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Polytope of Type {4,20,8}

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