Polytope of Type {4,40}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,40}*1280d
if this polytope has a name.
Group : SmallGroup(1280,90302)
Rank : 3
Schlafli Type : {4,40}
Number of vertices, edges, etc : 16, 320, 160
Order of s0s1s2 : 40
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,40}*640b
   4-fold quotients : {4,20}*320
   5-fold quotients : {4,8}*256d
   8-fold quotients : {4,20}*160
   10-fold quotients : {4,8}*128b
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {4,4}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*32
   64-fold quotients : {2,5}*20
   80-fold quotients : {2,4}*16, {4,2}*16
   160-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*s2*s1*s0*s1*s2*s1*s2> of order 2.
      80 facets:
         80 of {4}*8
      12 vertex figures:
         4 of {40}*80
         8 of {20}*40
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      40 facets:
         40 of {4}*8
      8 vertex figures:
         2 of {40}*80
         4 of {10}*20
         2 of {20}*40

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

Twisty Puzzle