Polytope of Type {16,20}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,20}*1280a
if this polytope has a name.
Group : SmallGroup(1280,81666)
Rank : 3
Schlafli Type : {16,20}
Number of vertices, edges, etc : 32, 320, 40
Order of s0s1s2 : 80
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 : {8,20}*640a, {16,20}*640a, {16,20}*640b
   4-fold quotients : {4,20}*320, {8,20}*320a, {8,20}*320b, {16,10}*320
   5-fold quotients : {16,4}*256a
   8-fold quotients : {4,20}*160, {8,10}*160
   10-fold quotients : {8,4}*128a, {16,4}*128a, {16,4}*128b
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64, {16,2}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*32, {8,2}*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=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      20 facets:
         20 of {16}*32
      24 vertex figures:
         16 of {10}*20
         8 of {20}*40

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