Polytope of Type {16,4,10}

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