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}*1280c
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
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,4}*640a
   4-fold quotients : {20,4}*320
   5-fold quotients : {8,4}*256c
   8-fold quotients : {20,4}*160
   10-fold quotients : {4,4}*128
   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*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 2.
      8 facets:
         8 of {40}*80
      80 vertex figures:
         80 of {4}*8

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

Twisty Puzzle