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}*1792d
if this polytope has a name.
Group : SmallGroup(1792,90303)
Rank : 3
Schlafli Type : {8,28}
Number of vertices, edges, etc : 32, 448, 112
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 : {8,28}*896b
   4-fold quotients : {4,28}*448
   7-fold quotients : {8,4}*256d
   8-fold quotients : {4,28}*224
   14-fold quotients : {8,4}*128b
   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*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 2.
      84 facets:
         28 of {8}*16
         56 of {4}*8
      16 vertex figures:
         16 of {28}*56
   P/N, where N=<s0*s2*s1*s0*s1*s2> of order 4.
      56 facets:
         14 of {8}*16
         14 of {4}*8
         28 of {2}*4
      8 vertex figures:
         8 of {28}*56

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