Polytope of Type {4,4,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,4,10}*1280
Also Known As : {{4,4|2},{4,4|2},{4,10|2}}. if this polytope has another name.
Group : SmallGroup(1280,336970)
Rank : 5
Schlafli Type : {4,4,4,10}
Number of vertices, edges, etc : 4, 8, 8, 20, 10
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 : {2,4,4,10}*640, {4,4,2,10}*640, {4,2,4,10}*640
   4-fold quotients : {4,4,2,5}*320, {2,2,4,10}*320, {2,4,2,10}*320, {4,2,2,10}*320
   5-fold quotients : {4,4,4,2}*256
   8-fold quotients : {2,4,2,5}*160, {4,2,2,5}*160, {2,2,2,10}*160
   10-fold quotients : {2,4,4,2}*128, {4,4,2,2}*128, {4,2,4,2}*128
   16-fold quotients : {2,2,2,5}*80
   20-fold quotients : {2,2,4,2}*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.
Permutation Representation (GAP) : 
s0 := (  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)
(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)
( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)( 24,104)
( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)
( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)
( 41,121)( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)
( 49,129)( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)
( 57,137)( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)( 64,144)
( 65,145)( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)
( 73,153)( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)
(161,241)(162,242)(163,243)(164,244)(165,245)(166,246)(167,247)(168,248)
(169,249)(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)(176,256)
(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)(184,264)
(185,265)(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)(192,272)
(193,273)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)
(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)
(209,289)(210,290)(211,291)(212,292)(213,293)(214,294)(215,295)(216,296)
(217,297)(218,298)(219,299)(220,300)(221,301)(222,302)(223,303)(224,304)
(225,305)(226,306)(227,307)(228,308)(229,309)(230,310)(231,311)(232,312)
(233,313)(234,314)(235,315)(236,316)(237,317)(238,318)(239,319)(240,320)
(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)(328,408)
(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)(336,416)
(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)(344,424)
(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)(352,432)
(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)(360,440)
(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)(368,448)
(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)(376,456)
(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)(384,464)
(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)(392,472)
(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)(400,480)
(481,561)(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)(488,568)
(489,569)(490,570)(491,571)(492,572)(493,573)(494,574)(495,575)(496,576)
(497,577)(498,578)(499,579)(500,580)(501,581)(502,582)(503,583)(504,584)
(505,585)(506,586)(507,587)(508,588)(509,589)(510,590)(511,591)(512,592)
(513,593)(514,594)(515,595)(516,596)(517,597)(518,598)(519,599)(520,600)
(521,601)(522,602)(523,603)(524,604)(525,605)(526,606)(527,607)(528,608)
(529,609)(530,610)(531,611)(532,612)(533,613)(534,614)(535,615)(536,616)
(537,617)(538,618)(539,619)(540,620)(541,621)(542,622)(543,623)(544,624)
(545,625)(546,626)(547,627)(548,628)(549,629)(550,630)(551,631)(552,632)
(553,633)(554,634)(555,635)(556,636)(557,637)(558,638)(559,639)(560,640);;
s1 := (  1,321)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)(  8,328)
(  9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)( 16,336)
( 17,337)( 18,338)( 19,339)( 20,340)( 21,341)( 22,342)( 23,343)( 24,344)
( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)( 32,352)
( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)( 40,360)
( 41,361)( 42,362)( 43,363)( 44,364)( 45,365)( 46,366)( 47,367)( 48,368)
( 49,369)( 50,370)( 51,371)( 52,372)( 53,373)( 54,374)( 55,375)( 56,376)
( 57,377)( 58,378)( 59,379)( 60,380)( 61,381)( 62,382)( 63,383)( 64,384)
( 65,385)( 66,386)( 67,387)( 68,388)( 69,389)( 70,390)( 71,391)( 72,392)
( 73,393)( 74,394)( 75,395)( 76,396)( 77,397)( 78,398)( 79,399)( 80,400)
( 81,406)( 82,407)( 83,408)( 84,409)( 85,410)( 86,401)( 87,402)( 88,403)
( 89,404)( 90,405)( 91,416)( 92,417)( 93,418)( 94,419)( 95,420)( 96,411)
( 97,412)( 98,413)( 99,414)(100,415)(101,426)(102,427)(103,428)(104,429)
(105,430)(106,421)(107,422)(108,423)(109,424)(110,425)(111,436)(112,437)
(113,438)(114,439)(115,440)(116,431)(117,432)(118,433)(119,434)(120,435)
(121,446)(122,447)(123,448)(124,449)(125,450)(126,441)(127,442)(128,443)
(129,444)(130,445)(131,456)(132,457)(133,458)(134,459)(135,460)(136,451)
(137,452)(138,453)(139,454)(140,455)(141,466)(142,467)(143,468)(144,469)
(145,470)(146,461)(147,462)(148,463)(149,464)(150,465)(151,476)(152,477)
(153,478)(154,479)(155,480)(156,471)(157,472)(158,473)(159,474)(160,475)
(161,486)(162,487)(163,488)(164,489)(165,490)(166,481)(167,482)(168,483)
(169,484)(170,485)(171,496)(172,497)(173,498)(174,499)(175,500)(176,491)
(177,492)(178,493)(179,494)(180,495)(181,506)(182,507)(183,508)(184,509)
(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(191,516)(192,517)
(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)(200,515)
(201,526)(202,527)(203,528)(204,529)(205,530)(206,521)(207,522)(208,523)
(209,524)(210,525)(211,536)(212,537)(213,538)(214,539)(215,540)(216,531)
(217,532)(218,533)(219,534)(220,535)(221,546)(222,547)(223,548)(224,549)
(225,550)(226,541)(227,542)(228,543)(229,544)(230,545)(231,556)(232,557)
(233,558)(234,559)(235,560)(236,551)(237,552)(238,553)(239,554)(240,555)
(241,561)(242,562)(243,563)(244,564)(245,565)(246,566)(247,567)(248,568)
(249,569)(250,570)(251,571)(252,572)(253,573)(254,574)(255,575)(256,576)
(257,577)(258,578)(259,579)(260,580)(261,581)(262,582)(263,583)(264,584)
(265,585)(266,586)(267,587)(268,588)(269,589)(270,590)(271,591)(272,592)
(273,593)(274,594)(275,595)(276,596)(277,597)(278,598)(279,599)(280,600)
(281,601)(282,602)(283,603)(284,604)(285,605)(286,606)(287,607)(288,608)
(289,609)(290,610)(291,611)(292,612)(293,613)(294,614)(295,615)(296,616)
(297,617)(298,618)(299,619)(300,620)(301,621)(302,622)(303,623)(304,624)
(305,625)(306,626)(307,627)(308,628)(309,629)(310,630)(311,631)(312,632)
(313,633)(314,634)(315,635)(316,636)(317,637)(318,638)(319,639)(320,640);;
s2 := (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);;
s3 := (  1,281)(  2,285)(  3,284)(  4,283)(  5,282)(  6,286)(  7,290)(  8,289)
(  9,288)( 10,287)( 11,291)( 12,295)( 13,294)( 14,293)( 15,292)( 16,296)
( 17,300)( 18,299)( 19,298)( 20,297)( 21,301)( 22,305)( 23,304)( 24,303)
( 25,302)( 26,306)( 27,310)( 28,309)( 29,308)( 30,307)( 31,311)( 32,315)
( 33,314)( 34,313)( 35,312)( 36,316)( 37,320)( 38,319)( 39,318)( 40,317)
( 41,241)( 42,245)( 43,244)( 44,243)( 45,242)( 46,246)( 47,250)( 48,249)
( 49,248)( 50,247)( 51,251)( 52,255)( 53,254)( 54,253)( 55,252)( 56,256)
( 57,260)( 58,259)( 59,258)( 60,257)( 61,261)( 62,265)( 63,264)( 64,263)
( 65,262)( 66,266)( 67,270)( 68,269)( 69,268)( 70,267)( 71,271)( 72,275)
( 73,274)( 74,273)( 75,272)( 76,276)( 77,280)( 78,279)( 79,278)( 80,277)
( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)( 88,209)
( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,216)
( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)(104,223)
(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)(112,235)
(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)(120,237)
(121,161)(122,165)(123,164)(124,163)(125,162)(126,166)(127,170)(128,169)
(129,168)(130,167)(131,171)(132,175)(133,174)(134,173)(135,172)(136,176)
(137,180)(138,179)(139,178)(140,177)(141,181)(142,185)(143,184)(144,183)
(145,182)(146,186)(147,190)(148,189)(149,188)(150,187)(151,191)(152,195)
(153,194)(154,193)(155,192)(156,196)(157,200)(158,199)(159,198)(160,197)
(321,601)(322,605)(323,604)(324,603)(325,602)(326,606)(327,610)(328,609)
(329,608)(330,607)(331,611)(332,615)(333,614)(334,613)(335,612)(336,616)
(337,620)(338,619)(339,618)(340,617)(341,621)(342,625)(343,624)(344,623)
(345,622)(346,626)(347,630)(348,629)(349,628)(350,627)(351,631)(352,635)
(353,634)(354,633)(355,632)(356,636)(357,640)(358,639)(359,638)(360,637)
(361,561)(362,565)(363,564)(364,563)(365,562)(366,566)(367,570)(368,569)
(369,568)(370,567)(371,571)(372,575)(373,574)(374,573)(375,572)(376,576)
(377,580)(378,579)(379,578)(380,577)(381,581)(382,585)(383,584)(384,583)
(385,582)(386,586)(387,590)(388,589)(389,588)(390,587)(391,591)(392,595)
(393,594)(394,593)(395,592)(396,596)(397,600)(398,599)(399,598)(400,597)
(401,521)(402,525)(403,524)(404,523)(405,522)(406,526)(407,530)(408,529)
(409,528)(410,527)(411,531)(412,535)(413,534)(414,533)(415,532)(416,536)
(417,540)(418,539)(419,538)(420,537)(421,541)(422,545)(423,544)(424,543)
(425,542)(426,546)(427,550)(428,549)(429,548)(430,547)(431,551)(432,555)
(433,554)(434,553)(435,552)(436,556)(437,560)(438,559)(439,558)(440,557)
(441,481)(442,485)(443,484)(444,483)(445,482)(446,486)(447,490)(448,489)
(449,488)(450,487)(451,491)(452,495)(453,494)(454,493)(455,492)(456,496)
(457,500)(458,499)(459,498)(460,497)(461,501)(462,505)(463,504)(464,503)
(465,502)(466,506)(467,510)(468,509)(469,508)(470,507)(471,511)(472,515)
(473,514)(474,513)(475,512)(476,516)(477,520)(478,519)(479,518)(480,517);;
s4 := (  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);;
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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(640)!(  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)
(  8, 88)(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)
( 16, 96)( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)
( 24,104)( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)
( 32,112)( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)
( 40,120)( 41,121)( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)
( 48,128)( 49,129)( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)
( 56,136)( 57,137)( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)
( 64,144)( 65,145)( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)
( 72,152)( 73,153)( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)
( 80,160)(161,241)(162,242)(163,243)(164,244)(165,245)(166,246)(167,247)
(168,248)(169,249)(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)
(176,256)(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)
(184,264)(185,265)(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)
(192,272)(193,273)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)
(200,280)(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)
(208,288)(209,289)(210,290)(211,291)(212,292)(213,293)(214,294)(215,295)
(216,296)(217,297)(218,298)(219,299)(220,300)(221,301)(222,302)(223,303)
(224,304)(225,305)(226,306)(227,307)(228,308)(229,309)(230,310)(231,311)
(232,312)(233,313)(234,314)(235,315)(236,316)(237,317)(238,318)(239,319)
(240,320)(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)
(328,408)(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)
(336,416)(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)
(344,424)(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)
(352,432)(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)
(360,440)(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)
(368,448)(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)
(376,456)(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)
(384,464)(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)
(392,472)(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)
(400,480)(481,561)(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)
(488,568)(489,569)(490,570)(491,571)(492,572)(493,573)(494,574)(495,575)
(496,576)(497,577)(498,578)(499,579)(500,580)(501,581)(502,582)(503,583)
(504,584)(505,585)(506,586)(507,587)(508,588)(509,589)(510,590)(511,591)
(512,592)(513,593)(514,594)(515,595)(516,596)(517,597)(518,598)(519,599)
(520,600)(521,601)(522,602)(523,603)(524,604)(525,605)(526,606)(527,607)
(528,608)(529,609)(530,610)(531,611)(532,612)(533,613)(534,614)(535,615)
(536,616)(537,617)(538,618)(539,619)(540,620)(541,621)(542,622)(543,623)
(544,624)(545,625)(546,626)(547,627)(548,628)(549,629)(550,630)(551,631)
(552,632)(553,633)(554,634)(555,635)(556,636)(557,637)(558,638)(559,639)
(560,640);
s1 := Sym(640)!(  1,321)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)
(  8,328)(  9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)
( 16,336)( 17,337)( 18,338)( 19,339)( 20,340)( 21,341)( 22,342)( 23,343)
( 24,344)( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)
( 32,352)( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)
( 40,360)( 41,361)( 42,362)( 43,363)( 44,364)( 45,365)( 46,366)( 47,367)
( 48,368)( 49,369)( 50,370)( 51,371)( 52,372)( 53,373)( 54,374)( 55,375)
( 56,376)( 57,377)( 58,378)( 59,379)( 60,380)( 61,381)( 62,382)( 63,383)
( 64,384)( 65,385)( 66,386)( 67,387)( 68,388)( 69,389)( 70,390)( 71,391)
( 72,392)( 73,393)( 74,394)( 75,395)( 76,396)( 77,397)( 78,398)( 79,399)
( 80,400)( 81,406)( 82,407)( 83,408)( 84,409)( 85,410)( 86,401)( 87,402)
( 88,403)( 89,404)( 90,405)( 91,416)( 92,417)( 93,418)( 94,419)( 95,420)
( 96,411)( 97,412)( 98,413)( 99,414)(100,415)(101,426)(102,427)(103,428)
(104,429)(105,430)(106,421)(107,422)(108,423)(109,424)(110,425)(111,436)
(112,437)(113,438)(114,439)(115,440)(116,431)(117,432)(118,433)(119,434)
(120,435)(121,446)(122,447)(123,448)(124,449)(125,450)(126,441)(127,442)
(128,443)(129,444)(130,445)(131,456)(132,457)(133,458)(134,459)(135,460)
(136,451)(137,452)(138,453)(139,454)(140,455)(141,466)(142,467)(143,468)
(144,469)(145,470)(146,461)(147,462)(148,463)(149,464)(150,465)(151,476)
(152,477)(153,478)(154,479)(155,480)(156,471)(157,472)(158,473)(159,474)
(160,475)(161,486)(162,487)(163,488)(164,489)(165,490)(166,481)(167,482)
(168,483)(169,484)(170,485)(171,496)(172,497)(173,498)(174,499)(175,500)
(176,491)(177,492)(178,493)(179,494)(180,495)(181,506)(182,507)(183,508)
(184,509)(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(191,516)
(192,517)(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)
(200,515)(201,526)(202,527)(203,528)(204,529)(205,530)(206,521)(207,522)
(208,523)(209,524)(210,525)(211,536)(212,537)(213,538)(214,539)(215,540)
(216,531)(217,532)(218,533)(219,534)(220,535)(221,546)(222,547)(223,548)
(224,549)(225,550)(226,541)(227,542)(228,543)(229,544)(230,545)(231,556)
(232,557)(233,558)(234,559)(235,560)(236,551)(237,552)(238,553)(239,554)
(240,555)(241,561)(242,562)(243,563)(244,564)(245,565)(246,566)(247,567)
(248,568)(249,569)(250,570)(251,571)(252,572)(253,573)(254,574)(255,575)
(256,576)(257,577)(258,578)(259,579)(260,580)(261,581)(262,582)(263,583)
(264,584)(265,585)(266,586)(267,587)(268,588)(269,589)(270,590)(271,591)
(272,592)(273,593)(274,594)(275,595)(276,596)(277,597)(278,598)(279,599)
(280,600)(281,601)(282,602)(283,603)(284,604)(285,605)(286,606)(287,607)
(288,608)(289,609)(290,610)(291,611)(292,612)(293,613)(294,614)(295,615)
(296,616)(297,617)(298,618)(299,619)(300,620)(301,621)(302,622)(303,623)
(304,624)(305,625)(306,626)(307,627)(308,628)(309,629)(310,630)(311,631)
(312,632)(313,633)(314,634)(315,635)(316,636)(317,637)(318,638)(319,639)
(320,640);
s2 := 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);
s3 := Sym(640)!(  1,281)(  2,285)(  3,284)(  4,283)(  5,282)(  6,286)(  7,290)
(  8,289)(  9,288)( 10,287)( 11,291)( 12,295)( 13,294)( 14,293)( 15,292)
( 16,296)( 17,300)( 18,299)( 19,298)( 20,297)( 21,301)( 22,305)( 23,304)
( 24,303)( 25,302)( 26,306)( 27,310)( 28,309)( 29,308)( 30,307)( 31,311)
( 32,315)( 33,314)( 34,313)( 35,312)( 36,316)( 37,320)( 38,319)( 39,318)
( 40,317)( 41,241)( 42,245)( 43,244)( 44,243)( 45,242)( 46,246)( 47,250)
( 48,249)( 49,248)( 50,247)( 51,251)( 52,255)( 53,254)( 54,253)( 55,252)
( 56,256)( 57,260)( 58,259)( 59,258)( 60,257)( 61,261)( 62,265)( 63,264)
( 64,263)( 65,262)( 66,266)( 67,270)( 68,269)( 69,268)( 70,267)( 71,271)
( 72,275)( 73,274)( 74,273)( 75,272)( 76,276)( 77,280)( 78,279)( 79,278)
( 80,277)( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)
( 88,209)( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,216)( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)
(104,223)(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)
(112,235)(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)
(120,237)(121,161)(122,165)(123,164)(124,163)(125,162)(126,166)(127,170)
(128,169)(129,168)(130,167)(131,171)(132,175)(133,174)(134,173)(135,172)
(136,176)(137,180)(138,179)(139,178)(140,177)(141,181)(142,185)(143,184)
(144,183)(145,182)(146,186)(147,190)(148,189)(149,188)(150,187)(151,191)
(152,195)(153,194)(154,193)(155,192)(156,196)(157,200)(158,199)(159,198)
(160,197)(321,601)(322,605)(323,604)(324,603)(325,602)(326,606)(327,610)
(328,609)(329,608)(330,607)(331,611)(332,615)(333,614)(334,613)(335,612)
(336,616)(337,620)(338,619)(339,618)(340,617)(341,621)(342,625)(343,624)
(344,623)(345,622)(346,626)(347,630)(348,629)(349,628)(350,627)(351,631)
(352,635)(353,634)(354,633)(355,632)(356,636)(357,640)(358,639)(359,638)
(360,637)(361,561)(362,565)(363,564)(364,563)(365,562)(366,566)(367,570)
(368,569)(369,568)(370,567)(371,571)(372,575)(373,574)(374,573)(375,572)
(376,576)(377,580)(378,579)(379,578)(380,577)(381,581)(382,585)(383,584)
(384,583)(385,582)(386,586)(387,590)(388,589)(389,588)(390,587)(391,591)
(392,595)(393,594)(394,593)(395,592)(396,596)(397,600)(398,599)(399,598)
(400,597)(401,521)(402,525)(403,524)(404,523)(405,522)(406,526)(407,530)
(408,529)(409,528)(410,527)(411,531)(412,535)(413,534)(414,533)(415,532)
(416,536)(417,540)(418,539)(419,538)(420,537)(421,541)(422,545)(423,544)
(424,543)(425,542)(426,546)(427,550)(428,549)(429,548)(430,547)(431,551)
(432,555)(433,554)(434,553)(435,552)(436,556)(437,560)(438,559)(439,558)
(440,557)(441,481)(442,485)(443,484)(444,483)(445,482)(446,486)(447,490)
(448,489)(449,488)(450,487)(451,491)(452,495)(453,494)(454,493)(455,492)
(456,496)(457,500)(458,499)(459,498)(460,497)(461,501)(462,505)(463,504)
(464,503)(465,502)(466,506)(467,510)(468,509)(469,508)(470,507)(471,511)
(472,515)(473,514)(474,513)(475,512)(476,516)(477,520)(478,519)(479,518)
(480,517);
s4 := 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);
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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope