Polytope of Type {10,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,8}*1280a
if this polytope has a name.
Group : SmallGroup(1280,141629)
Rank : 4
Schlafli Type : {10,4,8}
Number of vertices, edges, etc : 10, 40, 32, 16
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 : {10,4,8}*640a, {10,4,8}*640b, {10,4,4}*640
4-fold quotients : {10,4,4}*320, {10,2,8}*320
5-fold quotients : {2,4,8}*256a
8-fold quotients : {5,2,8}*160, {10,2,4}*160, {10,4,2}*160
10-fold quotients : {2,4,8}*128a, {2,4,8}*128b, {2,4,4}*128
16-fold quotients : {5,2,4}*80, {10,2,2}*80
20-fold quotients : {2,4,4}*64, {2,2,8}*64
32-fold quotients : {5,2,2}*40
40-fold quotients : {2,2,4}*32, {2,4,2}*32
80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)( 8, 89)
( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)
( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)( 24,103)
( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)( 32,115)
( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,121)( 42,125)( 43,124)( 44,123)( 45,122)( 46,126)( 47,130)( 48,129)
( 49,128)( 50,127)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,136)
( 57,140)( 58,139)( 59,138)( 60,137)( 61,141)( 62,145)( 63,144)( 64,143)
( 65,142)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,151)( 72,155)
( 73,154)( 74,153)( 75,152)( 76,156)( 77,160)( 78,159)( 79,158)( 80,157)
(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)(168,249)
(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)(176,256)
(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)(184,263)
(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)(192,275)
(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)(200,277)
(201,281)(202,285)(203,284)(204,283)(205,282)(206,286)(207,290)(208,289)
(209,288)(210,287)(211,291)(212,295)(213,294)(214,293)(215,292)(216,296)
(217,300)(218,299)(219,298)(220,297)(221,301)(222,305)(223,304)(224,303)
(225,302)(226,306)(227,310)(228,309)(229,308)(230,307)(231,311)(232,315)
(233,314)(234,313)(235,312)(236,316)(237,320)(238,319)(239,318)(240,317)
(321,401)(322,405)(323,404)(324,403)(325,402)(326,406)(327,410)(328,409)
(329,408)(330,407)(331,411)(332,415)(333,414)(334,413)(335,412)(336,416)
(337,420)(338,419)(339,418)(340,417)(341,421)(342,425)(343,424)(344,423)
(345,422)(346,426)(347,430)(348,429)(349,428)(350,427)(351,431)(352,435)
(353,434)(354,433)(355,432)(356,436)(357,440)(358,439)(359,438)(360,437)
(361,441)(362,445)(363,444)(364,443)(365,442)(366,446)(367,450)(368,449)
(369,448)(370,447)(371,451)(372,455)(373,454)(374,453)(375,452)(376,456)
(377,460)(378,459)(379,458)(380,457)(381,461)(382,465)(383,464)(384,463)
(385,462)(386,466)(387,470)(388,469)(389,468)(390,467)(391,471)(392,475)
(393,474)(394,473)(395,472)(396,476)(397,480)(398,479)(399,478)(400,477)
(481,561)(482,565)(483,564)(484,563)(485,562)(486,566)(487,570)(488,569)
(489,568)(490,567)(491,571)(492,575)(493,574)(494,573)(495,572)(496,576)
(497,580)(498,579)(499,578)(500,577)(501,581)(502,585)(503,584)(504,583)
(505,582)(506,586)(507,590)(508,589)(509,588)(510,587)(511,591)(512,595)
(513,594)(514,593)(515,592)(516,596)(517,600)(518,599)(519,598)(520,597)
(521,601)(522,605)(523,604)(524,603)(525,602)(526,606)(527,610)(528,609)
(529,608)(530,607)(531,611)(532,615)(533,614)(534,613)(535,612)(536,616)
(537,620)(538,619)(539,618)(540,617)(541,621)(542,625)(543,624)(544,623)
(545,622)(546,626)(547,630)(548,629)(549,628)(550,627)(551,631)(552,635)
(553,634)(554,633)(555,632)(556,636)(557,640)(558,639)(559,638)(560,637);;
s1 := ( 1,243)( 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)( 21,263)( 22,262)( 23,261)( 24,265)
( 25,264)( 26,268)( 27,267)( 28,266)( 29,270)( 30,269)( 31,273)( 32,272)
( 33,271)( 34,275)( 35,274)( 36,278)( 37,277)( 38,276)( 39,280)( 40,279)
( 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)( 61,308)( 62,307)( 63,306)( 64,310)
( 65,309)( 66,303)( 67,302)( 68,301)( 69,305)( 70,304)( 71,318)( 72,317)
( 73,316)( 74,320)( 75,319)( 76,313)( 77,312)( 78,311)( 79,315)( 80,314)
( 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)(101,183)(102,182)(103,181)(104,185)
(105,184)(106,188)(107,187)(108,186)(109,190)(110,189)(111,193)(112,192)
(113,191)(114,195)(115,194)(116,198)(117,197)(118,196)(119,200)(120,199)
(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)(141,228)(142,227)(143,226)(144,230)
(145,229)(146,223)(147,222)(148,221)(149,225)(150,224)(151,238)(152,237)
(153,236)(154,240)(155,239)(156,233)(157,232)(158,231)(159,235)(160,234)
(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)(341,583)(342,582)(343,581)(344,585)
(345,584)(346,588)(347,587)(348,586)(349,590)(350,589)(351,593)(352,592)
(353,591)(354,595)(355,594)(356,598)(357,597)(358,596)(359,600)(360,599)
(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)(381,628)(382,627)(383,626)(384,630)
(385,629)(386,623)(387,622)(388,621)(389,625)(390,624)(391,638)(392,637)
(393,636)(394,640)(395,639)(396,633)(397,632)(398,631)(399,635)(400,634)
(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)(421,503)(422,502)(423,501)(424,505)
(425,504)(426,508)(427,507)(428,506)(429,510)(430,509)(431,513)(432,512)
(433,511)(434,515)(435,514)(436,518)(437,517)(438,516)(439,520)(440,519)
(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)(461,548)(462,547)(463,546)(464,550)
(465,549)(466,543)(467,542)(468,541)(469,545)(470,544)(471,558)(472,557)
(473,556)(474,560)(475,559)(476,553)(477,552)(478,551)(479,555)(480,554);;
s2 := ( 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)(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)(171,191)(172,192)(173,193)(174,194)(175,195)(176,196)
(177,197)(178,198)(179,199)(180,200)(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)(251,271)(252,272)(253,273)(254,274)(255,275)(256,276)
(257,277)(258,278)(259,279)(260,280)(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)(331,371)(332,372)(333,373)(334,374)(335,375)(336,376)
(337,377)(338,378)(339,379)(340,380)(341,381)(342,382)(343,383)(344,384)
(345,385)(346,386)(347,387)(348,388)(349,389)(350,390)(351,391)(352,392)
(353,393)(354,394)(355,395)(356,396)(357,397)(358,398)(359,399)(360,400)
(401,441)(402,442)(403,443)(404,444)(405,445)(406,446)(407,447)(408,448)
(409,449)(410,450)(411,451)(412,452)(413,453)(414,454)(415,455)(416,456)
(417,457)(418,458)(419,459)(420,460)(421,461)(422,462)(423,463)(424,464)
(425,465)(426,466)(427,467)(428,468)(429,469)(430,470)(431,471)(432,472)
(433,473)(434,474)(435,475)(436,476)(437,477)(438,478)(439,479)(440,480)
(481,546)(482,547)(483,548)(484,549)(485,550)(486,541)(487,542)(488,543)
(489,544)(490,545)(491,556)(492,557)(493,558)(494,559)(495,560)(496,551)
(497,552)(498,553)(499,554)(500,555)(501,526)(502,527)(503,528)(504,529)
(505,530)(506,521)(507,522)(508,523)(509,524)(510,525)(511,536)(512,537)
(513,538)(514,539)(515,540)(516,531)(517,532)(518,533)(519,534)(520,535)
(561,626)(562,627)(563,628)(564,629)(565,630)(566,621)(567,622)(568,623)
(569,624)(570,625)(571,636)(572,637)(573,638)(574,639)(575,640)(576,631)
(577,632)(578,633)(579,634)(580,635)(581,606)(582,607)(583,608)(584,609)
(585,610)(586,601)(587,602)(588,603)(589,604)(590,605)(591,616)(592,617)
(593,618)(594,619)(595,620)(596,611)(597,612)(598,613)(599,614)(600,615);;
s3 := ( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)( 8,328)
( 9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)( 16,336)
( 17,337)( 18,338)( 19,339)( 20,340)( 21,346)( 22,347)( 23,348)( 24,349)
( 25,350)( 26,341)( 27,342)( 28,343)( 29,344)( 30,345)( 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)( 61,396)( 62,397)( 63,398)( 64,399)
( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)( 72,387)
( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)( 80,385)
( 81,401)( 82,402)( 83,403)( 84,404)( 85,405)( 86,406)( 87,407)( 88,408)
( 89,409)( 90,410)( 91,411)( 92,412)( 93,413)( 94,414)( 95,415)( 96,416)
( 97,417)( 98,418)( 99,419)(100,420)(101,426)(102,427)(103,428)(104,429)
(105,430)(106,421)(107,422)(108,423)(109,424)(110,425)(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)(141,476)(142,477)(143,478)(144,479)
(145,480)(146,471)(147,472)(148,473)(149,474)(150,475)(151,466)(152,467)
(153,468)(154,469)(155,470)(156,461)(157,462)(158,463)(159,464)(160,465)
(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)
(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)(176,496)
(177,497)(178,498)(179,499)(180,500)(181,506)(182,507)(183,508)(184,509)
(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(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)(221,556)(222,557)(223,558)(224,559)
(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)(232,547)
(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)(240,545)
(241,561)(242,562)(243,563)(244,564)(245,565)(246,566)(247,567)(248,568)
(249,569)(250,570)(251,571)(252,572)(253,573)(254,574)(255,575)(256,576)
(257,577)(258,578)(259,579)(260,580)(261,586)(262,587)(263,588)(264,589)
(265,590)(266,581)(267,582)(268,583)(269,584)(270,585)(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)(301,636)(302,637)(303,638)(304,639)
(305,640)(306,631)(307,632)(308,633)(309,634)(310,635)(311,626)(312,627)
(313,628)(314,629)(315,630)(316,621)(317,622)(318,623)(319,624)(320,625);;
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*s1*s2*s1*s3*s2*s3*s2*s1*s2,
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(640)!( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)
( 8, 89)( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)
( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)
( 24,103)( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)
( 32,115)( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,121)( 42,125)( 43,124)( 44,123)( 45,122)( 46,126)( 47,130)
( 48,129)( 49,128)( 50,127)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)
( 56,136)( 57,140)( 58,139)( 59,138)( 60,137)( 61,141)( 62,145)( 63,144)
( 64,143)( 65,142)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,151)
( 72,155)( 73,154)( 74,153)( 75,152)( 76,156)( 77,160)( 78,159)( 79,158)
( 80,157)(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)
(168,249)(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)
(176,256)(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)
(184,263)(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)
(192,275)(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)
(200,277)(201,281)(202,285)(203,284)(204,283)(205,282)(206,286)(207,290)
(208,289)(209,288)(210,287)(211,291)(212,295)(213,294)(214,293)(215,292)
(216,296)(217,300)(218,299)(219,298)(220,297)(221,301)(222,305)(223,304)
(224,303)(225,302)(226,306)(227,310)(228,309)(229,308)(230,307)(231,311)
(232,315)(233,314)(234,313)(235,312)(236,316)(237,320)(238,319)(239,318)
(240,317)(321,401)(322,405)(323,404)(324,403)(325,402)(326,406)(327,410)
(328,409)(329,408)(330,407)(331,411)(332,415)(333,414)(334,413)(335,412)
(336,416)(337,420)(338,419)(339,418)(340,417)(341,421)(342,425)(343,424)
(344,423)(345,422)(346,426)(347,430)(348,429)(349,428)(350,427)(351,431)
(352,435)(353,434)(354,433)(355,432)(356,436)(357,440)(358,439)(359,438)
(360,437)(361,441)(362,445)(363,444)(364,443)(365,442)(366,446)(367,450)
(368,449)(369,448)(370,447)(371,451)(372,455)(373,454)(374,453)(375,452)
(376,456)(377,460)(378,459)(379,458)(380,457)(381,461)(382,465)(383,464)
(384,463)(385,462)(386,466)(387,470)(388,469)(389,468)(390,467)(391,471)
(392,475)(393,474)(394,473)(395,472)(396,476)(397,480)(398,479)(399,478)
(400,477)(481,561)(482,565)(483,564)(484,563)(485,562)(486,566)(487,570)
(488,569)(489,568)(490,567)(491,571)(492,575)(493,574)(494,573)(495,572)
(496,576)(497,580)(498,579)(499,578)(500,577)(501,581)(502,585)(503,584)
(504,583)(505,582)(506,586)(507,590)(508,589)(509,588)(510,587)(511,591)
(512,595)(513,594)(514,593)(515,592)(516,596)(517,600)(518,599)(519,598)
(520,597)(521,601)(522,605)(523,604)(524,603)(525,602)(526,606)(527,610)
(528,609)(529,608)(530,607)(531,611)(532,615)(533,614)(534,613)(535,612)
(536,616)(537,620)(538,619)(539,618)(540,617)(541,621)(542,625)(543,624)
(544,623)(545,622)(546,626)(547,630)(548,629)(549,628)(550,627)(551,631)
(552,635)(553,634)(554,633)(555,632)(556,636)(557,640)(558,639)(559,638)
(560,637);
s1 := Sym(640)!( 1,243)( 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)( 21,263)( 22,262)( 23,261)
( 24,265)( 25,264)( 26,268)( 27,267)( 28,266)( 29,270)( 30,269)( 31,273)
( 32,272)( 33,271)( 34,275)( 35,274)( 36,278)( 37,277)( 38,276)( 39,280)
( 40,279)( 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)( 61,308)( 62,307)( 63,306)
( 64,310)( 65,309)( 66,303)( 67,302)( 68,301)( 69,305)( 70,304)( 71,318)
( 72,317)( 73,316)( 74,320)( 75,319)( 76,313)( 77,312)( 78,311)( 79,315)
( 80,314)( 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)(101,183)(102,182)(103,181)
(104,185)(105,184)(106,188)(107,187)(108,186)(109,190)(110,189)(111,193)
(112,192)(113,191)(114,195)(115,194)(116,198)(117,197)(118,196)(119,200)
(120,199)(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)(141,228)(142,227)(143,226)
(144,230)(145,229)(146,223)(147,222)(148,221)(149,225)(150,224)(151,238)
(152,237)(153,236)(154,240)(155,239)(156,233)(157,232)(158,231)(159,235)
(160,234)(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)(341,583)(342,582)(343,581)
(344,585)(345,584)(346,588)(347,587)(348,586)(349,590)(350,589)(351,593)
(352,592)(353,591)(354,595)(355,594)(356,598)(357,597)(358,596)(359,600)
(360,599)(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)(381,628)(382,627)(383,626)
(384,630)(385,629)(386,623)(387,622)(388,621)(389,625)(390,624)(391,638)
(392,637)(393,636)(394,640)(395,639)(396,633)(397,632)(398,631)(399,635)
(400,634)(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)(421,503)(422,502)(423,501)
(424,505)(425,504)(426,508)(427,507)(428,506)(429,510)(430,509)(431,513)
(432,512)(433,511)(434,515)(435,514)(436,518)(437,517)(438,516)(439,520)
(440,519)(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)(461,548)(462,547)(463,546)
(464,550)(465,549)(466,543)(467,542)(468,541)(469,545)(470,544)(471,558)
(472,557)(473,556)(474,560)(475,559)(476,553)(477,552)(478,551)(479,555)
(480,554);
s2 := Sym(640)!( 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)(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)(171,191)(172,192)(173,193)(174,194)(175,195)
(176,196)(177,197)(178,198)(179,199)(180,200)(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)(251,271)(252,272)(253,273)(254,274)(255,275)
(256,276)(257,277)(258,278)(259,279)(260,280)(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)(331,371)(332,372)(333,373)(334,374)(335,375)
(336,376)(337,377)(338,378)(339,379)(340,380)(341,381)(342,382)(343,383)
(344,384)(345,385)(346,386)(347,387)(348,388)(349,389)(350,390)(351,391)
(352,392)(353,393)(354,394)(355,395)(356,396)(357,397)(358,398)(359,399)
(360,400)(401,441)(402,442)(403,443)(404,444)(405,445)(406,446)(407,447)
(408,448)(409,449)(410,450)(411,451)(412,452)(413,453)(414,454)(415,455)
(416,456)(417,457)(418,458)(419,459)(420,460)(421,461)(422,462)(423,463)
(424,464)(425,465)(426,466)(427,467)(428,468)(429,469)(430,470)(431,471)
(432,472)(433,473)(434,474)(435,475)(436,476)(437,477)(438,478)(439,479)
(440,480)(481,546)(482,547)(483,548)(484,549)(485,550)(486,541)(487,542)
(488,543)(489,544)(490,545)(491,556)(492,557)(493,558)(494,559)(495,560)
(496,551)(497,552)(498,553)(499,554)(500,555)(501,526)(502,527)(503,528)
(504,529)(505,530)(506,521)(507,522)(508,523)(509,524)(510,525)(511,536)
(512,537)(513,538)(514,539)(515,540)(516,531)(517,532)(518,533)(519,534)
(520,535)(561,626)(562,627)(563,628)(564,629)(565,630)(566,621)(567,622)
(568,623)(569,624)(570,625)(571,636)(572,637)(573,638)(574,639)(575,640)
(576,631)(577,632)(578,633)(579,634)(580,635)(581,606)(582,607)(583,608)
(584,609)(585,610)(586,601)(587,602)(588,603)(589,604)(590,605)(591,616)
(592,617)(593,618)(594,619)(595,620)(596,611)(597,612)(598,613)(599,614)
(600,615);
s3 := Sym(640)!( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)
( 8,328)( 9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)
( 16,336)( 17,337)( 18,338)( 19,339)( 20,340)( 21,346)( 22,347)( 23,348)
( 24,349)( 25,350)( 26,341)( 27,342)( 28,343)( 29,344)( 30,345)( 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)( 61,396)( 62,397)( 63,398)
( 64,399)( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)
( 72,387)( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)
( 80,385)( 81,401)( 82,402)( 83,403)( 84,404)( 85,405)( 86,406)( 87,407)
( 88,408)( 89,409)( 90,410)( 91,411)( 92,412)( 93,413)( 94,414)( 95,415)
( 96,416)( 97,417)( 98,418)( 99,419)(100,420)(101,426)(102,427)(103,428)
(104,429)(105,430)(106,421)(107,422)(108,423)(109,424)(110,425)(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)(141,476)(142,477)(143,478)
(144,479)(145,480)(146,471)(147,472)(148,473)(149,474)(150,475)(151,466)
(152,467)(153,468)(154,469)(155,470)(156,461)(157,462)(158,463)(159,464)
(160,465)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)
(168,488)(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)
(176,496)(177,497)(178,498)(179,499)(180,500)(181,506)(182,507)(183,508)
(184,509)(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(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)(221,556)(222,557)(223,558)
(224,559)(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)
(232,547)(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)
(240,545)(241,561)(242,562)(243,563)(244,564)(245,565)(246,566)(247,567)
(248,568)(249,569)(250,570)(251,571)(252,572)(253,573)(254,574)(255,575)
(256,576)(257,577)(258,578)(259,579)(260,580)(261,586)(262,587)(263,588)
(264,589)(265,590)(266,581)(267,582)(268,583)(269,584)(270,585)(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)(301,636)(302,637)(303,638)
(304,639)(305,640)(306,631)(307,632)(308,633)(309,634)(310,635)(311,626)
(312,627)(313,628)(314,629)(315,630)(316,621)(317,622)(318,623)(319,624)
(320,625);
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*s1*s2*s1*s3*s2*s3*s2*s1*s2,
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 >;
References : None.
to this polytope