Polytope of Type {4,40,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,40,4}*1280d
Also Known As : {{4,40|2},{40,4|2}}. if this polytope has another name.
Group : SmallGroup(1280,201310)
Rank : 4
Schlafli Type : {4,40,4}
Number of vertices, edges, etc : 4, 80, 80, 4
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Self-Dual
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, {2,40,4}*640a, {4,40,2}*640a
4-fold quotients : {2,20,4}*320, {4,20,2}*320, {4,10,4}*320, {2,40,2}*320
5-fold quotients : {4,8,4}*256d
8-fold quotients : {2,20,2}*160, {2,10,4}*160, {4,10,2}*160
10-fold quotients : {4,4,4}*128, {2,8,4}*128a, {4,8,2}*128a
16-fold quotients : {2,10,2}*80
20-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,8,2}*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.
Irregular Quotients (of which this is a minimal cover):
None.
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)( 41,121)( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)( 49,129)( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)( 57,137)( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)( 64,144)( 65,145)( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)( 73,153)( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)(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)(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)(209,289)(210,290)(211,291)(212,292)(213,293)(214,294)(215,295)(216,296)(217,297)(218,298)(219,299)(220,300)(221,301)(222,302)(223,303)(224,304)(225,305)(226,306)(227,307)(228,308)(229,309)(230,310)(231,311)(232,312)(233,313)(234,314)(235,315)(236,316)(237,317)(238,318)(239,319)(240,320)(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)(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)(368,448)(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)(376,456)(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)(384,464)(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)(392,472)(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)(400,480)(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)(521,601)(522,602)(523,603)(524,604)(525,605)(526,606)(527,607)(528,608)(529,609)(530,610)(531,611)(532,612)(533,613)(534,614)(535,615)(536,616)(537,617)(538,618)(539,619)(540,620)(541,621)(542,622)(543,623)(544,624)(545,625)(546,626)(547,627)(548,628)(549,629)(550,630)(551,631)(552,632)(553,633)(554,634)(555,635)(556,636)(557,637)(558,638)(559,639)(560,640);;
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)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 71, 76)( 72, 80)( 73, 79)( 74, 78)( 75, 77)( 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)(201,221)(202,225)(203,224)(204,223)(205,222)(206,226)(207,230)(208,229)(209,228)(210,227)(211,231)(212,235)(213,234)(214,233)(215,232)(216,236)(217,240)(218,239)(219,238)(220,237)(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)(442,445)(443,444)(447,450)(448,449)(452,455)(453,454)(457,460)(458,459)(461,466)(462,470)(463,469)(464,468)(465,467)(471,476)(472,480)(473,479)(474,478)(475,477)(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)(601,621)(602,625)(603,624)(604,623)(605,622)(606,626)(607,630)(608,629)(609,628)(610,627)(611,631)(612,635)(613,634)(614,633)(615,632)(616,636)(617,640)(618,639)(619,638)(620,637);;
s2 := ( 1,163)( 2,162)( 3,161)( 4,165)( 5,164)( 6,168)( 7,167)( 8,166)( 9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)( 16,178)( 17,177)( 18,176)( 19,180)( 20,179)( 21,188)( 22,187)( 23,186)( 24,190)( 25,189)( 26,183)( 27,182)( 28,181)( 29,185)( 30,184)( 31,198)( 32,197)( 33,196)( 34,200)( 35,199)( 36,193)( 37,192)( 38,191)( 39,195)( 40,194)( 41,203)( 42,202)( 43,201)( 44,205)( 45,204)( 46,208)( 47,207)( 48,206)( 49,210)( 50,209)( 51,213)( 52,212)( 53,211)( 54,215)( 55,214)( 56,218)( 57,217)( 58,216)( 59,220)( 60,219)( 61,228)( 62,227)( 63,226)( 64,230)( 65,229)( 66,223)( 67,222)( 68,221)( 69,225)( 70,224)( 71,238)( 72,237)( 73,236)( 74,240)( 75,239)( 76,233)( 77,232)( 78,231)( 79,235)( 80,234)( 81,243)( 82,242)( 83,241)( 84,245)( 85,244)( 86,248)( 87,247)( 88,246)( 89,250)( 90,249)( 91,253)( 92,252)( 93,251)( 94,255)( 95,254)( 96,258)( 97,257)( 98,256)( 99,260)(100,259)(101,268)(102,267)(103,266)(104,270)(105,269)(106,263)(107,262)(108,261)(109,265)(110,264)(111,278)(112,277)(113,276)(114,280)(115,279)(116,273)(117,272)(118,271)(119,275)(120,274)(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)(128,286)(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)(136,298)(137,297)(138,296)(139,300)(140,299)(141,308)(142,307)(143,306)(144,310)(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)(152,317)(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)(160,314)(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)(328,486)(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)(336,498)(337,497)(338,496)(339,500)(340,499)(341,508)(342,507)(343,506)(344,510)(345,509)(346,503)(347,502)(348,501)(349,505)(350,504)(351,518)(352,517)(353,516)(354,520)(355,519)(356,513)(357,512)(358,511)(359,515)(360,514)(361,523)(362,522)(363,521)(364,525)(365,524)(366,528)(367,527)(368,526)(369,530)(370,529)(371,533)(372,532)(373,531)(374,535)(375,534)(376,538)(377,537)(378,536)(379,540)(380,539)(381,548)(382,547)(383,546)(384,550)(385,549)(386,543)(387,542)(388,541)(389,545)(390,544)(391,558)(392,557)(393,556)(394,560)(395,559)(396,553)(397,552)(398,551)(399,555)(400,554)(401,563)(402,562)(403,561)(404,565)(405,564)(406,568)(407,567)(408,566)(409,570)(410,569)(411,573)(412,572)(413,571)(414,575)(415,574)(416,578)(417,577)(418,576)(419,580)(420,579)(421,588)(422,587)(423,586)(424,590)(425,589)(426,583)(427,582)(428,581)(429,585)(430,584)(431,598)(432,597)(433,596)(434,600)(435,599)(436,593)(437,592)(438,591)(439,595)(440,594)(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)(448,606)(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)(456,618)(457,617)(458,616)(459,620)(460,619)(461,628)(462,627)(463,626)(464,630)(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)(472,637)(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)(480,634);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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*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)( 41,121)( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)( 49,129)( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)( 57,137)( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)( 64,144)( 65,145)( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)( 73,153)( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)(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)(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)(209,289)(210,290)(211,291)(212,292)(213,293)(214,294)(215,295)(216,296)(217,297)(218,298)(219,299)(220,300)(221,301)(222,302)(223,303)(224,304)(225,305)(226,306)(227,307)(228,308)(229,309)(230,310)(231,311)(232,312)(233,313)(234,314)(235,315)(236,316)(237,317)(238,318)(239,319)(240,320)(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)(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)(368,448)(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)(376,456)(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)(384,464)(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)(392,472)(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)(400,480)(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)(521,601)(522,602)(523,603)(524,604)(525,605)(526,606)(527,607)(528,608)(529,609)(530,610)(531,611)(532,612)(533,613)(534,614)(535,615)(536,616)(537,617)(538,618)(539,619)(540,620)(541,621)(542,622)(543,623)(544,624)(545,625)(546,626)(547,627)(548,628)(549,629)(550,630)(551,631)(552,632)(553,633)(554,634)(555,635)(556,636)(557,637)(558,638)(559,639)(560,640);
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)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 71, 76)( 72, 80)( 73, 79)( 74, 78)( 75, 77)( 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)(201,221)(202,225)(203,224)(204,223)(205,222)(206,226)(207,230)(208,229)(209,228)(210,227)(211,231)(212,235)(213,234)(214,233)(215,232)(216,236)(217,240)(218,239)(219,238)(220,237)(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)(442,445)(443,444)(447,450)(448,449)(452,455)(453,454)(457,460)(458,459)(461,466)(462,470)(463,469)(464,468)(465,467)(471,476)(472,480)(473,479)(474,478)(475,477)(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)(601,621)(602,625)(603,624)(604,623)(605,622)(606,626)(607,630)(608,629)(609,628)(610,627)(611,631)(612,635)(613,634)(614,633)(615,632)(616,636)(617,640)(618,639)(619,638)(620,637);
s2 := Sym(640)!( 1,163)( 2,162)( 3,161)( 4,165)( 5,164)( 6,168)( 7,167)( 8,166)( 9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)( 16,178)( 17,177)( 18,176)( 19,180)( 20,179)( 21,188)( 22,187)( 23,186)( 24,190)( 25,189)( 26,183)( 27,182)( 28,181)( 29,185)( 30,184)( 31,198)( 32,197)( 33,196)( 34,200)( 35,199)( 36,193)( 37,192)( 38,191)( 39,195)( 40,194)( 41,203)( 42,202)( 43,201)( 44,205)( 45,204)( 46,208)( 47,207)( 48,206)( 49,210)( 50,209)( 51,213)( 52,212)( 53,211)( 54,215)( 55,214)( 56,218)( 57,217)( 58,216)( 59,220)( 60,219)( 61,228)( 62,227)( 63,226)( 64,230)( 65,229)( 66,223)( 67,222)( 68,221)( 69,225)( 70,224)( 71,238)( 72,237)( 73,236)( 74,240)( 75,239)( 76,233)( 77,232)( 78,231)( 79,235)( 80,234)( 81,243)( 82,242)( 83,241)( 84,245)( 85,244)( 86,248)( 87,247)( 88,246)( 89,250)( 90,249)( 91,253)( 92,252)( 93,251)( 94,255)( 95,254)( 96,258)( 97,257)( 98,256)( 99,260)(100,259)(101,268)(102,267)(103,266)(104,270)(105,269)(106,263)(107,262)(108,261)(109,265)(110,264)(111,278)(112,277)(113,276)(114,280)(115,279)(116,273)(117,272)(118,271)(119,275)(120,274)(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)(128,286)(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)(136,298)(137,297)(138,296)(139,300)(140,299)(141,308)(142,307)(143,306)(144,310)(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)(152,317)(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)(160,314)(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)(328,486)(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)(336,498)(337,497)(338,496)(339,500)(340,499)(341,508)(342,507)(343,506)(344,510)(345,509)(346,503)(347,502)(348,501)(349,505)(350,504)(351,518)(352,517)(353,516)(354,520)(355,519)(356,513)(357,512)(358,511)(359,515)(360,514)(361,523)(362,522)(363,521)(364,525)(365,524)(366,528)(367,527)(368,526)(369,530)(370,529)(371,533)(372,532)(373,531)(374,535)(375,534)(376,538)(377,537)(378,536)(379,540)(380,539)(381,548)(382,547)(383,546)(384,550)(385,549)(386,543)(387,542)(388,541)(389,545)(390,544)(391,558)(392,557)(393,556)(394,560)(395,559)(396,553)(397,552)(398,551)(399,555)(400,554)(401,563)(402,562)(403,561)(404,565)(405,564)(406,568)(407,567)(408,566)(409,570)(410,569)(411,573)(412,572)(413,571)(414,575)(415,574)(416,578)(417,577)(418,576)(419,580)(420,579)(421,588)(422,587)(423,586)(424,590)(425,589)(426,583)(427,582)(428,581)(429,585)(430,584)(431,598)(432,597)(433,596)(434,600)(435,599)(436,593)(437,592)(438,591)(439,595)(440,594)(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)(448,606)(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)(456,618)(457,617)(458,616)(459,620)(460,619)(461,628)(462,627)(463,626)(464,630)(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)(472,637)(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)(480,634);
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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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*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