Polytope of Type {10,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,16}*1280a
Also Known As : {{10,4|2},{4,16|2}}. if this polytope has another name.
Group : SmallGroup(1280,323301)
Rank : 4
Schlafli Type : {10,4,16}
Number of vertices, edges, etc : 10, 20, 32, 16
Order of s0s1s2s3 : 80
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 : {10,4,8}*640a, {10,2,16}*640
   4-fold quotients : {5,2,16}*320, {10,4,4}*320, {10,2,8}*320
   5-fold quotients : {2,4,16}*256a
   8-fold quotients : {5,2,8}*160, {10,2,4}*160, {10,4,2}*160
   10-fold quotients : {2,4,8}*128a, {2,2,16}*128
   16-fold quotients : {5,2,4}*80, {10,2,2}*80
   20-fold quotients : {2,4,4}*64, {2,2,8}*64
   32-fold quotients : {5,2,2}*40
   40-fold quotients : {2,2,4}*32, {2,4,2}*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)
( 41,121)( 42,125)( 43,124)( 44,123)( 45,122)( 46,126)( 47,130)( 48,129)
( 49,128)( 50,127)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,136)
( 57,140)( 58,139)( 59,138)( 60,137)( 61,141)( 62,145)( 63,144)( 64,143)
( 65,142)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,151)( 72,155)
( 73,154)( 74,153)( 75,152)( 76,156)( 77,160)( 78,159)( 79,158)( 80,157)
(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)
(201,281)(202,285)(203,284)(204,283)(205,282)(206,286)(207,290)(208,289)
(209,288)(210,287)(211,291)(212,295)(213,294)(214,293)(215,292)(216,296)
(217,300)(218,299)(219,298)(220,297)(221,301)(222,305)(223,304)(224,303)
(225,302)(226,306)(227,310)(228,309)(229,308)(230,307)(231,311)(232,315)
(233,314)(234,313)(235,312)(236,316)(237,320)(238,319)(239,318)(240,317)
(321,401)(322,405)(323,404)(324,403)(325,402)(326,406)(327,410)(328,409)
(329,408)(330,407)(331,411)(332,415)(333,414)(334,413)(335,412)(336,416)
(337,420)(338,419)(339,418)(340,417)(341,421)(342,425)(343,424)(344,423)
(345,422)(346,426)(347,430)(348,429)(349,428)(350,427)(351,431)(352,435)
(353,434)(354,433)(355,432)(356,436)(357,440)(358,439)(359,438)(360,437)
(361,441)(362,445)(363,444)(364,443)(365,442)(366,446)(367,450)(368,449)
(369,448)(370,447)(371,451)(372,455)(373,454)(374,453)(375,452)(376,456)
(377,460)(378,459)(379,458)(380,457)(381,461)(382,465)(383,464)(384,463)
(385,462)(386,466)(387,470)(388,469)(389,468)(390,467)(391,471)(392,475)
(393,474)(394,473)(395,472)(396,476)(397,480)(398,479)(399,478)(400,477)
(481,561)(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)
(521,601)(522,605)(523,604)(524,603)(525,602)(526,606)(527,610)(528,609)
(529,608)(530,607)(531,611)(532,615)(533,614)(534,613)(535,612)(536,616)
(537,620)(538,619)(539,618)(540,617)(541,621)(542,625)(543,624)(544,623)
(545,622)(546,626)(547,630)(548,629)(549,628)(550,627)(551,631)(552,635)
(553,634)(554,633)(555,632)(556,636)(557,640)(558,639)(559,638)(560,637);;
s1 := (  1,243)(  2,242)(  3,241)(  4,245)(  5,244)(  6,248)(  7,247)(  8,246)
(  9,250)( 10,249)( 11,253)( 12,252)( 13,251)( 14,255)( 15,254)( 16,258)
( 17,257)( 18,256)( 19,260)( 20,259)( 21,263)( 22,262)( 23,261)( 24,265)
( 25,264)( 26,268)( 27,267)( 28,266)( 29,270)( 30,269)( 31,273)( 32,272)
( 33,271)( 34,275)( 35,274)( 36,278)( 37,277)( 38,276)( 39,280)( 40,279)
( 41,283)( 42,282)( 43,281)( 44,285)( 45,284)( 46,288)( 47,287)( 48,286)
( 49,290)( 50,289)( 51,293)( 52,292)( 53,291)( 54,295)( 55,294)( 56,298)
( 57,297)( 58,296)( 59,300)( 60,299)( 61,303)( 62,302)( 63,301)( 64,305)
( 65,304)( 66,308)( 67,307)( 68,306)( 69,310)( 70,309)( 71,313)( 72,312)
( 73,311)( 74,315)( 75,314)( 76,318)( 77,317)( 78,316)( 79,320)( 80,319)
( 81,163)( 82,162)( 83,161)( 84,165)( 85,164)( 86,168)( 87,167)( 88,166)
( 89,170)( 90,169)( 91,173)( 92,172)( 93,171)( 94,175)( 95,174)( 96,178)
( 97,177)( 98,176)( 99,180)(100,179)(101,183)(102,182)(103,181)(104,185)
(105,184)(106,188)(107,187)(108,186)(109,190)(110,189)(111,193)(112,192)
(113,191)(114,195)(115,194)(116,198)(117,197)(118,196)(119,200)(120,199)
(121,203)(122,202)(123,201)(124,205)(125,204)(126,208)(127,207)(128,206)
(129,210)(130,209)(131,213)(132,212)(133,211)(134,215)(135,214)(136,218)
(137,217)(138,216)(139,220)(140,219)(141,223)(142,222)(143,221)(144,225)
(145,224)(146,228)(147,227)(148,226)(149,230)(150,229)(151,233)(152,232)
(153,231)(154,235)(155,234)(156,238)(157,237)(158,236)(159,240)(160,239)
(321,563)(322,562)(323,561)(324,565)(325,564)(326,568)(327,567)(328,566)
(329,570)(330,569)(331,573)(332,572)(333,571)(334,575)(335,574)(336,578)
(337,577)(338,576)(339,580)(340,579)(341,583)(342,582)(343,581)(344,585)
(345,584)(346,588)(347,587)(348,586)(349,590)(350,589)(351,593)(352,592)
(353,591)(354,595)(355,594)(356,598)(357,597)(358,596)(359,600)(360,599)
(361,603)(362,602)(363,601)(364,605)(365,604)(366,608)(367,607)(368,606)
(369,610)(370,609)(371,613)(372,612)(373,611)(374,615)(375,614)(376,618)
(377,617)(378,616)(379,620)(380,619)(381,623)(382,622)(383,621)(384,625)
(385,624)(386,628)(387,627)(388,626)(389,630)(390,629)(391,633)(392,632)
(393,631)(394,635)(395,634)(396,638)(397,637)(398,636)(399,640)(400,639)
(401,483)(402,482)(403,481)(404,485)(405,484)(406,488)(407,487)(408,486)
(409,490)(410,489)(411,493)(412,492)(413,491)(414,495)(415,494)(416,498)
(417,497)(418,496)(419,500)(420,499)(421,503)(422,502)(423,501)(424,505)
(425,504)(426,508)(427,507)(428,506)(429,510)(430,509)(431,513)(432,512)
(433,511)(434,515)(435,514)(436,518)(437,517)(438,516)(439,520)(440,519)
(441,523)(442,522)(443,521)(444,525)(445,524)(446,528)(447,527)(448,526)
(449,530)(450,529)(451,533)(452,532)(453,531)(454,535)(455,534)(456,538)
(457,537)(458,536)(459,540)(460,539)(461,543)(462,542)(463,541)(464,545)
(465,544)(466,548)(467,547)(468,546)(469,550)(470,549)(471,553)(472,552)
(473,551)(474,555)(475,554)(476,558)(477,557)(478,556)(479,560)(480,559);;
s2 := ( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 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, 71)( 62, 72)( 63, 73)( 64, 74)
( 65, 75)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 91, 96)( 92, 97)
( 93, 98)( 94, 99)( 95,100)(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)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)
(147,157)(148,158)(149,159)(150,160)(161,181)(162,182)(163,183)(164,184)
(165,185)(166,186)(167,187)(168,188)(169,189)(170,190)(171,196)(172,197)
(173,198)(174,199)(175,200)(176,191)(177,192)(178,193)(179,194)(180,195)
(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)(251,276)(252,277)
(253,278)(254,279)(255,280)(256,271)(257,272)(258,273)(259,274)(260,275)
(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)(331,376)(332,377)
(333,378)(334,379)(335,380)(336,371)(337,372)(338,373)(339,374)(340,375)
(341,381)(342,382)(343,383)(344,384)(345,385)(346,386)(347,387)(348,388)
(349,389)(350,390)(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)(411,456)(412,457)
(413,458)(414,459)(415,460)(416,451)(417,452)(418,453)(419,454)(420,455)
(421,461)(422,462)(423,463)(424,464)(425,465)(426,466)(427,467)(428,468)
(429,469)(430,470)(431,476)(432,477)(433,478)(434,479)(435,480)(436,471)
(437,472)(438,473)(439,474)(440,475)(481,541)(482,542)(483,543)(484,544)
(485,545)(486,546)(487,547)(488,548)(489,549)(490,550)(491,556)(492,557)
(493,558)(494,559)(495,560)(496,551)(497,552)(498,553)(499,554)(500,555)
(501,521)(502,522)(503,523)(504,524)(505,525)(506,526)(507,527)(508,528)
(509,529)(510,530)(511,536)(512,537)(513,538)(514,539)(515,540)(516,531)
(517,532)(518,533)(519,534)(520,535)(561,621)(562,622)(563,623)(564,624)
(565,625)(566,626)(567,627)(568,628)(569,629)(570,630)(571,636)(572,637)
(573,638)(574,639)(575,640)(576,631)(577,632)(578,633)(579,634)(580,635)
(581,601)(582,602)(583,603)(584,604)(585,605)(586,606)(587,607)(588,608)
(589,609)(590,610)(591,616)(592,617)(593,618)(594,619)(595,620)(596,611)
(597,612)(598,613)(599,614)(600,615);;
s3 := (  1,321)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)(  8,328)
(  9,329)( 10,330)( 11,336)( 12,337)( 13,338)( 14,339)( 15,340)( 16,331)
( 17,332)( 18,333)( 19,334)( 20,335)( 21,341)( 22,342)( 23,343)( 24,344)
( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,356)( 32,357)
( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)( 40,355)
( 41,371)( 42,372)( 43,373)( 44,374)( 45,375)( 46,376)( 47,377)( 48,378)
( 49,379)( 50,380)( 51,361)( 52,362)( 53,363)( 54,364)( 55,365)( 56,366)
( 57,367)( 58,368)( 59,369)( 60,370)( 61,391)( 62,392)( 63,393)( 64,394)
( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)( 72,382)
( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)( 80,390)
( 81,401)( 82,402)( 83,403)( 84,404)( 85,405)( 86,406)( 87,407)( 88,408)
( 89,409)( 90,410)( 91,416)( 92,417)( 93,418)( 94,419)( 95,420)( 96,411)
( 97,412)( 98,413)( 99,414)(100,415)(101,421)(102,422)(103,423)(104,424)
(105,425)(106,426)(107,427)(108,428)(109,429)(110,430)(111,436)(112,437)
(113,438)(114,439)(115,440)(116,431)(117,432)(118,433)(119,434)(120,435)
(121,451)(122,452)(123,453)(124,454)(125,455)(126,456)(127,457)(128,458)
(129,459)(130,460)(131,441)(132,442)(133,443)(134,444)(135,445)(136,446)
(137,447)(138,448)(139,449)(140,450)(141,471)(142,472)(143,473)(144,474)
(145,475)(146,476)(147,477)(148,478)(149,479)(150,480)(151,461)(152,462)
(153,463)(154,464)(155,465)(156,466)(157,467)(158,468)(159,469)(160,470)
(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)
(169,489)(170,490)(171,496)(172,497)(173,498)(174,499)(175,500)(176,491)
(177,492)(178,493)(179,494)(180,495)(181,501)(182,502)(183,503)(184,504)
(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,516)(192,517)
(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)(200,515)
(201,531)(202,532)(203,533)(204,534)(205,535)(206,536)(207,537)(208,538)
(209,539)(210,540)(211,521)(212,522)(213,523)(214,524)(215,525)(216,526)
(217,527)(218,528)(219,529)(220,530)(221,551)(222,552)(223,553)(224,554)
(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)(232,542)
(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)(240,550)
(241,561)(242,562)(243,563)(244,564)(245,565)(246,566)(247,567)(248,568)
(249,569)(250,570)(251,576)(252,577)(253,578)(254,579)(255,580)(256,571)
(257,572)(258,573)(259,574)(260,575)(261,581)(262,582)(263,583)(264,584)
(265,585)(266,586)(267,587)(268,588)(269,589)(270,590)(271,596)(272,597)
(273,598)(274,599)(275,600)(276,591)(277,592)(278,593)(279,594)(280,595)
(281,611)(282,612)(283,613)(284,614)(285,615)(286,616)(287,617)(288,618)
(289,619)(290,620)(291,601)(292,602)(293,603)(294,604)(295,605)(296,606)
(297,607)(298,608)(299,609)(300,610)(301,631)(302,632)(303,633)(304,634)
(305,635)(306,636)(307,637)(308,638)(309,639)(310,640)(311,621)(312,622)
(313,623)(314,624)(315,625)(316,626)(317,627)(318,628)(319,629)(320,630);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(640)!(  1, 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)( 41,121)( 42,125)( 43,124)( 44,123)( 45,122)( 46,126)( 47,130)
( 48,129)( 49,128)( 50,127)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)
( 56,136)( 57,140)( 58,139)( 59,138)( 60,137)( 61,141)( 62,145)( 63,144)
( 64,143)( 65,142)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,151)
( 72,155)( 73,154)( 74,153)( 75,152)( 76,156)( 77,160)( 78,159)( 79,158)
( 80,157)(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)(201,281)(202,285)(203,284)(204,283)(205,282)(206,286)(207,290)
(208,289)(209,288)(210,287)(211,291)(212,295)(213,294)(214,293)(215,292)
(216,296)(217,300)(218,299)(219,298)(220,297)(221,301)(222,305)(223,304)
(224,303)(225,302)(226,306)(227,310)(228,309)(229,308)(230,307)(231,311)
(232,315)(233,314)(234,313)(235,312)(236,316)(237,320)(238,319)(239,318)
(240,317)(321,401)(322,405)(323,404)(324,403)(325,402)(326,406)(327,410)
(328,409)(329,408)(330,407)(331,411)(332,415)(333,414)(334,413)(335,412)
(336,416)(337,420)(338,419)(339,418)(340,417)(341,421)(342,425)(343,424)
(344,423)(345,422)(346,426)(347,430)(348,429)(349,428)(350,427)(351,431)
(352,435)(353,434)(354,433)(355,432)(356,436)(357,440)(358,439)(359,438)
(360,437)(361,441)(362,445)(363,444)(364,443)(365,442)(366,446)(367,450)
(368,449)(369,448)(370,447)(371,451)(372,455)(373,454)(374,453)(375,452)
(376,456)(377,460)(378,459)(379,458)(380,457)(381,461)(382,465)(383,464)
(384,463)(385,462)(386,466)(387,470)(388,469)(389,468)(390,467)(391,471)
(392,475)(393,474)(394,473)(395,472)(396,476)(397,480)(398,479)(399,478)
(400,477)(481,561)(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)(521,601)(522,605)(523,604)(524,603)(525,602)(526,606)(527,610)
(528,609)(529,608)(530,607)(531,611)(532,615)(533,614)(534,613)(535,612)
(536,616)(537,620)(538,619)(539,618)(540,617)(541,621)(542,625)(543,624)
(544,623)(545,622)(546,626)(547,630)(548,629)(549,628)(550,627)(551,631)
(552,635)(553,634)(554,633)(555,632)(556,636)(557,640)(558,639)(559,638)
(560,637);
s1 := Sym(640)!(  1,243)(  2,242)(  3,241)(  4,245)(  5,244)(  6,248)(  7,247)
(  8,246)(  9,250)( 10,249)( 11,253)( 12,252)( 13,251)( 14,255)( 15,254)
( 16,258)( 17,257)( 18,256)( 19,260)( 20,259)( 21,263)( 22,262)( 23,261)
( 24,265)( 25,264)( 26,268)( 27,267)( 28,266)( 29,270)( 30,269)( 31,273)
( 32,272)( 33,271)( 34,275)( 35,274)( 36,278)( 37,277)( 38,276)( 39,280)
( 40,279)( 41,283)( 42,282)( 43,281)( 44,285)( 45,284)( 46,288)( 47,287)
( 48,286)( 49,290)( 50,289)( 51,293)( 52,292)( 53,291)( 54,295)( 55,294)
( 56,298)( 57,297)( 58,296)( 59,300)( 60,299)( 61,303)( 62,302)( 63,301)
( 64,305)( 65,304)( 66,308)( 67,307)( 68,306)( 69,310)( 70,309)( 71,313)
( 72,312)( 73,311)( 74,315)( 75,314)( 76,318)( 77,317)( 78,316)( 79,320)
( 80,319)( 81,163)( 82,162)( 83,161)( 84,165)( 85,164)( 86,168)( 87,167)
( 88,166)( 89,170)( 90,169)( 91,173)( 92,172)( 93,171)( 94,175)( 95,174)
( 96,178)( 97,177)( 98,176)( 99,180)(100,179)(101,183)(102,182)(103,181)
(104,185)(105,184)(106,188)(107,187)(108,186)(109,190)(110,189)(111,193)
(112,192)(113,191)(114,195)(115,194)(116,198)(117,197)(118,196)(119,200)
(120,199)(121,203)(122,202)(123,201)(124,205)(125,204)(126,208)(127,207)
(128,206)(129,210)(130,209)(131,213)(132,212)(133,211)(134,215)(135,214)
(136,218)(137,217)(138,216)(139,220)(140,219)(141,223)(142,222)(143,221)
(144,225)(145,224)(146,228)(147,227)(148,226)(149,230)(150,229)(151,233)
(152,232)(153,231)(154,235)(155,234)(156,238)(157,237)(158,236)(159,240)
(160,239)(321,563)(322,562)(323,561)(324,565)(325,564)(326,568)(327,567)
(328,566)(329,570)(330,569)(331,573)(332,572)(333,571)(334,575)(335,574)
(336,578)(337,577)(338,576)(339,580)(340,579)(341,583)(342,582)(343,581)
(344,585)(345,584)(346,588)(347,587)(348,586)(349,590)(350,589)(351,593)
(352,592)(353,591)(354,595)(355,594)(356,598)(357,597)(358,596)(359,600)
(360,599)(361,603)(362,602)(363,601)(364,605)(365,604)(366,608)(367,607)
(368,606)(369,610)(370,609)(371,613)(372,612)(373,611)(374,615)(375,614)
(376,618)(377,617)(378,616)(379,620)(380,619)(381,623)(382,622)(383,621)
(384,625)(385,624)(386,628)(387,627)(388,626)(389,630)(390,629)(391,633)
(392,632)(393,631)(394,635)(395,634)(396,638)(397,637)(398,636)(399,640)
(400,639)(401,483)(402,482)(403,481)(404,485)(405,484)(406,488)(407,487)
(408,486)(409,490)(410,489)(411,493)(412,492)(413,491)(414,495)(415,494)
(416,498)(417,497)(418,496)(419,500)(420,499)(421,503)(422,502)(423,501)
(424,505)(425,504)(426,508)(427,507)(428,506)(429,510)(430,509)(431,513)
(432,512)(433,511)(434,515)(435,514)(436,518)(437,517)(438,516)(439,520)
(440,519)(441,523)(442,522)(443,521)(444,525)(445,524)(446,528)(447,527)
(448,526)(449,530)(450,529)(451,533)(452,532)(453,531)(454,535)(455,534)
(456,538)(457,537)(458,536)(459,540)(460,539)(461,543)(462,542)(463,541)
(464,545)(465,544)(466,548)(467,547)(468,546)(469,550)(470,549)(471,553)
(472,552)(473,551)(474,555)(475,554)(476,558)(477,557)(478,556)(479,560)
(480,559);
s2 := Sym(640)!( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 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, 71)( 62, 72)( 63, 73)
( 64, 74)( 65, 75)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 91, 96)
( 92, 97)( 93, 98)( 94, 99)( 95,100)(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)(141,151)(142,152)(143,153)(144,154)(145,155)
(146,156)(147,157)(148,158)(149,159)(150,160)(161,181)(162,182)(163,183)
(164,184)(165,185)(166,186)(167,187)(168,188)(169,189)(170,190)(171,196)
(172,197)(173,198)(174,199)(175,200)(176,191)(177,192)(178,193)(179,194)
(180,195)(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)(251,276)
(252,277)(253,278)(254,279)(255,280)(256,271)(257,272)(258,273)(259,274)
(260,275)(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)(331,376)
(332,377)(333,378)(334,379)(335,380)(336,371)(337,372)(338,373)(339,374)
(340,375)(341,381)(342,382)(343,383)(344,384)(345,385)(346,386)(347,387)
(348,388)(349,389)(350,390)(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)(411,456)
(412,457)(413,458)(414,459)(415,460)(416,451)(417,452)(418,453)(419,454)
(420,455)(421,461)(422,462)(423,463)(424,464)(425,465)(426,466)(427,467)
(428,468)(429,469)(430,470)(431,476)(432,477)(433,478)(434,479)(435,480)
(436,471)(437,472)(438,473)(439,474)(440,475)(481,541)(482,542)(483,543)
(484,544)(485,545)(486,546)(487,547)(488,548)(489,549)(490,550)(491,556)
(492,557)(493,558)(494,559)(495,560)(496,551)(497,552)(498,553)(499,554)
(500,555)(501,521)(502,522)(503,523)(504,524)(505,525)(506,526)(507,527)
(508,528)(509,529)(510,530)(511,536)(512,537)(513,538)(514,539)(515,540)
(516,531)(517,532)(518,533)(519,534)(520,535)(561,621)(562,622)(563,623)
(564,624)(565,625)(566,626)(567,627)(568,628)(569,629)(570,630)(571,636)
(572,637)(573,638)(574,639)(575,640)(576,631)(577,632)(578,633)(579,634)
(580,635)(581,601)(582,602)(583,603)(584,604)(585,605)(586,606)(587,607)
(588,608)(589,609)(590,610)(591,616)(592,617)(593,618)(594,619)(595,620)
(596,611)(597,612)(598,613)(599,614)(600,615);
s3 := Sym(640)!(  1,321)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)
(  8,328)(  9,329)( 10,330)( 11,336)( 12,337)( 13,338)( 14,339)( 15,340)
( 16,331)( 17,332)( 18,333)( 19,334)( 20,335)( 21,341)( 22,342)( 23,343)
( 24,344)( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,356)
( 32,357)( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)
( 40,355)( 41,371)( 42,372)( 43,373)( 44,374)( 45,375)( 46,376)( 47,377)
( 48,378)( 49,379)( 50,380)( 51,361)( 52,362)( 53,363)( 54,364)( 55,365)
( 56,366)( 57,367)( 58,368)( 59,369)( 60,370)( 61,391)( 62,392)( 63,393)
( 64,394)( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)
( 72,382)( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)
( 80,390)( 81,401)( 82,402)( 83,403)( 84,404)( 85,405)( 86,406)( 87,407)
( 88,408)( 89,409)( 90,410)( 91,416)( 92,417)( 93,418)( 94,419)( 95,420)
( 96,411)( 97,412)( 98,413)( 99,414)(100,415)(101,421)(102,422)(103,423)
(104,424)(105,425)(106,426)(107,427)(108,428)(109,429)(110,430)(111,436)
(112,437)(113,438)(114,439)(115,440)(116,431)(117,432)(118,433)(119,434)
(120,435)(121,451)(122,452)(123,453)(124,454)(125,455)(126,456)(127,457)
(128,458)(129,459)(130,460)(131,441)(132,442)(133,443)(134,444)(135,445)
(136,446)(137,447)(138,448)(139,449)(140,450)(141,471)(142,472)(143,473)
(144,474)(145,475)(146,476)(147,477)(148,478)(149,479)(150,480)(151,461)
(152,462)(153,463)(154,464)(155,465)(156,466)(157,467)(158,468)(159,469)
(160,470)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)
(168,488)(169,489)(170,490)(171,496)(172,497)(173,498)(174,499)(175,500)
(176,491)(177,492)(178,493)(179,494)(180,495)(181,501)(182,502)(183,503)
(184,504)(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,516)
(192,517)(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)
(200,515)(201,531)(202,532)(203,533)(204,534)(205,535)(206,536)(207,537)
(208,538)(209,539)(210,540)(211,521)(212,522)(213,523)(214,524)(215,525)
(216,526)(217,527)(218,528)(219,529)(220,530)(221,551)(222,552)(223,553)
(224,554)(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)
(232,542)(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)
(240,550)(241,561)(242,562)(243,563)(244,564)(245,565)(246,566)(247,567)
(248,568)(249,569)(250,570)(251,576)(252,577)(253,578)(254,579)(255,580)
(256,571)(257,572)(258,573)(259,574)(260,575)(261,581)(262,582)(263,583)
(264,584)(265,585)(266,586)(267,587)(268,588)(269,589)(270,590)(271,596)
(272,597)(273,598)(274,599)(275,600)(276,591)(277,592)(278,593)(279,594)
(280,595)(281,611)(282,612)(283,613)(284,614)(285,615)(286,616)(287,617)
(288,618)(289,619)(290,620)(291,601)(292,602)(293,603)(294,604)(295,605)
(296,606)(297,607)(298,608)(299,609)(300,610)(301,631)(302,632)(303,633)
(304,634)(305,635)(306,636)(307,637)(308,638)(309,639)(310,640)(311,621)
(312,622)(313,623)(314,624)(315,625)(316,626)(317,627)(318,628)(319,629)
(320,630);
poly := sub<Sym(640)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope