Polytope of Type {20,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8}*1280d
if this polytope has a name.
Group : SmallGroup(1280,90303)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 80, 320, 32
Order of s0s1s2 : 40
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {20,8}*640b
   4-fold quotients : {20,4}*320
   5-fold quotients : {4,8}*256d
   8-fold quotients : {20,4}*160
   10-fold quotients : {4,8}*128b
   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*s2*s1*s2*s1*s0*s2> of order 2.
      16 facets:
         16 of {20}*40
      60 vertex figures:
         20 of {8}*16
         40 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2> of order 4.
      8 facets:
         8 of {20}*40
      40 vertex figures:
         10 of {8}*16
         10 of {4}*8
         20 of {2}*4

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