Polytope of Type {40,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,4,4}*1280b
if this polytope has a name.
Group : SmallGroup(1280,200909)
Rank : 4
Schlafli Type : {40,4,4}
Number of vertices, edges, etc : 40, 80, 8, 4
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 : {20,4,4}*640, {40,4,2}*640b
4-fold quotients : {20,4,2}*320, {20,2,4}*320, {10,4,4}*320
5-fold quotients : {8,4,4}*256b
8-fold quotients : {20,2,2}*160, {10,2,4}*160, {10,4,2}*160
10-fold quotients : {4,4,4}*128, {8,4,2}*128b
16-fold quotients : {5,2,4}*80, {10,2,2}*80
20-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
32-fold quotients : {5,2,2}*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.
Permutation Representation (GAP) :
s0 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)( 8, 89)
( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)
( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)( 24,103)
( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)( 32,115)
( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,126)( 42,130)( 43,129)( 44,128)( 45,127)( 46,121)( 47,125)( 48,124)
( 49,123)( 50,122)( 51,136)( 52,140)( 53,139)( 54,138)( 55,137)( 56,131)
( 57,135)( 58,134)( 59,133)( 60,132)( 61,146)( 62,150)( 63,149)( 64,148)
( 65,147)( 66,141)( 67,145)( 68,144)( 69,143)( 70,142)( 71,156)( 72,160)
( 73,159)( 74,158)( 75,157)( 76,151)( 77,155)( 78,154)( 79,153)( 80,152)
(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)(168,249)
(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)(176,256)
(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)(184,263)
(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)(192,275)
(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)(200,277)
(201,286)(202,290)(203,289)(204,288)(205,287)(206,281)(207,285)(208,284)
(209,283)(210,282)(211,296)(212,300)(213,299)(214,298)(215,297)(216,291)
(217,295)(218,294)(219,293)(220,292)(221,306)(222,310)(223,309)(224,308)
(225,307)(226,301)(227,305)(228,304)(229,303)(230,302)(231,316)(232,320)
(233,319)(234,318)(235,317)(236,311)(237,315)(238,314)(239,313)(240,312)
(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)
(361,446)(362,450)(363,449)(364,448)(365,447)(366,441)(367,445)(368,444)
(369,443)(370,442)(371,456)(372,460)(373,459)(374,458)(375,457)(376,451)
(377,455)(378,454)(379,453)(380,452)(381,466)(382,470)(383,469)(384,468)
(385,467)(386,461)(387,465)(388,464)(389,463)(390,462)(391,476)(392,480)
(393,479)(394,478)(395,477)(396,471)(397,475)(398,474)(399,473)(400,472)
(481,561)(482,565)(483,564)(484,563)(485,562)(486,566)(487,570)(488,569)
(489,568)(490,567)(491,571)(492,575)(493,574)(494,573)(495,572)(496,576)
(497,580)(498,579)(499,578)(500,577)(501,581)(502,585)(503,584)(504,583)
(505,582)(506,586)(507,590)(508,589)(509,588)(510,587)(511,591)(512,595)
(513,594)(514,593)(515,592)(516,596)(517,600)(518,599)(519,598)(520,597)
(521,606)(522,610)(523,609)(524,608)(525,607)(526,601)(527,605)(528,604)
(529,603)(530,602)(531,616)(532,620)(533,619)(534,618)(535,617)(536,611)
(537,615)(538,614)(539,613)(540,612)(541,626)(542,630)(543,629)(544,628)
(545,627)(546,621)(547,625)(548,624)(549,623)(550,622)(551,636)(552,640)
(553,639)(554,638)(555,637)(556,631)(557,635)(558,634)(559,633)(560,632);;
s1 := ( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)
( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 38)( 32, 37)( 33, 36)
( 34, 40)( 35, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 58)
( 52, 57)( 53, 56)( 54, 60)( 55, 59)( 61, 63)( 64, 65)( 66, 68)( 69, 70)
( 71, 73)( 74, 75)( 76, 78)( 79, 80)( 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)
(101,148)(102,147)(103,146)(104,150)(105,149)(106,143)(107,142)(108,141)
(109,145)(110,144)(111,158)(112,157)(113,156)(114,160)(115,159)(116,153)
(117,152)(118,151)(119,155)(120,154)(161,183)(162,182)(163,181)(164,185)
(165,184)(166,188)(167,187)(168,186)(169,190)(170,189)(171,193)(172,192)
(173,191)(174,195)(175,194)(176,198)(177,197)(178,196)(179,200)(180,199)
(201,228)(202,227)(203,226)(204,230)(205,229)(206,223)(207,222)(208,221)
(209,225)(210,224)(211,238)(212,237)(213,236)(214,240)(215,239)(216,233)
(217,232)(218,231)(219,235)(220,234)(241,303)(242,302)(243,301)(244,305)
(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)(252,312)
(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)
(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)(268,286)
(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)(275,294)(276,298)
(277,297)(278,296)(279,300)(280,299)(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)
(341,388)(342,387)(343,386)(344,390)(345,389)(346,383)(347,382)(348,381)
(349,385)(350,384)(351,398)(352,397)(353,396)(354,400)(355,399)(356,393)
(357,392)(358,391)(359,395)(360,394)(401,403)(404,405)(406,408)(409,410)
(411,413)(414,415)(416,418)(419,420)(421,428)(422,427)(423,426)(424,430)
(425,429)(431,438)(432,437)(433,436)(434,440)(435,439)(441,448)(442,447)
(443,446)(444,450)(445,449)(451,458)(452,457)(453,456)(454,460)(455,459)
(461,463)(464,465)(466,468)(469,470)(471,473)(474,475)(476,478)(479,480)
(481,543)(482,542)(483,541)(484,545)(485,544)(486,548)(487,547)(488,546)
(489,550)(490,549)(491,553)(492,552)(493,551)(494,555)(495,554)(496,558)
(497,557)(498,556)(499,560)(500,559)(501,523)(502,522)(503,521)(504,525)
(505,524)(506,528)(507,527)(508,526)(509,530)(510,529)(511,533)(512,532)
(513,531)(514,535)(515,534)(516,538)(517,537)(518,536)(519,540)(520,539)
(561,583)(562,582)(563,581)(564,585)(565,584)(566,588)(567,587)(568,586)
(569,590)(570,589)(571,593)(572,592)(573,591)(574,595)(575,594)(576,598)
(577,597)(578,596)(579,600)(580,599)(601,628)(602,627)(603,626)(604,630)
(605,629)(606,623)(607,622)(608,621)(609,625)(610,624)(611,638)(612,637)
(613,636)(614,640)(615,639)(616,633)(617,632)(618,631)(619,635)(620,634);;
s2 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)
( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)( 24,269)
( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,276)( 32,277)
( 33,278)( 34,279)( 35,280)( 36,271)( 37,272)( 38,273)( 39,274)( 40,275)
( 41,286)( 42,287)( 43,288)( 44,289)( 45,290)( 46,281)( 47,282)( 48,283)
( 49,284)( 50,285)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,291)
( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,161)( 82,162)( 83,163)( 84,164)( 85,165)( 86,166)( 87,167)( 88,168)
( 89,169)( 90,170)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)( 96,176)
( 97,177)( 98,178)( 99,179)(100,180)(101,186)(102,187)(103,188)(104,189)
(105,190)(106,181)(107,182)(108,183)(109,184)(110,185)(111,196)(112,197)
(113,198)(114,199)(115,200)(116,191)(117,192)(118,193)(119,194)(120,195)
(121,206)(122,207)(123,208)(124,209)(125,210)(126,201)(127,202)(128,203)
(129,204)(130,205)(131,216)(132,217)(133,218)(134,219)(135,220)(136,211)
(137,212)(138,213)(139,214)(140,215)(141,221)(142,222)(143,223)(144,224)
(145,225)(146,226)(147,227)(148,228)(149,229)(150,230)(151,231)(152,232)
(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)(160,240)
(321,561)(322,562)(323,563)(324,564)(325,565)(326,566)(327,567)(328,568)
(329,569)(330,570)(331,571)(332,572)(333,573)(334,574)(335,575)(336,576)
(337,577)(338,578)(339,579)(340,580)(341,586)(342,587)(343,588)(344,589)
(345,590)(346,581)(347,582)(348,583)(349,584)(350,585)(351,596)(352,597)
(353,598)(354,599)(355,600)(356,591)(357,592)(358,593)(359,594)(360,595)
(361,606)(362,607)(363,608)(364,609)(365,610)(366,601)(367,602)(368,603)
(369,604)(370,605)(371,616)(372,617)(373,618)(374,619)(375,620)(376,611)
(377,612)(378,613)(379,614)(380,615)(381,621)(382,622)(383,623)(384,624)
(385,625)(386,626)(387,627)(388,628)(389,629)(390,630)(391,631)(392,632)
(393,633)(394,634)(395,635)(396,636)(397,637)(398,638)(399,639)(400,640)
(401,481)(402,482)(403,483)(404,484)(405,485)(406,486)(407,487)(408,488)
(409,489)(410,490)(411,491)(412,492)(413,493)(414,494)(415,495)(416,496)
(417,497)(418,498)(419,499)(420,500)(421,506)(422,507)(423,508)(424,509)
(425,510)(426,501)(427,502)(428,503)(429,504)(430,505)(431,516)(432,517)
(433,518)(434,519)(435,520)(436,511)(437,512)(438,513)(439,514)(440,515)
(441,526)(442,527)(443,528)(444,529)(445,530)(446,521)(447,522)(448,523)
(449,524)(450,525)(451,536)(452,537)(453,538)(454,539)(455,540)(456,531)
(457,532)(458,533)(459,534)(460,535)(461,541)(462,542)(463,543)(464,544)
(465,545)(466,546)(467,547)(468,548)(469,549)(470,550)(471,551)(472,552)
(473,553)(474,554)(475,555)(476,556)(477,557)(478,558)(479,559)(480,560);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(640)!( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)
( 8, 89)( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)
( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)
( 24,103)( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)
( 32,115)( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,126)( 42,130)( 43,129)( 44,128)( 45,127)( 46,121)( 47,125)
( 48,124)( 49,123)( 50,122)( 51,136)( 52,140)( 53,139)( 54,138)( 55,137)
( 56,131)( 57,135)( 58,134)( 59,133)( 60,132)( 61,146)( 62,150)( 63,149)
( 64,148)( 65,147)( 66,141)( 67,145)( 68,144)( 69,143)( 70,142)( 71,156)
( 72,160)( 73,159)( 74,158)( 75,157)( 76,151)( 77,155)( 78,154)( 79,153)
( 80,152)(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)
(168,249)(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)
(176,256)(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)
(184,263)(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)
(192,275)(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)
(200,277)(201,286)(202,290)(203,289)(204,288)(205,287)(206,281)(207,285)
(208,284)(209,283)(210,282)(211,296)(212,300)(213,299)(214,298)(215,297)
(216,291)(217,295)(218,294)(219,293)(220,292)(221,306)(222,310)(223,309)
(224,308)(225,307)(226,301)(227,305)(228,304)(229,303)(230,302)(231,316)
(232,320)(233,319)(234,318)(235,317)(236,311)(237,315)(238,314)(239,313)
(240,312)(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)(361,446)(362,450)(363,449)(364,448)(365,447)(366,441)(367,445)
(368,444)(369,443)(370,442)(371,456)(372,460)(373,459)(374,458)(375,457)
(376,451)(377,455)(378,454)(379,453)(380,452)(381,466)(382,470)(383,469)
(384,468)(385,467)(386,461)(387,465)(388,464)(389,463)(390,462)(391,476)
(392,480)(393,479)(394,478)(395,477)(396,471)(397,475)(398,474)(399,473)
(400,472)(481,561)(482,565)(483,564)(484,563)(485,562)(486,566)(487,570)
(488,569)(489,568)(490,567)(491,571)(492,575)(493,574)(494,573)(495,572)
(496,576)(497,580)(498,579)(499,578)(500,577)(501,581)(502,585)(503,584)
(504,583)(505,582)(506,586)(507,590)(508,589)(509,588)(510,587)(511,591)
(512,595)(513,594)(514,593)(515,592)(516,596)(517,600)(518,599)(519,598)
(520,597)(521,606)(522,610)(523,609)(524,608)(525,607)(526,601)(527,605)
(528,604)(529,603)(530,602)(531,616)(532,620)(533,619)(534,618)(535,617)
(536,611)(537,615)(538,614)(539,613)(540,612)(541,626)(542,630)(543,629)
(544,628)(545,627)(546,621)(547,625)(548,624)(549,623)(550,622)(551,636)
(552,640)(553,639)(554,638)(555,637)(556,631)(557,635)(558,634)(559,633)
(560,632);
s1 := Sym(640)!( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 13)( 14, 15)( 16, 18)
( 19, 20)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 38)( 32, 37)
( 33, 36)( 34, 40)( 35, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)
( 51, 58)( 52, 57)( 53, 56)( 54, 60)( 55, 59)( 61, 63)( 64, 65)( 66, 68)
( 69, 70)( 71, 73)( 74, 75)( 76, 78)( 79, 80)( 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)(101,148)(102,147)(103,146)(104,150)(105,149)(106,143)(107,142)
(108,141)(109,145)(110,144)(111,158)(112,157)(113,156)(114,160)(115,159)
(116,153)(117,152)(118,151)(119,155)(120,154)(161,183)(162,182)(163,181)
(164,185)(165,184)(166,188)(167,187)(168,186)(169,190)(170,189)(171,193)
(172,192)(173,191)(174,195)(175,194)(176,198)(177,197)(178,196)(179,200)
(180,199)(201,228)(202,227)(203,226)(204,230)(205,229)(206,223)(207,222)
(208,221)(209,225)(210,224)(211,238)(212,237)(213,236)(214,240)(215,239)
(216,233)(217,232)(218,231)(219,235)(220,234)(241,303)(242,302)(243,301)
(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)
(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)
(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)
(268,286)(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)(275,294)
(276,298)(277,297)(278,296)(279,300)(280,299)(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)(341,388)(342,387)(343,386)(344,390)(345,389)(346,383)(347,382)
(348,381)(349,385)(350,384)(351,398)(352,397)(353,396)(354,400)(355,399)
(356,393)(357,392)(358,391)(359,395)(360,394)(401,403)(404,405)(406,408)
(409,410)(411,413)(414,415)(416,418)(419,420)(421,428)(422,427)(423,426)
(424,430)(425,429)(431,438)(432,437)(433,436)(434,440)(435,439)(441,448)
(442,447)(443,446)(444,450)(445,449)(451,458)(452,457)(453,456)(454,460)
(455,459)(461,463)(464,465)(466,468)(469,470)(471,473)(474,475)(476,478)
(479,480)(481,543)(482,542)(483,541)(484,545)(485,544)(486,548)(487,547)
(488,546)(489,550)(490,549)(491,553)(492,552)(493,551)(494,555)(495,554)
(496,558)(497,557)(498,556)(499,560)(500,559)(501,523)(502,522)(503,521)
(504,525)(505,524)(506,528)(507,527)(508,526)(509,530)(510,529)(511,533)
(512,532)(513,531)(514,535)(515,534)(516,538)(517,537)(518,536)(519,540)
(520,539)(561,583)(562,582)(563,581)(564,585)(565,584)(566,588)(567,587)
(568,586)(569,590)(570,589)(571,593)(572,592)(573,591)(574,595)(575,594)
(576,598)(577,597)(578,596)(579,600)(580,599)(601,628)(602,627)(603,626)
(604,630)(605,629)(606,623)(607,622)(608,621)(609,625)(610,624)(611,638)
(612,637)(613,636)(614,640)(615,639)(616,633)(617,632)(618,631)(619,635)
(620,634);
s2 := Sym(640)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)
( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)
( 24,269)( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,276)
( 32,277)( 33,278)( 34,279)( 35,280)( 36,271)( 37,272)( 38,273)( 39,274)
( 40,275)( 41,286)( 42,287)( 43,288)( 44,289)( 45,290)( 46,281)( 47,282)
( 48,283)( 49,284)( 50,285)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)
( 56,291)( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,161)( 82,162)( 83,163)( 84,164)( 85,165)( 86,166)( 87,167)
( 88,168)( 89,169)( 90,170)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)
( 96,176)( 97,177)( 98,178)( 99,179)(100,180)(101,186)(102,187)(103,188)
(104,189)(105,190)(106,181)(107,182)(108,183)(109,184)(110,185)(111,196)
(112,197)(113,198)(114,199)(115,200)(116,191)(117,192)(118,193)(119,194)
(120,195)(121,206)(122,207)(123,208)(124,209)(125,210)(126,201)(127,202)
(128,203)(129,204)(130,205)(131,216)(132,217)(133,218)(134,219)(135,220)
(136,211)(137,212)(138,213)(139,214)(140,215)(141,221)(142,222)(143,223)
(144,224)(145,225)(146,226)(147,227)(148,228)(149,229)(150,230)(151,231)
(152,232)(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)
(160,240)(321,561)(322,562)(323,563)(324,564)(325,565)(326,566)(327,567)
(328,568)(329,569)(330,570)(331,571)(332,572)(333,573)(334,574)(335,575)
(336,576)(337,577)(338,578)(339,579)(340,580)(341,586)(342,587)(343,588)
(344,589)(345,590)(346,581)(347,582)(348,583)(349,584)(350,585)(351,596)
(352,597)(353,598)(354,599)(355,600)(356,591)(357,592)(358,593)(359,594)
(360,595)(361,606)(362,607)(363,608)(364,609)(365,610)(366,601)(367,602)
(368,603)(369,604)(370,605)(371,616)(372,617)(373,618)(374,619)(375,620)
(376,611)(377,612)(378,613)(379,614)(380,615)(381,621)(382,622)(383,623)
(384,624)(385,625)(386,626)(387,627)(388,628)(389,629)(390,630)(391,631)
(392,632)(393,633)(394,634)(395,635)(396,636)(397,637)(398,638)(399,639)
(400,640)(401,481)(402,482)(403,483)(404,484)(405,485)(406,486)(407,487)
(408,488)(409,489)(410,490)(411,491)(412,492)(413,493)(414,494)(415,495)
(416,496)(417,497)(418,498)(419,499)(420,500)(421,506)(422,507)(423,508)
(424,509)(425,510)(426,501)(427,502)(428,503)(429,504)(430,505)(431,516)
(432,517)(433,518)(434,519)(435,520)(436,511)(437,512)(438,513)(439,514)
(440,515)(441,526)(442,527)(443,528)(444,529)(445,530)(446,521)(447,522)
(448,523)(449,524)(450,525)(451,536)(452,537)(453,538)(454,539)(455,540)
(456,531)(457,532)(458,533)(459,534)(460,535)(461,541)(462,542)(463,543)
(464,544)(465,545)(466,546)(467,547)(468,548)(469,549)(470,550)(471,551)
(472,552)(473,553)(474,554)(475,555)(476,556)(477,557)(478,558)(479,559)
(480,560);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope