         16 of {28}*56
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 4.
      28 facets:
         28 of {8}*16
      8 vertex figures:
         8 of {28}*56
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      28 facets:
         28 of {8}*16
      8 vertex figures:
         8 of {28}*56
   P/N, where N=<s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1> of order 4.
      28 facets:
         28 of {8}*16
      10 vertex figures:
         4 of {14}*28
         6 of {28}*56
   P/N, where N=<s1*s0*s1*s2*s1*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> of order 4.
      28 facets:
         28 of {8}*16
      12 vertex figures:
         8 of {14}*28
         4 of {28}*56
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      28 facets:
         28 of {8}*16
      8 vertex figures:
         8 of {28}*56
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1> of order 4.
      28 facets:
         28 of {8}*16
      8 vertex figures:
         8 of {28}*56
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      28 facets:
         28 of {8}*16
      8 vertex figures:
         8 of {28}*56
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      28 facets:
         28 of {8}*16
      8 vertex figures:
         8 of {28}*56
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      28 facets:
         28 of {8}*16
      10 vertex figures:
         4 of {14}*28
         6 of {28}*56

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

Twisty Puzzle