Polytope of Type {8,40}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,40}*1280f
if this polytope has a name.
Group : SmallGroup(1280,90303)
Rank : 3
Schlafli Type : {8,40}
Number of vertices, edges, etc : 16, 320, 80
Order of s0s1s2 : 20
Order of s0s1s2s1 : 8
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}*640b
   4-fold quotients : {4,20}*320
   5-fold quotients : {8,8}*256f
   8-fold quotients : {4,20}*160
   10-fold quotients : {8,4}*128b
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {4,4}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*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 := (  1,481)(  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);;
s1 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)(101,116)(102,120)(103,119)(104,118)(105,117)(106,111)(107,115)(108,114)(109,113)(110,112)(121,126)(122,130)(123,129)(124,128)(125,127)(131,136)(132,140)(133,139)(134,138)(135,137)(141,156)(142,160)(143,159)(144,158)(145,157)(146,151)(147,155)(148,154)(149,153)(150,152)(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)(181,231)(182,235)(183,234)(184,233)(185,232)(186,236)(187,240)(188,239)(189,238)(190,237)(191,221)(192,225)(193,224)(194,223)(195,222)(196,226)(197,230)(198,229)(199,228)(200,227)(241,291)(242,295)(243,294)(244,293)(245,292)(246,296)(247,300)(248,299)(249,298)(250,297)(251,281)(252,285)(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)(260,287)(261,301)(262,305)(263,304)(264,303)(265,302)(266,306)(267,310)(268,309)(269,308)(270,307)(271,311)(272,315)(273,314)(274,313)(275,312)(276,316)(277,320)(278,319)(279,318)(280,317)(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)(341,431)(342,435)(343,434)(344,433)(345,432)(346,436)(347,440)(348,439)(349,438)(350,437)(351,421)(352,425)(353,424)(354,423)(355,422)(356,426)(357,430)(358,429)(359,428)(360,427)(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)(381,471)(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)(481,626)(482,630)(483,629)(484,628)(485,627)(486,621)(487,625)(488,624)(489,623)(490,622)(491,636)(492,640)(493,639)(494,638)(495,637)(496,631)(497,635)(498,634)(499,633)(500,632)(501,611)(502,615)(503,614)(504,613)(505,612)(506,616)(507,620)(508,619)(509,618)(510,617)(511,601)(512,605)(513,604)(514,603)(515,602)(516,606)(517,610)(518,609)(519,608)(520,607)(521,581)(522,585)(523,584)(524,583)(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)(532,595)(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)(540,597)(541,576)(542,580)(543,579)(544,578)(545,577)(546,571)(547,575)(548,574)(549,573)(550,572)(551,566)(552,570)(553,569)(554,568)(555,567)(556,561)(557,565)(558,564)(559,563)(560,562);;
s2 := (  1,323)(  2,322)(  3,321)(  4,325)(  5,324)(  6,328)(  7,327)(  8,326)(  9,330)( 10,329)( 11,338)( 12,337)( 13,336)( 14,340)( 15,339)( 16,333)( 17,332)( 18,331)( 19,335)( 20,334)( 21,343)( 22,342)( 23,341)( 24,345)( 25,344)( 26,348)( 27,347)( 28,346)( 29,350)( 30,349)( 31,358)( 32,357)( 33,356)( 34,360)( 35,359)( 36,353)( 37,352)( 38,351)( 39,355)( 40,354)( 41,398)( 42,397)( 43,396)( 44,400)( 45,399)( 46,393)( 47,392)( 48,391)( 49,395)( 50,394)( 51,383)( 52,382)( 53,381)( 54,385)( 55,384)( 56,388)( 57,387)( 58,386)( 59,390)( 60,389)( 61,373)( 62,372)( 63,371)( 64,375)( 65,374)( 66,378)( 67,377)( 68,376)( 69,380)( 70,379)( 71,368)( 72,367)( 73,366)( 74,370)( 75,369)( 76,363)( 77,362)( 78,361)( 79,365)( 80,364)( 81,408)( 82,407)( 83,406)( 84,410)( 85,409)( 86,403)( 87,402)( 88,401)( 89,405)( 90,404)( 91,413)( 92,412)( 93,411)( 94,415)( 95,414)( 96,418)( 97,417)( 98,416)( 99,420)(100,419)(101,428)(102,427)(103,426)(104,430)(105,429)(106,423)(107,422)(108,421)(109,425)(110,424)(111,433)(112,432)(113,431)(114,435)(115,434)(116,438)(117,437)(118,436)(119,440)(120,439)(121,473)(122,472)(123,471)(124,475)(125,474)(126,478)(127,477)(128,476)(129,480)(130,479)(131,468)(132,467)(133,466)(134,470)(135,469)(136,463)(137,462)(138,461)(139,465)(140,464)(141,458)(142,457)(143,456)(144,460)(145,459)(146,453)(147,452)(148,451)(149,455)(150,454)(151,443)(152,442)(153,441)(154,445)(155,444)(156,448)(157,447)(158,446)(159,450)(160,449)(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)(168,486)(169,490)(170,489)(171,498)(172,497)(173,496)(174,500)(175,499)(176,493)(177,492)(178,491)(179,495)(180,494)(181,503)(182,502)(183,501)(184,505)(185,504)(186,508)(187,507)(188,506)(189,510)(190,509)(191,518)(192,517)(193,516)(194,520)(195,519)(196,513)(197,512)(198,511)(199,515)(200,514)(201,558)(202,557)(203,556)(204,560)(205,559)(206,553)(207,552)(208,551)(209,555)(210,554)(211,543)(212,542)(213,541)(214,545)(215,544)(216,548)(217,547)(218,546)(219,550)(220,549)(221,533)(222,532)(223,531)(224,535)(225,534)(226,538)(227,537)(228,536)(229,540)(230,539)(231,528)(232,527)(233,526)(234,530)(235,529)(236,523)(237,522)(238,521)(239,525)(240,524)(241,568)(242,567)(243,566)(244,570)(245,569)(246,563)(247,562)(248,561)(249,565)(250,564)(251,573)(252,572)(253,571)(254,575)(255,574)(256,578)(257,577)(258,576)(259,580)(260,579)(261,588)(262,587)(263,586)(264,590)(265,589)(266,583)(267,582)(268,581)(269,585)(270,584)(271,593)(272,592)(273,591)(274,595)(275,594)(276,598)(277,597)(278,596)(279,600)(280,599)(281,633)(282,632)(283,631)(284,635)(285,634)(286,638)(287,637)(288,636)(289,640)(290,639)(291,628)(292,627)(293,626)(294,630)(295,629)(296,623)(297,622)(298,621)(299,625)(300,624)(301,618)(302,617)(303,616)(304,620)(305,619)(306,613)(307,612)(308,611)(309,615)(310,614)(311,603)(312,602)(313,601)(314,605)(315,604)(316,608)(317,607)(318,606)(319,610)(320,609);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1, 
s1*s2*s1*s2*s1*s0*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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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);
s1 := Sym(640)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)(101,116)(102,120)(103,119)(104,118)(105,117)(106,111)(107,115)(108,114)(109,113)(110,112)(121,126)(122,130)(123,129)(124,128)(125,127)(131,136)(132,140)(133,139)(134,138)(135,137)(141,156)(142,160)(143,159)(144,158)(145,157)(146,151)(147,155)(148,154)(149,153)(150,152)(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)(181,231)(182,235)(183,234)(184,233)(185,232)(186,236)(187,240)(188,239)(189,238)(190,237)(191,221)(192,225)(193,224)(194,223)(195,222)(196,226)(197,230)(198,229)(199,228)(200,227)(241,291)(242,295)(243,294)(244,293)(245,292)(246,296)(247,300)(248,299)(249,298)(250,297)(251,281)(252,285)(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)(260,287)(261,301)(262,305)(263,304)(264,303)(265,302)(266,306)(267,310)(268,309)(269,308)(270,307)(271,311)(272,315)(273,314)(274,313)(275,312)(276,316)(277,320)(278,319)(279,318)(280,317)(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)(341,431)(342,435)(343,434)(344,433)(345,432)(346,436)(347,440)(348,439)(349,438)(350,437)(351,421)(352,425)(353,424)(354,423)(355,422)(356,426)(357,430)(358,429)(359,428)(360,427)(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)(381,471)(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)(481,626)(482,630)(483,629)(484,628)(485,627)(486,621)(487,625)(488,624)(489,623)(490,622)(491,636)(492,640)(493,639)(494,638)(495,637)(496,631)(497,635)(498,634)(499,633)(500,632)(501,611)(502,615)(503,614)(504,613)(505,612)(506,616)(507,620)(508,619)(509,618)(510,617)(511,601)(512,605)(513,604)(514,603)(515,602)(516,606)(517,610)(518,609)(519,608)(520,607)(521,581)(522,585)(523,584)(524,583)(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)(532,595)(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)(540,597)(541,576)(542,580)(543,579)(544,578)(545,577)(546,571)(547,575)(548,574)(549,573)(550,572)(551,566)(552,570)(553,569)(554,568)(555,567)(556,561)(557,565)(558,564)(559,563)(560,562);
s2 := Sym(640)!(  1,323)(  2,322)(  3,321)(  4,325)(  5,324)(  6,328)(  7,327)(  8,326)(  9,330)( 10,329)( 11,338)( 12,337)( 13,336)( 14,340)( 15,339)( 16,333)( 17,332)( 18,331)( 19,335)( 20,334)( 21,343)( 22,342)( 23,341)( 24,345)( 25,344)( 26,348)( 27,347)( 28,346)( 29,350)( 30,349)( 31,358)( 32,357)( 33,356)( 34,360)( 35,359)( 36,353)( 37,352)( 38,351)( 39,355)( 40,354)( 41,398)( 42,397)( 43,396)( 44,400)( 45,399)( 46,393)( 47,392)( 48,391)( 49,395)( 50,394)( 51,383)( 52,382)( 53,381)( 54,385)( 55,384)( 56,388)( 57,387)( 58,386)( 59,390)( 60,389)( 61,373)( 62,372)( 63,371)( 64,375)( 65,374)( 66,378)( 67,377)( 68,376)( 69,380)( 70,379)( 71,368)( 72,367)( 73,366)( 74,370)( 75,369)( 76,363)( 77,362)( 78,361)( 79,365)( 80,364)( 81,408)( 82,407)( 83,406)( 84,410)( 85,409)( 86,403)( 87,402)( 88,401)( 89,405)( 90,404)( 91,413)( 92,412)( 93,411)( 94,415)( 95,414)( 96,418)( 97,417)( 98,416)( 99,420)(100,419)(101,428)(102,427)(103,426)(104,430)(105,429)(106,423)(107,422)(108,421)(109,425)(110,424)(111,433)(112,432)(113,431)(114,435)(115,434)(116,438)(117,437)(118,436)(119,440)(120,439)(121,473)(122,472)(123,471)(124,475)(125,474)(126,478)(127,477)(128,476)(129,480)(130,479)(131,468)(132,467)(133,466)(134,470)(135,469)(136,463)(137,462)(138,461)(139,465)(140,464)(141,458)(142,457)(143,456)(144,460)(145,459)(146,453)(147,452)(148,451)(149,455)(150,454)(151,443)(152,442)(153,441)(154,445)(155,444)(156,448)(157,447)(158,446)(159,450)(160,449)(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)(168,486)(169,490)(170,489)(171,498)(172,497)(173,496)(174,500)(175,499)(176,493)(177,492)(178,491)(179,495)(180,494)(181,503)(182,502)(183,501)(184,505)(185,504)(186,508)(187,507)(188,506)(189,510)(190,509)(191,518)(192,517)(193,516)(194,520)(195,519)(196,513)(197,512)(198,511)(199,515)(200,514)(201,558)(202,557)(203,556)(204,560)(205,559)(206,553)(207,552)(208,551)(209,555)(210,554)(211,543)(212,542)(213,541)(214,545)(215,544)(216,548)(217,547)(218,546)(219,550)(220,549)(221,533)(222,532)(223,531)(224,535)(225,534)(226,538)(227,537)(228,536)(229,540)(230,539)(231,528)(232,527)(233,526)(234,530)(235,529)(236,523)(237,522)(238,521)(239,525)(240,524)(241,568)(242,567)(243,566)(244,570)(245,569)(246,563)(247,562)(248,561)(249,565)(250,564)(251,573)(252,572)(253,571)(254,575)(255,574)(256,578)(257,577)(258,576)(259,580)(260,579)(261,588)(262,587)(263,586)(264,590)(265,589)(266,583)(267,582)(268,581)(269,585)(270,584)(271,593)(272,592)(273,591)(274,595)(275,594)(276,598)(277,597)(278,596)(279,600)(280,599)(281,633)(282,632)(283,631)(284,635)(285,634)(286,638)(287,637)(288,636)(289,640)(290,639)(291,628)(292,627)(293,626)(294,630)(295,629)(296,623)(297,622)(298,621)(299,625)(300,624)(301,618)(302,617)(303,616)(304,620)(305,619)(306,613)(307,612)(308,611)(309,615)(310,614)(311,603)(312,602)(313,601)(314,605)(315,604)(316,608)(317,607)(318,606)(319,610)(320,609);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1, 
s1*s2*s1*s2*s1*s0*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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle