Polytope of Type {8,40}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,40}*1280c
if this polytope has a name.
Group : SmallGroup(1280,81632)
Rank : 3
Schlafli Type : {8,40}
Number of vertices, edges, etc : 16, 320, 80
Order of s0s1s2 : 40
Order of s0s1s2s1 : 4
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 : {8,20}*640a, {4,40}*640b
   4-fold quotients : {4,20}*320, {8,20}*320a, {8,20}*320b
   5-fold quotients : {8,8}*256d
   8-fold quotients : {4,20}*160, {8,10}*160
   10-fold quotients : {8,4}*128a, {4,8}*128b
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*32, {8,2}*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=<s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      40 facets:
         40 of {8}*16
      8 vertex figures:
         8 of {40}*80
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      40 facets:
         40 of {8}*16
      8 vertex figures:
         8 of {40}*80

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

Twisty Puzzle