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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,4,4}*1280
Also Known As : {{10,4|2},{4,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1280,336970)
Rank : 5
Schlafli Type : {10,4,4,4}
Number of vertices, edges, etc : 10, 20, 8, 8, 4
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,2,4,4}*640, {10,4,4,2}*640, {10,4,2,4}*640
   4-fold quotients : {5,2,4,4}*320, {10,2,2,4}*320, {10,2,4,2}*320, {10,4,2,2}*320
   5-fold quotients : {2,4,4,4}*256
   8-fold quotients : {5,2,2,4}*160, {5,2,4,2}*160, {10,2,2,2}*160
   10-fold quotients : {2,2,4,4}*128, {2,4,4,2}*128, {2,4,2,4}*128
   16-fold quotients : {5,2,2,2}*80
   20-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {2,4,2,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 41)(  2, 45)(  3, 44)(  4, 43)(  5, 42)(  6, 46)(  7, 50)(  8, 49)
(  9, 48)( 10, 47)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 56)
( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 61)( 22, 65)( 23, 64)( 24, 63)
( 25, 62)( 26, 66)( 27, 70)( 28, 69)( 29, 68)( 30, 67)( 31, 71)( 32, 75)
( 33, 74)( 34, 73)( 35, 72)( 36, 76)( 37, 80)( 38, 79)( 39, 78)( 40, 77)
( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)
( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)( 96,136)
( 97,140)( 98,139)( 99,138)(100,137)(101,141)(102,145)(103,144)(104,143)
(105,142)(106,146)(107,150)(108,149)(109,148)(110,147)(111,151)(112,155)
(113,154)(114,153)(115,152)(116,156)(117,160)(118,159)(119,158)(120,157)
(161,201)(162,205)(163,204)(164,203)(165,202)(166,206)(167,210)(168,209)
(169,208)(170,207)(171,211)(172,215)(173,214)(174,213)(175,212)(176,216)
(177,220)(178,219)(179,218)(180,217)(181,221)(182,225)(183,224)(184,223)
(185,222)(186,226)(187,230)(188,229)(189,228)(190,227)(191,231)(192,235)
(193,234)(194,233)(195,232)(196,236)(197,240)(198,239)(199,238)(200,237)
(241,281)(242,285)(243,284)(244,283)(245,282)(246,286)(247,290)(248,289)
(249,288)(250,287)(251,291)(252,295)(253,294)(254,293)(255,292)(256,296)
(257,300)(258,299)(259,298)(260,297)(261,301)(262,305)(263,304)(264,303)
(265,302)(266,306)(267,310)(268,309)(269,308)(270,307)(271,311)(272,315)
(273,314)(274,313)(275,312)(276,316)(277,320)(278,319)(279,318)(280,317)
(321,361)(322,365)(323,364)(324,363)(325,362)(326,366)(327,370)(328,369)
(329,368)(330,367)(331,371)(332,375)(333,374)(334,373)(335,372)(336,376)
(337,380)(338,379)(339,378)(340,377)(341,381)(342,385)(343,384)(344,383)
(345,382)(346,386)(347,390)(348,389)(349,388)(350,387)(351,391)(352,395)
(353,394)(354,393)(355,392)(356,396)(357,400)(358,399)(359,398)(360,397)
(401,441)(402,445)(403,444)(404,443)(405,442)(406,446)(407,450)(408,449)
(409,448)(410,447)(411,451)(412,455)(413,454)(414,453)(415,452)(416,456)
(417,460)(418,459)(419,458)(420,457)(421,461)(422,465)(423,464)(424,463)
(425,462)(426,466)(427,470)(428,469)(429,468)(430,467)(431,471)(432,475)
(433,474)(434,473)(435,472)(436,476)(437,480)(438,479)(439,478)(440,477)
(481,521)(482,525)(483,524)(484,523)(485,522)(486,526)(487,530)(488,529)
(489,528)(490,527)(491,531)(492,535)(493,534)(494,533)(495,532)(496,536)
(497,540)(498,539)(499,538)(500,537)(501,541)(502,545)(503,544)(504,543)
(505,542)(506,546)(507,550)(508,549)(509,548)(510,547)(511,551)(512,555)
(513,554)(514,553)(515,552)(516,556)(517,560)(518,559)(519,558)(520,557)
(561,601)(562,605)(563,604)(564,603)(565,602)(566,606)(567,610)(568,609)
(569,608)(570,607)(571,611)(572,615)(573,614)(574,613)(575,612)(576,616)
(577,620)(578,619)(579,618)(580,617)(581,621)(582,625)(583,624)(584,623)
(585,622)(586,626)(587,630)(588,629)(589,628)(590,627)(591,631)(592,635)
(593,634)(594,633)(595,632)(596,636)(597,640)(598,639)(599,638)(600,637);;
s1 := (  1,123)(  2,122)(  3,121)(  4,125)(  5,124)(  6,128)(  7,127)(  8,126)
(  9,130)( 10,129)( 11,133)( 12,132)( 13,131)( 14,135)( 15,134)( 16,138)
( 17,137)( 18,136)( 19,140)( 20,139)( 21,143)( 22,142)( 23,141)( 24,145)
( 25,144)( 26,148)( 27,147)( 28,146)( 29,150)( 30,149)( 31,153)( 32,152)
( 33,151)( 34,155)( 35,154)( 36,158)( 37,157)( 38,156)( 39,160)( 40,159)
( 41, 83)( 42, 82)( 43, 81)( 44, 85)( 45, 84)( 46, 88)( 47, 87)( 48, 86)
( 49, 90)( 50, 89)( 51, 93)( 52, 92)( 53, 91)( 54, 95)( 55, 94)( 56, 98)
( 57, 97)( 58, 96)( 59,100)( 60, 99)( 61,103)( 62,102)( 63,101)( 64,105)
( 65,104)( 66,108)( 67,107)( 68,106)( 69,110)( 70,109)( 71,113)( 72,112)
( 73,111)( 74,115)( 75,114)( 76,118)( 77,117)( 78,116)( 79,120)( 80,119)
(161,283)(162,282)(163,281)(164,285)(165,284)(166,288)(167,287)(168,286)
(169,290)(170,289)(171,293)(172,292)(173,291)(174,295)(175,294)(176,298)
(177,297)(178,296)(179,300)(180,299)(181,303)(182,302)(183,301)(184,305)
(185,304)(186,308)(187,307)(188,306)(189,310)(190,309)(191,313)(192,312)
(193,311)(194,315)(195,314)(196,318)(197,317)(198,316)(199,320)(200,319)
(201,243)(202,242)(203,241)(204,245)(205,244)(206,248)(207,247)(208,246)
(209,250)(210,249)(211,253)(212,252)(213,251)(214,255)(215,254)(216,258)
(217,257)(218,256)(219,260)(220,259)(221,263)(222,262)(223,261)(224,265)
(225,264)(226,268)(227,267)(228,266)(229,270)(230,269)(231,273)(232,272)
(233,271)(234,275)(235,274)(236,278)(237,277)(238,276)(239,280)(240,279)
(321,443)(322,442)(323,441)(324,445)(325,444)(326,448)(327,447)(328,446)
(329,450)(330,449)(331,453)(332,452)(333,451)(334,455)(335,454)(336,458)
(337,457)(338,456)(339,460)(340,459)(341,463)(342,462)(343,461)(344,465)
(345,464)(346,468)(347,467)(348,466)(349,470)(350,469)(351,473)(352,472)
(353,471)(354,475)(355,474)(356,478)(357,477)(358,476)(359,480)(360,479)
(361,403)(362,402)(363,401)(364,405)(365,404)(366,408)(367,407)(368,406)
(369,410)(370,409)(371,413)(372,412)(373,411)(374,415)(375,414)(376,418)
(377,417)(378,416)(379,420)(380,419)(381,423)(382,422)(383,421)(384,425)
(385,424)(386,428)(387,427)(388,426)(389,430)(390,429)(391,433)(392,432)
(393,431)(394,435)(395,434)(396,438)(397,437)(398,436)(399,440)(400,439)
(481,603)(482,602)(483,601)(484,605)(485,604)(486,608)(487,607)(488,606)
(489,610)(490,609)(491,613)(492,612)(493,611)(494,615)(495,614)(496,618)
(497,617)(498,616)(499,620)(500,619)(501,623)(502,622)(503,621)(504,625)
(505,624)(506,628)(507,627)(508,626)(509,630)(510,629)(511,633)(512,632)
(513,631)(514,635)(515,634)(516,638)(517,637)(518,636)(519,640)(520,639)
(521,563)(522,562)(523,561)(524,565)(525,564)(526,568)(527,567)(528,566)
(529,570)(530,569)(531,573)(532,572)(533,571)(534,575)(535,574)(536,578)
(537,577)(538,576)(539,580)(540,579)(541,583)(542,582)(543,581)(544,585)
(545,584)(546,588)(547,587)(548,586)(549,590)(550,589)(551,593)(552,592)
(553,591)(554,595)(555,594)(556,598)(557,597)(558,596)(559,600)(560,599);;
s2 := (  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);;
s3 := (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);;
s4 := (  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)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 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)(101,181)(102,182)(103,183)(104,184)
(105,185)(106,186)(107,187)(108,188)(109,189)(110,190)(111,191)(112,192)
(113,193)(114,194)(115,195)(116,196)(117,197)(118,198)(119,199)(120,200)
(121,201)(122,202)(123,203)(124,204)(125,205)(126,206)(127,207)(128,208)
(129,209)(130,210)(131,211)(132,212)(133,213)(134,214)(135,215)(136,216)
(137,217)(138,218)(139,219)(140,220)(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)(341,581)(342,582)(343,583)(344,584)
(345,585)(346,586)(347,587)(348,588)(349,589)(350,590)(351,591)(352,592)
(353,593)(354,594)(355,595)(356,596)(357,597)(358,598)(359,599)(360,600)
(361,601)(362,602)(363,603)(364,604)(365,605)(366,606)(367,607)(368,608)
(369,609)(370,610)(371,611)(372,612)(373,613)(374,614)(375,615)(376,616)
(377,617)(378,618)(379,619)(380,620)(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)(421,501)(422,502)(423,503)(424,504)
(425,505)(426,506)(427,507)(428,508)(429,509)(430,510)(431,511)(432,512)
(433,513)(434,514)(435,515)(436,516)(437,517)(438,518)(439,519)(440,520)
(441,521)(442,522)(443,523)(444,524)(445,525)(446,526)(447,527)(448,528)
(449,529)(450,530)(451,531)(452,532)(453,533)(454,534)(455,535)(456,536)
(457,537)(458,538)(459,539)(460,540)(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);;
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*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, 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, 41)(  2, 45)(  3, 44)(  4, 43)(  5, 42)(  6, 46)(  7, 50)
(  8, 49)(  9, 48)( 10, 47)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)
( 16, 56)( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 61)( 22, 65)( 23, 64)
( 24, 63)( 25, 62)( 26, 66)( 27, 70)( 28, 69)( 29, 68)( 30, 67)( 31, 71)
( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 76)( 37, 80)( 38, 79)( 39, 78)
( 40, 77)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)
( 88,129)( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)
( 96,136)( 97,140)( 98,139)( 99,138)(100,137)(101,141)(102,145)(103,144)
(104,143)(105,142)(106,146)(107,150)(108,149)(109,148)(110,147)(111,151)
(112,155)(113,154)(114,153)(115,152)(116,156)(117,160)(118,159)(119,158)
(120,157)(161,201)(162,205)(163,204)(164,203)(165,202)(166,206)(167,210)
(168,209)(169,208)(170,207)(171,211)(172,215)(173,214)(174,213)(175,212)
(176,216)(177,220)(178,219)(179,218)(180,217)(181,221)(182,225)(183,224)
(184,223)(185,222)(186,226)(187,230)(188,229)(189,228)(190,227)(191,231)
(192,235)(193,234)(194,233)(195,232)(196,236)(197,240)(198,239)(199,238)
(200,237)(241,281)(242,285)(243,284)(244,283)(245,282)(246,286)(247,290)
(248,289)(249,288)(250,287)(251,291)(252,295)(253,294)(254,293)(255,292)
(256,296)(257,300)(258,299)(259,298)(260,297)(261,301)(262,305)(263,304)
(264,303)(265,302)(266,306)(267,310)(268,309)(269,308)(270,307)(271,311)
(272,315)(273,314)(274,313)(275,312)(276,316)(277,320)(278,319)(279,318)
(280,317)(321,361)(322,365)(323,364)(324,363)(325,362)(326,366)(327,370)
(328,369)(329,368)(330,367)(331,371)(332,375)(333,374)(334,373)(335,372)
(336,376)(337,380)(338,379)(339,378)(340,377)(341,381)(342,385)(343,384)
(344,383)(345,382)(346,386)(347,390)(348,389)(349,388)(350,387)(351,391)
(352,395)(353,394)(354,393)(355,392)(356,396)(357,400)(358,399)(359,398)
(360,397)(401,441)(402,445)(403,444)(404,443)(405,442)(406,446)(407,450)
(408,449)(409,448)(410,447)(411,451)(412,455)(413,454)(414,453)(415,452)
(416,456)(417,460)(418,459)(419,458)(420,457)(421,461)(422,465)(423,464)
(424,463)(425,462)(426,466)(427,470)(428,469)(429,468)(430,467)(431,471)
(432,475)(433,474)(434,473)(435,472)(436,476)(437,480)(438,479)(439,478)
(440,477)(481,521)(482,525)(483,524)(484,523)(485,522)(486,526)(487,530)
(488,529)(489,528)(490,527)(491,531)(492,535)(493,534)(494,533)(495,532)
(496,536)(497,540)(498,539)(499,538)(500,537)(501,541)(502,545)(503,544)
(504,543)(505,542)(506,546)(507,550)(508,549)(509,548)(510,547)(511,551)
(512,555)(513,554)(514,553)(515,552)(516,556)(517,560)(518,559)(519,558)
(520,557)(561,601)(562,605)(563,604)(564,603)(565,602)(566,606)(567,610)
(568,609)(569,608)(570,607)(571,611)(572,615)(573,614)(574,613)(575,612)
(576,616)(577,620)(578,619)(579,618)(580,617)(581,621)(582,625)(583,624)
(584,623)(585,622)(586,626)(587,630)(588,629)(589,628)(590,627)(591,631)
(592,635)(593,634)(594,633)(595,632)(596,636)(597,640)(598,639)(599,638)
(600,637);
s1 := Sym(640)!(  1,123)(  2,122)(  3,121)(  4,125)(  5,124)(  6,128)(  7,127)
(  8,126)(  9,130)( 10,129)( 11,133)( 12,132)( 13,131)( 14,135)( 15,134)
( 16,138)( 17,137)( 18,136)( 19,140)( 20,139)( 21,143)( 22,142)( 23,141)
( 24,145)( 25,144)( 26,148)( 27,147)( 28,146)( 29,150)( 30,149)( 31,153)
( 32,152)( 33,151)( 34,155)( 35,154)( 36,158)( 37,157)( 38,156)( 39,160)
( 40,159)( 41, 83)( 42, 82)( 43, 81)( 44, 85)( 45, 84)( 46, 88)( 47, 87)
( 48, 86)( 49, 90)( 50, 89)( 51, 93)( 52, 92)( 53, 91)( 54, 95)( 55, 94)
( 56, 98)( 57, 97)( 58, 96)( 59,100)( 60, 99)( 61,103)( 62,102)( 63,101)
( 64,105)( 65,104)( 66,108)( 67,107)( 68,106)( 69,110)( 70,109)( 71,113)
( 72,112)( 73,111)( 74,115)( 75,114)( 76,118)( 77,117)( 78,116)( 79,120)
( 80,119)(161,283)(162,282)(163,281)(164,285)(165,284)(166,288)(167,287)
(168,286)(169,290)(170,289)(171,293)(172,292)(173,291)(174,295)(175,294)
(176,298)(177,297)(178,296)(179,300)(180,299)(181,303)(182,302)(183,301)
(184,305)(185,304)(186,308)(187,307)(188,306)(189,310)(190,309)(191,313)
(192,312)(193,311)(194,315)(195,314)(196,318)(197,317)(198,316)(199,320)
(200,319)(201,243)(202,242)(203,241)(204,245)(205,244)(206,248)(207,247)
(208,246)(209,250)(210,249)(211,253)(212,252)(213,251)(214,255)(215,254)
(216,258)(217,257)(218,256)(219,260)(220,259)(221,263)(222,262)(223,261)
(224,265)(225,264)(226,268)(227,267)(228,266)(229,270)(230,269)(231,273)
(232,272)(233,271)(234,275)(235,274)(236,278)(237,277)(238,276)(239,280)
(240,279)(321,443)(322,442)(323,441)(324,445)(325,444)(326,448)(327,447)
(328,446)(329,450)(330,449)(331,453)(332,452)(333,451)(334,455)(335,454)
(336,458)(337,457)(338,456)(339,460)(340,459)(341,463)(342,462)(343,461)
(344,465)(345,464)(346,468)(347,467)(348,466)(349,470)(350,469)(351,473)
(352,472)(353,471)(354,475)(355,474)(356,478)(357,477)(358,476)(359,480)
(360,479)(361,403)(362,402)(363,401)(364,405)(365,404)(366,408)(367,407)
(368,406)(369,410)(370,409)(371,413)(372,412)(373,411)(374,415)(375,414)
(376,418)(377,417)(378,416)(379,420)(380,419)(381,423)(382,422)(383,421)
(384,425)(385,424)(386,428)(387,427)(388,426)(389,430)(390,429)(391,433)
(392,432)(393,431)(394,435)(395,434)(396,438)(397,437)(398,436)(399,440)
(400,439)(481,603)(482,602)(483,601)(484,605)(485,604)(486,608)(487,607)
(488,606)(489,610)(490,609)(491,613)(492,612)(493,611)(494,615)(495,614)
(496,618)(497,617)(498,616)(499,620)(500,619)(501,623)(502,622)(503,621)
(504,625)(505,624)(506,628)(507,627)(508,626)(509,630)(510,629)(511,633)
(512,632)(513,631)(514,635)(515,634)(516,638)(517,637)(518,636)(519,640)
(520,639)(521,563)(522,562)(523,561)(524,565)(525,564)(526,568)(527,567)
(528,566)(529,570)(530,569)(531,573)(532,572)(533,571)(534,575)(535,574)
(536,578)(537,577)(538,576)(539,580)(540,579)(541,583)(542,582)(543,581)
(544,585)(545,584)(546,588)(547,587)(548,586)(549,590)(550,589)(551,593)
(552,592)(553,591)(554,595)(555,594)(556,598)(557,597)(558,596)(559,600)
(560,599);
s2 := 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);
s3 := 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);
s4 := 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)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 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)(101,181)(102,182)(103,183)
(104,184)(105,185)(106,186)(107,187)(108,188)(109,189)(110,190)(111,191)
(112,192)(113,193)(114,194)(115,195)(116,196)(117,197)(118,198)(119,199)
(120,200)(121,201)(122,202)(123,203)(124,204)(125,205)(126,206)(127,207)
(128,208)(129,209)(130,210)(131,211)(132,212)(133,213)(134,214)(135,215)
(136,216)(137,217)(138,218)(139,219)(140,220)(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)(341,581)(342,582)(343,583)
(344,584)(345,585)(346,586)(347,587)(348,588)(349,589)(350,590)(351,591)
(352,592)(353,593)(354,594)(355,595)(356,596)(357,597)(358,598)(359,599)
(360,600)(361,601)(362,602)(363,603)(364,604)(365,605)(366,606)(367,607)
(368,608)(369,609)(370,610)(371,611)(372,612)(373,613)(374,614)(375,615)
(376,616)(377,617)(378,618)(379,619)(380,620)(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)(421,501)(422,502)(423,503)
(424,504)(425,505)(426,506)(427,507)(428,508)(429,509)(430,510)(431,511)
(432,512)(433,513)(434,514)(435,515)(436,516)(437,517)(438,518)(439,519)
(440,520)(441,521)(442,522)(443,523)(444,524)(445,525)(446,526)(447,527)
(448,528)(449,529)(450,530)(451,531)(452,532)(453,533)(454,534)(455,535)
(456,536)(457,537)(458,538)(459,539)(460,540)(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);
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*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, 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