Polytope of Type {8,20}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20}*1600b
if this polytope has a name.
Group : SmallGroup(1600,6743)
Rank : 3
Schlafli Type : {8,20}
Number of vertices, edges, etc : 40, 400, 100
Order of s0s1s2 : 8
Order of s0s1s2s1 : 20
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 : {4,20}*800
   4-fold quotients : {4,10}*400
   8-fold quotients : {4,10}*200
   25-fold quotients : {8,4}*64b
   50-fold quotients : {4,4}*32
   100-fold quotients : {2,4}*16, {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*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      50 facets:
         50 of {8}*16
      20 vertex figures:
         20 of {20}*40
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2> of order 5.
      20 facets:
         20 of {8}*16
      8 vertex figures:
         8 of {20}*40
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2> of order 5.
      20 facets:
         20 of {8}*16
      24 vertex figures:
         20 of {4}*8
         4 of {20}*40
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 5.
      20 facets:
         20 of {8}*16
      8 vertex figures:
         8 of {20}*40

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

Twisty Puzzle