Polytope of Type {111,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {111,4}*1776
if this polytope has a name.
Group : SmallGroup(1776,245)
Rank : 3
Schlafli Type : {111,4}
Number of vertices, edges, etc : 222, 444, 8
Order of s0s1s2 : 222
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {111,4}*888
   4-fold quotients : {111,2}*444
   12-fold quotients : {37,2}*148
   37-fold quotients : {3,4}*48
   74-fold quotients : {3,4}*24
   148-fold quotients : {3,2}*12
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*s1*s2*s1> of order 2.
      4 facets:
         4 of {111}*222
      148 vertex figures:
         74 of {4}*8
         74 of {2}*4

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

Twisty Puzzle