Polytope of Type {16,40}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,40}*1280e
if this polytope has a name.
Group : SmallGroup(1280,83049)
Rank : 3
Schlafli Type : {16,40}
Number of vertices, edges, etc : 16, 320, 40
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {8,40}*640d, {16,20}*640b
   4-fold quotients : {4,40}*320b, {8,20}*320a
   5-fold quotients : {16,8}*256e
   8-fold quotients : {4,20}*160, {8,10}*160
   10-fold quotients : {8,8}*128c, {16,4}*128b
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {8,4}*64a, {4,8}*64b
   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):
   None.

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)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 46, 51)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 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)(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)(127,155)(128,154)(129,153)(130,152)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(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)(361,456)(362,460)(363,459)(364,458)(365,457)(366,451)(367,455)(368,454)(369,453)(370,452)(371,446)(372,450)(373,449)(374,448)(375,447)(376,441)(377,445)(378,444)(379,443)(380,442)(381,471)(382,475)(383,474)(384,473)(385,472)(386,476)(387,480)(388,479)(389,478)(390,477)(391,461)(392,465)(393,464)(394,463)(395,462)(396,466)(397,470)(398,469)(399,468)(400,467)(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)( 41,218)( 42,217)( 43,216)( 44,220)( 45,219)( 46,213)( 47,212)( 48,211)( 49,215)( 50,214)( 51,208)( 52,207)( 53,206)( 54,210)( 55,209)( 56,203)( 57,202)( 58,201)( 59,205)( 60,204)( 61,238)( 62,237)( 63,236)( 64,240)( 65,239)( 66,233)( 67,232)( 68,231)( 69,235)( 70,234)( 71,228)( 72,227)( 73,226)( 74,230)( 75,229)( 76,223)( 77,222)( 78,221)( 79,225)( 80,224)( 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)(121,288)(122,287)(123,286)(124,290)(125,289)(126,283)(127,282)(128,281)(129,285)(130,284)(131,298)(132,297)(133,296)(134,300)(135,299)(136,293)(137,292)(138,291)(139,295)(140,294)(141,308)(142,307)(143,306)(144,310)(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)(152,317)(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)(160,314)(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)(361,538)(362,537)(363,536)(364,540)(365,539)(366,533)(367,532)(368,531)(369,535)(370,534)(371,528)(372,527)(373,526)(374,530)(375,529)(376,523)(377,522)(378,521)(379,525)(380,524)(381,558)(382,557)(383,556)(384,560)(385,559)(386,553)(387,552)(388,551)(389,555)(390,554)(391,548)(392,547)(393,546)(394,550)(395,549)(396,543)(397,542)(398,541)(399,545)(400,544)(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)(441,608)(442,607)(443,606)(444,610)(445,609)(446,603)(447,602)(448,601)(449,605)(450,604)(451,618)(452,617)(453,616)(454,620)(455,619)(456,613)(457,612)(458,611)(459,615)(460,614)(461,628)(462,627)(463,626)(464,630)(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)(472,637)(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)(480,634);;
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*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*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)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 46, 51)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 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)(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)(127,155)(128,154)(129,153)(130,152)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)(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)(361,456)(362,460)(363,459)(364,458)(365,457)(366,451)(367,455)(368,454)(369,453)(370,452)(371,446)(372,450)(373,449)(374,448)(375,447)(376,441)(377,445)(378,444)(379,443)(380,442)(381,471)(382,475)(383,474)(384,473)(385,472)(386,476)(387,480)(388,479)(389,478)(390,477)(391,461)(392,465)(393,464)(394,463)(395,462)(396,466)(397,470)(398,469)(399,468)(400,467)(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)( 41,218)( 42,217)( 43,216)( 44,220)( 45,219)( 46,213)( 47,212)( 48,211)( 49,215)( 50,214)( 51,208)( 52,207)( 53,206)( 54,210)( 55,209)( 56,203)( 57,202)( 58,201)( 59,205)( 60,204)( 61,238)( 62,237)( 63,236)( 64,240)( 65,239)( 66,233)( 67,232)( 68,231)( 69,235)( 70,234)( 71,228)( 72,227)( 73,226)( 74,230)( 75,229)( 76,223)( 77,222)( 78,221)( 79,225)( 80,224)( 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)(121,288)(122,287)(123,286)(124,290)(125,289)(126,283)(127,282)(128,281)(129,285)(130,284)(131,298)(132,297)(133,296)(134,300)(135,299)(136,293)(137,292)(138,291)(139,295)(140,294)(141,308)(142,307)(143,306)(144,310)(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)(152,317)(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)(160,314)(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)(361,538)(362,537)(363,536)(364,540)(365,539)(366,533)(367,532)(368,531)(369,535)(370,534)(371,528)(372,527)(373,526)(374,530)(375,529)(376,523)(377,522)(378,521)(379,525)(380,524)(381,558)(382,557)(383,556)(384,560)(385,559)(386,553)(387,552)(388,551)(389,555)(390,554)(391,548)(392,547)(393,546)(394,550)(395,549)(396,543)(397,542)(398,541)(399,545)(400,544)(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)(441,608)(442,607)(443,606)(444,610)(445,609)(446,603)(447,602)(448,601)(449,605)(450,604)(451,618)(452,617)(453,616)(454,620)(455,619)(456,613)(457,612)(458,611)(459,615)(460,614)(461,628)(462,627)(463,626)(464,630)(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)(472,637)(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)(480,634);
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*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle