Polytope of Type {8,8,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8,10}*1280a
if this polytope has a name.
Group : SmallGroup(1280,145169)
Rank : 4
Schlafli Type : {8,8,10}
Number of vertices, edges, etc : 8, 32, 40, 10
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 : {4,8,10}*640a, {8,4,10}*640b
4-fold quotients : {4,4,10}*320, {2,8,10}*320
5-fold quotients : {8,8,2}*256a
8-fold quotients : {2,4,10}*160, {4,2,10}*160
10-fold quotients : {4,8,2}*128a, {8,4,2}*128b
16-fold quotients : {4,2,5}*80, {2,2,10}*80
20-fold quotients : {4,4,2}*64, {2,8,2}*64
32-fold quotients : {2,2,5}*40
40-fold quotients : {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 := ( 1,161)( 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)( 21,186)( 22,187)( 23,188)( 24,189)( 25,190)( 26,181)( 27,182)( 28,183)( 29,184)( 30,185)( 31,196)( 32,197)( 33,198)( 34,199)( 35,200)( 36,191)( 37,192)( 38,193)( 39,194)( 40,195)( 41,206)( 42,207)( 43,208)( 44,209)( 45,210)( 46,201)( 47,202)( 48,203)( 49,204)( 50,205)( 51,216)( 52,217)( 53,218)( 54,219)( 55,220)( 56,211)( 57,212)( 58,213)( 59,214)( 60,215)( 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)(101,266)(102,267)(103,268)(104,269)(105,270)(106,261)(107,262)(108,263)(109,264)(110,265)(111,276)(112,277)(113,278)(114,279)(115,280)(116,271)(117,272)(118,273)(119,274)(120,275)(121,286)(122,287)(123,288)(124,289)(125,290)(126,281)(127,282)(128,283)(129,284)(130,285)(131,296)(132,297)(133,298)(134,299)(135,300)(136,291)(137,292)(138,293)(139,294)(140,295)(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)(341,506)(342,507)(343,508)(344,509)(345,510)(346,501)(347,502)(348,503)(349,504)(350,505)(351,516)(352,517)(353,518)(354,519)(355,520)(356,511)(357,512)(358,513)(359,514)(360,515)(361,526)(362,527)(363,528)(364,529)(365,530)(366,521)(367,522)(368,523)(369,524)(370,525)(371,536)(372,537)(373,538)(374,539)(375,540)(376,531)(377,532)(378,533)(379,534)(380,535)(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)(421,586)(422,587)(423,588)(424,589)(425,590)(426,581)(427,582)(428,583)(429,584)(430,585)(431,596)(432,597)(433,598)(434,599)(435,600)(436,591)(437,592)(438,593)(439,594)(440,595)(441,606)(442,607)(443,608)(444,609)(445,610)(446,601)(447,602)(448,603)(449,604)(450,605)(451,616)(452,617)(453,618)(454,619)(455,620)(456,611)(457,612)(458,613)(459,614)(460,615)(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 := ( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 41, 51)( 42, 52)( 43, 53)( 44, 54)( 45, 55)( 46, 56)( 47, 57)( 48, 58)( 49, 59)( 50, 60)( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)(101,106)(102,107)(103,108)(104,109)(105,110)(111,116)(112,117)(113,118)(114,119)(115,120)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140)(141,156)(142,157)(143,158)(144,159)(145,160)(146,151)(147,152)(148,153)(149,154)(150,155)(161,181)(162,182)(163,183)(164,184)(165,185)(166,186)(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)(173,193)(174,194)(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)(207,237)(208,238)(209,239)(210,240)(211,221)(212,222)(213,223)(214,224)(215,225)(216,226)(217,227)(218,228)(219,229)(220,230)(241,261)(242,262)(243,263)(244,264)(245,265)(246,266)(247,267)(248,268)(249,269)(250,270)(251,271)(252,272)(253,273)(254,274)(255,275)(256,276)(257,277)(258,278)(259,279)(260,280)(281,311)(282,312)(283,313)(284,314)(285,315)(286,316)(287,317)(288,318)(289,319)(290,320)(291,301)(292,302)(293,303)(294,304)(295,305)(296,306)(297,307)(298,308)(299,309)(300,310)(321,361)(322,362)(323,363)(324,364)(325,365)(326,366)(327,367)(328,368)(329,369)(330,370)(331,371)(332,372)(333,373)(334,374)(335,375)(336,376)(337,377)(338,378)(339,379)(340,380)(341,386)(342,387)(343,388)(344,389)(345,390)(346,381)(347,382)(348,383)(349,384)(350,385)(351,396)(352,397)(353,398)(354,399)(355,400)(356,391)(357,392)(358,393)(359,394)(360,395)(401,441)(402,442)(403,443)(404,444)(405,445)(406,446)(407,447)(408,448)(409,449)(410,450)(411,451)(412,452)(413,453)(414,454)(415,455)(416,456)(417,457)(418,458)(419,459)(420,460)(421,466)(422,467)(423,468)(424,469)(425,470)(426,461)(427,462)(428,463)(429,464)(430,465)(431,476)(432,477)(433,478)(434,479)(435,480)(436,471)(437,472)(438,473)(439,474)(440,475)(481,546)(482,547)(483,548)(484,549)(485,550)(486,541)(487,542)(488,543)(489,544)(490,545)(491,556)(492,557)(493,558)(494,559)(495,560)(496,551)(497,552)(498,553)(499,554)(500,555)(501,526)(502,527)(503,528)(504,529)(505,530)(506,521)(507,522)(508,523)(509,524)(510,525)(511,536)(512,537)(513,538)(514,539)(515,540)(516,531)(517,532)(518,533)(519,534)(520,535)(561,626)(562,627)(563,628)(564,629)(565,630)(566,621)(567,622)(568,623)(569,624)(570,625)(571,636)(572,637)(573,638)(574,639)(575,640)(576,631)(577,632)(578,633)(579,634)(580,635)(581,606)(582,607)(583,608)(584,609)(585,610)(586,601)(587,602)(588,603)(589,604)(590,605)(591,616)(592,617)(593,618)(594,619)(595,620)(596,611)(597,612)(598,613)(599,614)(600,615);;
s2 := ( 1,401)( 2,405)( 3,404)( 4,403)( 5,402)( 6,406)( 7,410)( 8,409)( 9,408)( 10,407)( 11,411)( 12,415)( 13,414)( 14,413)( 15,412)( 16,416)( 17,420)( 18,419)( 19,418)( 20,417)( 21,426)( 22,430)( 23,429)( 24,428)( 25,427)( 26,421)( 27,425)( 28,424)( 29,423)( 30,422)( 31,436)( 32,440)( 33,439)( 34,438)( 35,437)( 36,431)( 37,435)( 38,434)( 39,433)( 40,432)( 41,451)( 42,455)( 43,454)( 44,453)( 45,452)( 46,456)( 47,460)( 48,459)( 49,458)( 50,457)( 51,441)( 52,445)( 53,444)( 54,443)( 55,442)( 56,446)( 57,450)( 58,449)( 59,448)( 60,447)( 61,476)( 62,480)( 63,479)( 64,478)( 65,477)( 66,471)( 67,475)( 68,474)( 69,473)( 70,472)( 71,466)( 72,470)( 73,469)( 74,468)( 75,467)( 76,461)( 77,465)( 78,464)( 79,463)( 80,462)( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)( 88,329)( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,336)( 97,340)( 98,339)( 99,338)(100,337)(101,346)(102,350)(103,349)(104,348)(105,347)(106,341)(107,345)(108,344)(109,343)(110,342)(111,356)(112,360)(113,359)(114,358)(115,357)(116,351)(117,355)(118,354)(119,353)(120,352)(121,371)(122,375)(123,374)(124,373)(125,372)(126,376)(127,380)(128,379)(129,378)(130,377)(131,361)(132,365)(133,364)(134,363)(135,362)(136,366)(137,370)(138,369)(139,368)(140,367)(141,396)(142,400)(143,399)(144,398)(145,397)(146,391)(147,395)(148,394)(149,393)(150,392)(151,386)(152,390)(153,389)(154,388)(155,387)(156,381)(157,385)(158,384)(159,383)(160,382)(161,561)(162,565)(163,564)(164,563)(165,562)(166,566)(167,570)(168,569)(169,568)(170,567)(171,571)(172,575)(173,574)(174,573)(175,572)(176,576)(177,580)(178,579)(179,578)(180,577)(181,586)(182,590)(183,589)(184,588)(185,587)(186,581)(187,585)(188,584)(189,583)(190,582)(191,596)(192,600)(193,599)(194,598)(195,597)(196,591)(197,595)(198,594)(199,593)(200,592)(201,611)(202,615)(203,614)(204,613)(205,612)(206,616)(207,620)(208,619)(209,618)(210,617)(211,601)(212,605)(213,604)(214,603)(215,602)(216,606)(217,610)(218,609)(219,608)(220,607)(221,636)(222,640)(223,639)(224,638)(225,637)(226,631)(227,635)(228,634)(229,633)(230,632)(231,626)(232,630)(233,629)(234,628)(235,627)(236,621)(237,625)(238,624)(239,623)(240,622)(241,481)(242,485)(243,484)(244,483)(245,482)(246,486)(247,490)(248,489)(249,488)(250,487)(251,491)(252,495)(253,494)(254,493)(255,492)(256,496)(257,500)(258,499)(259,498)(260,497)(261,506)(262,510)(263,509)(264,508)(265,507)(266,501)(267,505)(268,504)(269,503)(270,502)(271,516)(272,520)(273,519)(274,518)(275,517)(276,511)(277,515)(278,514)(279,513)(280,512)(281,531)(282,535)(283,534)(284,533)(285,532)(286,536)(287,540)(288,539)(289,538)(290,537)(291,521)(292,525)(293,524)(294,523)(295,522)(296,526)(297,530)(298,529)(299,528)(300,527)(301,556)(302,560)(303,559)(304,558)(305,557)(306,551)(307,555)(308,554)(309,553)(310,552)(311,546)(312,550)(313,549)(314,548)(315,547)(316,541)(317,545)(318,544)(319,543)(320,542);;
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)( 41,123)( 42,122)( 43,121)( 44,125)( 45,124)( 46,128)( 47,127)( 48,126)( 49,130)( 50,129)( 51,133)( 52,132)( 53,131)( 54,135)( 55,134)( 56,138)( 57,137)( 58,136)( 59,140)( 60,139)( 61,143)( 62,142)( 63,141)( 64,145)( 65,144)( 66,148)( 67,147)( 68,146)( 69,150)( 70,149)( 71,153)( 72,152)( 73,151)( 74,155)( 75,154)( 76,158)( 77,157)( 78,156)( 79,160)( 80,159)(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)(201,283)(202,282)(203,281)(204,285)(205,284)(206,288)(207,287)(208,286)(209,290)(210,289)(211,293)(212,292)(213,291)(214,295)(215,294)(216,298)(217,297)(218,296)(219,300)(220,299)(221,303)(222,302)(223,301)(224,305)(225,304)(226,308)(227,307)(228,306)(229,310)(230,309)(231,313)(232,312)(233,311)(234,315)(235,314)(236,318)(237,317)(238,316)(239,320)(240,319)(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)(361,443)(362,442)(363,441)(364,445)(365,444)(366,448)(367,447)(368,446)(369,450)(370,449)(371,453)(372,452)(373,451)(374,455)(375,454)(376,458)(377,457)(378,456)(379,460)(380,459)(381,463)(382,462)(383,461)(384,465)(385,464)(386,468)(387,467)(388,466)(389,470)(390,469)(391,473)(392,472)(393,471)(394,475)(395,474)(396,478)(397,477)(398,476)(399,480)(400,479)(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)(521,603)(522,602)(523,601)(524,605)(525,604)(526,608)(527,607)(528,606)(529,610)(530,609)(531,613)(532,612)(533,611)(534,615)(535,614)(536,618)(537,617)(538,616)(539,620)(540,619)(541,623)(542,622)(543,621)(544,625)(545,624)(546,628)(547,627)(548,626)(549,630)(550,629)(551,633)(552,632)(553,631)(554,635)(555,634)(556,638)(557,637)(558,636)(559,640)(560,639);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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 ];;
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)( 21,186)( 22,187)( 23,188)( 24,189)( 25,190)( 26,181)( 27,182)( 28,183)( 29,184)( 30,185)( 31,196)( 32,197)( 33,198)( 34,199)( 35,200)( 36,191)( 37,192)( 38,193)( 39,194)( 40,195)( 41,206)( 42,207)( 43,208)( 44,209)( 45,210)( 46,201)( 47,202)( 48,203)( 49,204)( 50,205)( 51,216)( 52,217)( 53,218)( 54,219)( 55,220)( 56,211)( 57,212)( 58,213)( 59,214)( 60,215)( 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)(101,266)(102,267)(103,268)(104,269)(105,270)(106,261)(107,262)(108,263)(109,264)(110,265)(111,276)(112,277)(113,278)(114,279)(115,280)(116,271)(117,272)(118,273)(119,274)(120,275)(121,286)(122,287)(123,288)(124,289)(125,290)(126,281)(127,282)(128,283)(129,284)(130,285)(131,296)(132,297)(133,298)(134,299)(135,300)(136,291)(137,292)(138,293)(139,294)(140,295)(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)(341,506)(342,507)(343,508)(344,509)(345,510)(346,501)(347,502)(348,503)(349,504)(350,505)(351,516)(352,517)(353,518)(354,519)(355,520)(356,511)(357,512)(358,513)(359,514)(360,515)(361,526)(362,527)(363,528)(364,529)(365,530)(366,521)(367,522)(368,523)(369,524)(370,525)(371,536)(372,537)(373,538)(374,539)(375,540)(376,531)(377,532)(378,533)(379,534)(380,535)(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)(421,586)(422,587)(423,588)(424,589)(425,590)(426,581)(427,582)(428,583)(429,584)(430,585)(431,596)(432,597)(433,598)(434,599)(435,600)(436,591)(437,592)(438,593)(439,594)(440,595)(441,606)(442,607)(443,608)(444,609)(445,610)(446,601)(447,602)(448,603)(449,604)(450,605)(451,616)(452,617)(453,618)(454,619)(455,620)(456,611)(457,612)(458,613)(459,614)(460,615)(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)!( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 41, 51)( 42, 52)( 43, 53)( 44, 54)( 45, 55)( 46, 56)( 47, 57)( 48, 58)( 49, 59)( 50, 60)( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)(101,106)(102,107)(103,108)(104,109)(105,110)(111,116)(112,117)(113,118)(114,119)(115,120)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)(129,139)(130,140)(141,156)(142,157)(143,158)(144,159)(145,160)(146,151)(147,152)(148,153)(149,154)(150,155)(161,181)(162,182)(163,183)(164,184)(165,185)(166,186)(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)(173,193)(174,194)(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)(207,237)(208,238)(209,239)(210,240)(211,221)(212,222)(213,223)(214,224)(215,225)(216,226)(217,227)(218,228)(219,229)(220,230)(241,261)(242,262)(243,263)(244,264)(245,265)(246,266)(247,267)(248,268)(249,269)(250,270)(251,271)(252,272)(253,273)(254,274)(255,275)(256,276)(257,277)(258,278)(259,279)(260,280)(281,311)(282,312)(283,313)(284,314)(285,315)(286,316)(287,317)(288,318)(289,319)(290,320)(291,301)(292,302)(293,303)(294,304)(295,305)(296,306)(297,307)(298,308)(299,309)(300,310)(321,361)(322,362)(323,363)(324,364)(325,365)(326,366)(327,367)(328,368)(329,369)(330,370)(331,371)(332,372)(333,373)(334,374)(335,375)(336,376)(337,377)(338,378)(339,379)(340,380)(341,386)(342,387)(343,388)(344,389)(345,390)(346,381)(347,382)(348,383)(349,384)(350,385)(351,396)(352,397)(353,398)(354,399)(355,400)(356,391)(357,392)(358,393)(359,394)(360,395)(401,441)(402,442)(403,443)(404,444)(405,445)(406,446)(407,447)(408,448)(409,449)(410,450)(411,451)(412,452)(413,453)(414,454)(415,455)(416,456)(417,457)(418,458)(419,459)(420,460)(421,466)(422,467)(423,468)(424,469)(425,470)(426,461)(427,462)(428,463)(429,464)(430,465)(431,476)(432,477)(433,478)(434,479)(435,480)(436,471)(437,472)(438,473)(439,474)(440,475)(481,546)(482,547)(483,548)(484,549)(485,550)(486,541)(487,542)(488,543)(489,544)(490,545)(491,556)(492,557)(493,558)(494,559)(495,560)(496,551)(497,552)(498,553)(499,554)(500,555)(501,526)(502,527)(503,528)(504,529)(505,530)(506,521)(507,522)(508,523)(509,524)(510,525)(511,536)(512,537)(513,538)(514,539)(515,540)(516,531)(517,532)(518,533)(519,534)(520,535)(561,626)(562,627)(563,628)(564,629)(565,630)(566,621)(567,622)(568,623)(569,624)(570,625)(571,636)(572,637)(573,638)(574,639)(575,640)(576,631)(577,632)(578,633)(579,634)(580,635)(581,606)(582,607)(583,608)(584,609)(585,610)(586,601)(587,602)(588,603)(589,604)(590,605)(591,616)(592,617)(593,618)(594,619)(595,620)(596,611)(597,612)(598,613)(599,614)(600,615);
s2 := Sym(640)!( 1,401)( 2,405)( 3,404)( 4,403)( 5,402)( 6,406)( 7,410)( 8,409)( 9,408)( 10,407)( 11,411)( 12,415)( 13,414)( 14,413)( 15,412)( 16,416)( 17,420)( 18,419)( 19,418)( 20,417)( 21,426)( 22,430)( 23,429)( 24,428)( 25,427)( 26,421)( 27,425)( 28,424)( 29,423)( 30,422)( 31,436)( 32,440)( 33,439)( 34,438)( 35,437)( 36,431)( 37,435)( 38,434)( 39,433)( 40,432)( 41,451)( 42,455)( 43,454)( 44,453)( 45,452)( 46,456)( 47,460)( 48,459)( 49,458)( 50,457)( 51,441)( 52,445)( 53,444)( 54,443)( 55,442)( 56,446)( 57,450)( 58,449)( 59,448)( 60,447)( 61,476)( 62,480)( 63,479)( 64,478)( 65,477)( 66,471)( 67,475)( 68,474)( 69,473)( 70,472)( 71,466)( 72,470)( 73,469)( 74,468)( 75,467)( 76,461)( 77,465)( 78,464)( 79,463)( 80,462)( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)( 88,329)( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,336)( 97,340)( 98,339)( 99,338)(100,337)(101,346)(102,350)(103,349)(104,348)(105,347)(106,341)(107,345)(108,344)(109,343)(110,342)(111,356)(112,360)(113,359)(114,358)(115,357)(116,351)(117,355)(118,354)(119,353)(120,352)(121,371)(122,375)(123,374)(124,373)(125,372)(126,376)(127,380)(128,379)(129,378)(130,377)(131,361)(132,365)(133,364)(134,363)(135,362)(136,366)(137,370)(138,369)(139,368)(140,367)(141,396)(142,400)(143,399)(144,398)(145,397)(146,391)(147,395)(148,394)(149,393)(150,392)(151,386)(152,390)(153,389)(154,388)(155,387)(156,381)(157,385)(158,384)(159,383)(160,382)(161,561)(162,565)(163,564)(164,563)(165,562)(166,566)(167,570)(168,569)(169,568)(170,567)(171,571)(172,575)(173,574)(174,573)(175,572)(176,576)(177,580)(178,579)(179,578)(180,577)(181,586)(182,590)(183,589)(184,588)(185,587)(186,581)(187,585)(188,584)(189,583)(190,582)(191,596)(192,600)(193,599)(194,598)(195,597)(196,591)(197,595)(198,594)(199,593)(200,592)(201,611)(202,615)(203,614)(204,613)(205,612)(206,616)(207,620)(208,619)(209,618)(210,617)(211,601)(212,605)(213,604)(214,603)(215,602)(216,606)(217,610)(218,609)(219,608)(220,607)(221,636)(222,640)(223,639)(224,638)(225,637)(226,631)(227,635)(228,634)(229,633)(230,632)(231,626)(232,630)(233,629)(234,628)(235,627)(236,621)(237,625)(238,624)(239,623)(240,622)(241,481)(242,485)(243,484)(244,483)(245,482)(246,486)(247,490)(248,489)(249,488)(250,487)(251,491)(252,495)(253,494)(254,493)(255,492)(256,496)(257,500)(258,499)(259,498)(260,497)(261,506)(262,510)(263,509)(264,508)(265,507)(266,501)(267,505)(268,504)(269,503)(270,502)(271,516)(272,520)(273,519)(274,518)(275,517)(276,511)(277,515)(278,514)(279,513)(280,512)(281,531)(282,535)(283,534)(284,533)(285,532)(286,536)(287,540)(288,539)(289,538)(290,537)(291,521)(292,525)(293,524)(294,523)(295,522)(296,526)(297,530)(298,529)(299,528)(300,527)(301,556)(302,560)(303,559)(304,558)(305,557)(306,551)(307,555)(308,554)(309,553)(310,552)(311,546)(312,550)(313,549)(314,548)(315,547)(316,541)(317,545)(318,544)(319,543)(320,542);
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)( 41,123)( 42,122)( 43,121)( 44,125)( 45,124)( 46,128)( 47,127)( 48,126)( 49,130)( 50,129)( 51,133)( 52,132)( 53,131)( 54,135)( 55,134)( 56,138)( 57,137)( 58,136)( 59,140)( 60,139)( 61,143)( 62,142)( 63,141)( 64,145)( 65,144)( 66,148)( 67,147)( 68,146)( 69,150)( 70,149)( 71,153)( 72,152)( 73,151)( 74,155)( 75,154)( 76,158)( 77,157)( 78,156)( 79,160)( 80,159)(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)(201,283)(202,282)(203,281)(204,285)(205,284)(206,288)(207,287)(208,286)(209,290)(210,289)(211,293)(212,292)(213,291)(214,295)(215,294)(216,298)(217,297)(218,296)(219,300)(220,299)(221,303)(222,302)(223,301)(224,305)(225,304)(226,308)(227,307)(228,306)(229,310)(230,309)(231,313)(232,312)(233,311)(234,315)(235,314)(236,318)(237,317)(238,316)(239,320)(240,319)(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)(361,443)(362,442)(363,441)(364,445)(365,444)(366,448)(367,447)(368,446)(369,450)(370,449)(371,453)(372,452)(373,451)(374,455)(375,454)(376,458)(377,457)(378,456)(379,460)(380,459)(381,463)(382,462)(383,461)(384,465)(385,464)(386,468)(387,467)(388,466)(389,470)(390,469)(391,473)(392,472)(393,471)(394,475)(395,474)(396,478)(397,477)(398,476)(399,480)(400,479)(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)(521,603)(522,602)(523,601)(524,605)(525,604)(526,608)(527,607)(528,606)(529,610)(530,609)(531,613)(532,612)(533,611)(534,615)(535,614)(536,618)(537,617)(538,616)(539,620)(540,619)(541,623)(542,622)(543,621)(544,625)(545,624)(546,628)(547,627)(548,626)(549,630)(550,629)(551,633)(552,632)(553,631)(554,635)(555,634)(556,638)(557,637)(558,636)(559,640)(560,639);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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 >;
References : None.
to this polytope