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}*1280c
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 : {4,20}*640a
   4-fold quotients : {4,20}*320
   5-fold quotients : {4,8}*256c
   8-fold quotients : {4,20}*160
   10-fold quotients : {4,4}*128
   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*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 2.
      80 facets:
         80 of {4}*8
      8 vertex figures:
         8 of {40}*80

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

Twisty Puzzle