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}*1280d
if this polytope has a name.
Group : SmallGroup(1280,81633)
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 : {4,40}*640a, {8,20}*640b
   4-fold quotients : {4,40}*320a, {4,20}*320, {4,40}*320b
   5-fold quotients : {8,8}*256c
   8-fold quotients : {4,20}*160, {2,40}*160
   10-fold quotients : {4,8}*128a, {8,4}*128b
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*32, {2,8}*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*s1*s2*s1> of order 2.
      40 facets:
         40 of {8}*16
      8 vertex figures:
         8 of {40}*80
   P/N, where N=<s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      40 facets:
         40 of {8}*16
      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)( 11,171)( 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);;
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 := (  1,323)(  2,322)(  3,321)(  4,325)(  5,324)(  6,328)(  7,327)(  8,326)(  9,330)( 10,329)( 11,333)( 12,332)( 13,331)( 14,335)( 15,334)( 16,338)( 17,337)( 18,336)( 19,340)( 20,339)( 21,343)( 22,342)( 23,341)( 24,345)( 25,344)( 26,348)( 27,347)( 28,346)( 29,350)( 30,349)( 31,353)( 32,352)( 33,351)( 34,355)( 35,354)( 36,358)( 37,357)( 38,356)( 39,360)( 40,359)( 41,378)( 42,377)( 43,376)( 44,380)( 45,379)( 46,373)( 47,372)( 48,371)( 49,375)( 50,374)( 51,368)( 52,367)( 53,366)( 54,370)( 55,369)( 56,363)( 57,362)( 58,361)( 59,365)( 60,364)( 61,398)( 62,397)( 63,396)( 64,400)( 65,399)( 66,393)( 67,392)( 68,391)( 69,395)( 70,394)( 71,388)( 72,387)( 73,386)( 74,390)( 75,389)( 76,383)( 77,382)( 78,381)( 79,385)( 80,384)( 81,423)( 82,422)( 83,421)( 84,425)( 85,424)( 86,428)( 87,427)( 88,426)( 89,430)( 90,429)( 91,433)( 92,432)( 93,431)( 94,435)( 95,434)( 96,438)( 97,437)( 98,436)( 99,440)(100,439)(101,403)(102,402)(103,401)(104,405)(105,404)(106,408)(107,407)(108,406)(109,410)(110,409)(111,413)(112,412)(113,411)(114,415)(115,414)(116,418)(117,417)(118,416)(119,420)(120,419)(121,478)(122,477)(123,476)(124,480)(125,479)(126,473)(127,472)(128,471)(129,475)(130,474)(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)(151,448)(152,447)(153,446)(154,450)(155,449)(156,443)(157,442)(158,441)(159,445)(160,444)(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)(168,486)(169,490)(170,489)(171,493)(172,492)(173,491)(174,495)(175,494)(176,498)(177,497)(178,496)(179,500)(180,499)(181,503)(182,502)(183,501)(184,505)(185,504)(186,508)(187,507)(188,506)(189,510)(190,509)(191,513)(192,512)(193,511)(194,515)(195,514)(196,518)(197,517)(198,516)(199,520)(200,519)(201,538)(202,537)(203,536)(204,540)(205,539)(206,533)(207,532)(208,531)(209,535)(210,534)(211,528)(212,527)(213,526)(214,530)(215,529)(216,523)(217,522)(218,521)(219,525)(220,524)(221,558)(222,557)(223,556)(224,560)(225,559)(226,553)(227,552)(228,551)(229,555)(230,554)(231,548)(232,547)(233,546)(234,550)(235,549)(236,543)(237,542)(238,541)(239,545)(240,544)(241,583)(242,582)(243,581)(244,585)(245,584)(246,588)(247,587)(248,586)(249,590)(250,589)(251,593)(252,592)(253,591)(254,595)(255,594)(256,598)(257,597)(258,596)(259,600)(260,599)(261,563)(262,562)(263,561)(264,565)(265,564)(266,568)(267,567)(268,566)(269,570)(270,569)(271,573)(272,572)(273,571)(274,575)(275,574)(276,578)(277,577)(278,576)(279,580)(280,579)(281,638)(282,637)(283,636)(284,640)(285,639)(286,633)(287,632)(288,631)(289,635)(290,634)(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)(311,608)(312,607)(313,606)(314,610)(315,609)(316,603)(317,602)(318,601)(319,605)(320,604);;
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*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)( 11,171)( 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);
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)!(  1,323)(  2,322)(  3,321)(  4,325)(  5,324)(  6,328)(  7,327)(  8,326)(  9,330)( 10,329)( 11,333)( 12,332)( 13,331)( 14,335)( 15,334)( 16,338)( 17,337)( 18,336)( 19,340)( 20,339)( 21,343)( 22,342)( 23,341)( 24,345)( 25,344)( 26,348)( 27,347)( 28,346)( 29,350)( 30,349)( 31,353)( 32,352)( 33,351)( 34,355)( 35,354)( 36,358)( 37,357)( 38,356)( 39,360)( 40,359)( 41,378)( 42,377)( 43,376)( 44,380)( 45,379)( 46,373)( 47,372)( 48,371)( 49,375)( 50,374)( 51,368)( 52,367)( 53,366)( 54,370)( 55,369)( 56,363)( 57,362)( 58,361)( 59,365)( 60,364)( 61,398)( 62,397)( 63,396)( 64,400)( 65,399)( 66,393)( 67,392)( 68,391)( 69,395)( 70,394)( 71,388)( 72,387)( 73,386)( 74,390)( 75,389)( 76,383)( 77,382)( 78,381)( 79,385)( 80,384)( 81,423)( 82,422)( 83,421)( 84,425)( 85,424)( 86,428)( 87,427)( 88,426)( 89,430)( 90,429)( 91,433)( 92,432)( 93,431)( 94,435)( 95,434)( 96,438)( 97,437)( 98,436)( 99,440)(100,439)(101,403)(102,402)(103,401)(104,405)(105,404)(106,408)(107,407)(108,406)(109,410)(110,409)(111,413)(112,412)(113,411)(114,415)(115,414)(116,418)(117,417)(118,416)(119,420)(120,419)(121,478)(122,477)(123,476)(124,480)(125,479)(126,473)(127,472)(128,471)(129,475)(130,474)(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)(151,448)(152,447)(153,446)(154,450)(155,449)(156,443)(157,442)(158,441)(159,445)(160,444)(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)(168,486)(169,490)(170,489)(171,493)(172,492)(173,491)(174,495)(175,494)(176,498)(177,497)(178,496)(179,500)(180,499)(181,503)(182,502)(183,501)(184,505)(185,504)(186,508)(187,507)(188,506)(189,510)(190,509)(191,513)(192,512)(193,511)(194,515)(195,514)(196,518)(197,517)(198,516)(199,520)(200,519)(201,538)(202,537)(203,536)(204,540)(205,539)(206,533)(207,532)(208,531)(209,535)(210,534)(211,528)(212,527)(213,526)(214,530)(215,529)(216,523)(217,522)(218,521)(219,525)(220,524)(221,558)(222,557)(223,556)(224,560)(225,559)(226,553)(227,552)(228,551)(229,555)(230,554)(231,548)(232,547)(233,546)(234,550)(235,549)(236,543)(237,542)(238,541)(239,545)(240,544)(241,583)(242,582)(243,581)(244,585)(245,584)(246,588)(247,587)(248,586)(249,590)(250,589)(251,593)(252,592)(253,591)(254,595)(255,594)(256,598)(257,597)(258,596)(259,600)(260,599)(261,563)(262,562)(263,561)(264,565)(265,564)(266,568)(267,567)(268,566)(269,570)(270,569)(271,573)(272,572)(273,571)(274,575)(275,574)(276,578)(277,577)(278,576)(279,580)(280,579)(281,638)(282,637)(283,636)(284,640)(285,639)(286,633)(287,632)(288,631)(289,635)(290,634)(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)(311,608)(312,607)(313,606)(314,610)(315,609)(316,603)(317,602)(318,601)(319,605)(320,604);
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*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle