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Polytope of Type {80,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {80,4}*1280b
if this polytope has a name.
Group : SmallGroup(1280,81735)
Rank : 3
Schlafli Type : {80,4}
Number of vertices, edges, etc : 160, 320, 8
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {40,4}*640a
   4-fold quotients : {40,4}*320a, {20,4}*320, {40,4}*320b
   5-fold quotients : {16,4}*256b
   8-fold quotients : {20,4}*160, {40,2}*160
   10-fold quotients : {8,4}*128a
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32, {8,2}*32
   64-fold quotients : {5,2}*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.
Permutation Representation (GAP) :
s0 := (  1,321)(  2,325)(  3,324)(  4,323)(  5,322)(  6,326)(  7,330)(  8,329)
(  9,328)( 10,327)( 11,331)( 12,335)( 13,334)( 14,333)( 15,332)( 16,336)
( 17,340)( 18,339)( 19,338)( 20,337)( 21,346)( 22,350)( 23,349)( 24,348)
( 25,347)( 26,341)( 27,345)( 28,344)( 29,343)( 30,342)( 31,356)( 32,360)
( 33,359)( 34,358)( 35,357)( 36,351)( 37,355)( 38,354)( 39,353)( 40,352)
( 41,376)( 42,380)( 43,379)( 44,378)( 45,377)( 46,371)( 47,375)( 48,374)
( 49,373)( 50,372)( 51,366)( 52,370)( 53,369)( 54,368)( 55,367)( 56,361)
( 57,365)( 58,364)( 59,363)( 60,362)( 61,391)( 62,395)( 63,394)( 64,393)
( 65,392)( 66,396)( 67,400)( 68,399)( 69,398)( 70,397)( 71,381)( 72,385)
( 73,384)( 74,383)( 75,382)( 76,386)( 77,390)( 78,389)( 79,388)( 80,387)
( 81,421)( 82,425)( 83,424)( 84,423)( 85,422)( 86,426)( 87,430)( 88,429)
( 89,428)( 90,427)( 91,431)( 92,435)( 93,434)( 94,433)( 95,432)( 96,436)
( 97,440)( 98,439)( 99,438)(100,437)(101,401)(102,405)(103,404)(104,403)
(105,402)(106,406)(107,410)(108,409)(109,408)(110,407)(111,411)(112,415)
(113,414)(114,413)(115,412)(116,416)(117,420)(118,419)(119,418)(120,417)
(121,476)(122,480)(123,479)(124,478)(125,477)(126,471)(127,475)(128,474)
(129,473)(130,472)(131,466)(132,470)(133,469)(134,468)(135,467)(136,461)
(137,465)(138,464)(139,463)(140,462)(141,456)(142,460)(143,459)(144,458)
(145,457)(146,451)(147,455)(148,454)(149,453)(150,452)(151,446)(152,450)
(153,449)(154,448)(155,447)(156,441)(157,445)(158,444)(159,443)(160,442)
(161,481)(162,485)(163,484)(164,483)(165,482)(166,486)(167,490)(168,489)
(169,488)(170,487)(171,491)(172,495)(173,494)(174,493)(175,492)(176,496)
(177,500)(178,499)(179,498)(180,497)(181,506)(182,510)(183,509)(184,508)
(185,507)(186,501)(187,505)(188,504)(189,503)(190,502)(191,516)(192,520)
(193,519)(194,518)(195,517)(196,511)(197,515)(198,514)(199,513)(200,512)
(201,536)(202,540)(203,539)(204,538)(205,537)(206,531)(207,535)(208,534)
(209,533)(210,532)(211,526)(212,530)(213,529)(214,528)(215,527)(216,521)
(217,525)(218,524)(219,523)(220,522)(221,551)(222,555)(223,554)(224,553)
(225,552)(226,556)(227,560)(228,559)(229,558)(230,557)(231,541)(232,545)
(233,544)(234,543)(235,542)(236,546)(237,550)(238,549)(239,548)(240,547)
(241,581)(242,585)(243,584)(244,583)(245,582)(246,586)(247,590)(248,589)
(249,588)(250,587)(251,591)(252,595)(253,594)(254,593)(255,592)(256,596)
(257,600)(258,599)(259,598)(260,597)(261,561)(262,565)(263,564)(264,563)
(265,562)(266,566)(267,570)(268,569)(269,568)(270,567)(271,571)(272,575)
(273,574)(274,573)(275,572)(276,576)(277,580)(278,579)(279,578)(280,577)
(281,636)(282,640)(283,639)(284,638)(285,637)(286,631)(287,635)(288,634)
(289,633)(290,632)(291,626)(292,630)(293,629)(294,628)(295,627)(296,621)
(297,625)(298,624)(299,623)(300,622)(301,616)(302,620)(303,619)(304,618)
(305,617)(306,611)(307,615)(308,614)(309,613)(310,612)(311,606)(312,610)
(313,609)(314,608)(315,607)(316,601)(317,605)(318,604)(319,603)(320,602);;
s1 := (  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 18)( 12, 17)( 13, 16)( 14, 20)
( 15, 19)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 33)( 34, 35)
( 36, 38)( 39, 40)( 41, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 58)( 52, 57)
( 53, 56)( 54, 60)( 55, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 70)( 65, 69)
( 71, 73)( 74, 75)( 76, 78)( 79, 80)( 81,103)( 82,102)( 83,101)( 84,105)
( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,118)( 92,117)
( 93,116)( 94,120)( 95,119)( 96,113)( 97,112)( 98,111)( 99,115)(100,114)
(121,143)(122,142)(123,141)(124,145)(125,144)(126,148)(127,147)(128,146)
(129,150)(130,149)(131,158)(132,157)(133,156)(134,160)(135,159)(136,153)
(137,152)(138,151)(139,155)(140,154)(161,203)(162,202)(163,201)(164,205)
(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,218)(172,217)
(173,216)(174,220)(175,219)(176,213)(177,212)(178,211)(179,215)(180,214)
(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)(187,222)(188,221)
(189,225)(190,224)(191,233)(192,232)(193,231)(194,235)(195,234)(196,238)
(197,237)(198,236)(199,240)(200,239)(241,308)(242,307)(243,306)(244,310)
(245,309)(246,303)(247,302)(248,301)(249,305)(250,304)(251,313)(252,312)
(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)
(261,288)(262,287)(263,286)(264,290)(265,289)(266,283)(267,282)(268,281)
(269,285)(270,284)(271,293)(272,292)(273,291)(274,295)(275,294)(276,298)
(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)(323,401)(324,405)
(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)(331,418)(332,417)
(333,416)(334,420)(335,419)(336,413)(337,412)(338,411)(339,415)(340,414)
(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)(347,422)(348,421)
(349,425)(350,424)(351,433)(352,432)(353,431)(354,435)(355,434)(356,438)
(357,437)(358,436)(359,440)(360,439)(361,443)(362,442)(363,441)(364,445)
(365,444)(366,448)(367,447)(368,446)(369,450)(370,449)(371,458)(372,457)
(373,456)(374,460)(375,459)(376,453)(377,452)(378,451)(379,455)(380,454)
(381,468)(382,467)(383,466)(384,470)(385,469)(386,463)(387,462)(388,461)
(389,465)(390,464)(391,473)(392,472)(393,471)(394,475)(395,474)(396,478)
(397,477)(398,476)(399,480)(400,479)(481,613)(482,612)(483,611)(484,615)
(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,608)(492,607)
(493,606)(494,610)(495,609)(496,603)(497,602)(498,601)(499,605)(500,604)
(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)(507,632)(508,631)
(509,635)(510,634)(511,623)(512,622)(513,621)(514,625)(515,624)(516,628)
(517,627)(518,626)(519,630)(520,629)(521,573)(522,572)(523,571)(524,575)
(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,568)(532,567)
(533,566)(534,570)(535,569)(536,563)(537,562)(538,561)(539,565)(540,564)
(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)(547,592)(548,591)
(549,595)(550,594)(551,583)(552,582)(553,581)(554,585)(555,584)(556,588)
(557,587)(558,586)(559,590)(560,589);;
s2 := (  1,161)(  2,162)(  3,163)(  4,164)(  5,165)(  6,166)(  7,167)(  8,168)
(  9,169)( 10,170)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)( 16,176)
( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)( 24,184)
( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,191)( 32,192)
( 33,193)( 34,194)( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)( 40,200)
( 41,201)( 42,202)( 43,203)( 44,204)( 45,205)( 46,206)( 47,207)( 48,208)
( 49,209)( 50,210)( 51,211)( 52,212)( 53,213)( 54,214)( 55,215)( 56,216)
( 57,217)( 58,218)( 59,219)( 60,220)( 61,221)( 62,222)( 63,223)( 64,224)
( 65,225)( 66,226)( 67,227)( 68,228)( 69,229)( 70,230)( 71,231)( 72,232)
( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)( 80,240)
( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,256)( 87,257)( 88,258)
( 89,259)( 90,260)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,246)
( 97,247)( 98,248)( 99,249)(100,250)(101,271)(102,272)(103,273)(104,274)
(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,261)(112,262)
(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)
(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)(128,298)
(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,311)(142,312)(143,313)(144,314)
(145,315)(146,316)(147,317)(148,318)(149,319)(150,320)(151,301)(152,302)
(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)(160,310)
(321,481)(322,482)(323,483)(324,484)(325,485)(326,486)(327,487)(328,488)
(329,489)(330,490)(331,491)(332,492)(333,493)(334,494)(335,495)(336,496)
(337,497)(338,498)(339,499)(340,500)(341,501)(342,502)(343,503)(344,504)
(345,505)(346,506)(347,507)(348,508)(349,509)(350,510)(351,511)(352,512)
(353,513)(354,514)(355,515)(356,516)(357,517)(358,518)(359,519)(360,520)
(361,521)(362,522)(363,523)(364,524)(365,525)(366,526)(367,527)(368,528)
(369,529)(370,530)(371,531)(372,532)(373,533)(374,534)(375,535)(376,536)
(377,537)(378,538)(379,539)(380,540)(381,541)(382,542)(383,543)(384,544)
(385,545)(386,546)(387,547)(388,548)(389,549)(390,550)(391,551)(392,552)
(393,553)(394,554)(395,555)(396,556)(397,557)(398,558)(399,559)(400,560)
(401,571)(402,572)(403,573)(404,574)(405,575)(406,576)(407,577)(408,578)
(409,579)(410,580)(411,561)(412,562)(413,563)(414,564)(415,565)(416,566)
(417,567)(418,568)(419,569)(420,570)(421,591)(422,592)(423,593)(424,594)
(425,595)(426,596)(427,597)(428,598)(429,599)(430,600)(431,581)(432,582)
(433,583)(434,584)(435,585)(436,586)(437,587)(438,588)(439,589)(440,590)
(441,611)(442,612)(443,613)(444,614)(445,615)(446,616)(447,617)(448,618)
(449,619)(450,620)(451,601)(452,602)(453,603)(454,604)(455,605)(456,606)
(457,607)(458,608)(459,609)(460,610)(461,631)(462,632)(463,633)(464,634)
(465,635)(466,636)(467,637)(468,638)(469,639)(470,640)(471,621)(472,622)
(473,623)(474,624)(475,625)(476,626)(477,627)(478,628)(479,629)(480,630);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*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, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*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*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(640)!(  1,321)(  2,325)(  3,324)(  4,323)(  5,322)(  6,326)(  7,330)
(  8,329)(  9,328)( 10,327)( 11,331)( 12,335)( 13,334)( 14,333)( 15,332)
( 16,336)( 17,340)( 18,339)( 19,338)( 20,337)( 21,346)( 22,350)( 23,349)
( 24,348)( 25,347)( 26,341)( 27,345)( 28,344)( 29,343)( 30,342)( 31,356)
( 32,360)( 33,359)( 34,358)( 35,357)( 36,351)( 37,355)( 38,354)( 39,353)
( 40,352)( 41,376)( 42,380)( 43,379)( 44,378)( 45,377)( 46,371)( 47,375)
( 48,374)( 49,373)( 50,372)( 51,366)( 52,370)( 53,369)( 54,368)( 55,367)
( 56,361)( 57,365)( 58,364)( 59,363)( 60,362)( 61,391)( 62,395)( 63,394)
( 64,393)( 65,392)( 66,396)( 67,400)( 68,399)( 69,398)( 70,397)( 71,381)
( 72,385)( 73,384)( 74,383)( 75,382)( 76,386)( 77,390)( 78,389)( 79,388)
( 80,387)( 81,421)( 82,425)( 83,424)( 84,423)( 85,422)( 86,426)( 87,430)
( 88,429)( 89,428)( 90,427)( 91,431)( 92,435)( 93,434)( 94,433)( 95,432)
( 96,436)( 97,440)( 98,439)( 99,438)(100,437)(101,401)(102,405)(103,404)
(104,403)(105,402)(106,406)(107,410)(108,409)(109,408)(110,407)(111,411)
(112,415)(113,414)(114,413)(115,412)(116,416)(117,420)(118,419)(119,418)
(120,417)(121,476)(122,480)(123,479)(124,478)(125,477)(126,471)(127,475)
(128,474)(129,473)(130,472)(131,466)(132,470)(133,469)(134,468)(135,467)
(136,461)(137,465)(138,464)(139,463)(140,462)(141,456)(142,460)(143,459)
(144,458)(145,457)(146,451)(147,455)(148,454)(149,453)(150,452)(151,446)
(152,450)(153,449)(154,448)(155,447)(156,441)(157,445)(158,444)(159,443)
(160,442)(161,481)(162,485)(163,484)(164,483)(165,482)(166,486)(167,490)
(168,489)(169,488)(170,487)(171,491)(172,495)(173,494)(174,493)(175,492)
(176,496)(177,500)(178,499)(179,498)(180,497)(181,506)(182,510)(183,509)
(184,508)(185,507)(186,501)(187,505)(188,504)(189,503)(190,502)(191,516)
(192,520)(193,519)(194,518)(195,517)(196,511)(197,515)(198,514)(199,513)
(200,512)(201,536)(202,540)(203,539)(204,538)(205,537)(206,531)(207,535)
(208,534)(209,533)(210,532)(211,526)(212,530)(213,529)(214,528)(215,527)
(216,521)(217,525)(218,524)(219,523)(220,522)(221,551)(222,555)(223,554)
(224,553)(225,552)(226,556)(227,560)(228,559)(229,558)(230,557)(231,541)
(232,545)(233,544)(234,543)(235,542)(236,546)(237,550)(238,549)(239,548)
(240,547)(241,581)(242,585)(243,584)(244,583)(245,582)(246,586)(247,590)
(248,589)(249,588)(250,587)(251,591)(252,595)(253,594)(254,593)(255,592)
(256,596)(257,600)(258,599)(259,598)(260,597)(261,561)(262,565)(263,564)
(264,563)(265,562)(266,566)(267,570)(268,569)(269,568)(270,567)(271,571)
(272,575)(273,574)(274,573)(275,572)(276,576)(277,580)(278,579)(279,578)
(280,577)(281,636)(282,640)(283,639)(284,638)(285,637)(286,631)(287,635)
(288,634)(289,633)(290,632)(291,626)(292,630)(293,629)(294,628)(295,627)
(296,621)(297,625)(298,624)(299,623)(300,622)(301,616)(302,620)(303,619)
(304,618)(305,617)(306,611)(307,615)(308,614)(309,613)(310,612)(311,606)
(312,610)(313,609)(314,608)(315,607)(316,601)(317,605)(318,604)(319,603)
(320,602);
s1 := Sym(640)!(  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 18)( 12, 17)( 13, 16)
( 14, 20)( 15, 19)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 33)
( 34, 35)( 36, 38)( 39, 40)( 41, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 58)
( 52, 57)( 53, 56)( 54, 60)( 55, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 70)
( 65, 69)( 71, 73)( 74, 75)( 76, 78)( 79, 80)( 81,103)( 82,102)( 83,101)
( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,118)
( 92,117)( 93,116)( 94,120)( 95,119)( 96,113)( 97,112)( 98,111)( 99,115)
(100,114)(121,143)(122,142)(123,141)(124,145)(125,144)(126,148)(127,147)
(128,146)(129,150)(130,149)(131,158)(132,157)(133,156)(134,160)(135,159)
(136,153)(137,152)(138,151)(139,155)(140,154)(161,203)(162,202)(163,201)
(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,218)
(172,217)(173,216)(174,220)(175,219)(176,213)(177,212)(178,211)(179,215)
(180,214)(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)(187,222)
(188,221)(189,225)(190,224)(191,233)(192,232)(193,231)(194,235)(195,234)
(196,238)(197,237)(198,236)(199,240)(200,239)(241,308)(242,307)(243,306)
(244,310)(245,309)(246,303)(247,302)(248,301)(249,305)(250,304)(251,313)
(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)
(260,319)(261,288)(262,287)(263,286)(264,290)(265,289)(266,283)(267,282)
(268,281)(269,285)(270,284)(271,293)(272,292)(273,291)(274,295)(275,294)
(276,298)(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)(323,401)
(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)(331,418)
(332,417)(333,416)(334,420)(335,419)(336,413)(337,412)(338,411)(339,415)
(340,414)(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)(347,422)
(348,421)(349,425)(350,424)(351,433)(352,432)(353,431)(354,435)(355,434)
(356,438)(357,437)(358,436)(359,440)(360,439)(361,443)(362,442)(363,441)
(364,445)(365,444)(366,448)(367,447)(368,446)(369,450)(370,449)(371,458)
(372,457)(373,456)(374,460)(375,459)(376,453)(377,452)(378,451)(379,455)
(380,454)(381,468)(382,467)(383,466)(384,470)(385,469)(386,463)(387,462)
(388,461)(389,465)(390,464)(391,473)(392,472)(393,471)(394,475)(395,474)
(396,478)(397,477)(398,476)(399,480)(400,479)(481,613)(482,612)(483,611)
(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,608)
(492,607)(493,606)(494,610)(495,609)(496,603)(497,602)(498,601)(499,605)
(500,604)(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)(507,632)
(508,631)(509,635)(510,634)(511,623)(512,622)(513,621)(514,625)(515,624)
(516,628)(517,627)(518,626)(519,630)(520,629)(521,573)(522,572)(523,571)
(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,568)
(532,567)(533,566)(534,570)(535,569)(536,563)(537,562)(538,561)(539,565)
(540,564)(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)(547,592)
(548,591)(549,595)(550,594)(551,583)(552,582)(553,581)(554,585)(555,584)
(556,588)(557,587)(558,586)(559,590)(560,589);
s2 := Sym(640)!(  1,161)(  2,162)(  3,163)(  4,164)(  5,165)(  6,166)(  7,167)
(  8,168)(  9,169)( 10,170)( 11,171)( 12,172)( 13,173)( 14,174)( 15,175)
( 16,176)( 17,177)( 18,178)( 19,179)( 20,180)( 21,181)( 22,182)( 23,183)
( 24,184)( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,191)
( 32,192)( 33,193)( 34,194)( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)
( 40,200)( 41,201)( 42,202)( 43,203)( 44,204)( 45,205)( 46,206)( 47,207)
( 48,208)( 49,209)( 50,210)( 51,211)( 52,212)( 53,213)( 54,214)( 55,215)
( 56,216)( 57,217)( 58,218)( 59,219)( 60,220)( 61,221)( 62,222)( 63,223)
( 64,224)( 65,225)( 66,226)( 67,227)( 68,228)( 69,229)( 70,230)( 71,231)
( 72,232)( 73,233)( 74,234)( 75,235)( 76,236)( 77,237)( 78,238)( 79,239)
( 80,240)( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,256)( 87,257)
( 88,258)( 89,259)( 90,260)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,246)( 97,247)( 98,248)( 99,249)(100,250)(101,271)(102,272)(103,273)
(104,274)(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,261)
(112,262)(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)
(120,270)(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)
(128,298)(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,311)(142,312)(143,313)
(144,314)(145,315)(146,316)(147,317)(148,318)(149,319)(150,320)(151,301)
(152,302)(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)
(160,310)(321,481)(322,482)(323,483)(324,484)(325,485)(326,486)(327,487)
(328,488)(329,489)(330,490)(331,491)(332,492)(333,493)(334,494)(335,495)
(336,496)(337,497)(338,498)(339,499)(340,500)(341,501)(342,502)(343,503)
(344,504)(345,505)(346,506)(347,507)(348,508)(349,509)(350,510)(351,511)
(352,512)(353,513)(354,514)(355,515)(356,516)(357,517)(358,518)(359,519)
(360,520)(361,521)(362,522)(363,523)(364,524)(365,525)(366,526)(367,527)
(368,528)(369,529)(370,530)(371,531)(372,532)(373,533)(374,534)(375,535)
(376,536)(377,537)(378,538)(379,539)(380,540)(381,541)(382,542)(383,543)
(384,544)(385,545)(386,546)(387,547)(388,548)(389,549)(390,550)(391,551)
(392,552)(393,553)(394,554)(395,555)(396,556)(397,557)(398,558)(399,559)
(400,560)(401,571)(402,572)(403,573)(404,574)(405,575)(406,576)(407,577)
(408,578)(409,579)(410,580)(411,561)(412,562)(413,563)(414,564)(415,565)
(416,566)(417,567)(418,568)(419,569)(420,570)(421,591)(422,592)(423,593)
(424,594)(425,595)(426,596)(427,597)(428,598)(429,599)(430,600)(431,581)
(432,582)(433,583)(434,584)(435,585)(436,586)(437,587)(438,588)(439,589)
(440,590)(441,611)(442,612)(443,613)(444,614)(445,615)(446,616)(447,617)
(448,618)(449,619)(450,620)(451,601)(452,602)(453,603)(454,604)(455,605)
(456,606)(457,607)(458,608)(459,609)(460,610)(461,631)(462,632)(463,633)
(464,634)(465,635)(466,636)(467,637)(468,638)(469,639)(470,640)(471,621)
(472,622)(473,623)(474,624)(475,625)(476,626)(477,627)(478,628)(479,629)
(480,630);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*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, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*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*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 >; 
 
References : None.
to this polytope