Polytope of Type {20,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,8}*1280b
if this polytope has a name.
Group : SmallGroup(1280,200904)
Rank : 4
Schlafli Type : {20,4,8}
Number of vertices, edges, etc : 20, 40, 16, 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 : {20,4,4}*640, {10,4,8}*640b
   4-fold quotients : {20,4,2}*320, {20,2,4}*320, {10,4,4}*320
   5-fold quotients : {4,4,8}*256b
   8-fold quotients : {20,2,2}*160, {10,2,4}*160, {10,4,2}*160
   10-fold quotients : {4,4,4}*128, {2,4,8}*128b
   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
   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 := (  1,243)(  2,242)(  3,241)(  4,245)(  5,244)(  6,248)(  7,247)(  8,246)
(  9,250)( 10,249)( 11,253)( 12,252)( 13,251)( 14,255)( 15,254)( 16,258)
( 17,257)( 18,256)( 19,260)( 20,259)( 21,268)( 22,267)( 23,266)( 24,270)
( 25,269)( 26,263)( 27,262)( 28,261)( 29,265)( 30,264)( 31,278)( 32,277)
( 33,276)( 34,280)( 35,279)( 36,273)( 37,272)( 38,271)( 39,275)( 40,274)
( 41,288)( 42,287)( 43,286)( 44,290)( 45,289)( 46,283)( 47,282)( 48,281)
( 49,285)( 50,284)( 51,298)( 52,297)( 53,296)( 54,300)( 55,299)( 56,293)
( 57,292)( 58,291)( 59,295)( 60,294)( 61,303)( 62,302)( 63,301)( 64,305)
( 65,304)( 66,308)( 67,307)( 68,306)( 69,310)( 70,309)( 71,313)( 72,312)
( 73,311)( 74,315)( 75,314)( 76,318)( 77,317)( 78,316)( 79,320)( 80,319)
( 81,163)( 82,162)( 83,161)( 84,165)( 85,164)( 86,168)( 87,167)( 88,166)
( 89,170)( 90,169)( 91,173)( 92,172)( 93,171)( 94,175)( 95,174)( 96,178)
( 97,177)( 98,176)( 99,180)(100,179)(101,188)(102,187)(103,186)(104,190)
(105,189)(106,183)(107,182)(108,181)(109,185)(110,184)(111,198)(112,197)
(113,196)(114,200)(115,199)(116,193)(117,192)(118,191)(119,195)(120,194)
(121,208)(122,207)(123,206)(124,210)(125,209)(126,203)(127,202)(128,201)
(129,205)(130,204)(131,218)(132,217)(133,216)(134,220)(135,219)(136,213)
(137,212)(138,211)(139,215)(140,214)(141,223)(142,222)(143,221)(144,225)
(145,224)(146,228)(147,227)(148,226)(149,230)(150,229)(151,233)(152,232)
(153,231)(154,235)(155,234)(156,238)(157,237)(158,236)(159,240)(160,239)
(321,563)(322,562)(323,561)(324,565)(325,564)(326,568)(327,567)(328,566)
(329,570)(330,569)(331,573)(332,572)(333,571)(334,575)(335,574)(336,578)
(337,577)(338,576)(339,580)(340,579)(341,588)(342,587)(343,586)(344,590)
(345,589)(346,583)(347,582)(348,581)(349,585)(350,584)(351,598)(352,597)
(353,596)(354,600)(355,599)(356,593)(357,592)(358,591)(359,595)(360,594)
(361,608)(362,607)(363,606)(364,610)(365,609)(366,603)(367,602)(368,601)
(369,605)(370,604)(371,618)(372,617)(373,616)(374,620)(375,619)(376,613)
(377,612)(378,611)(379,615)(380,614)(381,623)(382,622)(383,621)(384,625)
(385,624)(386,628)(387,627)(388,626)(389,630)(390,629)(391,633)(392,632)
(393,631)(394,635)(395,634)(396,638)(397,637)(398,636)(399,640)(400,639)
(401,483)(402,482)(403,481)(404,485)(405,484)(406,488)(407,487)(408,486)
(409,490)(410,489)(411,493)(412,492)(413,491)(414,495)(415,494)(416,498)
(417,497)(418,496)(419,500)(420,499)(421,508)(422,507)(423,506)(424,510)
(425,509)(426,503)(427,502)(428,501)(429,505)(430,504)(431,518)(432,517)
(433,516)(434,520)(435,519)(436,513)(437,512)(438,511)(439,515)(440,514)
(441,528)(442,527)(443,526)(444,530)(445,529)(446,523)(447,522)(448,521)
(449,525)(450,524)(451,538)(452,537)(453,536)(454,540)(455,539)(456,533)
(457,532)(458,531)(459,535)(460,534)(461,543)(462,542)(463,541)(464,545)
(465,544)(466,548)(467,547)(468,546)(469,550)(470,549)(471,553)(472,552)
(473,551)(474,555)(475,554)(476,558)(477,557)(478,556)(479,560)(480,559);;
s2 := ( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)( 33, 38)
( 34, 39)( 35, 40)( 41, 46)( 42, 47)( 43, 48)( 44, 49)( 45, 50)( 51, 56)
( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 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)
(201,226)(202,227)(203,228)(204,229)(205,230)(206,221)(207,222)(208,223)
(209,224)(210,225)(211,236)(212,237)(213,238)(214,239)(215,240)(216,231)
(217,232)(218,233)(219,234)(220,235)(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)(441,446)(442,447)
(443,448)(444,449)(445,450)(451,456)(452,457)(453,458)(454,459)(455,460)
(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)(601,626)(602,627)(603,628)(604,629)
(605,630)(606,621)(607,622)(608,623)(609,624)(610,625)(611,636)(612,637)
(613,638)(614,639)(615,640)(616,631)(617,632)(618,633)(619,634)(620,635);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*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)!(  1,243)(  2,242)(  3,241)(  4,245)(  5,244)(  6,248)(  7,247)
(  8,246)(  9,250)( 10,249)( 11,253)( 12,252)( 13,251)( 14,255)( 15,254)
( 16,258)( 17,257)( 18,256)( 19,260)( 20,259)( 21,268)( 22,267)( 23,266)
( 24,270)( 25,269)( 26,263)( 27,262)( 28,261)( 29,265)( 30,264)( 31,278)
( 32,277)( 33,276)( 34,280)( 35,279)( 36,273)( 37,272)( 38,271)( 39,275)
( 40,274)( 41,288)( 42,287)( 43,286)( 44,290)( 45,289)( 46,283)( 47,282)
( 48,281)( 49,285)( 50,284)( 51,298)( 52,297)( 53,296)( 54,300)( 55,299)
( 56,293)( 57,292)( 58,291)( 59,295)( 60,294)( 61,303)( 62,302)( 63,301)
( 64,305)( 65,304)( 66,308)( 67,307)( 68,306)( 69,310)( 70,309)( 71,313)
( 72,312)( 73,311)( 74,315)( 75,314)( 76,318)( 77,317)( 78,316)( 79,320)
( 80,319)( 81,163)( 82,162)( 83,161)( 84,165)( 85,164)( 86,168)( 87,167)
( 88,166)( 89,170)( 90,169)( 91,173)( 92,172)( 93,171)( 94,175)( 95,174)
( 96,178)( 97,177)( 98,176)( 99,180)(100,179)(101,188)(102,187)(103,186)
(104,190)(105,189)(106,183)(107,182)(108,181)(109,185)(110,184)(111,198)
(112,197)(113,196)(114,200)(115,199)(116,193)(117,192)(118,191)(119,195)
(120,194)(121,208)(122,207)(123,206)(124,210)(125,209)(126,203)(127,202)
(128,201)(129,205)(130,204)(131,218)(132,217)(133,216)(134,220)(135,219)
(136,213)(137,212)(138,211)(139,215)(140,214)(141,223)(142,222)(143,221)
(144,225)(145,224)(146,228)(147,227)(148,226)(149,230)(150,229)(151,233)
(152,232)(153,231)(154,235)(155,234)(156,238)(157,237)(158,236)(159,240)
(160,239)(321,563)(322,562)(323,561)(324,565)(325,564)(326,568)(327,567)
(328,566)(329,570)(330,569)(331,573)(332,572)(333,571)(334,575)(335,574)
(336,578)(337,577)(338,576)(339,580)(340,579)(341,588)(342,587)(343,586)
(344,590)(345,589)(346,583)(347,582)(348,581)(349,585)(350,584)(351,598)
(352,597)(353,596)(354,600)(355,599)(356,593)(357,592)(358,591)(359,595)
(360,594)(361,608)(362,607)(363,606)(364,610)(365,609)(366,603)(367,602)
(368,601)(369,605)(370,604)(371,618)(372,617)(373,616)(374,620)(375,619)
(376,613)(377,612)(378,611)(379,615)(380,614)(381,623)(382,622)(383,621)
(384,625)(385,624)(386,628)(387,627)(388,626)(389,630)(390,629)(391,633)
(392,632)(393,631)(394,635)(395,634)(396,638)(397,637)(398,636)(399,640)
(400,639)(401,483)(402,482)(403,481)(404,485)(405,484)(406,488)(407,487)
(408,486)(409,490)(410,489)(411,493)(412,492)(413,491)(414,495)(415,494)
(416,498)(417,497)(418,496)(419,500)(420,499)(421,508)(422,507)(423,506)
(424,510)(425,509)(426,503)(427,502)(428,501)(429,505)(430,504)(431,518)
(432,517)(433,516)(434,520)(435,519)(436,513)(437,512)(438,511)(439,515)
(440,514)(441,528)(442,527)(443,526)(444,530)(445,529)(446,523)(447,522)
(448,521)(449,525)(450,524)(451,538)(452,537)(453,536)(454,540)(455,539)
(456,533)(457,532)(458,531)(459,535)(460,534)(461,543)(462,542)(463,541)
(464,545)(465,544)(466,548)(467,547)(468,546)(469,550)(470,549)(471,553)
(472,552)(473,551)(474,555)(475,554)(476,558)(477,557)(478,556)(479,560)
(480,559);
s2 := Sym(640)!( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)
( 33, 38)( 34, 39)( 35, 40)( 41, 46)( 42, 47)( 43, 48)( 44, 49)( 45, 50)
( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 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)(201,226)(202,227)(203,228)(204,229)(205,230)(206,221)(207,222)
(208,223)(209,224)(210,225)(211,236)(212,237)(213,238)(214,239)(215,240)
(216,231)(217,232)(218,233)(219,234)(220,235)(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)(441,446)
(442,447)(443,448)(444,449)(445,450)(451,456)(452,457)(453,458)(454,459)
(455,460)(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)(601,626)(602,627)(603,628)
(604,629)(605,630)(606,621)(607,622)(608,623)(609,624)(610,625)(611,636)
(612,637)(613,638)(614,639)(615,640)(616,631)(617,632)(618,633)(619,634)
(620,635);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*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