Polytope of Type {4,4,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,40}*1280b
if this polytope has a name.
Group : SmallGroup(1280,200909)
Rank : 4
Schlafli Type : {4,4,40}
Number of vertices, edges, etc : 4, 8, 80, 40
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 : {4,4,20}*640, {2,4,40}*640b
   4-fold quotients : {2,4,20}*320, {4,2,20}*320, {4,4,10}*320
   5-fold quotients : {4,4,8}*256b
   8-fold quotients : {2,2,20}*160, {2,4,10}*160, {4,2,10}*160
   10-fold quotients : {4,4,4}*128, {2,4,8}*128b
   16-fold quotients : {4,2,5}*80, {2,2,10}*80
   20-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   32-fold quotients : {2,2,5}*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)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)( 24,269)
( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,276)( 32,277)
( 33,278)( 34,279)( 35,280)( 36,271)( 37,272)( 38,273)( 39,274)( 40,275)
( 41,286)( 42,287)( 43,288)( 44,289)( 45,290)( 46,281)( 47,282)( 48,283)
( 49,284)( 50,285)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,291)
( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,161)( 82,162)( 83,163)( 84,164)( 85,165)( 86,166)( 87,167)( 88,168)
( 89,169)( 90,170)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)( 96,176)
( 97,177)( 98,178)( 99,179)(100,180)(101,186)(102,187)(103,188)(104,189)
(105,190)(106,181)(107,182)(108,183)(109,184)(110,185)(111,196)(112,197)
(113,198)(114,199)(115,200)(116,191)(117,192)(118,193)(119,194)(120,195)
(121,206)(122,207)(123,208)(124,209)(125,210)(126,201)(127,202)(128,203)
(129,204)(130,205)(131,216)(132,217)(133,218)(134,219)(135,220)(136,211)
(137,212)(138,213)(139,214)(140,215)(141,221)(142,222)(143,223)(144,224)
(145,225)(146,226)(147,227)(148,228)(149,229)(150,230)(151,231)(152,232)
(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)(160,240)
(321,561)(322,562)(323,563)(324,564)(325,565)(326,566)(327,567)(328,568)
(329,569)(330,570)(331,571)(332,572)(333,573)(334,574)(335,575)(336,576)
(337,577)(338,578)(339,579)(340,580)(341,586)(342,587)(343,588)(344,589)
(345,590)(346,581)(347,582)(348,583)(349,584)(350,585)(351,596)(352,597)
(353,598)(354,599)(355,600)(356,591)(357,592)(358,593)(359,594)(360,595)
(361,606)(362,607)(363,608)(364,609)(365,610)(366,601)(367,602)(368,603)
(369,604)(370,605)(371,616)(372,617)(373,618)(374,619)(375,620)(376,611)
(377,612)(378,613)(379,614)(380,615)(381,621)(382,622)(383,623)(384,624)
(385,625)(386,626)(387,627)(388,628)(389,629)(390,630)(391,631)(392,632)
(393,633)(394,634)(395,635)(396,636)(397,637)(398,638)(399,639)(400,640)
(401,481)(402,482)(403,483)(404,484)(405,485)(406,486)(407,487)(408,488)
(409,489)(410,490)(411,491)(412,492)(413,493)(414,494)(415,495)(416,496)
(417,497)(418,498)(419,499)(420,500)(421,506)(422,507)(423,508)(424,509)
(425,510)(426,501)(427,502)(428,503)(429,504)(430,505)(431,516)(432,517)
(433,518)(434,519)(435,520)(436,511)(437,512)(438,513)(439,514)(440,515)
(441,526)(442,527)(443,528)(444,529)(445,530)(446,521)(447,522)(448,523)
(449,524)(450,525)(451,536)(452,537)(453,538)(454,539)(455,540)(456,531)
(457,532)(458,533)(459,534)(460,535)(461,541)(462,542)(463,543)(464,544)
(465,545)(466,546)(467,547)(468,548)(469,549)(470,550)(471,551)(472,552)
(473,553)(474,554)(475,555)(476,556)(477,557)(478,558)(479,559)(480,560);;
s2 := (  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);;
s3 := (  1, 83)(  2, 82)(  3, 81)(  4, 85)(  5, 84)(  6, 88)(  7, 87)(  8, 86)
(  9, 90)( 10, 89)( 11, 93)( 12, 92)( 13, 91)( 14, 95)( 15, 94)( 16, 98)
( 17, 97)( 18, 96)( 19,100)( 20, 99)( 21,103)( 22,102)( 23,101)( 24,105)
( 25,104)( 26,108)( 27,107)( 28,106)( 29,110)( 30,109)( 31,113)( 32,112)
( 33,111)( 34,115)( 35,114)( 36,118)( 37,117)( 38,116)( 39,120)( 40,119)
( 41,128)( 42,127)( 43,126)( 44,130)( 45,129)( 46,123)( 47,122)( 48,121)
( 49,125)( 50,124)( 51,138)( 52,137)( 53,136)( 54,140)( 55,139)( 56,133)
( 57,132)( 58,131)( 59,135)( 60,134)( 61,148)( 62,147)( 63,146)( 64,150)
( 65,149)( 66,143)( 67,142)( 68,141)( 69,145)( 70,144)( 71,158)( 72,157)
( 73,156)( 74,160)( 75,159)( 76,153)( 77,152)( 78,151)( 79,155)( 80,154)
(161,243)(162,242)(163,241)(164,245)(165,244)(166,248)(167,247)(168,246)
(169,250)(170,249)(171,253)(172,252)(173,251)(174,255)(175,254)(176,258)
(177,257)(178,256)(179,260)(180,259)(181,263)(182,262)(183,261)(184,265)
(185,264)(186,268)(187,267)(188,266)(189,270)(190,269)(191,273)(192,272)
(193,271)(194,275)(195,274)(196,278)(197,277)(198,276)(199,280)(200,279)
(201,288)(202,287)(203,286)(204,290)(205,289)(206,283)(207,282)(208,281)
(209,285)(210,284)(211,298)(212,297)(213,296)(214,300)(215,299)(216,293)
(217,292)(218,291)(219,295)(220,294)(221,308)(222,307)(223,306)(224,310)
(225,309)(226,303)(227,302)(228,301)(229,305)(230,304)(231,318)(232,317)
(233,316)(234,320)(235,319)(236,313)(237,312)(238,311)(239,315)(240,314)
(321,403)(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)
(329,410)(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)(336,418)
(337,417)(338,416)(339,420)(340,419)(341,423)(342,422)(343,421)(344,425)
(345,424)(346,428)(347,427)(348,426)(349,430)(350,429)(351,433)(352,432)
(353,431)(354,435)(355,434)(356,438)(357,437)(358,436)(359,440)(360,439)
(361,448)(362,447)(363,446)(364,450)(365,449)(366,443)(367,442)(368,441)
(369,445)(370,444)(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)(391,478)(392,477)
(393,476)(394,480)(395,479)(396,473)(397,472)(398,471)(399,475)(400,474)
(481,563)(482,562)(483,561)(484,565)(485,564)(486,568)(487,567)(488,566)
(489,570)(490,569)(491,573)(492,572)(493,571)(494,575)(495,574)(496,578)
(497,577)(498,576)(499,580)(500,579)(501,583)(502,582)(503,581)(504,585)
(505,584)(506,588)(507,587)(508,586)(509,590)(510,589)(511,593)(512,592)
(513,591)(514,595)(515,594)(516,598)(517,597)(518,596)(519,600)(520,599)
(521,608)(522,607)(523,606)(524,610)(525,609)(526,603)(527,602)(528,601)
(529,605)(530,604)(531,618)(532,617)(533,616)(534,620)(535,619)(536,613)
(537,612)(538,611)(539,615)(540,614)(541,628)(542,627)(543,626)(544,630)
(545,629)(546,623)(547,622)(548,621)(549,625)(550,624)(551,638)(552,637)
(553,636)(554,640)(555,639)(556,633)(557,632)(558,631)(559,635)(560,634);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*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)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)
( 24,269)( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,276)
( 32,277)( 33,278)( 34,279)( 35,280)( 36,271)( 37,272)( 38,273)( 39,274)
( 40,275)( 41,286)( 42,287)( 43,288)( 44,289)( 45,290)( 46,281)( 47,282)
( 48,283)( 49,284)( 50,285)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)
( 56,291)( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,161)( 82,162)( 83,163)( 84,164)( 85,165)( 86,166)( 87,167)
( 88,168)( 89,169)( 90,170)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)
( 96,176)( 97,177)( 98,178)( 99,179)(100,180)(101,186)(102,187)(103,188)
(104,189)(105,190)(106,181)(107,182)(108,183)(109,184)(110,185)(111,196)
(112,197)(113,198)(114,199)(115,200)(116,191)(117,192)(118,193)(119,194)
(120,195)(121,206)(122,207)(123,208)(124,209)(125,210)(126,201)(127,202)
(128,203)(129,204)(130,205)(131,216)(132,217)(133,218)(134,219)(135,220)
(136,211)(137,212)(138,213)(139,214)(140,215)(141,221)(142,222)(143,223)
(144,224)(145,225)(146,226)(147,227)(148,228)(149,229)(150,230)(151,231)
(152,232)(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)
(160,240)(321,561)(322,562)(323,563)(324,564)(325,565)(326,566)(327,567)
(328,568)(329,569)(330,570)(331,571)(332,572)(333,573)(334,574)(335,575)
(336,576)(337,577)(338,578)(339,579)(340,580)(341,586)(342,587)(343,588)
(344,589)(345,590)(346,581)(347,582)(348,583)(349,584)(350,585)(351,596)
(352,597)(353,598)(354,599)(355,600)(356,591)(357,592)(358,593)(359,594)
(360,595)(361,606)(362,607)(363,608)(364,609)(365,610)(366,601)(367,602)
(368,603)(369,604)(370,605)(371,616)(372,617)(373,618)(374,619)(375,620)
(376,611)(377,612)(378,613)(379,614)(380,615)(381,621)(382,622)(383,623)
(384,624)(385,625)(386,626)(387,627)(388,628)(389,629)(390,630)(391,631)
(392,632)(393,633)(394,634)(395,635)(396,636)(397,637)(398,638)(399,639)
(400,640)(401,481)(402,482)(403,483)(404,484)(405,485)(406,486)(407,487)
(408,488)(409,489)(410,490)(411,491)(412,492)(413,493)(414,494)(415,495)
(416,496)(417,497)(418,498)(419,499)(420,500)(421,506)(422,507)(423,508)
(424,509)(425,510)(426,501)(427,502)(428,503)(429,504)(430,505)(431,516)
(432,517)(433,518)(434,519)(435,520)(436,511)(437,512)(438,513)(439,514)
(440,515)(441,526)(442,527)(443,528)(444,529)(445,530)(446,521)(447,522)
(448,523)(449,524)(450,525)(451,536)(452,537)(453,538)(454,539)(455,540)
(456,531)(457,532)(458,533)(459,534)(460,535)(461,541)(462,542)(463,543)
(464,544)(465,545)(466,546)(467,547)(468,548)(469,549)(470,550)(471,551)
(472,552)(473,553)(474,554)(475,555)(476,556)(477,557)(478,558)(479,559)
(480,560);
s2 := 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);
s3 := Sym(640)!(  1, 83)(  2, 82)(  3, 81)(  4, 85)(  5, 84)(  6, 88)(  7, 87)
(  8, 86)(  9, 90)( 10, 89)( 11, 93)( 12, 92)( 13, 91)( 14, 95)( 15, 94)
( 16, 98)( 17, 97)( 18, 96)( 19,100)( 20, 99)( 21,103)( 22,102)( 23,101)
( 24,105)( 25,104)( 26,108)( 27,107)( 28,106)( 29,110)( 30,109)( 31,113)
( 32,112)( 33,111)( 34,115)( 35,114)( 36,118)( 37,117)( 38,116)( 39,120)
( 40,119)( 41,128)( 42,127)( 43,126)( 44,130)( 45,129)( 46,123)( 47,122)
( 48,121)( 49,125)( 50,124)( 51,138)( 52,137)( 53,136)( 54,140)( 55,139)
( 56,133)( 57,132)( 58,131)( 59,135)( 60,134)( 61,148)( 62,147)( 63,146)
( 64,150)( 65,149)( 66,143)( 67,142)( 68,141)( 69,145)( 70,144)( 71,158)
( 72,157)( 73,156)( 74,160)( 75,159)( 76,153)( 77,152)( 78,151)( 79,155)
( 80,154)(161,243)(162,242)(163,241)(164,245)(165,244)(166,248)(167,247)
(168,246)(169,250)(170,249)(171,253)(172,252)(173,251)(174,255)(175,254)
(176,258)(177,257)(178,256)(179,260)(180,259)(181,263)(182,262)(183,261)
(184,265)(185,264)(186,268)(187,267)(188,266)(189,270)(190,269)(191,273)
(192,272)(193,271)(194,275)(195,274)(196,278)(197,277)(198,276)(199,280)
(200,279)(201,288)(202,287)(203,286)(204,290)(205,289)(206,283)(207,282)
(208,281)(209,285)(210,284)(211,298)(212,297)(213,296)(214,300)(215,299)
(216,293)(217,292)(218,291)(219,295)(220,294)(221,308)(222,307)(223,306)
(224,310)(225,309)(226,303)(227,302)(228,301)(229,305)(230,304)(231,318)
(232,317)(233,316)(234,320)(235,319)(236,313)(237,312)(238,311)(239,315)
(240,314)(321,403)(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)
(328,406)(329,410)(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)
(336,418)(337,417)(338,416)(339,420)(340,419)(341,423)(342,422)(343,421)
(344,425)(345,424)(346,428)(347,427)(348,426)(349,430)(350,429)(351,433)
(352,432)(353,431)(354,435)(355,434)(356,438)(357,437)(358,436)(359,440)
(360,439)(361,448)(362,447)(363,446)(364,450)(365,449)(366,443)(367,442)
(368,441)(369,445)(370,444)(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)(391,478)
(392,477)(393,476)(394,480)(395,479)(396,473)(397,472)(398,471)(399,475)
(400,474)(481,563)(482,562)(483,561)(484,565)(485,564)(486,568)(487,567)
(488,566)(489,570)(490,569)(491,573)(492,572)(493,571)(494,575)(495,574)
(496,578)(497,577)(498,576)(499,580)(500,579)(501,583)(502,582)(503,581)
(504,585)(505,584)(506,588)(507,587)(508,586)(509,590)(510,589)(511,593)
(512,592)(513,591)(514,595)(515,594)(516,598)(517,597)(518,596)(519,600)
(520,599)(521,608)(522,607)(523,606)(524,610)(525,609)(526,603)(527,602)
(528,601)(529,605)(530,604)(531,618)(532,617)(533,616)(534,620)(535,619)
(536,613)(537,612)(538,611)(539,615)(540,614)(541,628)(542,627)(543,626)
(544,630)(545,629)(546,623)(547,622)(548,621)(549,625)(550,624)(551,638)
(552,637)(553,636)(554,640)(555,639)(556,633)(557,632)(558,631)(559,635)
(560,634);
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 >;
References : None.
to this polytope