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Polytope of Type {8,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20,4}*1280b
if this polytope has a name.
Group : SmallGroup(1280,200907)
Rank : 4
Schlafli Type : {8,20,4}
Number of vertices, edges, etc : 8, 80, 40, 4
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {4,20,4}*640, {8,20,2}*640b
   4-fold quotients : {2,20,4}*320, {4,20,2}*320, {4,10,4}*320
   5-fold quotients : {8,4,4}*256b
   8-fold quotients : {2,20,2}*160, {2,10,4}*160, {4,10,2}*160
   10-fold quotients : {4,4,4}*128, {8,4,2}*128b
   16-fold quotients : {2,10,2}*80
   20-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   32-fold quotients : {2,5,2}*40
   40-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)
(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)
( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)( 24,104)
( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)
( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)
( 41,126)( 42,127)( 43,128)( 44,129)( 45,130)( 46,121)( 47,122)( 48,123)
( 49,124)( 50,125)( 51,136)( 52,137)( 53,138)( 54,139)( 55,140)( 56,131)
( 57,132)( 58,133)( 59,134)( 60,135)( 61,146)( 62,147)( 63,148)( 64,149)
( 65,150)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,156)( 72,157)
( 73,158)( 74,159)( 75,160)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)
(161,241)(162,242)(163,243)(164,244)(165,245)(166,246)(167,247)(168,248)
(169,249)(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)(176,256)
(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)(184,264)
(185,265)(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)(192,272)
(193,273)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)
(201,286)(202,287)(203,288)(204,289)(205,290)(206,281)(207,282)(208,283)
(209,284)(210,285)(211,296)(212,297)(213,298)(214,299)(215,300)(216,291)
(217,292)(218,293)(219,294)(220,295)(221,306)(222,307)(223,308)(224,309)
(225,310)(226,301)(227,302)(228,303)(229,304)(230,305)(231,316)(232,317)
(233,318)(234,319)(235,320)(236,311)(237,312)(238,313)(239,314)(240,315)
(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)(328,408)
(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)(336,416)
(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)(344,424)
(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)(352,432)
(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)(360,440)
(361,446)(362,447)(363,448)(364,449)(365,450)(366,441)(367,442)(368,443)
(369,444)(370,445)(371,456)(372,457)(373,458)(374,459)(375,460)(376,451)
(377,452)(378,453)(379,454)(380,455)(381,466)(382,467)(383,468)(384,469)
(385,470)(386,461)(387,462)(388,463)(389,464)(390,465)(391,476)(392,477)
(393,478)(394,479)(395,480)(396,471)(397,472)(398,473)(399,474)(400,475)
(481,561)(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)(488,568)
(489,569)(490,570)(491,571)(492,572)(493,573)(494,574)(495,575)(496,576)
(497,577)(498,578)(499,579)(500,580)(501,581)(502,582)(503,583)(504,584)
(505,585)(506,586)(507,587)(508,588)(509,589)(510,590)(511,591)(512,592)
(513,593)(514,594)(515,595)(516,596)(517,597)(518,598)(519,599)(520,600)
(521,606)(522,607)(523,608)(524,609)(525,610)(526,601)(527,602)(528,603)
(529,604)(530,605)(531,616)(532,617)(533,618)(534,619)(535,620)(536,611)
(537,612)(538,613)(539,614)(540,615)(541,626)(542,627)(543,628)(544,629)
(545,630)(546,621)(547,622)(548,623)(549,624)(550,625)(551,636)(552,637)
(553,638)(554,639)(555,640)(556,631)(557,632)(558,633)(559,634)(560,635);;
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, 46)( 42, 50)( 43, 49)( 44, 48)( 45, 47)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 67, 70)( 68, 69)
( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 81,121)( 82,125)( 83,124)( 84,123)
( 85,122)( 86,126)( 87,130)( 88,129)( 89,128)( 90,127)( 91,131)( 92,135)
( 93,134)( 94,133)( 95,132)( 96,136)( 97,140)( 98,139)( 99,138)(100,137)
(101,146)(102,150)(103,149)(104,148)(105,147)(106,141)(107,145)(108,144)
(109,143)(110,142)(111,156)(112,160)(113,159)(114,158)(115,157)(116,151)
(117,155)(118,154)(119,153)(120,152)(161,181)(162,185)(163,184)(164,183)
(165,182)(166,186)(167,190)(168,189)(169,188)(170,187)(171,191)(172,195)
(173,194)(174,193)(175,192)(176,196)(177,200)(178,199)(179,198)(180,197)
(201,226)(202,230)(203,229)(204,228)(205,227)(206,221)(207,225)(208,224)
(209,223)(210,222)(211,236)(212,240)(213,239)(214,238)(215,237)(216,231)
(217,235)(218,234)(219,233)(220,232)(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)(321,361)(322,365)(323,364)(324,363)
(325,362)(326,366)(327,370)(328,369)(329,368)(330,367)(331,371)(332,375)
(333,374)(334,373)(335,372)(336,376)(337,380)(338,379)(339,378)(340,377)
(341,386)(342,390)(343,389)(344,388)(345,387)(346,381)(347,385)(348,384)
(349,383)(350,382)(351,396)(352,400)(353,399)(354,398)(355,397)(356,391)
(357,395)(358,394)(359,393)(360,392)(402,405)(403,404)(407,410)(408,409)
(412,415)(413,414)(417,420)(418,419)(421,426)(422,430)(423,429)(424,428)
(425,427)(431,436)(432,440)(433,439)(434,438)(435,437)(441,446)(442,450)
(443,449)(444,448)(445,447)(451,456)(452,460)(453,459)(454,458)(455,457)
(462,465)(463,464)(467,470)(468,469)(472,475)(473,474)(477,480)(478,479)
(481,541)(482,545)(483,544)(484,543)(485,542)(486,546)(487,550)(488,549)
(489,548)(490,547)(491,551)(492,555)(493,554)(494,553)(495,552)(496,556)
(497,560)(498,559)(499,558)(500,557)(501,521)(502,525)(503,524)(504,523)
(505,522)(506,526)(507,530)(508,529)(509,528)(510,527)(511,531)(512,535)
(513,534)(514,533)(515,532)(516,536)(517,540)(518,539)(519,538)(520,537)
(561,581)(562,585)(563,584)(564,583)(565,582)(566,586)(567,590)(568,589)
(569,588)(570,587)(571,591)(572,595)(573,594)(574,593)(575,592)(576,596)
(577,600)(578,599)(579,598)(580,597)(601,626)(602,630)(603,629)(604,628)
(605,627)(606,621)(607,625)(608,624)(609,623)(610,622)(611,636)(612,640)
(613,639)(614,638)(615,637)(616,631)(617,635)(618,634)(619,633)(620,632);;
s2 := (  1,243)(  2,242)(  3,241)(  4,245)(  5,244)(  6,248)(  7,247)(  8,246)
(  9,250)( 10,249)( 11,253)( 12,252)( 13,251)( 14,255)( 15,254)( 16,258)
( 17,257)( 18,256)( 19,260)( 20,259)( 21,268)( 22,267)( 23,266)( 24,270)
( 25,269)( 26,263)( 27,262)( 28,261)( 29,265)( 30,264)( 31,278)( 32,277)
( 33,276)( 34,280)( 35,279)( 36,273)( 37,272)( 38,271)( 39,275)( 40,274)
( 41,288)( 42,287)( 43,286)( 44,290)( 45,289)( 46,283)( 47,282)( 48,281)
( 49,285)( 50,284)( 51,298)( 52,297)( 53,296)( 54,300)( 55,299)( 56,293)
( 57,292)( 58,291)( 59,295)( 60,294)( 61,303)( 62,302)( 63,301)( 64,305)
( 65,304)( 66,308)( 67,307)( 68,306)( 69,310)( 70,309)( 71,313)( 72,312)
( 73,311)( 74,315)( 75,314)( 76,318)( 77,317)( 78,316)( 79,320)( 80,319)
( 81,163)( 82,162)( 83,161)( 84,165)( 85,164)( 86,168)( 87,167)( 88,166)
( 89,170)( 90,169)( 91,173)( 92,172)( 93,171)( 94,175)( 95,174)( 96,178)
( 97,177)( 98,176)( 99,180)(100,179)(101,188)(102,187)(103,186)(104,190)
(105,189)(106,183)(107,182)(108,181)(109,185)(110,184)(111,198)(112,197)
(113,196)(114,200)(115,199)(116,193)(117,192)(118,191)(119,195)(120,194)
(121,208)(122,207)(123,206)(124,210)(125,209)(126,203)(127,202)(128,201)
(129,205)(130,204)(131,218)(132,217)(133,216)(134,220)(135,219)(136,213)
(137,212)(138,211)(139,215)(140,214)(141,223)(142,222)(143,221)(144,225)
(145,224)(146,228)(147,227)(148,226)(149,230)(150,229)(151,233)(152,232)
(153,231)(154,235)(155,234)(156,238)(157,237)(158,236)(159,240)(160,239)
(321,563)(322,562)(323,561)(324,565)(325,564)(326,568)(327,567)(328,566)
(329,570)(330,569)(331,573)(332,572)(333,571)(334,575)(335,574)(336,578)
(337,577)(338,576)(339,580)(340,579)(341,588)(342,587)(343,586)(344,590)
(345,589)(346,583)(347,582)(348,581)(349,585)(350,584)(351,598)(352,597)
(353,596)(354,600)(355,599)(356,593)(357,592)(358,591)(359,595)(360,594)
(361,608)(362,607)(363,606)(364,610)(365,609)(366,603)(367,602)(368,601)
(369,605)(370,604)(371,618)(372,617)(373,616)(374,620)(375,619)(376,613)
(377,612)(378,611)(379,615)(380,614)(381,623)(382,622)(383,621)(384,625)
(385,624)(386,628)(387,627)(388,626)(389,630)(390,629)(391,633)(392,632)
(393,631)(394,635)(395,634)(396,638)(397,637)(398,636)(399,640)(400,639)
(401,483)(402,482)(403,481)(404,485)(405,484)(406,488)(407,487)(408,486)
(409,490)(410,489)(411,493)(412,492)(413,491)(414,495)(415,494)(416,498)
(417,497)(418,496)(419,500)(420,499)(421,508)(422,507)(423,506)(424,510)
(425,509)(426,503)(427,502)(428,501)(429,505)(430,504)(431,518)(432,517)
(433,516)(434,520)(435,519)(436,513)(437,512)(438,511)(439,515)(440,514)
(441,528)(442,527)(443,526)(444,530)(445,529)(446,523)(447,522)(448,521)
(449,525)(450,524)(451,538)(452,537)(453,536)(454,540)(455,539)(456,533)
(457,532)(458,531)(459,535)(460,534)(461,543)(462,542)(463,541)(464,545)
(465,544)(466,548)(467,547)(468,546)(469,550)(470,549)(471,553)(472,552)
(473,551)(474,555)(475,554)(476,558)(477,557)(478,556)(479,560)(480,559);;
s3 := (  1,401)(  2,402)(  3,403)(  4,404)(  5,405)(  6,406)(  7,407)(  8,408)
(  9,409)( 10,410)( 11,411)( 12,412)( 13,413)( 14,414)( 15,415)( 16,416)
( 17,417)( 18,418)( 19,419)( 20,420)( 21,421)( 22,422)( 23,423)( 24,424)
( 25,425)( 26,426)( 27,427)( 28,428)( 29,429)( 30,430)( 31,431)( 32,432)
( 33,433)( 34,434)( 35,435)( 36,436)( 37,437)( 38,438)( 39,439)( 40,440)
( 41,441)( 42,442)( 43,443)( 44,444)( 45,445)( 46,446)( 47,447)( 48,448)
( 49,449)( 50,450)( 51,451)( 52,452)( 53,453)( 54,454)( 55,455)( 56,456)
( 57,457)( 58,458)( 59,459)( 60,460)( 61,461)( 62,462)( 63,463)( 64,464)
( 65,465)( 66,466)( 67,467)( 68,468)( 69,469)( 70,470)( 71,471)( 72,472)
( 73,473)( 74,474)( 75,475)( 76,476)( 77,477)( 78,478)( 79,479)( 80,480)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,571)(162,572)(163,573)(164,574)(165,575)(166,576)(167,577)(168,578)
(169,579)(170,580)(171,561)(172,562)(173,563)(174,564)(175,565)(176,566)
(177,567)(178,568)(179,569)(180,570)(181,591)(182,592)(183,593)(184,594)
(185,595)(186,596)(187,597)(188,598)(189,599)(190,600)(191,581)(192,582)
(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)(200,590)
(201,611)(202,612)(203,613)(204,614)(205,615)(206,616)(207,617)(208,618)
(209,619)(210,620)(211,601)(212,602)(213,603)(214,604)(215,605)(216,606)
(217,607)(218,608)(219,609)(220,610)(221,631)(222,632)(223,633)(224,634)
(225,635)(226,636)(227,637)(228,638)(229,639)(230,640)(231,621)(232,622)
(233,623)(234,624)(235,625)(236,626)(237,627)(238,628)(239,629)(240,630)
(241,491)(242,492)(243,493)(244,494)(245,495)(246,496)(247,497)(248,498)
(249,499)(250,500)(251,481)(252,482)(253,483)(254,484)(255,485)(256,486)
(257,487)(258,488)(259,489)(260,490)(261,511)(262,512)(263,513)(264,514)
(265,515)(266,516)(267,517)(268,518)(269,519)(270,520)(271,501)(272,502)
(273,503)(274,504)(275,505)(276,506)(277,507)(278,508)(279,509)(280,510)
(281,531)(282,532)(283,533)(284,534)(285,535)(286,536)(287,537)(288,538)
(289,539)(290,540)(291,521)(292,522)(293,523)(294,524)(295,525)(296,526)
(297,527)(298,528)(299,529)(300,530)(301,551)(302,552)(303,553)(304,554)
(305,555)(306,556)(307,557)(308,558)(309,559)(310,560)(311,541)(312,542)
(313,543)(314,544)(315,545)(316,546)(317,547)(318,548)(319,549)(320,550);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(640)!(  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)
(  8, 88)(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)
( 16, 96)( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)
( 24,104)( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)
( 32,112)( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)
( 40,120)( 41,126)( 42,127)( 43,128)( 44,129)( 45,130)( 46,121)( 47,122)
( 48,123)( 49,124)( 50,125)( 51,136)( 52,137)( 53,138)( 54,139)( 55,140)
( 56,131)( 57,132)( 58,133)( 59,134)( 60,135)( 61,146)( 62,147)( 63,148)
( 64,149)( 65,150)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,156)
( 72,157)( 73,158)( 74,159)( 75,160)( 76,151)( 77,152)( 78,153)( 79,154)
( 80,155)(161,241)(162,242)(163,243)(164,244)(165,245)(166,246)(167,247)
(168,248)(169,249)(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)
(176,256)(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)
(184,264)(185,265)(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)
(192,272)(193,273)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)
(200,280)(201,286)(202,287)(203,288)(204,289)(205,290)(206,281)(207,282)
(208,283)(209,284)(210,285)(211,296)(212,297)(213,298)(214,299)(215,300)
(216,291)(217,292)(218,293)(219,294)(220,295)(221,306)(222,307)(223,308)
(224,309)(225,310)(226,301)(227,302)(228,303)(229,304)(230,305)(231,316)
(232,317)(233,318)(234,319)(235,320)(236,311)(237,312)(238,313)(239,314)
(240,315)(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)
(328,408)(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)
(336,416)(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)
(344,424)(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)
(352,432)(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)
(360,440)(361,446)(362,447)(363,448)(364,449)(365,450)(366,441)(367,442)
(368,443)(369,444)(370,445)(371,456)(372,457)(373,458)(374,459)(375,460)
(376,451)(377,452)(378,453)(379,454)(380,455)(381,466)(382,467)(383,468)
(384,469)(385,470)(386,461)(387,462)(388,463)(389,464)(390,465)(391,476)
(392,477)(393,478)(394,479)(395,480)(396,471)(397,472)(398,473)(399,474)
(400,475)(481,561)(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)
(488,568)(489,569)(490,570)(491,571)(492,572)(493,573)(494,574)(495,575)
(496,576)(497,577)(498,578)(499,579)(500,580)(501,581)(502,582)(503,583)
(504,584)(505,585)(506,586)(507,587)(508,588)(509,589)(510,590)(511,591)
(512,592)(513,593)(514,594)(515,595)(516,596)(517,597)(518,598)(519,599)
(520,600)(521,606)(522,607)(523,608)(524,609)(525,610)(526,601)(527,602)
(528,603)(529,604)(530,605)(531,616)(532,617)(533,618)(534,619)(535,620)
(536,611)(537,612)(538,613)(539,614)(540,615)(541,626)(542,627)(543,628)
(544,629)(545,630)(546,621)(547,622)(548,623)(549,624)(550,625)(551,636)
(552,637)(553,638)(554,639)(555,640)(556,631)(557,632)(558,633)(559,634)
(560,635);
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, 46)( 42, 50)( 43, 49)( 44, 48)( 45, 47)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 67, 70)
( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 81,121)( 82,125)( 83,124)
( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)( 89,128)( 90,127)( 91,131)
( 92,135)( 93,134)( 94,133)( 95,132)( 96,136)( 97,140)( 98,139)( 99,138)
(100,137)(101,146)(102,150)(103,149)(104,148)(105,147)(106,141)(107,145)
(108,144)(109,143)(110,142)(111,156)(112,160)(113,159)(114,158)(115,157)
(116,151)(117,155)(118,154)(119,153)(120,152)(161,181)(162,185)(163,184)
(164,183)(165,182)(166,186)(167,190)(168,189)(169,188)(170,187)(171,191)
(172,195)(173,194)(174,193)(175,192)(176,196)(177,200)(178,199)(179,198)
(180,197)(201,226)(202,230)(203,229)(204,228)(205,227)(206,221)(207,225)
(208,224)(209,223)(210,222)(211,236)(212,240)(213,239)(214,238)(215,237)
(216,231)(217,235)(218,234)(219,233)(220,232)(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)(321,361)(322,365)(323,364)
(324,363)(325,362)(326,366)(327,370)(328,369)(329,368)(330,367)(331,371)
(332,375)(333,374)(334,373)(335,372)(336,376)(337,380)(338,379)(339,378)
(340,377)(341,386)(342,390)(343,389)(344,388)(345,387)(346,381)(347,385)
(348,384)(349,383)(350,382)(351,396)(352,400)(353,399)(354,398)(355,397)
(356,391)(357,395)(358,394)(359,393)(360,392)(402,405)(403,404)(407,410)
(408,409)(412,415)(413,414)(417,420)(418,419)(421,426)(422,430)(423,429)
(424,428)(425,427)(431,436)(432,440)(433,439)(434,438)(435,437)(441,446)
(442,450)(443,449)(444,448)(445,447)(451,456)(452,460)(453,459)(454,458)
(455,457)(462,465)(463,464)(467,470)(468,469)(472,475)(473,474)(477,480)
(478,479)(481,541)(482,545)(483,544)(484,543)(485,542)(486,546)(487,550)
(488,549)(489,548)(490,547)(491,551)(492,555)(493,554)(494,553)(495,552)
(496,556)(497,560)(498,559)(499,558)(500,557)(501,521)(502,525)(503,524)
(504,523)(505,522)(506,526)(507,530)(508,529)(509,528)(510,527)(511,531)
(512,535)(513,534)(514,533)(515,532)(516,536)(517,540)(518,539)(519,538)
(520,537)(561,581)(562,585)(563,584)(564,583)(565,582)(566,586)(567,590)
(568,589)(569,588)(570,587)(571,591)(572,595)(573,594)(574,593)(575,592)
(576,596)(577,600)(578,599)(579,598)(580,597)(601,626)(602,630)(603,629)
(604,628)(605,627)(606,621)(607,625)(608,624)(609,623)(610,622)(611,636)
(612,640)(613,639)(614,638)(615,637)(616,631)(617,635)(618,634)(619,633)
(620,632);
s2 := Sym(640)!(  1,243)(  2,242)(  3,241)(  4,245)(  5,244)(  6,248)(  7,247)
(  8,246)(  9,250)( 10,249)( 11,253)( 12,252)( 13,251)( 14,255)( 15,254)
( 16,258)( 17,257)( 18,256)( 19,260)( 20,259)( 21,268)( 22,267)( 23,266)
( 24,270)( 25,269)( 26,263)( 27,262)( 28,261)( 29,265)( 30,264)( 31,278)
( 32,277)( 33,276)( 34,280)( 35,279)( 36,273)( 37,272)( 38,271)( 39,275)
( 40,274)( 41,288)( 42,287)( 43,286)( 44,290)( 45,289)( 46,283)( 47,282)
( 48,281)( 49,285)( 50,284)( 51,298)( 52,297)( 53,296)( 54,300)( 55,299)
( 56,293)( 57,292)( 58,291)( 59,295)( 60,294)( 61,303)( 62,302)( 63,301)
( 64,305)( 65,304)( 66,308)( 67,307)( 68,306)( 69,310)( 70,309)( 71,313)
( 72,312)( 73,311)( 74,315)( 75,314)( 76,318)( 77,317)( 78,316)( 79,320)
( 80,319)( 81,163)( 82,162)( 83,161)( 84,165)( 85,164)( 86,168)( 87,167)
( 88,166)( 89,170)( 90,169)( 91,173)( 92,172)( 93,171)( 94,175)( 95,174)
( 96,178)( 97,177)( 98,176)( 99,180)(100,179)(101,188)(102,187)(103,186)
(104,190)(105,189)(106,183)(107,182)(108,181)(109,185)(110,184)(111,198)
(112,197)(113,196)(114,200)(115,199)(116,193)(117,192)(118,191)(119,195)
(120,194)(121,208)(122,207)(123,206)(124,210)(125,209)(126,203)(127,202)
(128,201)(129,205)(130,204)(131,218)(132,217)(133,216)(134,220)(135,219)
(136,213)(137,212)(138,211)(139,215)(140,214)(141,223)(142,222)(143,221)
(144,225)(145,224)(146,228)(147,227)(148,226)(149,230)(150,229)(151,233)
(152,232)(153,231)(154,235)(155,234)(156,238)(157,237)(158,236)(159,240)
(160,239)(321,563)(322,562)(323,561)(324,565)(325,564)(326,568)(327,567)
(328,566)(329,570)(330,569)(331,573)(332,572)(333,571)(334,575)(335,574)
(336,578)(337,577)(338,576)(339,580)(340,579)(341,588)(342,587)(343,586)
(344,590)(345,589)(346,583)(347,582)(348,581)(349,585)(350,584)(351,598)
(352,597)(353,596)(354,600)(355,599)(356,593)(357,592)(358,591)(359,595)
(360,594)(361,608)(362,607)(363,606)(364,610)(365,609)(366,603)(367,602)
(368,601)(369,605)(370,604)(371,618)(372,617)(373,616)(374,620)(375,619)
(376,613)(377,612)(378,611)(379,615)(380,614)(381,623)(382,622)(383,621)
(384,625)(385,624)(386,628)(387,627)(388,626)(389,630)(390,629)(391,633)
(392,632)(393,631)(394,635)(395,634)(396,638)(397,637)(398,636)(399,640)
(400,639)(401,483)(402,482)(403,481)(404,485)(405,484)(406,488)(407,487)
(408,486)(409,490)(410,489)(411,493)(412,492)(413,491)(414,495)(415,494)
(416,498)(417,497)(418,496)(419,500)(420,499)(421,508)(422,507)(423,506)
(424,510)(425,509)(426,503)(427,502)(428,501)(429,505)(430,504)(431,518)
(432,517)(433,516)(434,520)(435,519)(436,513)(437,512)(438,511)(439,515)
(440,514)(441,528)(442,527)(443,526)(444,530)(445,529)(446,523)(447,522)
(448,521)(449,525)(450,524)(451,538)(452,537)(453,536)(454,540)(455,539)
(456,533)(457,532)(458,531)(459,535)(460,534)(461,543)(462,542)(463,541)
(464,545)(465,544)(466,548)(467,547)(468,546)(469,550)(470,549)(471,553)
(472,552)(473,551)(474,555)(475,554)(476,558)(477,557)(478,556)(479,560)
(480,559);
s3 := Sym(640)!(  1,401)(  2,402)(  3,403)(  4,404)(  5,405)(  6,406)(  7,407)
(  8,408)(  9,409)( 10,410)( 11,411)( 12,412)( 13,413)( 14,414)( 15,415)
( 16,416)( 17,417)( 18,418)( 19,419)( 20,420)( 21,421)( 22,422)( 23,423)
( 24,424)( 25,425)( 26,426)( 27,427)( 28,428)( 29,429)( 30,430)( 31,431)
( 32,432)( 33,433)( 34,434)( 35,435)( 36,436)( 37,437)( 38,438)( 39,439)
( 40,440)( 41,441)( 42,442)( 43,443)( 44,444)( 45,445)( 46,446)( 47,447)
( 48,448)( 49,449)( 50,450)( 51,451)( 52,452)( 53,453)( 54,454)( 55,455)
( 56,456)( 57,457)( 58,458)( 59,459)( 60,460)( 61,461)( 62,462)( 63,463)
( 64,464)( 65,465)( 66,466)( 67,467)( 68,468)( 69,469)( 70,470)( 71,471)
( 72,472)( 73,473)( 74,474)( 75,475)( 76,476)( 77,477)( 78,478)( 79,479)
( 80,480)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,571)(162,572)(163,573)(164,574)(165,575)(166,576)(167,577)
(168,578)(169,579)(170,580)(171,561)(172,562)(173,563)(174,564)(175,565)
(176,566)(177,567)(178,568)(179,569)(180,570)(181,591)(182,592)(183,593)
(184,594)(185,595)(186,596)(187,597)(188,598)(189,599)(190,600)(191,581)
(192,582)(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)
(200,590)(201,611)(202,612)(203,613)(204,614)(205,615)(206,616)(207,617)
(208,618)(209,619)(210,620)(211,601)(212,602)(213,603)(214,604)(215,605)
(216,606)(217,607)(218,608)(219,609)(220,610)(221,631)(222,632)(223,633)
(224,634)(225,635)(226,636)(227,637)(228,638)(229,639)(230,640)(231,621)
(232,622)(233,623)(234,624)(235,625)(236,626)(237,627)(238,628)(239,629)
(240,630)(241,491)(242,492)(243,493)(244,494)(245,495)(246,496)(247,497)
(248,498)(249,499)(250,500)(251,481)(252,482)(253,483)(254,484)(255,485)
(256,486)(257,487)(258,488)(259,489)(260,490)(261,511)(262,512)(263,513)
(264,514)(265,515)(266,516)(267,517)(268,518)(269,519)(270,520)(271,501)
(272,502)(273,503)(274,504)(275,505)(276,506)(277,507)(278,508)(279,509)
(280,510)(281,531)(282,532)(283,533)(284,534)(285,535)(286,536)(287,537)
(288,538)(289,539)(290,540)(291,521)(292,522)(293,523)(294,524)(295,525)
(296,526)(297,527)(298,528)(299,529)(300,530)(301,551)(302,552)(303,553)
(304,554)(305,555)(306,556)(307,557)(308,558)(309,559)(310,560)(311,541)
(312,542)(313,543)(314,544)(315,545)(316,546)(317,547)(318,548)(319,549)
(320,550);
poly := sub<Sym(640)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope