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Polytope of Type {8,8,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8,10}*1280c
if this polytope has a name.
Group : SmallGroup(1280,145169)
Rank : 4
Schlafli Type : {8,8,10}
Number of vertices, edges, etc : 8, 32, 40, 10
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 : {8,4,10}*640a, {4,8,10}*640b
   4-fold quotients : {4,4,10}*320, {8,2,10}*320
   5-fold quotients : {8,8,2}*256c
   8-fold quotients : {8,2,5}*160, {2,4,10}*160, {4,2,10}*160
   10-fold quotients : {8,4,2}*128a, {4,8,2}*128b
   16-fold quotients : {4,2,5}*80, {2,2,10}*80
   20-fold quotients : {4,4,2}*64, {8,2,2}*64
   32-fold quotients : {2,2,5}*40
   40-fold quotients : {2,4,2}*32, {4,2,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,321)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)(  8,328)
(  9,329)( 10,330)( 11,331)( 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);;
s1 := ( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)( 33, 38)
( 34, 39)( 35, 40)( 41, 51)( 42, 52)( 43, 53)( 44, 54)( 45, 55)( 46, 56)
( 47, 57)( 48, 58)( 49, 59)( 50, 60)( 61, 76)( 62, 77)( 63, 78)( 64, 79)
( 65, 80)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)(101,106)(102,107)
(103,108)(104,109)(105,110)(111,116)(112,117)(113,118)(114,119)(115,120)
(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)(128,138)
(129,139)(130,140)(141,156)(142,157)(143,158)(144,159)(145,160)(146,151)
(147,152)(148,153)(149,154)(150,155)(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)
(201,231)(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)
(341,386)(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)(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)
(421,466)(422,467)(423,468)(424,469)(425,470)(426,461)(427,462)(428,463)
(429,464)(430,465)(431,476)(432,477)(433,478)(434,479)(435,480)(436,471)
(437,472)(438,473)(439,474)(440,475)(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);;
s2 := (  1,241)(  2,245)(  3,244)(  4,243)(  5,242)(  6,246)(  7,250)(  8,249)
(  9,248)( 10,247)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)( 16,256)
( 17,260)( 18,259)( 19,258)( 20,257)( 21,266)( 22,270)( 23,269)( 24,268)
( 25,267)( 26,261)( 27,265)( 28,264)( 29,263)( 30,262)( 31,276)( 32,280)
( 33,279)( 34,278)( 35,277)( 36,271)( 37,275)( 38,274)( 39,273)( 40,272)
( 41,286)( 42,290)( 43,289)( 44,288)( 45,287)( 46,281)( 47,285)( 48,284)
( 49,283)( 50,282)( 51,296)( 52,300)( 53,299)( 54,298)( 55,297)( 56,291)
( 57,295)( 58,294)( 59,293)( 60,292)( 61,301)( 62,305)( 63,304)( 64,303)
( 65,302)( 66,306)( 67,310)( 68,309)( 69,308)( 70,307)( 71,311)( 72,315)
( 73,314)( 74,313)( 75,312)( 76,316)( 77,320)( 78,319)( 79,318)( 80,317)
( 81,161)( 82,165)( 83,164)( 84,163)( 85,162)( 86,166)( 87,170)( 88,169)
( 89,168)( 90,167)( 91,171)( 92,175)( 93,174)( 94,173)( 95,172)( 96,176)
( 97,180)( 98,179)( 99,178)(100,177)(101,186)(102,190)(103,189)(104,188)
(105,187)(106,181)(107,185)(108,184)(109,183)(110,182)(111,196)(112,200)
(113,199)(114,198)(115,197)(116,191)(117,195)(118,194)(119,193)(120,192)
(121,206)(122,210)(123,209)(124,208)(125,207)(126,201)(127,205)(128,204)
(129,203)(130,202)(131,216)(132,220)(133,219)(134,218)(135,217)(136,211)
(137,215)(138,214)(139,213)(140,212)(141,221)(142,225)(143,224)(144,223)
(145,222)(146,226)(147,230)(148,229)(149,228)(150,227)(151,231)(152,235)
(153,234)(154,233)(155,232)(156,236)(157,240)(158,239)(159,238)(160,237)
(321,561)(322,565)(323,564)(324,563)(325,562)(326,566)(327,570)(328,569)
(329,568)(330,567)(331,571)(332,575)(333,574)(334,573)(335,572)(336,576)
(337,580)(338,579)(339,578)(340,577)(341,586)(342,590)(343,589)(344,588)
(345,587)(346,581)(347,585)(348,584)(349,583)(350,582)(351,596)(352,600)
(353,599)(354,598)(355,597)(356,591)(357,595)(358,594)(359,593)(360,592)
(361,606)(362,610)(363,609)(364,608)(365,607)(366,601)(367,605)(368,604)
(369,603)(370,602)(371,616)(372,620)(373,619)(374,618)(375,617)(376,611)
(377,615)(378,614)(379,613)(380,612)(381,621)(382,625)(383,624)(384,623)
(385,622)(386,626)(387,630)(388,629)(389,628)(390,627)(391,631)(392,635)
(393,634)(394,633)(395,632)(396,636)(397,640)(398,639)(399,638)(400,637)
(401,481)(402,485)(403,484)(404,483)(405,482)(406,486)(407,490)(408,489)
(409,488)(410,487)(411,491)(412,495)(413,494)(414,493)(415,492)(416,496)
(417,500)(418,499)(419,498)(420,497)(421,506)(422,510)(423,509)(424,508)
(425,507)(426,501)(427,505)(428,504)(429,503)(430,502)(431,516)(432,520)
(433,519)(434,518)(435,517)(436,511)(437,515)(438,514)(439,513)(440,512)
(441,526)(442,530)(443,529)(444,528)(445,527)(446,521)(447,525)(448,524)
(449,523)(450,522)(451,536)(452,540)(453,539)(454,538)(455,537)(456,531)
(457,535)(458,534)(459,533)(460,532)(461,541)(462,545)(463,544)(464,543)
(465,542)(466,546)(467,550)(468,549)(469,548)(470,547)(471,551)(472,555)
(473,554)(474,553)(475,552)(476,556)(477,560)(478,559)(479,558)(480,557);;
s3 := (  1, 83)(  2, 82)(  3, 81)(  4, 85)(  5, 84)(  6, 88)(  7, 87)(  8, 86)
(  9, 90)( 10, 89)( 11, 93)( 12, 92)( 13, 91)( 14, 95)( 15, 94)( 16, 98)
( 17, 97)( 18, 96)( 19,100)( 20, 99)( 21,103)( 22,102)( 23,101)( 24,105)
( 25,104)( 26,108)( 27,107)( 28,106)( 29,110)( 30,109)( 31,113)( 32,112)
( 33,111)( 34,115)( 35,114)( 36,118)( 37,117)( 38,116)( 39,120)( 40,119)
( 41,123)( 42,122)( 43,121)( 44,125)( 45,124)( 46,128)( 47,127)( 48,126)
( 49,130)( 50,129)( 51,133)( 52,132)( 53,131)( 54,135)( 55,134)( 56,138)
( 57,137)( 58,136)( 59,140)( 60,139)( 61,143)( 62,142)( 63,141)( 64,145)
( 65,144)( 66,148)( 67,147)( 68,146)( 69,150)( 70,149)( 71,153)( 72,152)
( 73,151)( 74,155)( 75,154)( 76,158)( 77,157)( 78,156)( 79,160)( 80,159)
(161,243)(162,242)(163,241)(164,245)(165,244)(166,248)(167,247)(168,246)
(169,250)(170,249)(171,253)(172,252)(173,251)(174,255)(175,254)(176,258)
(177,257)(178,256)(179,260)(180,259)(181,263)(182,262)(183,261)(184,265)
(185,264)(186,268)(187,267)(188,266)(189,270)(190,269)(191,273)(192,272)
(193,271)(194,275)(195,274)(196,278)(197,277)(198,276)(199,280)(200,279)
(201,283)(202,282)(203,281)(204,285)(205,284)(206,288)(207,287)(208,286)
(209,290)(210,289)(211,293)(212,292)(213,291)(214,295)(215,294)(216,298)
(217,297)(218,296)(219,300)(220,299)(221,303)(222,302)(223,301)(224,305)
(225,304)(226,308)(227,307)(228,306)(229,310)(230,309)(231,313)(232,312)
(233,311)(234,315)(235,314)(236,318)(237,317)(238,316)(239,320)(240,319)
(321,403)(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)
(329,410)(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)(336,418)
(337,417)(338,416)(339,420)(340,419)(341,423)(342,422)(343,421)(344,425)
(345,424)(346,428)(347,427)(348,426)(349,430)(350,429)(351,433)(352,432)
(353,431)(354,435)(355,434)(356,438)(357,437)(358,436)(359,440)(360,439)
(361,443)(362,442)(363,441)(364,445)(365,444)(366,448)(367,447)(368,446)
(369,450)(370,449)(371,453)(372,452)(373,451)(374,455)(375,454)(376,458)
(377,457)(378,456)(379,460)(380,459)(381,463)(382,462)(383,461)(384,465)
(385,464)(386,468)(387,467)(388,466)(389,470)(390,469)(391,473)(392,472)
(393,471)(394,475)(395,474)(396,478)(397,477)(398,476)(399,480)(400,479)
(481,563)(482,562)(483,561)(484,565)(485,564)(486,568)(487,567)(488,566)
(489,570)(490,569)(491,573)(492,572)(493,571)(494,575)(495,574)(496,578)
(497,577)(498,576)(499,580)(500,579)(501,583)(502,582)(503,581)(504,585)
(505,584)(506,588)(507,587)(508,586)(509,590)(510,589)(511,593)(512,592)
(513,591)(514,595)(515,594)(516,598)(517,597)(518,596)(519,600)(520,599)
(521,603)(522,602)(523,601)(524,605)(525,604)(526,608)(527,607)(528,606)
(529,610)(530,609)(531,613)(532,612)(533,611)(534,615)(535,614)(536,618)
(537,617)(538,616)(539,620)(540,619)(541,623)(542,622)(543,621)(544,625)
(545,624)(546,628)(547,627)(548,626)(549,630)(550,629)(551,633)(552,632)
(553,631)(554,635)(555,634)(556,638)(557,637)(558,636)(559,640)(560,639);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(640)!(  1,321)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)
(  8,328)(  9,329)( 10,330)( 11,331)( 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);
s1 := Sym(640)!( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 36)( 32, 37)
( 33, 38)( 34, 39)( 35, 40)( 41, 51)( 42, 52)( 43, 53)( 44, 54)( 45, 55)
( 46, 56)( 47, 57)( 48, 58)( 49, 59)( 50, 60)( 61, 76)( 62, 77)( 63, 78)
( 64, 79)( 65, 80)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)(101,106)
(102,107)(103,108)(104,109)(105,110)(111,116)(112,117)(113,118)(114,119)
(115,120)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(127,137)
(128,138)(129,139)(130,140)(141,156)(142,157)(143,158)(144,159)(145,160)
(146,151)(147,152)(148,153)(149,154)(150,155)(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)(201,231)(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)(341,386)(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)(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)(421,466)(422,467)(423,468)(424,469)(425,470)(426,461)(427,462)
(428,463)(429,464)(430,465)(431,476)(432,477)(433,478)(434,479)(435,480)
(436,471)(437,472)(438,473)(439,474)(440,475)(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);
s2 := Sym(640)!(  1,241)(  2,245)(  3,244)(  4,243)(  5,242)(  6,246)(  7,250)
(  8,249)(  9,248)( 10,247)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)
( 16,256)( 17,260)( 18,259)( 19,258)( 20,257)( 21,266)( 22,270)( 23,269)
( 24,268)( 25,267)( 26,261)( 27,265)( 28,264)( 29,263)( 30,262)( 31,276)
( 32,280)( 33,279)( 34,278)( 35,277)( 36,271)( 37,275)( 38,274)( 39,273)
( 40,272)( 41,286)( 42,290)( 43,289)( 44,288)( 45,287)( 46,281)( 47,285)
( 48,284)( 49,283)( 50,282)( 51,296)( 52,300)( 53,299)( 54,298)( 55,297)
( 56,291)( 57,295)( 58,294)( 59,293)( 60,292)( 61,301)( 62,305)( 63,304)
( 64,303)( 65,302)( 66,306)( 67,310)( 68,309)( 69,308)( 70,307)( 71,311)
( 72,315)( 73,314)( 74,313)( 75,312)( 76,316)( 77,320)( 78,319)( 79,318)
( 80,317)( 81,161)( 82,165)( 83,164)( 84,163)( 85,162)( 86,166)( 87,170)
( 88,169)( 89,168)( 90,167)( 91,171)( 92,175)( 93,174)( 94,173)( 95,172)
( 96,176)( 97,180)( 98,179)( 99,178)(100,177)(101,186)(102,190)(103,189)
(104,188)(105,187)(106,181)(107,185)(108,184)(109,183)(110,182)(111,196)
(112,200)(113,199)(114,198)(115,197)(116,191)(117,195)(118,194)(119,193)
(120,192)(121,206)(122,210)(123,209)(124,208)(125,207)(126,201)(127,205)
(128,204)(129,203)(130,202)(131,216)(132,220)(133,219)(134,218)(135,217)
(136,211)(137,215)(138,214)(139,213)(140,212)(141,221)(142,225)(143,224)
(144,223)(145,222)(146,226)(147,230)(148,229)(149,228)(150,227)(151,231)
(152,235)(153,234)(154,233)(155,232)(156,236)(157,240)(158,239)(159,238)
(160,237)(321,561)(322,565)(323,564)(324,563)(325,562)(326,566)(327,570)
(328,569)(329,568)(330,567)(331,571)(332,575)(333,574)(334,573)(335,572)
(336,576)(337,580)(338,579)(339,578)(340,577)(341,586)(342,590)(343,589)
(344,588)(345,587)(346,581)(347,585)(348,584)(349,583)(350,582)(351,596)
(352,600)(353,599)(354,598)(355,597)(356,591)(357,595)(358,594)(359,593)
(360,592)(361,606)(362,610)(363,609)(364,608)(365,607)(366,601)(367,605)
(368,604)(369,603)(370,602)(371,616)(372,620)(373,619)(374,618)(375,617)
(376,611)(377,615)(378,614)(379,613)(380,612)(381,621)(382,625)(383,624)
(384,623)(385,622)(386,626)(387,630)(388,629)(389,628)(390,627)(391,631)
(392,635)(393,634)(394,633)(395,632)(396,636)(397,640)(398,639)(399,638)
(400,637)(401,481)(402,485)(403,484)(404,483)(405,482)(406,486)(407,490)
(408,489)(409,488)(410,487)(411,491)(412,495)(413,494)(414,493)(415,492)
(416,496)(417,500)(418,499)(419,498)(420,497)(421,506)(422,510)(423,509)
(424,508)(425,507)(426,501)(427,505)(428,504)(429,503)(430,502)(431,516)
(432,520)(433,519)(434,518)(435,517)(436,511)(437,515)(438,514)(439,513)
(440,512)(441,526)(442,530)(443,529)(444,528)(445,527)(446,521)(447,525)
(448,524)(449,523)(450,522)(451,536)(452,540)(453,539)(454,538)(455,537)
(456,531)(457,535)(458,534)(459,533)(460,532)(461,541)(462,545)(463,544)
(464,543)(465,542)(466,546)(467,550)(468,549)(469,548)(470,547)(471,551)
(472,555)(473,554)(474,553)(475,552)(476,556)(477,560)(478,559)(479,558)
(480,557);
s3 := Sym(640)!(  1, 83)(  2, 82)(  3, 81)(  4, 85)(  5, 84)(  6, 88)(  7, 87)
(  8, 86)(  9, 90)( 10, 89)( 11, 93)( 12, 92)( 13, 91)( 14, 95)( 15, 94)
( 16, 98)( 17, 97)( 18, 96)( 19,100)( 20, 99)( 21,103)( 22,102)( 23,101)
( 24,105)( 25,104)( 26,108)( 27,107)( 28,106)( 29,110)( 30,109)( 31,113)
( 32,112)( 33,111)( 34,115)( 35,114)( 36,118)( 37,117)( 38,116)( 39,120)
( 40,119)( 41,123)( 42,122)( 43,121)( 44,125)( 45,124)( 46,128)( 47,127)
( 48,126)( 49,130)( 50,129)( 51,133)( 52,132)( 53,131)( 54,135)( 55,134)
( 56,138)( 57,137)( 58,136)( 59,140)( 60,139)( 61,143)( 62,142)( 63,141)
( 64,145)( 65,144)( 66,148)( 67,147)( 68,146)( 69,150)( 70,149)( 71,153)
( 72,152)( 73,151)( 74,155)( 75,154)( 76,158)( 77,157)( 78,156)( 79,160)
( 80,159)(161,243)(162,242)(163,241)(164,245)(165,244)(166,248)(167,247)
(168,246)(169,250)(170,249)(171,253)(172,252)(173,251)(174,255)(175,254)
(176,258)(177,257)(178,256)(179,260)(180,259)(181,263)(182,262)(183,261)
(184,265)(185,264)(186,268)(187,267)(188,266)(189,270)(190,269)(191,273)
(192,272)(193,271)(194,275)(195,274)(196,278)(197,277)(198,276)(199,280)
(200,279)(201,283)(202,282)(203,281)(204,285)(205,284)(206,288)(207,287)
(208,286)(209,290)(210,289)(211,293)(212,292)(213,291)(214,295)(215,294)
(216,298)(217,297)(218,296)(219,300)(220,299)(221,303)(222,302)(223,301)
(224,305)(225,304)(226,308)(227,307)(228,306)(229,310)(230,309)(231,313)
(232,312)(233,311)(234,315)(235,314)(236,318)(237,317)(238,316)(239,320)
(240,319)(321,403)(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)
(328,406)(329,410)(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)
(336,418)(337,417)(338,416)(339,420)(340,419)(341,423)(342,422)(343,421)
(344,425)(345,424)(346,428)(347,427)(348,426)(349,430)(350,429)(351,433)
(352,432)(353,431)(354,435)(355,434)(356,438)(357,437)(358,436)(359,440)
(360,439)(361,443)(362,442)(363,441)(364,445)(365,444)(366,448)(367,447)
(368,446)(369,450)(370,449)(371,453)(372,452)(373,451)(374,455)(375,454)
(376,458)(377,457)(378,456)(379,460)(380,459)(381,463)(382,462)(383,461)
(384,465)(385,464)(386,468)(387,467)(388,466)(389,470)(390,469)(391,473)
(392,472)(393,471)(394,475)(395,474)(396,478)(397,477)(398,476)(399,480)
(400,479)(481,563)(482,562)(483,561)(484,565)(485,564)(486,568)(487,567)
(488,566)(489,570)(490,569)(491,573)(492,572)(493,571)(494,575)(495,574)
(496,578)(497,577)(498,576)(499,580)(500,579)(501,583)(502,582)(503,581)
(504,585)(505,584)(506,588)(507,587)(508,586)(509,590)(510,589)(511,593)
(512,592)(513,591)(514,595)(515,594)(516,598)(517,597)(518,596)(519,600)
(520,599)(521,603)(522,602)(523,601)(524,605)(525,604)(526,608)(527,607)
(528,606)(529,610)(530,609)(531,613)(532,612)(533,611)(534,615)(535,614)
(536,618)(537,617)(538,616)(539,620)(540,619)(541,623)(542,622)(543,621)
(544,625)(545,624)(546,628)(547,627)(548,626)(549,630)(550,629)(551,633)
(552,632)(553,631)(554,635)(555,634)(556,638)(557,637)(558,636)(559,640)
(560,639);
poly := sub<Sym(640)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope