Polytope of Type {4,20,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20,8}*1280a
Also Known As : {{4,20|2},{20,8|2}}. if this polytope has another name.
Group : SmallGroup(1280,200567)
Rank : 4
Schlafli Type : {4,20,8}
Number of vertices, edges, etc : 4, 40, 80, 8
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 : {4,20,4}*640, {2,20,8}*640a, {4,10,8}*640
   4-fold quotients : {2,20,4}*320, {4,20,2}*320, {4,10,4}*320, {2,10,8}*320
   5-fold quotients : {4,4,8}*256a
   8-fold quotients : {2,20,2}*160, {2,10,4}*160, {4,10,2}*160
   10-fold quotients : {4,4,4}*128, {2,4,8}*128a, {4,2,8}*128
   16-fold quotients : {2,10,2}*80
   20-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64, {2,2,8}*64
   32-fold quotients : {2,5,2}*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)(  2,402)(  3,403)(  4,404)(  5,405)(  6,406)(  7,407)(  8,408)
(  9,409)( 10,410)( 11,411)( 12,412)( 13,413)( 14,414)( 15,415)( 16,416)
( 17,417)( 18,418)( 19,419)( 20,420)( 21,421)( 22,422)( 23,423)( 24,424)
( 25,425)( 26,426)( 27,427)( 28,428)( 29,429)( 30,430)( 31,431)( 32,432)
( 33,433)( 34,434)( 35,435)( 36,436)( 37,437)( 38,438)( 39,439)( 40,440)
( 41,441)( 42,442)( 43,443)( 44,444)( 45,445)( 46,446)( 47,447)( 48,448)
( 49,449)( 50,450)( 51,451)( 52,452)( 53,453)( 54,454)( 55,455)( 56,456)
( 57,457)( 58,458)( 59,459)( 60,460)( 61,461)( 62,462)( 63,463)( 64,464)
( 65,465)( 66,466)( 67,467)( 68,468)( 69,469)( 70,470)( 71,471)( 72,472)
( 73,473)( 74,474)( 75,475)( 76,476)( 77,477)( 78,478)( 79,479)( 80,480)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,571)(162,572)(163,573)(164,574)(165,575)(166,576)(167,577)(168,578)
(169,579)(170,580)(171,561)(172,562)(173,563)(174,564)(175,565)(176,566)
(177,567)(178,568)(179,569)(180,570)(181,591)(182,592)(183,593)(184,594)
(185,595)(186,596)(187,597)(188,598)(189,599)(190,600)(191,581)(192,582)
(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)(200,590)
(201,611)(202,612)(203,613)(204,614)(205,615)(206,616)(207,617)(208,618)
(209,619)(210,620)(211,601)(212,602)(213,603)(214,604)(215,605)(216,606)
(217,607)(218,608)(219,609)(220,610)(221,631)(222,632)(223,633)(224,634)
(225,635)(226,636)(227,637)(228,638)(229,639)(230,640)(231,621)(232,622)
(233,623)(234,624)(235,625)(236,626)(237,627)(238,628)(239,629)(240,630)
(241,491)(242,492)(243,493)(244,494)(245,495)(246,496)(247,497)(248,498)
(249,499)(250,500)(251,481)(252,482)(253,483)(254,484)(255,485)(256,486)
(257,487)(258,488)(259,489)(260,490)(261,511)(262,512)(263,513)(264,514)
(265,515)(266,516)(267,517)(268,518)(269,519)(270,520)(271,501)(272,502)
(273,503)(274,504)(275,505)(276,506)(277,507)(278,508)(279,509)(280,510)
(281,531)(282,532)(283,533)(284,534)(285,535)(286,536)(287,537)(288,538)
(289,539)(290,540)(291,521)(292,522)(293,523)(294,524)(295,525)(296,526)
(297,527)(298,528)(299,529)(300,530)(301,551)(302,552)(303,553)(304,554)
(305,555)(306,556)(307,557)(308,558)(309,559)(310,560)(311,541)(312,542)
(313,543)(314,544)(315,545)(316,546)(317,547)(318,548)(319,549)(320,550);;
s1 := (  1,161)(  2,165)(  3,164)(  4,163)(  5,162)(  6,166)(  7,170)(  8,169)
(  9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)( 16,176)
( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)( 24,183)
( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)( 32,195)
( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)( 40,197)
( 41,201)( 42,205)( 43,204)( 44,203)( 45,202)( 46,206)( 47,210)( 48,209)
( 49,208)( 50,207)( 51,211)( 52,215)( 53,214)( 54,213)( 55,212)( 56,216)
( 57,220)( 58,219)( 59,218)( 60,217)( 61,221)( 62,225)( 63,224)( 64,223)
( 65,222)( 66,226)( 67,230)( 68,229)( 69,228)( 70,227)( 71,231)( 72,235)
( 73,234)( 74,233)( 75,232)( 76,236)( 77,240)( 78,239)( 79,238)( 80,237)
( 81,241)( 82,245)( 83,244)( 84,243)( 85,242)( 86,246)( 87,250)( 88,249)
( 89,248)( 90,247)( 91,251)( 92,255)( 93,254)( 94,253)( 95,252)( 96,256)
( 97,260)( 98,259)( 99,258)(100,257)(101,261)(102,265)(103,264)(104,263)
(105,262)(106,266)(107,270)(108,269)(109,268)(110,267)(111,271)(112,275)
(113,274)(114,273)(115,272)(116,276)(117,280)(118,279)(119,278)(120,277)
(121,281)(122,285)(123,284)(124,283)(125,282)(126,286)(127,290)(128,289)
(129,288)(130,287)(131,291)(132,295)(133,294)(134,293)(135,292)(136,296)
(137,300)(138,299)(139,298)(140,297)(141,301)(142,305)(143,304)(144,303)
(145,302)(146,306)(147,310)(148,309)(149,308)(150,307)(151,311)(152,315)
(153,314)(154,313)(155,312)(156,316)(157,320)(158,319)(159,318)(160,317)
(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)(328,489)
(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)(336,496)
(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)(344,503)
(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)(352,515)
(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)(360,517)
(361,521)(362,525)(363,524)(364,523)(365,522)(366,526)(367,530)(368,529)
(369,528)(370,527)(371,531)(372,535)(373,534)(374,533)(375,532)(376,536)
(377,540)(378,539)(379,538)(380,537)(381,541)(382,545)(383,544)(384,543)
(385,542)(386,546)(387,550)(388,549)(389,548)(390,547)(391,551)(392,555)
(393,554)(394,553)(395,552)(396,556)(397,560)(398,559)(399,558)(400,557)
(401,561)(402,565)(403,564)(404,563)(405,562)(406,566)(407,570)(408,569)
(409,568)(410,567)(411,571)(412,575)(413,574)(414,573)(415,572)(416,576)
(417,580)(418,579)(419,578)(420,577)(421,581)(422,585)(423,584)(424,583)
(425,582)(426,586)(427,590)(428,589)(429,588)(430,587)(431,591)(432,595)
(433,594)(434,593)(435,592)(436,596)(437,600)(438,599)(439,598)(440,597)
(441,601)(442,605)(443,604)(444,603)(445,602)(446,606)(447,610)(448,609)
(449,608)(450,607)(451,611)(452,615)(453,614)(454,613)(455,612)(456,616)
(457,620)(458,619)(459,618)(460,617)(461,621)(462,625)(463,624)(464,623)
(465,622)(466,626)(467,630)(468,629)(469,628)(470,627)(471,631)(472,635)
(473,634)(474,633)(475,632)(476,636)(477,640)(478,639)(479,638)(480,637);;
s2 := (  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)
( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 33)( 34, 35)( 36, 38)( 39, 40)
( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 58)( 52, 57)( 53, 56)
( 54, 60)( 55, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 70)( 65, 69)( 71, 78)
( 72, 77)( 73, 76)( 74, 80)( 75, 79)( 81,123)( 82,122)( 83,121)( 84,125)
( 85,124)( 86,128)( 87,127)( 88,126)( 89,130)( 90,129)( 91,133)( 92,132)
( 93,131)( 94,135)( 95,134)( 96,138)( 97,137)( 98,136)( 99,140)(100,139)
(101,143)(102,142)(103,141)(104,145)(105,144)(106,148)(107,147)(108,146)
(109,150)(110,149)(111,153)(112,152)(113,151)(114,155)(115,154)(116,158)
(117,157)(118,156)(119,160)(120,159)(161,183)(162,182)(163,181)(164,185)
(165,184)(166,188)(167,187)(168,186)(169,190)(170,189)(171,193)(172,192)
(173,191)(174,195)(175,194)(176,198)(177,197)(178,196)(179,200)(180,199)
(201,228)(202,227)(203,226)(204,230)(205,229)(206,223)(207,222)(208,221)
(209,225)(210,224)(211,238)(212,237)(213,236)(214,240)(215,239)(216,233)
(217,232)(218,231)(219,235)(220,234)(241,303)(242,302)(243,301)(244,305)
(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)(252,312)
(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)
(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)(268,286)
(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)(275,294)(276,298)
(277,297)(278,296)(279,300)(280,299)(321,363)(322,362)(323,361)(324,365)
(325,364)(326,368)(327,367)(328,366)(329,370)(330,369)(331,373)(332,372)
(333,371)(334,375)(335,374)(336,378)(337,377)(338,376)(339,380)(340,379)
(341,383)(342,382)(343,381)(344,385)(345,384)(346,388)(347,387)(348,386)
(349,390)(350,389)(351,393)(352,392)(353,391)(354,395)(355,394)(356,398)
(357,397)(358,396)(359,400)(360,399)(401,403)(404,405)(406,408)(409,410)
(411,413)(414,415)(416,418)(419,420)(421,423)(424,425)(426,428)(429,430)
(431,433)(434,435)(436,438)(439,440)(441,448)(442,447)(443,446)(444,450)
(445,449)(451,458)(452,457)(453,456)(454,460)(455,459)(461,468)(462,467)
(463,466)(464,470)(465,469)(471,478)(472,477)(473,476)(474,480)(475,479)
(481,543)(482,542)(483,541)(484,545)(485,544)(486,548)(487,547)(488,546)
(489,550)(490,549)(491,553)(492,552)(493,551)(494,555)(495,554)(496,558)
(497,557)(498,556)(499,560)(500,559)(501,523)(502,522)(503,521)(504,525)
(505,524)(506,528)(507,527)(508,526)(509,530)(510,529)(511,533)(512,532)
(513,531)(514,535)(515,534)(516,538)(517,537)(518,536)(519,540)(520,539)
(561,583)(562,582)(563,581)(564,585)(565,584)(566,588)(567,587)(568,586)
(569,590)(570,589)(571,593)(572,592)(573,591)(574,595)(575,594)(576,598)
(577,597)(578,596)(579,600)(580,599)(601,628)(602,627)(603,626)(604,630)
(605,629)(606,623)(607,622)(608,621)(609,625)(610,624)(611,638)(612,637)
(613,636)(614,640)(615,639)(616,633)(617,632)(618,631)(619,635)(620,634);;
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)
( 41,126)( 42,127)( 43,128)( 44,129)( 45,130)( 46,121)( 47,122)( 48,123)
( 49,124)( 50,125)( 51,136)( 52,137)( 53,138)( 54,139)( 55,140)( 56,131)
( 57,132)( 58,133)( 59,134)( 60,135)( 61,146)( 62,147)( 63,148)( 64,149)
( 65,150)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,156)( 72,157)
( 73,158)( 74,159)( 75,160)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)
(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)
(201,286)(202,287)(203,288)(204,289)(205,290)(206,281)(207,282)(208,283)
(209,284)(210,285)(211,296)(212,297)(213,298)(214,299)(215,300)(216,291)
(217,292)(218,293)(219,294)(220,295)(221,306)(222,307)(223,308)(224,309)
(225,310)(226,301)(227,302)(228,303)(229,304)(230,305)(231,316)(232,317)
(233,318)(234,319)(235,320)(236,311)(237,312)(238,313)(239,314)(240,315)
(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)
(361,446)(362,447)(363,448)(364,449)(365,450)(366,441)(367,442)(368,443)
(369,444)(370,445)(371,456)(372,457)(373,458)(374,459)(375,460)(376,451)
(377,452)(378,453)(379,454)(380,455)(381,466)(382,467)(383,468)(384,469)
(385,470)(386,461)(387,462)(388,463)(389,464)(390,465)(391,476)(392,477)
(393,478)(394,479)(395,480)(396,471)(397,472)(398,473)(399,474)(400,475)
(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)
(521,606)(522,607)(523,608)(524,609)(525,610)(526,601)(527,602)(528,603)
(529,604)(530,605)(531,616)(532,617)(533,618)(534,619)(535,620)(536,611)
(537,612)(538,613)(539,614)(540,615)(541,626)(542,627)(543,628)(544,629)
(545,630)(546,621)(547,622)(548,623)(549,624)(550,625)(551,636)(552,637)
(553,638)(554,639)(555,640)(556,631)(557,632)(558,633)(559,634)(560,635);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(640)!(  1,401)(  2,402)(  3,403)(  4,404)(  5,405)(  6,406)(  7,407)
(  8,408)(  9,409)( 10,410)( 11,411)( 12,412)( 13,413)( 14,414)( 15,415)
( 16,416)( 17,417)( 18,418)( 19,419)( 20,420)( 21,421)( 22,422)( 23,423)
( 24,424)( 25,425)( 26,426)( 27,427)( 28,428)( 29,429)( 30,430)( 31,431)
( 32,432)( 33,433)( 34,434)( 35,435)( 36,436)( 37,437)( 38,438)( 39,439)
( 40,440)( 41,441)( 42,442)( 43,443)( 44,444)( 45,445)( 46,446)( 47,447)
( 48,448)( 49,449)( 50,450)( 51,451)( 52,452)( 53,453)( 54,454)( 55,455)
( 56,456)( 57,457)( 58,458)( 59,459)( 60,460)( 61,461)( 62,462)( 63,463)
( 64,464)( 65,465)( 66,466)( 67,467)( 68,468)( 69,469)( 70,470)( 71,471)
( 72,472)( 73,473)( 74,474)( 75,475)( 76,476)( 77,477)( 78,478)( 79,479)
( 80,480)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,571)(162,572)(163,573)(164,574)(165,575)(166,576)(167,577)
(168,578)(169,579)(170,580)(171,561)(172,562)(173,563)(174,564)(175,565)
(176,566)(177,567)(178,568)(179,569)(180,570)(181,591)(182,592)(183,593)
(184,594)(185,595)(186,596)(187,597)(188,598)(189,599)(190,600)(191,581)
(192,582)(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)
(200,590)(201,611)(202,612)(203,613)(204,614)(205,615)(206,616)(207,617)
(208,618)(209,619)(210,620)(211,601)(212,602)(213,603)(214,604)(215,605)
(216,606)(217,607)(218,608)(219,609)(220,610)(221,631)(222,632)(223,633)
(224,634)(225,635)(226,636)(227,637)(228,638)(229,639)(230,640)(231,621)
(232,622)(233,623)(234,624)(235,625)(236,626)(237,627)(238,628)(239,629)
(240,630)(241,491)(242,492)(243,493)(244,494)(245,495)(246,496)(247,497)
(248,498)(249,499)(250,500)(251,481)(252,482)(253,483)(254,484)(255,485)
(256,486)(257,487)(258,488)(259,489)(260,490)(261,511)(262,512)(263,513)
(264,514)(265,515)(266,516)(267,517)(268,518)(269,519)(270,520)(271,501)
(272,502)(273,503)(274,504)(275,505)(276,506)(277,507)(278,508)(279,509)
(280,510)(281,531)(282,532)(283,533)(284,534)(285,535)(286,536)(287,537)
(288,538)(289,539)(290,540)(291,521)(292,522)(293,523)(294,524)(295,525)
(296,526)(297,527)(298,528)(299,529)(300,530)(301,551)(302,552)(303,553)
(304,554)(305,555)(306,556)(307,557)(308,558)(309,559)(310,560)(311,541)
(312,542)(313,543)(314,544)(315,545)(316,546)(317,547)(318,548)(319,549)
(320,550);
s1 := Sym(640)!(  1,161)(  2,165)(  3,164)(  4,163)(  5,162)(  6,166)(  7,170)
(  8,169)(  9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)
( 16,176)( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)
( 24,183)( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)
( 32,195)( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)
( 40,197)( 41,201)( 42,205)( 43,204)( 44,203)( 45,202)( 46,206)( 47,210)
( 48,209)( 49,208)( 50,207)( 51,211)( 52,215)( 53,214)( 54,213)( 55,212)
( 56,216)( 57,220)( 58,219)( 59,218)( 60,217)( 61,221)( 62,225)( 63,224)
( 64,223)( 65,222)( 66,226)( 67,230)( 68,229)( 69,228)( 70,227)( 71,231)
( 72,235)( 73,234)( 74,233)( 75,232)( 76,236)( 77,240)( 78,239)( 79,238)
( 80,237)( 81,241)( 82,245)( 83,244)( 84,243)( 85,242)( 86,246)( 87,250)
( 88,249)( 89,248)( 90,247)( 91,251)( 92,255)( 93,254)( 94,253)( 95,252)
( 96,256)( 97,260)( 98,259)( 99,258)(100,257)(101,261)(102,265)(103,264)
(104,263)(105,262)(106,266)(107,270)(108,269)(109,268)(110,267)(111,271)
(112,275)(113,274)(114,273)(115,272)(116,276)(117,280)(118,279)(119,278)
(120,277)(121,281)(122,285)(123,284)(124,283)(125,282)(126,286)(127,290)
(128,289)(129,288)(130,287)(131,291)(132,295)(133,294)(134,293)(135,292)
(136,296)(137,300)(138,299)(139,298)(140,297)(141,301)(142,305)(143,304)
(144,303)(145,302)(146,306)(147,310)(148,309)(149,308)(150,307)(151,311)
(152,315)(153,314)(154,313)(155,312)(156,316)(157,320)(158,319)(159,318)
(160,317)(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)
(328,489)(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)
(336,496)(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)
(344,503)(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)
(352,515)(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)
(360,517)(361,521)(362,525)(363,524)(364,523)(365,522)(366,526)(367,530)
(368,529)(369,528)(370,527)(371,531)(372,535)(373,534)(374,533)(375,532)
(376,536)(377,540)(378,539)(379,538)(380,537)(381,541)(382,545)(383,544)
(384,543)(385,542)(386,546)(387,550)(388,549)(389,548)(390,547)(391,551)
(392,555)(393,554)(394,553)(395,552)(396,556)(397,560)(398,559)(399,558)
(400,557)(401,561)(402,565)(403,564)(404,563)(405,562)(406,566)(407,570)
(408,569)(409,568)(410,567)(411,571)(412,575)(413,574)(414,573)(415,572)
(416,576)(417,580)(418,579)(419,578)(420,577)(421,581)(422,585)(423,584)
(424,583)(425,582)(426,586)(427,590)(428,589)(429,588)(430,587)(431,591)
(432,595)(433,594)(434,593)(435,592)(436,596)(437,600)(438,599)(439,598)
(440,597)(441,601)(442,605)(443,604)(444,603)(445,602)(446,606)(447,610)
(448,609)(449,608)(450,607)(451,611)(452,615)(453,614)(454,613)(455,612)
(456,616)(457,620)(458,619)(459,618)(460,617)(461,621)(462,625)(463,624)
(464,623)(465,622)(466,626)(467,630)(468,629)(469,628)(470,627)(471,631)
(472,635)(473,634)(474,633)(475,632)(476,636)(477,640)(478,639)(479,638)
(480,637);
s2 := Sym(640)!(  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)
( 19, 20)( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 33)( 34, 35)( 36, 38)
( 39, 40)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 58)( 52, 57)
( 53, 56)( 54, 60)( 55, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 70)( 65, 69)
( 71, 78)( 72, 77)( 73, 76)( 74, 80)( 75, 79)( 81,123)( 82,122)( 83,121)
( 84,125)( 85,124)( 86,128)( 87,127)( 88,126)( 89,130)( 90,129)( 91,133)
( 92,132)( 93,131)( 94,135)( 95,134)( 96,138)( 97,137)( 98,136)( 99,140)
(100,139)(101,143)(102,142)(103,141)(104,145)(105,144)(106,148)(107,147)
(108,146)(109,150)(110,149)(111,153)(112,152)(113,151)(114,155)(115,154)
(116,158)(117,157)(118,156)(119,160)(120,159)(161,183)(162,182)(163,181)
(164,185)(165,184)(166,188)(167,187)(168,186)(169,190)(170,189)(171,193)
(172,192)(173,191)(174,195)(175,194)(176,198)(177,197)(178,196)(179,200)
(180,199)(201,228)(202,227)(203,226)(204,230)(205,229)(206,223)(207,222)
(208,221)(209,225)(210,224)(211,238)(212,237)(213,236)(214,240)(215,239)
(216,233)(217,232)(218,231)(219,235)(220,234)(241,303)(242,302)(243,301)
(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)
(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)
(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)
(268,286)(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)(275,294)
(276,298)(277,297)(278,296)(279,300)(280,299)(321,363)(322,362)(323,361)
(324,365)(325,364)(326,368)(327,367)(328,366)(329,370)(330,369)(331,373)
(332,372)(333,371)(334,375)(335,374)(336,378)(337,377)(338,376)(339,380)
(340,379)(341,383)(342,382)(343,381)(344,385)(345,384)(346,388)(347,387)
(348,386)(349,390)(350,389)(351,393)(352,392)(353,391)(354,395)(355,394)
(356,398)(357,397)(358,396)(359,400)(360,399)(401,403)(404,405)(406,408)
(409,410)(411,413)(414,415)(416,418)(419,420)(421,423)(424,425)(426,428)
(429,430)(431,433)(434,435)(436,438)(439,440)(441,448)(442,447)(443,446)
(444,450)(445,449)(451,458)(452,457)(453,456)(454,460)(455,459)(461,468)
(462,467)(463,466)(464,470)(465,469)(471,478)(472,477)(473,476)(474,480)
(475,479)(481,543)(482,542)(483,541)(484,545)(485,544)(486,548)(487,547)
(488,546)(489,550)(490,549)(491,553)(492,552)(493,551)(494,555)(495,554)
(496,558)(497,557)(498,556)(499,560)(500,559)(501,523)(502,522)(503,521)
(504,525)(505,524)(506,528)(507,527)(508,526)(509,530)(510,529)(511,533)
(512,532)(513,531)(514,535)(515,534)(516,538)(517,537)(518,536)(519,540)
(520,539)(561,583)(562,582)(563,581)(564,585)(565,584)(566,588)(567,587)
(568,586)(569,590)(570,589)(571,593)(572,592)(573,591)(574,595)(575,594)
(576,598)(577,597)(578,596)(579,600)(580,599)(601,628)(602,627)(603,626)
(604,630)(605,629)(606,623)(607,622)(608,621)(609,625)(610,624)(611,638)
(612,637)(613,636)(614,640)(615,639)(616,633)(617,632)(618,631)(619,635)
(620,634);
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)( 41,126)( 42,127)( 43,128)( 44,129)( 45,130)( 46,121)( 47,122)
( 48,123)( 49,124)( 50,125)( 51,136)( 52,137)( 53,138)( 54,139)( 55,140)
( 56,131)( 57,132)( 58,133)( 59,134)( 60,135)( 61,146)( 62,147)( 63,148)
( 64,149)( 65,150)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,156)
( 72,157)( 73,158)( 74,159)( 75,160)( 76,151)( 77,152)( 78,153)( 79,154)
( 80,155)(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)(201,286)(202,287)(203,288)(204,289)(205,290)(206,281)(207,282)
(208,283)(209,284)(210,285)(211,296)(212,297)(213,298)(214,299)(215,300)
(216,291)(217,292)(218,293)(219,294)(220,295)(221,306)(222,307)(223,308)
(224,309)(225,310)(226,301)(227,302)(228,303)(229,304)(230,305)(231,316)
(232,317)(233,318)(234,319)(235,320)(236,311)(237,312)(238,313)(239,314)
(240,315)(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)(361,446)(362,447)(363,448)(364,449)(365,450)(366,441)(367,442)
(368,443)(369,444)(370,445)(371,456)(372,457)(373,458)(374,459)(375,460)
(376,451)(377,452)(378,453)(379,454)(380,455)(381,466)(382,467)(383,468)
(384,469)(385,470)(386,461)(387,462)(388,463)(389,464)(390,465)(391,476)
(392,477)(393,478)(394,479)(395,480)(396,471)(397,472)(398,473)(399,474)
(400,475)(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)(521,606)(522,607)(523,608)(524,609)(525,610)(526,601)(527,602)
(528,603)(529,604)(530,605)(531,616)(532,617)(533,618)(534,619)(535,620)
(536,611)(537,612)(538,613)(539,614)(540,615)(541,626)(542,627)(543,628)
(544,629)(545,630)(546,621)(547,622)(548,623)(549,624)(550,625)(551,636)
(552,637)(553,638)(554,639)(555,640)(556,631)(557,632)(558,633)(559,634)
(560,635);
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope