Polytope of Type {40,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,4}*1280d
if this polytope has a name.
Group : SmallGroup(1280,90302)
Rank : 3
Schlafli Type : {40,4}
Number of vertices, edges, etc : 160, 320, 16
Order of s0s1s2 : 40
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {40,4}*640b
   4-fold quotients : {20,4}*320
   5-fold quotients : {8,4}*256d
   8-fold quotients : {20,4}*160
   10-fold quotients : {8,4}*128b
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {4,4}*64
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32
   64-fold quotients : {5,2}*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.
      12 facets:
         4 of {40}*80
         8 of {20}*40
      80 vertex figures:
         80 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         2 of {40}*80
         4 of {10}*20
         2 of {20}*40
      40 vertex figures:
         40 of {4}*8

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

Twisty Puzzle