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}*1280e
if this polytope has a name.
Group : SmallGroup(1280,90301)
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 : {4,40}*640b
   4-fold quotients : {4,20}*320
   5-fold quotients : {8,8}*256e
   8-fold quotients : {4,20}*160
   10-fold quotients : {4,8}*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 := (  1,321)(  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);;
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 := (  1,483)(  2,482)(  3,481)(  4,485)(  5,484)(  6,488)(  7,487)(  8,486)(  9,490)( 10,489)( 11,493)( 12,492)( 13,491)( 14,495)( 15,494)( 16,498)( 17,497)( 18,496)( 19,500)( 20,499)( 21,508)( 22,507)( 23,506)( 24,510)( 25,509)( 26,503)( 27,502)( 28,501)( 29,505)( 30,504)( 31,518)( 32,517)( 33,516)( 34,520)( 35,519)( 36,513)( 37,512)( 38,511)( 39,515)( 40,514)( 41,558)( 42,557)( 43,556)( 44,560)( 45,559)( 46,553)( 47,552)( 48,551)( 49,555)( 50,554)( 51,548)( 52,547)( 53,546)( 54,550)( 55,549)( 56,543)( 57,542)( 58,541)( 59,545)( 60,544)( 61,538)( 62,537)( 63,536)( 64,540)( 65,539)( 66,533)( 67,532)( 68,531)( 69,535)( 70,534)( 71,528)( 72,527)( 73,526)( 74,530)( 75,529)( 76,523)( 77,522)( 78,521)( 79,525)( 80,524)( 81,588)( 82,587)( 83,586)( 84,590)( 85,589)( 86,583)( 87,582)( 88,581)( 89,585)( 90,584)( 91,598)( 92,597)( 93,596)( 94,600)( 95,599)( 96,593)( 97,592)( 98,591)( 99,595)(100,594)(101,568)(102,567)(103,566)(104,570)(105,569)(106,563)(107,562)(108,561)(109,565)(110,564)(111,578)(112,577)(113,576)(114,580)(115,579)(116,573)(117,572)(118,571)(119,575)(120,574)(121,613)(122,612)(123,611)(124,615)(125,614)(126,618)(127,617)(128,616)(129,620)(130,619)(131,603)(132,602)(133,601)(134,605)(135,604)(136,608)(137,607)(138,606)(139,610)(140,609)(141,638)(142,637)(143,636)(144,640)(145,639)(146,633)(147,632)(148,631)(149,635)(150,634)(151,628)(152,627)(153,626)(154,630)(155,629)(156,623)(157,622)(158,621)(159,625)(160,624)(161,323)(162,322)(163,321)(164,325)(165,324)(166,328)(167,327)(168,326)(169,330)(170,329)(171,333)(172,332)(173,331)(174,335)(175,334)(176,338)(177,337)(178,336)(179,340)(180,339)(181,348)(182,347)(183,346)(184,350)(185,349)(186,343)(187,342)(188,341)(189,345)(190,344)(191,358)(192,357)(193,356)(194,360)(195,359)(196,353)(197,352)(198,351)(199,355)(200,354)(201,398)(202,397)(203,396)(204,400)(205,399)(206,393)(207,392)(208,391)(209,395)(210,394)(211,388)(212,387)(213,386)(214,390)(215,389)(216,383)(217,382)(218,381)(219,385)(220,384)(221,378)(222,377)(223,376)(224,380)(225,379)(226,373)(227,372)(228,371)(229,375)(230,374)(231,368)(232,367)(233,366)(234,370)(235,369)(236,363)(237,362)(238,361)(239,365)(240,364)(241,428)(242,427)(243,426)(244,430)(245,429)(246,423)(247,422)(248,421)(249,425)(250,424)(251,438)(252,437)(253,436)(254,440)(255,439)(256,433)(257,432)(258,431)(259,435)(260,434)(261,408)(262,407)(263,406)(264,410)(265,409)(266,403)(267,402)(268,401)(269,405)(270,404)(271,418)(272,417)(273,416)(274,420)(275,419)(276,413)(277,412)(278,411)(279,415)(280,414)(281,453)(282,452)(283,451)(284,455)(285,454)(286,458)(287,457)(288,456)(289,460)(290,459)(291,443)(292,442)(293,441)(294,445)(295,444)(296,448)(297,447)(298,446)(299,450)(300,449)(301,478)(302,477)(303,476)(304,480)(305,479)(306,473)(307,472)(308,471)(309,475)(310,474)(311,468)(312,467)(313,466)(314,470)(315,469)(316,463)(317,462)(318,461)(319,465)(320,464);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2, 
s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*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*s0*s1 ];;
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)( 11,336)( 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);
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)!(  1,483)(  2,482)(  3,481)(  4,485)(  5,484)(  6,488)(  7,487)(  8,486)(  9,490)( 10,489)( 11,493)( 12,492)( 13,491)( 14,495)( 15,494)( 16,498)( 17,497)( 18,496)( 19,500)( 20,499)( 21,508)( 22,507)( 23,506)( 24,510)( 25,509)( 26,503)( 27,502)( 28,501)( 29,505)( 30,504)( 31,518)( 32,517)( 33,516)( 34,520)( 35,519)( 36,513)( 37,512)( 38,511)( 39,515)( 40,514)( 41,558)( 42,557)( 43,556)( 44,560)( 45,559)( 46,553)( 47,552)( 48,551)( 49,555)( 50,554)( 51,548)( 52,547)( 53,546)( 54,550)( 55,549)( 56,543)( 57,542)( 58,541)( 59,545)( 60,544)( 61,538)( 62,537)( 63,536)( 64,540)( 65,539)( 66,533)( 67,532)( 68,531)( 69,535)( 70,534)( 71,528)( 72,527)( 73,526)( 74,530)( 75,529)( 76,523)( 77,522)( 78,521)( 79,525)( 80,524)( 81,588)( 82,587)( 83,586)( 84,590)( 85,589)( 86,583)( 87,582)( 88,581)( 89,585)( 90,584)( 91,598)( 92,597)( 93,596)( 94,600)( 95,599)( 96,593)( 97,592)( 98,591)( 99,595)(100,594)(101,568)(102,567)(103,566)(104,570)(105,569)(106,563)(107,562)(108,561)(109,565)(110,564)(111,578)(112,577)(113,576)(114,580)(115,579)(116,573)(117,572)(118,571)(119,575)(120,574)(121,613)(122,612)(123,611)(124,615)(125,614)(126,618)(127,617)(128,616)(129,620)(130,619)(131,603)(132,602)(133,601)(134,605)(135,604)(136,608)(137,607)(138,606)(139,610)(140,609)(141,638)(142,637)(143,636)(144,640)(145,639)(146,633)(147,632)(148,631)(149,635)(150,634)(151,628)(152,627)(153,626)(154,630)(155,629)(156,623)(157,622)(158,621)(159,625)(160,624)(161,323)(162,322)(163,321)(164,325)(165,324)(166,328)(167,327)(168,326)(169,330)(170,329)(171,333)(172,332)(173,331)(174,335)(175,334)(176,338)(177,337)(178,336)(179,340)(180,339)(181,348)(182,347)(183,346)(184,350)(185,349)(186,343)(187,342)(188,341)(189,345)(190,344)(191,358)(192,357)(193,356)(194,360)(195,359)(196,353)(197,352)(198,351)(199,355)(200,354)(201,398)(202,397)(203,396)(204,400)(205,399)(206,393)(207,392)(208,391)(209,395)(210,394)(211,388)(212,387)(213,386)(214,390)(215,389)(216,383)(217,382)(218,381)(219,385)(220,384)(221,378)(222,377)(223,376)(224,380)(225,379)(226,373)(227,372)(228,371)(229,375)(230,374)(231,368)(232,367)(233,366)(234,370)(235,369)(236,363)(237,362)(238,361)(239,365)(240,364)(241,428)(242,427)(243,426)(244,430)(245,429)(246,423)(247,422)(248,421)(249,425)(250,424)(251,438)(252,437)(253,436)(254,440)(255,439)(256,433)(257,432)(258,431)(259,435)(260,434)(261,408)(262,407)(263,406)(264,410)(265,409)(266,403)(267,402)(268,401)(269,405)(270,404)(271,418)(272,417)(273,416)(274,420)(275,419)(276,413)(277,412)(278,411)(279,415)(280,414)(281,453)(282,452)(283,451)(284,455)(285,454)(286,458)(287,457)(288,456)(289,460)(290,459)(291,443)(292,442)(293,441)(294,445)(295,444)(296,448)(297,447)(298,446)(299,450)(300,449)(301,478)(302,477)(303,476)(304,480)(305,479)(306,473)(307,472)(308,471)(309,475)(310,474)(311,468)(312,467)(313,466)(314,470)(315,469)(316,463)(317,462)(318,461)(319,465)(320,464);
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2, 
s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*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*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle