Polytope of Type {80,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {80,8}*1280f
if this polytope has a name.
Group : SmallGroup(1280,83050)
Rank : 3
Schlafli Type : {80,8}
Number of vertices, edges, etc : 80, 320, 8
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {40,8}*640b, {80,4}*640b
   4-fold quotients : {40,4}*320a, {20,8}*320a
   5-fold quotients : {16,8}*256f
   8-fold quotients : {20,4}*160, {40,2}*160, {10,8}*160
   10-fold quotients : {8,8}*128b, {16,4}*128b
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {4,8}*64a, {8,4}*64a
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32, {2,8}*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):
   None.

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