Polytope of Type {16,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,10}*1600
if this polytope has a name.
Group : SmallGroup(1600,6492)
Rank : 3
Schlafli Type : {16,10}
Number of vertices, edges, etc : 80, 400, 50
Order of s0s1s2 : 16
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,10}*800
   4-fold quotients : {4,10}*400
   8-fold quotients : {4,10}*200
   25-fold quotients : {16,2}*64
   50-fold quotients : {8,2}*32
   100-fold quotients : {4,2}*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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1> of order 5.
      10 facets:
         10 of {16}*32
      16 vertex figures:
         16 of {10}*20
   P/N, where N=<s1*s2*s1*s2> of order 5.
      10 facets:
         10 of {16}*32
      48 vertex figures:
         40 of {2}*4
         8 of {10}*20
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 5.
      10 facets:
         10 of {16}*32
      16 vertex figures:
         16 of {10}*20

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