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}*1280c
if this polytope has a name.
Group : SmallGroup(1280,90301)
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 : {20,4}*640a
   4-fold quotients : {20,4}*320
   5-fold quotients : {4,8}*256c
   8-fold quotients : {20,4}*160
   10-fold quotients : {4,4}*128
   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*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 2.
      16 facets:
         16 of {20}*40
      40 vertex figures:
         40 of {8}*16

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

Twisty Puzzle