Polytope of Type {4,10,16} with group SmallGroup(1280,326216)

Overview

Group: SmallGroup(1280,326216)
Rank: 4
Schläfli Type: {4,10,16}
Vertices, edges, …: 4, 20, 80, 16
Order of s₀s₁s₂s₃: 80
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{4,10|2},{10,16|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

{4,2,16}*256

8-fold

10-fold

16-fold

{2,10,2}*80

20-fold

32-fold

{2,5,2}*40

40-fold

80-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References