Polytope of Type {40,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,8}*1280d
if this polytope has a name.
Group : SmallGroup(1280,81633)
Rank : 3
Schlafli Type : {40,8}
Number of vertices, edges, etc : 80, 320, 16
Order of s0s1s2 : 40
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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}*640a, {20,8}*640b
   4-fold quotients : {40,4}*320a, {20,4}*320, {40,4}*320b
   5-fold quotients : {8,8}*256d
   8-fold quotients : {20,4}*160, {40,2}*160
   10-fold quotients : {8,4}*128a, {4,8}*128b
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32, {8,2}*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=<s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      8 facets:
         8 of {40}*80
      40 vertex figures:
         40 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      8 facets:
         8 of {40}*80
      40 vertex figures:
         40 of {8}*16

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

Twisty Puzzle