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}*1280b
if this polytope has a name.
Group : SmallGroup(1280,81734)
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
   4-fold quotients : {4,20}*320, {8,20}*320a, {8,20}*320b
   5-fold quotients : {16,4}*256b
   8-fold quotients : {4,20}*160, {8,10}*160
   10-fold quotients : {8,4}*128a
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*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*s0*s1*s2*s1*s0*s1*s2> of order 2.
      20 facets:
         20 of {16}*32
      16 vertex figures:
         16 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)( 41,376)( 42,377)( 43,378)( 44,379)( 45,380)( 46,371)( 47,372)( 48,373)( 49,374)( 50,375)( 51,366)( 52,367)( 53,368)( 54,369)( 55,370)( 56,361)( 57,362)( 58,363)( 59,364)( 60,365)( 61,391)( 62,392)( 63,393)( 64,394)( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)( 72,382)( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)( 80,390)( 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)(121,476)(122,477)(123,478)(124,479)(125,480)(126,471)(127,472)(128,473)(129,474)(130,475)(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)(151,446)(152,447)(153,448)(154,449)(155,450)(156,441)(157,442)(158,443)(159,444)(160,445)(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)(201,536)(202,537)(203,538)(204,539)(205,540)(206,531)(207,532)(208,533)(209,534)(210,535)(211,526)(212,527)(213,528)(214,529)(215,530)(216,521)(217,522)(218,523)(219,524)(220,525)(221,551)(222,552)(223,553)(224,554)(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)(232,542)(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)(240,550)(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)(281,636)(282,637)(283,638)(284,639)(285,640)(286,631)(287,632)(288,633)(289,634)(290,635)(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)(311,606)(312,607)(313,608)(314,609)(315,610)(316,601)(317,602)(318,603)(319,604)(320,605);;
s1 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 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)(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)(128,149)(129,148)(130,147)(131,156)(132,160)(133,159)(134,158)(135,157)(136,151)(137,155)(138,154)(139,153)(140,152)(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)(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)(187,225)(188,224)(189,223)(190,222)(191,231)(192,235)(193,234)(194,233)(195,232)(196,236)(197,240)(198,239)(199,238)(200,237)(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)(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)(347,425)(348,424)(349,423)(350,422)(351,431)(352,435)(353,434)(354,433)(355,432)(356,436)(357,440)(358,439)(359,438)(360,437)(361,441)(362,445)(363,444)(364,443)(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,456)(372,460)(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)(380,452)(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)(501,636)(502,640)(503,639)(504,638)(505,637)(506,631)(507,635)(508,634)(509,633)(510,632)(511,621)(512,625)(513,624)(514,623)(515,622)(516,626)(517,630)(518,629)(519,628)(520,627)(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)(541,596)(542,600)(543,599)(544,598)(545,597)(546,591)(547,595)(548,594)(549,593)(550,592)(551,581)(552,585)(553,584)(554,583)(555,582)(556,586)(557,590)(558,589)(559,588)(560,587);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*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)( 41,376)( 42,377)( 43,378)( 44,379)( 45,380)( 46,371)( 47,372)( 48,373)( 49,374)( 50,375)( 51,366)( 52,367)( 53,368)( 54,369)( 55,370)( 56,361)( 57,362)( 58,363)( 59,364)( 60,365)( 61,391)( 62,392)( 63,393)( 64,394)( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)( 72,382)( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)( 80,390)( 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)(121,476)(122,477)(123,478)(124,479)(125,480)(126,471)(127,472)(128,473)(129,474)(130,475)(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)(151,446)(152,447)(153,448)(154,449)(155,450)(156,441)(157,442)(158,443)(159,444)(160,445)(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)(201,536)(202,537)(203,538)(204,539)(205,540)(206,531)(207,532)(208,533)(209,534)(210,535)(211,526)(212,527)(213,528)(214,529)(215,530)(216,521)(217,522)(218,523)(219,524)(220,525)(221,551)(222,552)(223,553)(224,554)(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)(232,542)(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)(240,550)(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)(281,636)(282,637)(283,638)(284,639)(285,640)(286,631)(287,632)(288,633)(289,634)(290,635)(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)(311,606)(312,607)(313,608)(314,609)(315,610)(316,601)(317,602)(318,603)(319,604)(320,605);
s1 := Sym(640)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 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)(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)(128,149)(129,148)(130,147)(131,156)(132,160)(133,159)(134,158)(135,157)(136,151)(137,155)(138,154)(139,153)(140,152)(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)(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)(187,225)(188,224)(189,223)(190,222)(191,231)(192,235)(193,234)(194,233)(195,232)(196,236)(197,240)(198,239)(199,238)(200,237)(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)(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)(347,425)(348,424)(349,423)(350,422)(351,431)(352,435)(353,434)(354,433)(355,432)(356,436)(357,440)(358,439)(359,438)(360,437)(361,441)(362,445)(363,444)(364,443)(365,442)(366,446)(367,450)(368,449)(369,448)(370,447)(371,456)(372,460)(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)(380,452)(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)(501,636)(502,640)(503,639)(504,638)(505,637)(506,631)(507,635)(508,634)(509,633)(510,632)(511,621)(512,625)(513,624)(514,623)(515,622)(516,626)(517,630)(518,629)(519,628)(520,627)(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)(541,596)(542,600)(543,599)(544,598)(545,597)(546,591)(547,595)(548,594)(549,593)(550,592)(551,581)(552,585)(553,584)(554,583)(555,582)(556,586)(557,590)(558,589)(559,588)(560,587);
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*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