Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,40}

Atlas Canonical Name {8,40}*1280h

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1280,90329)
Rank
3
Schläfli Type
{8,40}
Vertices, edges, …
16, 320, 80
Order of s0s1s2
40
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

8-fold

10-fold

16-fold

20-fold

32-fold

40-fold

64-fold

80-fold

160-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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)( 41,551)( 42,552)( 43,553)( 44,554)( 45,555)( 46,556)( 47,557)( 48,558)( 49,559)( 50,560)( 51,541)( 52,542)( 53,543)( 54,544)( 55,545)( 56,546)( 57,547)( 58,548)( 59,549)( 60,550)( 61,531)( 62,532)( 63,533)( 64,534)( 65,535)( 66,536)( 67,537)( 68,538)( 69,539)( 70,540)( 71,521)( 72,522)( 73,523)( 74,524)( 75,525)( 76,526)( 77,527)( 78,528)( 79,529)( 80,530)( 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)(121,616)(122,617)(123,618)(124,619)(125,620)(126,611)(127,612)(128,613)(129,614)(130,615)(131,606)(132,607)(133,608)(134,609)(135,610)(136,601)(137,602)(138,603)(139,604)(140,605)(141,631)(142,632)(143,633)(144,634)(145,635)(146,636)(147,637)(148,638)(149,639)(150,640)(151,621)(152,622)(153,623)(154,624)(155,625)(156,626)(157,627)(158,628)(159,629)(160,630)(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)(201,391)(202,392)(203,393)(204,394)(205,395)(206,396)(207,397)(208,398)(209,399)(210,400)(211,381)(212,382)(213,383)(214,384)(215,385)(216,386)(217,387)(218,388)(219,389)(220,390)(221,371)(222,372)(223,373)(224,374)(225,375)(226,376)(227,377)(228,378)(229,379)(230,380)(231,361)(232,362)(233,363)(234,364)(235,365)(236,366)(237,367)(238,368)(239,369)(240,370)(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)(281,456)(282,457)(283,458)(284,459)(285,460)(286,451)(287,452)(288,453)(289,454)(290,455)(291,446)(292,447)(293,448)(294,449)(295,450)(296,441)(297,442)(298,443)(299,444)(300,445)(301,471)(302,472)(303,473)(304,474)(305,475)(306,476)(307,477)(308,478)(309,479)(310,480)(311,461)(312,462)(313,463)(314,464)(315,465)(316,466)(317,467)(318,468)(319,469)(320,470);;
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)( 41, 46)( 42, 50)( 43, 49)( 44, 48)( 45, 47)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 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)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(141,151)(142,155)(143,154)(144,153)(145,152)(146,156)(147,160)(148,159)(149,158)(150,157)(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)(181,231)(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)(361,446)(362,450)(363,449)(364,448)(365,447)(366,441)(367,445)(368,444)(369,443)(370,442)(371,456)(372,460)(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)(380,452)(381,476)(382,480)(383,479)(384,478)(385,477)(386,471)(387,475)(388,474)(389,473)(390,472)(391,466)(392,470)(393,469)(394,468)(395,467)(396,461)(397,465)(398,464)(399,463)(400,462)(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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*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*s0*s1*s2*s1 ];;
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)( 41,551)( 42,552)( 43,553)( 44,554)( 45,555)( 46,556)( 47,557)( 48,558)( 49,559)( 50,560)( 51,541)( 52,542)( 53,543)( 54,544)( 55,545)( 56,546)( 57,547)( 58,548)( 59,549)( 60,550)( 61,531)( 62,532)( 63,533)( 64,534)( 65,535)( 66,536)( 67,537)( 68,538)( 69,539)( 70,540)( 71,521)( 72,522)( 73,523)( 74,524)( 75,525)( 76,526)( 77,527)( 78,528)( 79,529)( 80,530)( 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)(121,616)(122,617)(123,618)(124,619)(125,620)(126,611)(127,612)(128,613)(129,614)(130,615)(131,606)(132,607)(133,608)(134,609)(135,610)(136,601)(137,602)(138,603)(139,604)(140,605)(141,631)(142,632)(143,633)(144,634)(145,635)(146,636)(147,637)(148,638)(149,639)(150,640)(151,621)(152,622)(153,623)(154,624)(155,625)(156,626)(157,627)(158,628)(159,629)(160,630)(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)(201,391)(202,392)(203,393)(204,394)(205,395)(206,396)(207,397)(208,398)(209,399)(210,400)(211,381)(212,382)(213,383)(214,384)(215,385)(216,386)(217,387)(218,388)(219,389)(220,390)(221,371)(222,372)(223,373)(224,374)(225,375)(226,376)(227,377)(228,378)(229,379)(230,380)(231,361)(232,362)(233,363)(234,364)(235,365)(236,366)(237,367)(238,368)(239,369)(240,370)(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)(281,456)(282,457)(283,458)(284,459)(285,460)(286,451)(287,452)(288,453)(289,454)(290,455)(291,446)(292,447)(293,448)(294,449)(295,450)(296,441)(297,442)(298,443)(299,444)(300,445)(301,471)(302,472)(303,473)(304,474)(305,475)(306,476)(307,477)(308,478)(309,479)(310,480)(311,461)(312,462)(313,463)(314,464)(315,465)(316,466)(317,467)(318,468)(319,469)(320,470);
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)( 41, 46)( 42, 50)( 43, 49)( 44, 48)( 45, 47)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 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)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(141,151)(142,155)(143,154)(144,153)(145,152)(146,156)(147,160)(148,159)(149,158)(150,157)(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)(181,231)(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)(361,446)(362,450)(363,449)(364,448)(365,447)(366,441)(367,445)(368,444)(369,443)(370,442)(371,456)(372,460)(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)(380,452)(381,476)(382,480)(383,479)(384,478)(385,477)(386,471)(387,475)(388,474)(389,473)(390,472)(391,466)(392,470)(393,469)(394,468)(395,467)(396,461)(397,465)(398,464)(399,463)(400,462)(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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*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*s0*s1*s2*s1 >; 

References

None.

to this polytope.

Twisty Puzzle