Polytope of Type {20,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8,4}*1280d
Also Known As : {{20,8|2},{8,4|2}}. if this polytope has another name.
Group : SmallGroup(1280,201309)
Rank : 4
Schlafli Type : {20,8,4}
Number of vertices, edges, etc : 20, 80, 16, 4
Order of s0s1s2s3 : 40
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 : {20,4,4}*640, {20,8,2}*640a, {10,8,4}*640a
   4-fold quotients : {20,4,2}*320, {20,2,4}*320, {10,4,4}*320, {10,8,2}*320
   5-fold quotients : {4,8,4}*256d
   8-fold quotients : {20,2,2}*160, {10,2,4}*160, {10,4,2}*160
   10-fold quotients : {4,4,4}*128, {2,8,4}*128a, {4,8,2}*128a
   16-fold quotients : {5,2,4}*80, {10,2,2}*80
   20-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,8,2}*64
   32-fold quotients : {5,2,2}*40
   40-fold quotients : {2,2,4}*32, {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 := (  1,401)(  2,405)(  3,404)(  4,403)(  5,402)(  6,406)(  7,410)(  8,409)
(  9,408)( 10,407)( 11,411)( 12,415)( 13,414)( 14,413)( 15,412)( 16,416)
( 17,420)( 18,419)( 19,418)( 20,417)( 21,421)( 22,425)( 23,424)( 24,423)
( 25,422)( 26,426)( 27,430)( 28,429)( 29,428)( 30,427)( 31,431)( 32,435)
( 33,434)( 34,433)( 35,432)( 36,436)( 37,440)( 38,439)( 39,438)( 40,437)
( 41,441)( 42,445)( 43,444)( 44,443)( 45,442)( 46,446)( 47,450)( 48,449)
( 49,448)( 50,447)( 51,451)( 52,455)( 53,454)( 54,453)( 55,452)( 56,456)
( 57,460)( 58,459)( 59,458)( 60,457)( 61,461)( 62,465)( 63,464)( 64,463)
( 65,462)( 66,466)( 67,470)( 68,469)( 69,468)( 70,467)( 71,471)( 72,475)
( 73,474)( 74,473)( 75,472)( 76,476)( 77,480)( 78,479)( 79,478)( 80,477)
( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)( 88,329)
( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,336)
( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,345)(103,344)(104,343)
(105,342)(106,346)(107,350)(108,349)(109,348)(110,347)(111,351)(112,355)
(113,354)(114,353)(115,352)(116,356)(117,360)(118,359)(119,358)(120,357)
(121,361)(122,365)(123,364)(124,363)(125,362)(126,366)(127,370)(128,369)
(129,368)(130,367)(131,371)(132,375)(133,374)(134,373)(135,372)(136,376)
(137,380)(138,379)(139,378)(140,377)(141,381)(142,385)(143,384)(144,383)
(145,382)(146,386)(147,390)(148,389)(149,388)(150,387)(151,391)(152,395)
(153,394)(154,393)(155,392)(156,396)(157,400)(158,399)(159,398)(160,397)
(161,571)(162,575)(163,574)(164,573)(165,572)(166,576)(167,580)(168,579)
(169,578)(170,577)(171,561)(172,565)(173,564)(174,563)(175,562)(176,566)
(177,570)(178,569)(179,568)(180,567)(181,591)(182,595)(183,594)(184,593)
(185,592)(186,596)(187,600)(188,599)(189,598)(190,597)(191,581)(192,585)
(193,584)(194,583)(195,582)(196,586)(197,590)(198,589)(199,588)(200,587)
(201,611)(202,615)(203,614)(204,613)(205,612)(206,616)(207,620)(208,619)
(209,618)(210,617)(211,601)(212,605)(213,604)(214,603)(215,602)(216,606)
(217,610)(218,609)(219,608)(220,607)(221,631)(222,635)(223,634)(224,633)
(225,632)(226,636)(227,640)(228,639)(229,638)(230,637)(231,621)(232,625)
(233,624)(234,623)(235,622)(236,626)(237,630)(238,629)(239,628)(240,627)
(241,491)(242,495)(243,494)(244,493)(245,492)(246,496)(247,500)(248,499)
(249,498)(250,497)(251,481)(252,485)(253,484)(254,483)(255,482)(256,486)
(257,490)(258,489)(259,488)(260,487)(261,511)(262,515)(263,514)(264,513)
(265,512)(266,516)(267,520)(268,519)(269,518)(270,517)(271,501)(272,505)
(273,504)(274,503)(275,502)(276,506)(277,510)(278,509)(279,508)(280,507)
(281,531)(282,535)(283,534)(284,533)(285,532)(286,536)(287,540)(288,539)
(289,538)(290,537)(291,521)(292,525)(293,524)(294,523)(295,522)(296,526)
(297,530)(298,529)(299,528)(300,527)(301,551)(302,555)(303,554)(304,553)
(305,552)(306,556)(307,560)(308,559)(309,558)(310,557)(311,541)(312,545)
(313,544)(314,543)(315,542)(316,546)(317,550)(318,549)(319,548)(320,547);;
s1 := (  1,163)(  2,162)(  3,161)(  4,165)(  5,164)(  6,168)(  7,167)(  8,166)
(  9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)( 16,178)
( 17,177)( 18,176)( 19,180)( 20,179)( 21,188)( 22,187)( 23,186)( 24,190)
( 25,189)( 26,183)( 27,182)( 28,181)( 29,185)( 30,184)( 31,198)( 32,197)
( 33,196)( 34,200)( 35,199)( 36,193)( 37,192)( 38,191)( 39,195)( 40,194)
( 41,203)( 42,202)( 43,201)( 44,205)( 45,204)( 46,208)( 47,207)( 48,206)
( 49,210)( 50,209)( 51,213)( 52,212)( 53,211)( 54,215)( 55,214)( 56,218)
( 57,217)( 58,216)( 59,220)( 60,219)( 61,228)( 62,227)( 63,226)( 64,230)
( 65,229)( 66,223)( 67,222)( 68,221)( 69,225)( 70,224)( 71,238)( 72,237)
( 73,236)( 74,240)( 75,239)( 76,233)( 77,232)( 78,231)( 79,235)( 80,234)
( 81,243)( 82,242)( 83,241)( 84,245)( 85,244)( 86,248)( 87,247)( 88,246)
( 89,250)( 90,249)( 91,253)( 92,252)( 93,251)( 94,255)( 95,254)( 96,258)
( 97,257)( 98,256)( 99,260)(100,259)(101,268)(102,267)(103,266)(104,270)
(105,269)(106,263)(107,262)(108,261)(109,265)(110,264)(111,278)(112,277)
(113,276)(114,280)(115,279)(116,273)(117,272)(118,271)(119,275)(120,274)
(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)(128,286)
(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)(136,298)
(137,297)(138,296)(139,300)(140,299)(141,308)(142,307)(143,306)(144,310)
(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)(152,317)
(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)(160,314)
(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)(328,486)
(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)(336,498)
(337,497)(338,496)(339,500)(340,499)(341,508)(342,507)(343,506)(344,510)
(345,509)(346,503)(347,502)(348,501)(349,505)(350,504)(351,518)(352,517)
(353,516)(354,520)(355,519)(356,513)(357,512)(358,511)(359,515)(360,514)
(361,523)(362,522)(363,521)(364,525)(365,524)(366,528)(367,527)(368,526)
(369,530)(370,529)(371,533)(372,532)(373,531)(374,535)(375,534)(376,538)
(377,537)(378,536)(379,540)(380,539)(381,548)(382,547)(383,546)(384,550)
(385,549)(386,543)(387,542)(388,541)(389,545)(390,544)(391,558)(392,557)
(393,556)(394,560)(395,559)(396,553)(397,552)(398,551)(399,555)(400,554)
(401,563)(402,562)(403,561)(404,565)(405,564)(406,568)(407,567)(408,566)
(409,570)(410,569)(411,573)(412,572)(413,571)(414,575)(415,574)(416,578)
(417,577)(418,576)(419,580)(420,579)(421,588)(422,587)(423,586)(424,590)
(425,589)(426,583)(427,582)(428,581)(429,585)(430,584)(431,598)(432,597)
(433,596)(434,600)(435,599)(436,593)(437,592)(438,591)(439,595)(440,594)
(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)(448,606)
(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)(456,618)
(457,617)(458,616)(459,620)(460,619)(461,628)(462,627)(463,626)(464,630)
(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)(472,637)
(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)(480,634);;
s2 := ( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)( 33, 38)
( 34, 39)( 35, 40)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 71, 76)
( 72, 77)( 73, 78)( 74, 79)( 75, 80)( 81,121)( 82,122)( 83,123)( 84,124)
( 85,125)( 86,126)( 87,127)( 88,128)( 89,129)( 90,130)( 91,131)( 92,132)
( 93,133)( 94,134)( 95,135)( 96,136)( 97,137)( 98,138)( 99,139)(100,140)
(101,146)(102,147)(103,148)(104,149)(105,150)(106,141)(107,142)(108,143)
(109,144)(110,145)(111,156)(112,157)(113,158)(114,159)(115,160)(116,151)
(117,152)(118,153)(119,154)(120,155)(161,181)(162,182)(163,183)(164,184)
(165,185)(166,186)(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)
(173,193)(174,194)(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)
(201,221)(202,222)(203,223)(204,224)(205,225)(206,226)(207,227)(208,228)
(209,229)(210,230)(211,231)(212,232)(213,233)(214,234)(215,235)(216,236)
(217,237)(218,238)(219,239)(220,240)(241,301)(242,302)(243,303)(244,304)
(245,305)(246,306)(247,307)(248,308)(249,309)(250,310)(251,311)(252,312)
(253,313)(254,314)(255,315)(256,316)(257,317)(258,318)(259,319)(260,320)
(261,281)(262,282)(263,283)(264,284)(265,285)(266,286)(267,287)(268,288)
(269,289)(270,290)(271,291)(272,292)(273,293)(274,294)(275,295)(276,296)
(277,297)(278,298)(279,299)(280,300)(321,361)(322,362)(323,363)(324,364)
(325,365)(326,366)(327,367)(328,368)(329,369)(330,370)(331,371)(332,372)
(333,373)(334,374)(335,375)(336,376)(337,377)(338,378)(339,379)(340,380)
(341,386)(342,387)(343,388)(344,389)(345,390)(346,381)(347,382)(348,383)
(349,384)(350,385)(351,396)(352,397)(353,398)(354,399)(355,400)(356,391)
(357,392)(358,393)(359,394)(360,395)(421,426)(422,427)(423,428)(424,429)
(425,430)(431,436)(432,437)(433,438)(434,439)(435,440)(461,466)(462,467)
(463,468)(464,469)(465,470)(471,476)(472,477)(473,478)(474,479)(475,480)
(481,541)(482,542)(483,543)(484,544)(485,545)(486,546)(487,547)(488,548)
(489,549)(490,550)(491,551)(492,552)(493,553)(494,554)(495,555)(496,556)
(497,557)(498,558)(499,559)(500,560)(501,521)(502,522)(503,523)(504,524)
(505,525)(506,526)(507,527)(508,528)(509,529)(510,530)(511,531)(512,532)
(513,533)(514,534)(515,535)(516,536)(517,537)(518,538)(519,539)(520,540)
(561,581)(562,582)(563,583)(564,584)(565,585)(566,586)(567,587)(568,588)
(569,589)(570,590)(571,591)(572,592)(573,593)(574,594)(575,595)(576,596)
(577,597)(578,598)(579,599)(580,600)(601,621)(602,622)(603,623)(604,624)
(605,625)(606,626)(607,627)(608,628)(609,629)(610,630)(611,631)(612,632)
(613,633)(614,634)(615,635)(616,636)(617,637)(618,638)(619,639)(620,640);;
s3 := (  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 88)
(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)
( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)( 24,104)
( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)
( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)
( 41,121)( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)
( 49,129)( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)
( 57,137)( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)( 64,144)
( 65,145)( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)
( 73,153)( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)
(161,241)(162,242)(163,243)(164,244)(165,245)(166,246)(167,247)(168,248)
(169,249)(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)(176,256)
(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)(184,264)
(185,265)(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)(192,272)
(193,273)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)
(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)
(209,289)(210,290)(211,291)(212,292)(213,293)(214,294)(215,295)(216,296)
(217,297)(218,298)(219,299)(220,300)(221,301)(222,302)(223,303)(224,304)
(225,305)(226,306)(227,307)(228,308)(229,309)(230,310)(231,311)(232,312)
(233,313)(234,314)(235,315)(236,316)(237,317)(238,318)(239,319)(240,320)
(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)(328,408)
(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)(336,416)
(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)(344,424)
(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)(352,432)
(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)(360,440)
(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)(368,448)
(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)(376,456)
(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)(384,464)
(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)(392,472)
(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)(400,480)
(481,561)(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)(488,568)
(489,569)(490,570)(491,571)(492,572)(493,573)(494,574)(495,575)(496,576)
(497,577)(498,578)(499,579)(500,580)(501,581)(502,582)(503,583)(504,584)
(505,585)(506,586)(507,587)(508,588)(509,589)(510,590)(511,591)(512,592)
(513,593)(514,594)(515,595)(516,596)(517,597)(518,598)(519,599)(520,600)
(521,601)(522,602)(523,603)(524,604)(525,605)(526,606)(527,607)(528,608)
(529,609)(530,610)(531,611)(532,612)(533,613)(534,614)(535,615)(536,616)
(537,617)(538,618)(539,619)(540,620)(541,621)(542,622)(543,623)(544,624)
(545,625)(546,626)(547,627)(548,628)(549,629)(550,630)(551,631)(552,632)
(553,633)(554,634)(555,635)(556,636)(557,637)(558,638)(559,639)(560,640);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(640)!(  1,401)(  2,405)(  3,404)(  4,403)(  5,402)(  6,406)(  7,410)
(  8,409)(  9,408)( 10,407)( 11,411)( 12,415)( 13,414)( 14,413)( 15,412)
( 16,416)( 17,420)( 18,419)( 19,418)( 20,417)( 21,421)( 22,425)( 23,424)
( 24,423)( 25,422)( 26,426)( 27,430)( 28,429)( 29,428)( 30,427)( 31,431)
( 32,435)( 33,434)( 34,433)( 35,432)( 36,436)( 37,440)( 38,439)( 39,438)
( 40,437)( 41,441)( 42,445)( 43,444)( 44,443)( 45,442)( 46,446)( 47,450)
( 48,449)( 49,448)( 50,447)( 51,451)( 52,455)( 53,454)( 54,453)( 55,452)
( 56,456)( 57,460)( 58,459)( 59,458)( 60,457)( 61,461)( 62,465)( 63,464)
( 64,463)( 65,462)( 66,466)( 67,470)( 68,469)( 69,468)( 70,467)( 71,471)
( 72,475)( 73,474)( 74,473)( 75,472)( 76,476)( 77,480)( 78,479)( 79,478)
( 80,477)( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)
( 88,329)( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)
( 96,336)( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,345)(103,344)
(104,343)(105,342)(106,346)(107,350)(108,349)(109,348)(110,347)(111,351)
(112,355)(113,354)(114,353)(115,352)(116,356)(117,360)(118,359)(119,358)
(120,357)(121,361)(122,365)(123,364)(124,363)(125,362)(126,366)(127,370)
(128,369)(129,368)(130,367)(131,371)(132,375)(133,374)(134,373)(135,372)
(136,376)(137,380)(138,379)(139,378)(140,377)(141,381)(142,385)(143,384)
(144,383)(145,382)(146,386)(147,390)(148,389)(149,388)(150,387)(151,391)
(152,395)(153,394)(154,393)(155,392)(156,396)(157,400)(158,399)(159,398)
(160,397)(161,571)(162,575)(163,574)(164,573)(165,572)(166,576)(167,580)
(168,579)(169,578)(170,577)(171,561)(172,565)(173,564)(174,563)(175,562)
(176,566)(177,570)(178,569)(179,568)(180,567)(181,591)(182,595)(183,594)
(184,593)(185,592)(186,596)(187,600)(188,599)(189,598)(190,597)(191,581)
(192,585)(193,584)(194,583)(195,582)(196,586)(197,590)(198,589)(199,588)
(200,587)(201,611)(202,615)(203,614)(204,613)(205,612)(206,616)(207,620)
(208,619)(209,618)(210,617)(211,601)(212,605)(213,604)(214,603)(215,602)
(216,606)(217,610)(218,609)(219,608)(220,607)(221,631)(222,635)(223,634)
(224,633)(225,632)(226,636)(227,640)(228,639)(229,638)(230,637)(231,621)
(232,625)(233,624)(234,623)(235,622)(236,626)(237,630)(238,629)(239,628)
(240,627)(241,491)(242,495)(243,494)(244,493)(245,492)(246,496)(247,500)
(248,499)(249,498)(250,497)(251,481)(252,485)(253,484)(254,483)(255,482)
(256,486)(257,490)(258,489)(259,488)(260,487)(261,511)(262,515)(263,514)
(264,513)(265,512)(266,516)(267,520)(268,519)(269,518)(270,517)(271,501)
(272,505)(273,504)(274,503)(275,502)(276,506)(277,510)(278,509)(279,508)
(280,507)(281,531)(282,535)(283,534)(284,533)(285,532)(286,536)(287,540)
(288,539)(289,538)(290,537)(291,521)(292,525)(293,524)(294,523)(295,522)
(296,526)(297,530)(298,529)(299,528)(300,527)(301,551)(302,555)(303,554)
(304,553)(305,552)(306,556)(307,560)(308,559)(309,558)(310,557)(311,541)
(312,545)(313,544)(314,543)(315,542)(316,546)(317,550)(318,549)(319,548)
(320,547);
s1 := Sym(640)!(  1,163)(  2,162)(  3,161)(  4,165)(  5,164)(  6,168)(  7,167)
(  8,166)(  9,170)( 10,169)( 11,173)( 12,172)( 13,171)( 14,175)( 15,174)
( 16,178)( 17,177)( 18,176)( 19,180)( 20,179)( 21,188)( 22,187)( 23,186)
( 24,190)( 25,189)( 26,183)( 27,182)( 28,181)( 29,185)( 30,184)( 31,198)
( 32,197)( 33,196)( 34,200)( 35,199)( 36,193)( 37,192)( 38,191)( 39,195)
( 40,194)( 41,203)( 42,202)( 43,201)( 44,205)( 45,204)( 46,208)( 47,207)
( 48,206)( 49,210)( 50,209)( 51,213)( 52,212)( 53,211)( 54,215)( 55,214)
( 56,218)( 57,217)( 58,216)( 59,220)( 60,219)( 61,228)( 62,227)( 63,226)
( 64,230)( 65,229)( 66,223)( 67,222)( 68,221)( 69,225)( 70,224)( 71,238)
( 72,237)( 73,236)( 74,240)( 75,239)( 76,233)( 77,232)( 78,231)( 79,235)
( 80,234)( 81,243)( 82,242)( 83,241)( 84,245)( 85,244)( 86,248)( 87,247)
( 88,246)( 89,250)( 90,249)( 91,253)( 92,252)( 93,251)( 94,255)( 95,254)
( 96,258)( 97,257)( 98,256)( 99,260)(100,259)(101,268)(102,267)(103,266)
(104,270)(105,269)(106,263)(107,262)(108,261)(109,265)(110,264)(111,278)
(112,277)(113,276)(114,280)(115,279)(116,273)(117,272)(118,271)(119,275)
(120,274)(121,283)(122,282)(123,281)(124,285)(125,284)(126,288)(127,287)
(128,286)(129,290)(130,289)(131,293)(132,292)(133,291)(134,295)(135,294)
(136,298)(137,297)(138,296)(139,300)(140,299)(141,308)(142,307)(143,306)
(144,310)(145,309)(146,303)(147,302)(148,301)(149,305)(150,304)(151,318)
(152,317)(153,316)(154,320)(155,319)(156,313)(157,312)(158,311)(159,315)
(160,314)(321,483)(322,482)(323,481)(324,485)(325,484)(326,488)(327,487)
(328,486)(329,490)(330,489)(331,493)(332,492)(333,491)(334,495)(335,494)
(336,498)(337,497)(338,496)(339,500)(340,499)(341,508)(342,507)(343,506)
(344,510)(345,509)(346,503)(347,502)(348,501)(349,505)(350,504)(351,518)
(352,517)(353,516)(354,520)(355,519)(356,513)(357,512)(358,511)(359,515)
(360,514)(361,523)(362,522)(363,521)(364,525)(365,524)(366,528)(367,527)
(368,526)(369,530)(370,529)(371,533)(372,532)(373,531)(374,535)(375,534)
(376,538)(377,537)(378,536)(379,540)(380,539)(381,548)(382,547)(383,546)
(384,550)(385,549)(386,543)(387,542)(388,541)(389,545)(390,544)(391,558)
(392,557)(393,556)(394,560)(395,559)(396,553)(397,552)(398,551)(399,555)
(400,554)(401,563)(402,562)(403,561)(404,565)(405,564)(406,568)(407,567)
(408,566)(409,570)(410,569)(411,573)(412,572)(413,571)(414,575)(415,574)
(416,578)(417,577)(418,576)(419,580)(420,579)(421,588)(422,587)(423,586)
(424,590)(425,589)(426,583)(427,582)(428,581)(429,585)(430,584)(431,598)
(432,597)(433,596)(434,600)(435,599)(436,593)(437,592)(438,591)(439,595)
(440,594)(441,603)(442,602)(443,601)(444,605)(445,604)(446,608)(447,607)
(448,606)(449,610)(450,609)(451,613)(452,612)(453,611)(454,615)(455,614)
(456,618)(457,617)(458,616)(459,620)(460,619)(461,628)(462,627)(463,626)
(464,630)(465,629)(466,623)(467,622)(468,621)(469,625)(470,624)(471,638)
(472,637)(473,636)(474,640)(475,639)(476,633)(477,632)(478,631)(479,635)
(480,634);
s2 := Sym(640)!( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)
( 33, 38)( 34, 39)( 35, 40)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)
( 71, 76)( 72, 77)( 73, 78)( 74, 79)( 75, 80)( 81,121)( 82,122)( 83,123)
( 84,124)( 85,125)( 86,126)( 87,127)( 88,128)( 89,129)( 90,130)( 91,131)
( 92,132)( 93,133)( 94,134)( 95,135)( 96,136)( 97,137)( 98,138)( 99,139)
(100,140)(101,146)(102,147)(103,148)(104,149)(105,150)(106,141)(107,142)
(108,143)(109,144)(110,145)(111,156)(112,157)(113,158)(114,159)(115,160)
(116,151)(117,152)(118,153)(119,154)(120,155)(161,181)(162,182)(163,183)
(164,184)(165,185)(166,186)(167,187)(168,188)(169,189)(170,190)(171,191)
(172,192)(173,193)(174,194)(175,195)(176,196)(177,197)(178,198)(179,199)
(180,200)(201,221)(202,222)(203,223)(204,224)(205,225)(206,226)(207,227)
(208,228)(209,229)(210,230)(211,231)(212,232)(213,233)(214,234)(215,235)
(216,236)(217,237)(218,238)(219,239)(220,240)(241,301)(242,302)(243,303)
(244,304)(245,305)(246,306)(247,307)(248,308)(249,309)(250,310)(251,311)
(252,312)(253,313)(254,314)(255,315)(256,316)(257,317)(258,318)(259,319)
(260,320)(261,281)(262,282)(263,283)(264,284)(265,285)(266,286)(267,287)
(268,288)(269,289)(270,290)(271,291)(272,292)(273,293)(274,294)(275,295)
(276,296)(277,297)(278,298)(279,299)(280,300)(321,361)(322,362)(323,363)
(324,364)(325,365)(326,366)(327,367)(328,368)(329,369)(330,370)(331,371)
(332,372)(333,373)(334,374)(335,375)(336,376)(337,377)(338,378)(339,379)
(340,380)(341,386)(342,387)(343,388)(344,389)(345,390)(346,381)(347,382)
(348,383)(349,384)(350,385)(351,396)(352,397)(353,398)(354,399)(355,400)
(356,391)(357,392)(358,393)(359,394)(360,395)(421,426)(422,427)(423,428)
(424,429)(425,430)(431,436)(432,437)(433,438)(434,439)(435,440)(461,466)
(462,467)(463,468)(464,469)(465,470)(471,476)(472,477)(473,478)(474,479)
(475,480)(481,541)(482,542)(483,543)(484,544)(485,545)(486,546)(487,547)
(488,548)(489,549)(490,550)(491,551)(492,552)(493,553)(494,554)(495,555)
(496,556)(497,557)(498,558)(499,559)(500,560)(501,521)(502,522)(503,523)
(504,524)(505,525)(506,526)(507,527)(508,528)(509,529)(510,530)(511,531)
(512,532)(513,533)(514,534)(515,535)(516,536)(517,537)(518,538)(519,539)
(520,540)(561,581)(562,582)(563,583)(564,584)(565,585)(566,586)(567,587)
(568,588)(569,589)(570,590)(571,591)(572,592)(573,593)(574,594)(575,595)
(576,596)(577,597)(578,598)(579,599)(580,600)(601,621)(602,622)(603,623)
(604,624)(605,625)(606,626)(607,627)(608,628)(609,629)(610,630)(611,631)
(612,632)(613,633)(614,634)(615,635)(616,636)(617,637)(618,638)(619,639)
(620,640);
s3 := Sym(640)!(  1, 81)(  2, 82)(  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)
(  8, 88)(  9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)
( 16, 96)( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)
( 24,104)( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)
( 32,112)( 33,113)( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)
( 40,120)( 41,121)( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)
( 48,128)( 49,129)( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)
( 56,136)( 57,137)( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)
( 64,144)( 65,145)( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)
( 72,152)( 73,153)( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)
( 80,160)(161,241)(162,242)(163,243)(164,244)(165,245)(166,246)(167,247)
(168,248)(169,249)(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)
(176,256)(177,257)(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)
(184,264)(185,265)(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)
(192,272)(193,273)(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)
(200,280)(201,281)(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)
(208,288)(209,289)(210,290)(211,291)(212,292)(213,293)(214,294)(215,295)
(216,296)(217,297)(218,298)(219,299)(220,300)(221,301)(222,302)(223,303)
(224,304)(225,305)(226,306)(227,307)(228,308)(229,309)(230,310)(231,311)
(232,312)(233,313)(234,314)(235,315)(236,316)(237,317)(238,318)(239,319)
(240,320)(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)
(328,408)(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)
(336,416)(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)
(344,424)(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)
(352,432)(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)
(360,440)(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)
(368,448)(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)
(376,456)(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)
(384,464)(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)
(392,472)(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)
(400,480)(481,561)(482,562)(483,563)(484,564)(485,565)(486,566)(487,567)
(488,568)(489,569)(490,570)(491,571)(492,572)(493,573)(494,574)(495,575)
(496,576)(497,577)(498,578)(499,579)(500,580)(501,581)(502,582)(503,583)
(504,584)(505,585)(506,586)(507,587)(508,588)(509,589)(510,590)(511,591)
(512,592)(513,593)(514,594)(515,595)(516,596)(517,597)(518,598)(519,599)
(520,600)(521,601)(522,602)(523,603)(524,604)(525,605)(526,606)(527,607)
(528,608)(529,609)(530,610)(531,611)(532,612)(533,613)(534,614)(535,615)
(536,616)(537,617)(538,618)(539,619)(540,620)(541,621)(542,622)(543,623)
(544,624)(545,625)(546,626)(547,627)(548,628)(549,629)(550,630)(551,631)
(552,632)(553,633)(554,634)(555,635)(556,636)(557,637)(558,638)(559,639)
(560,640);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope