Polytope of Type {10,16}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,16}*1600
if this polytope has a name.
Group : SmallGroup(1600,6492)
Rank : 3
Schlafli Type : {10,16}
Number of vertices, edges, etc : 50, 400, 80
Order of s0s1s2 : 16
Order of s0s1s2s1 : 10
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 : {10,8}*800
   4-fold quotients : {10,4}*400
   8-fold quotients : {10,4}*200
   25-fold quotients : {2,16}*64
   50-fold quotients : {2,8}*32
   100-fold quotients : {2,4}*16
   200-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*s2*s1*s0*s1*s2*s1*s0*s1> of order 5.
      16 facets:
         16 of {10}*20
      10 vertex figures:
         10 of {16}*32
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 5.
      16 facets:
         16 of {10}*20
      10 vertex figures:
         10 of {16}*32
   P/N, where N=<s0*s1*s0*s1> of order 5.
      48 facets:
         40 of {2}*4
         8 of {10}*20
      10 vertex figures:
         10 of {16}*32

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

Twisty Puzzle