Polytope of Type {4,4,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,10,4}*1280
Also Known As : {{4,4|2},{4,10|2},{10,4|2}}. if this polytope has another name.
Group : SmallGroup(1280,364857)
Rank : 5
Schlafli Type : {4,4,10,4}
Number of vertices, edges, etc : 4, 8, 20, 20, 4
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 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 : {4,4,10,2}*640, {2,4,10,4}*640, {4,2,10,4}*640
4-fold quotients : {2,2,10,4}*320, {2,4,10,2}*320, {4,2,10,2}*320
5-fold quotients : {4,4,2,4}*256
8-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
10-fold quotients : {4,4,2,2}*128, {2,4,2,4}*128, {4,2,2,4}*128
16-fold quotients : {2,2,5,2}*80
20-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64, {4,2,2,2}*64
40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
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)(161,566)(162,567)(163,568)(164,569)(165,570)(166,561)(167,562)(168,563)(169,564)(170,565)(171,576)(172,577)(173,578)(174,579)(175,580)(176,571)(177,572)(178,573)(179,574)(180,575)(181,586)(182,587)(183,588)(184,589)(185,590)(186,581)(187,582)(188,583)(189,584)(190,585)(191,596)(192,597)(193,598)(194,599)(195,600)(196,591)(197,592)(198,593)(199,594)(200,595)(201,606)(202,607)(203,608)(204,609)(205,610)(206,601)(207,602)(208,603)(209,604)(210,605)(211,616)(212,617)(213,618)(214,619)(215,620)(216,611)(217,612)(218,613)(219,614)(220,615)(221,626)(222,627)(223,628)(224,629)(225,630)(226,621)(227,622)(228,623)(229,624)(230,625)(231,636)(232,637)(233,638)(234,639)(235,640)(236,631)(237,632)(238,633)(239,634)(240,635)(241,486)(242,487)(243,488)(244,489)(245,490)(246,481)(247,482)(248,483)(249,484)(250,485)(251,496)(252,497)(253,498)(254,499)(255,500)(256,491)(257,492)(258,493)(259,494)(260,495)(261,506)(262,507)(263,508)(264,509)(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,516)(272,517)(273,518)(274,519)(275,520)(276,511)(277,512)(278,513)(279,514)(280,515)(281,526)(282,527)(283,528)(284,529)(285,530)(286,521)(287,522)(288,523)(289,524)(290,525)(291,536)(292,537)(293,538)(294,539)(295,540)(296,531)(297,532)(298,533)(299,534)(300,535)(301,546)(302,547)(303,548)(304,549)(305,550)(306,541)(307,542)(308,543)(309,544)(310,545)(311,556)(312,557)(313,558)(314,559)(315,560)(316,551)(317,552)(318,553)(319,554)(320,555);;
s1 := (161,171)(162,172)(163,173)(164,174)(165,175)(166,176)(167,177)(168,178)(169,179)(170,180)(181,191)(182,192)(183,193)(184,194)(185,195)(186,196)(187,197)(188,198)(189,199)(190,200)(201,211)(202,212)(203,213)(204,214)(205,215)(206,216)(207,217)(208,218)(209,219)(210,220)(221,231)(222,232)(223,233)(224,234)(225,235)(226,236)(227,237)(228,238)(229,239)(230,240)(241,251)(242,252)(243,253)(244,254)(245,255)(246,256)(247,257)(248,258)(249,259)(250,260)(261,271)(262,272)(263,273)(264,274)(265,275)(266,276)(267,277)(268,278)(269,279)(270,280)(281,291)(282,292)(283,293)(284,294)(285,295)(286,296)(287,297)(288,298)(289,299)(290,300)(301,311)(302,312)(303,313)(304,314)(305,315)(306,316)(307,317)(308,318)(309,319)(310,320)(321,341)(322,342)(323,343)(324,344)(325,345)(326,346)(327,347)(328,348)(329,349)(330,350)(331,351)(332,352)(333,353)(334,354)(335,355)(336,356)(337,357)(338,358)(339,359)(340,360)(361,381)(362,382)(363,383)(364,384)(365,385)(366,386)(367,387)(368,388)(369,389)(370,390)(371,391)(372,392)(373,393)(374,394)(375,395)(376,396)(377,397)(378,398)(379,399)(380,400)(401,421)(402,422)(403,423)(404,424)(405,425)(406,426)(407,427)(408,428)(409,429)(410,430)(411,431)(412,432)(413,433)(414,434)(415,435)(416,436)(417,437)(418,438)(419,439)(420,440)(441,461)(442,462)(443,463)(444,464)(445,465)(446,466)(447,467)(448,468)(449,469)(450,470)(451,471)(452,472)(453,473)(454,474)(455,475)(456,476)(457,477)(458,478)(459,479)(460,480)(481,511)(482,512)(483,513)(484,514)(485,515)(486,516)(487,517)(488,518)(489,519)(490,520)(491,501)(492,502)(493,503)(494,504)(495,505)(496,506)(497,507)(498,508)(499,509)(500,510)(521,551)(522,552)(523,553)(524,554)(525,555)(526,556)(527,557)(528,558)(529,559)(530,560)(531,541)(532,542)(533,543)(534,544)(535,545)(536,546)(537,547)(538,548)(539,549)(540,550)(561,591)(562,592)(563,593)(564,594)(565,595)(566,596)(567,597)(568,598)(569,599)(570,600)(571,581)(572,582)(573,583)(574,584)(575,585)(576,586)(577,587)(578,588)(579,589)(580,590)(601,631)(602,632)(603,633)(604,634)(605,635)(606,636)(607,637)(608,638)(609,639)(610,640)(611,621)(612,622)(613,623)(614,624)(615,625)(616,626)(617,627)(618,628)(619,629)(620,630);;
s2 := ( 1,201)( 2,205)( 3,204)( 4,203)( 5,202)( 6,206)( 7,210)( 8,209)( 9,208)( 10,207)( 11,211)( 12,215)( 13,214)( 14,213)( 15,212)( 16,216)( 17,220)( 18,219)( 19,218)( 20,217)( 21,221)( 22,225)( 23,224)( 24,223)( 25,222)( 26,226)( 27,230)( 28,229)( 29,228)( 30,227)( 31,231)( 32,235)( 33,234)( 34,233)( 35,232)( 36,236)( 37,240)( 38,239)( 39,238)( 40,237)( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)( 48,169)( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)( 64,183)( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)( 72,195)( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)( 81,286)( 82,290)( 83,289)( 84,288)( 85,287)( 86,281)( 87,285)( 88,284)( 89,283)( 90,282)( 91,296)( 92,300)( 93,299)( 94,298)( 95,297)( 96,291)( 97,295)( 98,294)( 99,293)(100,292)(101,306)(102,310)(103,309)(104,308)(105,307)(106,301)(107,305)(108,304)(109,303)(110,302)(111,316)(112,320)(113,319)(114,318)(115,317)(116,311)(117,315)(118,314)(119,313)(120,312)(121,246)(122,250)(123,249)(124,248)(125,247)(126,241)(127,245)(128,244)(129,243)(130,242)(131,256)(132,260)(133,259)(134,258)(135,257)(136,251)(137,255)(138,254)(139,253)(140,252)(141,266)(142,270)(143,269)(144,268)(145,267)(146,261)(147,265)(148,264)(149,263)(150,262)(151,276)(152,280)(153,279)(154,278)(155,277)(156,271)(157,275)(158,274)(159,273)(160,272)(321,521)(322,525)(323,524)(324,523)(325,522)(326,526)(327,530)(328,529)(329,528)(330,527)(331,531)(332,535)(333,534)(334,533)(335,532)(336,536)(337,540)(338,539)(339,538)(340,537)(341,541)(342,545)(343,544)(344,543)(345,542)(346,546)(347,550)(348,549)(349,548)(350,547)(351,551)(352,555)(353,554)(354,553)(355,552)(356,556)(357,560)(358,559)(359,558)(360,557)(361,481)(362,485)(363,484)(364,483)(365,482)(366,486)(367,490)(368,489)(369,488)(370,487)(371,491)(372,495)(373,494)(374,493)(375,492)(376,496)(377,500)(378,499)(379,498)(380,497)(381,501)(382,505)(383,504)(384,503)(385,502)(386,506)(387,510)(388,509)(389,508)(390,507)(391,511)(392,515)(393,514)(394,513)(395,512)(396,516)(397,520)(398,519)(399,518)(400,517)(401,606)(402,610)(403,609)(404,608)(405,607)(406,601)(407,605)(408,604)(409,603)(410,602)(411,616)(412,620)(413,619)(414,618)(415,617)(416,611)(417,615)(418,614)(419,613)(420,612)(421,626)(422,630)(423,629)(424,628)(425,627)(426,621)(427,625)(428,624)(429,623)(430,622)(431,636)(432,640)(433,639)(434,638)(435,637)(436,631)(437,635)(438,634)(439,633)(440,632)(441,566)(442,570)(443,569)(444,568)(445,567)(446,561)(447,565)(448,564)(449,563)(450,562)(451,576)(452,580)(453,579)(454,578)(455,577)(456,571)(457,575)(458,574)(459,573)(460,572)(461,586)(462,590)(463,589)(464,588)(465,587)(466,581)(467,585)(468,584)(469,583)(470,582)(471,596)(472,600)(473,599)(474,598)(475,597)(476,591)(477,595)(478,594)(479,593)(480,592);;
s3 := ( 1, 43)( 2, 42)( 3, 41)( 4, 45)( 5, 44)( 6, 48)( 7, 47)( 8, 46)( 9, 50)( 10, 49)( 11, 53)( 12, 52)( 13, 51)( 14, 55)( 15, 54)( 16, 58)( 17, 57)( 18, 56)( 19, 60)( 20, 59)( 21, 63)( 22, 62)( 23, 61)( 24, 65)( 25, 64)( 26, 68)( 27, 67)( 28, 66)( 29, 70)( 30, 69)( 31, 73)( 32, 72)( 33, 71)( 34, 75)( 35, 74)( 36, 78)( 37, 77)( 38, 76)( 39, 80)( 40, 79)( 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)(101,143)(102,142)(103,141)(104,145)(105,144)(106,148)(107,147)(108,146)(109,150)(110,149)(111,153)(112,152)(113,151)(114,155)(115,154)(116,158)(117,157)(118,156)(119,160)(120,159)(161,203)(162,202)(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,213)(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)(179,220)(180,219)(181,223)(182,222)(183,221)(184,225)(185,224)(186,228)(187,227)(188,226)(189,230)(190,229)(191,233)(192,232)(193,231)(194,235)(195,234)(196,238)(197,237)(198,236)(199,240)(200,239)(241,283)(242,282)(243,281)(244,285)(245,284)(246,288)(247,287)(248,286)(249,290)(250,289)(251,293)(252,292)(253,291)(254,295)(255,294)(256,298)(257,297)(258,296)(259,300)(260,299)(261,303)(262,302)(263,301)(264,305)(265,304)(266,308)(267,307)(268,306)(269,310)(270,309)(271,313)(272,312)(273,311)(274,315)(275,314)(276,318)(277,317)(278,316)(279,320)(280,319)(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)(341,383)(342,382)(343,381)(344,385)(345,384)(346,388)(347,387)(348,386)(349,390)(350,389)(351,393)(352,392)(353,391)(354,395)(355,394)(356,398)(357,397)(358,396)(359,400)(360,399)(401,443)(402,442)(403,441)(404,445)(405,444)(406,448)(407,447)(408,446)(409,450)(410,449)(411,453)(412,452)(413,451)(414,455)(415,454)(416,458)(417,457)(418,456)(419,460)(420,459)(421,463)(422,462)(423,461)(424,465)(425,464)(426,468)(427,467)(428,466)(429,470)(430,469)(431,473)(432,472)(433,471)(434,475)(435,474)(436,478)(437,477)(438,476)(439,480)(440,479)(481,523)(482,522)(483,521)(484,525)(485,524)(486,528)(487,527)(488,526)(489,530)(490,529)(491,533)(492,532)(493,531)(494,535)(495,534)(496,538)(497,537)(498,536)(499,540)(500,539)(501,543)(502,542)(503,541)(504,545)(505,544)(506,548)(507,547)(508,546)(509,550)(510,549)(511,553)(512,552)(513,551)(514,555)(515,554)(516,558)(517,557)(518,556)(519,560)(520,559)(561,603)(562,602)(563,601)(564,605)(565,604)(566,608)(567,607)(568,606)(569,610)(570,609)(571,613)(572,612)(573,611)(574,615)(575,614)(576,618)(577,617)(578,616)(579,620)(580,619)(581,623)(582,622)(583,621)(584,625)(585,624)(586,628)(587,627)(588,626)(589,630)(590,629)(591,633)(592,632)(593,631)(594,635)(595,634)(596,638)(597,637)(598,636)(599,640)(600,639);;
s4 := ( 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,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)(161,566)(162,567)(163,568)(164,569)(165,570)(166,561)(167,562)(168,563)(169,564)(170,565)(171,576)(172,577)(173,578)(174,579)(175,580)(176,571)(177,572)(178,573)(179,574)(180,575)(181,586)(182,587)(183,588)(184,589)(185,590)(186,581)(187,582)(188,583)(189,584)(190,585)(191,596)(192,597)(193,598)(194,599)(195,600)(196,591)(197,592)(198,593)(199,594)(200,595)(201,606)(202,607)(203,608)(204,609)(205,610)(206,601)(207,602)(208,603)(209,604)(210,605)(211,616)(212,617)(213,618)(214,619)(215,620)(216,611)(217,612)(218,613)(219,614)(220,615)(221,626)(222,627)(223,628)(224,629)(225,630)(226,621)(227,622)(228,623)(229,624)(230,625)(231,636)(232,637)(233,638)(234,639)(235,640)(236,631)(237,632)(238,633)(239,634)(240,635)(241,486)(242,487)(243,488)(244,489)(245,490)(246,481)(247,482)(248,483)(249,484)(250,485)(251,496)(252,497)(253,498)(254,499)(255,500)(256,491)(257,492)(258,493)(259,494)(260,495)(261,506)(262,507)(263,508)(264,509)(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,516)(272,517)(273,518)(274,519)(275,520)(276,511)(277,512)(278,513)(279,514)(280,515)(281,526)(282,527)(283,528)(284,529)(285,530)(286,521)(287,522)(288,523)(289,524)(290,525)(291,536)(292,537)(293,538)(294,539)(295,540)(296,531)(297,532)(298,533)(299,534)(300,535)(301,546)(302,547)(303,548)(304,549)(305,550)(306,541)(307,542)(308,543)(309,544)(310,545)(311,556)(312,557)(313,558)(314,559)(315,560)(316,551)(317,552)(318,553)(319,554)(320,555);
s1 := Sym(640)!(161,171)(162,172)(163,173)(164,174)(165,175)(166,176)(167,177)(168,178)(169,179)(170,180)(181,191)(182,192)(183,193)(184,194)(185,195)(186,196)(187,197)(188,198)(189,199)(190,200)(201,211)(202,212)(203,213)(204,214)(205,215)(206,216)(207,217)(208,218)(209,219)(210,220)(221,231)(222,232)(223,233)(224,234)(225,235)(226,236)(227,237)(228,238)(229,239)(230,240)(241,251)(242,252)(243,253)(244,254)(245,255)(246,256)(247,257)(248,258)(249,259)(250,260)(261,271)(262,272)(263,273)(264,274)(265,275)(266,276)(267,277)(268,278)(269,279)(270,280)(281,291)(282,292)(283,293)(284,294)(285,295)(286,296)(287,297)(288,298)(289,299)(290,300)(301,311)(302,312)(303,313)(304,314)(305,315)(306,316)(307,317)(308,318)(309,319)(310,320)(321,341)(322,342)(323,343)(324,344)(325,345)(326,346)(327,347)(328,348)(329,349)(330,350)(331,351)(332,352)(333,353)(334,354)(335,355)(336,356)(337,357)(338,358)(339,359)(340,360)(361,381)(362,382)(363,383)(364,384)(365,385)(366,386)(367,387)(368,388)(369,389)(370,390)(371,391)(372,392)(373,393)(374,394)(375,395)(376,396)(377,397)(378,398)(379,399)(380,400)(401,421)(402,422)(403,423)(404,424)(405,425)(406,426)(407,427)(408,428)(409,429)(410,430)(411,431)(412,432)(413,433)(414,434)(415,435)(416,436)(417,437)(418,438)(419,439)(420,440)(441,461)(442,462)(443,463)(444,464)(445,465)(446,466)(447,467)(448,468)(449,469)(450,470)(451,471)(452,472)(453,473)(454,474)(455,475)(456,476)(457,477)(458,478)(459,479)(460,480)(481,511)(482,512)(483,513)(484,514)(485,515)(486,516)(487,517)(488,518)(489,519)(490,520)(491,501)(492,502)(493,503)(494,504)(495,505)(496,506)(497,507)(498,508)(499,509)(500,510)(521,551)(522,552)(523,553)(524,554)(525,555)(526,556)(527,557)(528,558)(529,559)(530,560)(531,541)(532,542)(533,543)(534,544)(535,545)(536,546)(537,547)(538,548)(539,549)(540,550)(561,591)(562,592)(563,593)(564,594)(565,595)(566,596)(567,597)(568,598)(569,599)(570,600)(571,581)(572,582)(573,583)(574,584)(575,585)(576,586)(577,587)(578,588)(579,589)(580,590)(601,631)(602,632)(603,633)(604,634)(605,635)(606,636)(607,637)(608,638)(609,639)(610,640)(611,621)(612,622)(613,623)(614,624)(615,625)(616,626)(617,627)(618,628)(619,629)(620,630);
s2 := Sym(640)!( 1,201)( 2,205)( 3,204)( 4,203)( 5,202)( 6,206)( 7,210)( 8,209)( 9,208)( 10,207)( 11,211)( 12,215)( 13,214)( 14,213)( 15,212)( 16,216)( 17,220)( 18,219)( 19,218)( 20,217)( 21,221)( 22,225)( 23,224)( 24,223)( 25,222)( 26,226)( 27,230)( 28,229)( 29,228)( 30,227)( 31,231)( 32,235)( 33,234)( 34,233)( 35,232)( 36,236)( 37,240)( 38,239)( 39,238)( 40,237)( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)( 48,169)( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)( 64,183)( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)( 72,195)( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)( 81,286)( 82,290)( 83,289)( 84,288)( 85,287)( 86,281)( 87,285)( 88,284)( 89,283)( 90,282)( 91,296)( 92,300)( 93,299)( 94,298)( 95,297)( 96,291)( 97,295)( 98,294)( 99,293)(100,292)(101,306)(102,310)(103,309)(104,308)(105,307)(106,301)(107,305)(108,304)(109,303)(110,302)(111,316)(112,320)(113,319)(114,318)(115,317)(116,311)(117,315)(118,314)(119,313)(120,312)(121,246)(122,250)(123,249)(124,248)(125,247)(126,241)(127,245)(128,244)(129,243)(130,242)(131,256)(132,260)(133,259)(134,258)(135,257)(136,251)(137,255)(138,254)(139,253)(140,252)(141,266)(142,270)(143,269)(144,268)(145,267)(146,261)(147,265)(148,264)(149,263)(150,262)(151,276)(152,280)(153,279)(154,278)(155,277)(156,271)(157,275)(158,274)(159,273)(160,272)(321,521)(322,525)(323,524)(324,523)(325,522)(326,526)(327,530)(328,529)(329,528)(330,527)(331,531)(332,535)(333,534)(334,533)(335,532)(336,536)(337,540)(338,539)(339,538)(340,537)(341,541)(342,545)(343,544)(344,543)(345,542)(346,546)(347,550)(348,549)(349,548)(350,547)(351,551)(352,555)(353,554)(354,553)(355,552)(356,556)(357,560)(358,559)(359,558)(360,557)(361,481)(362,485)(363,484)(364,483)(365,482)(366,486)(367,490)(368,489)(369,488)(370,487)(371,491)(372,495)(373,494)(374,493)(375,492)(376,496)(377,500)(378,499)(379,498)(380,497)(381,501)(382,505)(383,504)(384,503)(385,502)(386,506)(387,510)(388,509)(389,508)(390,507)(391,511)(392,515)(393,514)(394,513)(395,512)(396,516)(397,520)(398,519)(399,518)(400,517)(401,606)(402,610)(403,609)(404,608)(405,607)(406,601)(407,605)(408,604)(409,603)(410,602)(411,616)(412,620)(413,619)(414,618)(415,617)(416,611)(417,615)(418,614)(419,613)(420,612)(421,626)(422,630)(423,629)(424,628)(425,627)(426,621)(427,625)(428,624)(429,623)(430,622)(431,636)(432,640)(433,639)(434,638)(435,637)(436,631)(437,635)(438,634)(439,633)(440,632)(441,566)(442,570)(443,569)(444,568)(445,567)(446,561)(447,565)(448,564)(449,563)(450,562)(451,576)(452,580)(453,579)(454,578)(455,577)(456,571)(457,575)(458,574)(459,573)(460,572)(461,586)(462,590)(463,589)(464,588)(465,587)(466,581)(467,585)(468,584)(469,583)(470,582)(471,596)(472,600)(473,599)(474,598)(475,597)(476,591)(477,595)(478,594)(479,593)(480,592);
s3 := Sym(640)!( 1, 43)( 2, 42)( 3, 41)( 4, 45)( 5, 44)( 6, 48)( 7, 47)( 8, 46)( 9, 50)( 10, 49)( 11, 53)( 12, 52)( 13, 51)( 14, 55)( 15, 54)( 16, 58)( 17, 57)( 18, 56)( 19, 60)( 20, 59)( 21, 63)( 22, 62)( 23, 61)( 24, 65)( 25, 64)( 26, 68)( 27, 67)( 28, 66)( 29, 70)( 30, 69)( 31, 73)( 32, 72)( 33, 71)( 34, 75)( 35, 74)( 36, 78)( 37, 77)( 38, 76)( 39, 80)( 40, 79)( 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)(101,143)(102,142)(103,141)(104,145)(105,144)(106,148)(107,147)(108,146)(109,150)(110,149)(111,153)(112,152)(113,151)(114,155)(115,154)(116,158)(117,157)(118,156)(119,160)(120,159)(161,203)(162,202)(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,213)(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)(179,220)(180,219)(181,223)(182,222)(183,221)(184,225)(185,224)(186,228)(187,227)(188,226)(189,230)(190,229)(191,233)(192,232)(193,231)(194,235)(195,234)(196,238)(197,237)(198,236)(199,240)(200,239)(241,283)(242,282)(243,281)(244,285)(245,284)(246,288)(247,287)(248,286)(249,290)(250,289)(251,293)(252,292)(253,291)(254,295)(255,294)(256,298)(257,297)(258,296)(259,300)(260,299)(261,303)(262,302)(263,301)(264,305)(265,304)(266,308)(267,307)(268,306)(269,310)(270,309)(271,313)(272,312)(273,311)(274,315)(275,314)(276,318)(277,317)(278,316)(279,320)(280,319)(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)(341,383)(342,382)(343,381)(344,385)(345,384)(346,388)(347,387)(348,386)(349,390)(350,389)(351,393)(352,392)(353,391)(354,395)(355,394)(356,398)(357,397)(358,396)(359,400)(360,399)(401,443)(402,442)(403,441)(404,445)(405,444)(406,448)(407,447)(408,446)(409,450)(410,449)(411,453)(412,452)(413,451)(414,455)(415,454)(416,458)(417,457)(418,456)(419,460)(420,459)(421,463)(422,462)(423,461)(424,465)(425,464)(426,468)(427,467)(428,466)(429,470)(430,469)(431,473)(432,472)(433,471)(434,475)(435,474)(436,478)(437,477)(438,476)(439,480)(440,479)(481,523)(482,522)(483,521)(484,525)(485,524)(486,528)(487,527)(488,526)(489,530)(490,529)(491,533)(492,532)(493,531)(494,535)(495,534)(496,538)(497,537)(498,536)(499,540)(500,539)(501,543)(502,542)(503,541)(504,545)(505,544)(506,548)(507,547)(508,546)(509,550)(510,549)(511,553)(512,552)(513,551)(514,555)(515,554)(516,558)(517,557)(518,556)(519,560)(520,559)(561,603)(562,602)(563,601)(564,605)(565,604)(566,608)(567,607)(568,606)(569,610)(570,609)(571,613)(572,612)(573,611)(574,615)(575,614)(576,618)(577,617)(578,616)(579,620)(580,619)(581,623)(582,622)(583,621)(584,625)(585,624)(586,628)(587,627)(588,626)(589,630)(590,629)(591,633)(592,632)(593,631)(594,635)(595,634)(596,638)(597,637)(598,636)(599,640)(600,639);
s4 := 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,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope