Polytope of Type {10,16,4}

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