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Polytope of Type {10,8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,8}*1280b
Also Known As : {{10,8|2},{8,8|2}}. if this polytope has another name.
Group : SmallGroup(1280,145169)
Rank : 4
Schlafli Type : {10,8,8}
Number of vertices, edges, etc : 10, 40, 32, 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 : {10,4,8}*640a, {10,8,4}*640a
   4-fold quotients : {10,4,4}*320, {10,2,8}*320, {10,8,2}*320
   5-fold quotients : {2,8,8}*256b
   8-fold quotients : {5,2,8}*160, {10,2,4}*160, {10,4,2}*160
   10-fold quotients : {2,4,8}*128a, {2,8,4}*128a
   16-fold quotients : {5,2,4}*80, {10,2,2}*80
   20-fold quotients : {2,4,4}*64, {2,2,8}*64, {2,8,2}*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)( 21,268)( 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, 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);;
s3 := (  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)(  8,488)
(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)
( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)
( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,531)( 47,532)( 48,533)
( 49,534)( 50,535)( 51,526)( 52,527)( 53,528)( 54,529)( 55,530)( 56,521)
( 57,522)( 58,523)( 59,524)( 60,525)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,551)( 67,552)( 68,553)( 69,554)( 70,555)( 71,546)( 72,547)
( 73,548)( 74,549)( 75,550)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)( 88,568)
( 89,569)( 90,570)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)( 96,576)
( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)(104,584)
(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)(112,592)
(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)(120,600)
(121,616)(122,617)(123,618)(124,619)(125,620)(126,611)(127,612)(128,613)
(129,614)(130,615)(131,606)(132,607)(133,608)(134,609)(135,610)(136,601)
(137,602)(138,603)(139,604)(140,605)(141,636)(142,637)(143,638)(144,639)
(145,640)(146,631)(147,632)(148,633)(149,634)(150,635)(151,626)(152,627)
(153,628)(154,629)(155,630)(156,621)(157,622)(158,623)(159,624)(160,625)
(161,321)(162,322)(163,323)(164,324)(165,325)(166,326)(167,327)(168,328)
(169,329)(170,330)(171,331)(172,332)(173,333)(174,334)(175,335)(176,336)
(177,337)(178,338)(179,339)(180,340)(181,341)(182,342)(183,343)(184,344)
(185,345)(186,346)(187,347)(188,348)(189,349)(190,350)(191,351)(192,352)
(193,353)(194,354)(195,355)(196,356)(197,357)(198,358)(199,359)(200,360)
(201,376)(202,377)(203,378)(204,379)(205,380)(206,371)(207,372)(208,373)
(209,374)(210,375)(211,366)(212,367)(213,368)(214,369)(215,370)(216,361)
(217,362)(218,363)(219,364)(220,365)(221,396)(222,397)(223,398)(224,399)
(225,400)(226,391)(227,392)(228,393)(229,394)(230,395)(231,386)(232,387)
(233,388)(234,389)(235,390)(236,381)(237,382)(238,383)(239,384)(240,385)
(241,401)(242,402)(243,403)(244,404)(245,405)(246,406)(247,407)(248,408)
(249,409)(250,410)(251,411)(252,412)(253,413)(254,414)(255,415)(256,416)
(257,417)(258,418)(259,419)(260,420)(261,421)(262,422)(263,423)(264,424)
(265,425)(266,426)(267,427)(268,428)(269,429)(270,430)(271,431)(272,432)
(273,433)(274,434)(275,435)(276,436)(277,437)(278,438)(279,439)(280,440)
(281,456)(282,457)(283,458)(284,459)(285,460)(286,451)(287,452)(288,453)
(289,454)(290,455)(291,446)(292,447)(293,448)(294,449)(295,450)(296,441)
(297,442)(298,443)(299,444)(300,445)(301,476)(302,477)(303,478)(304,479)
(305,480)(306,471)(307,472)(308,473)(309,474)(310,475)(311,466)(312,467)
(313,468)(314,469)(315,470)(316,461)(317,462)(318,463)(319,464)(320,465);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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)( 21,268)( 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, 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);
s3 := Sym(640)!(  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)
(  8,488)(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)
( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)
( 40,520)( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,531)( 47,532)
( 48,533)( 49,534)( 50,535)( 51,526)( 52,527)( 53,528)( 54,529)( 55,530)
( 56,521)( 57,522)( 58,523)( 59,524)( 60,525)( 61,556)( 62,557)( 63,558)
( 64,559)( 65,560)( 66,551)( 67,552)( 68,553)( 69,554)( 70,555)( 71,546)
( 72,547)( 73,548)( 74,549)( 75,550)( 76,541)( 77,542)( 78,543)( 79,544)
( 80,545)( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)
( 88,568)( 89,569)( 90,570)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)
( 96,576)( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)
(104,584)(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)
(112,592)(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)
(120,600)(121,616)(122,617)(123,618)(124,619)(125,620)(126,611)(127,612)
(128,613)(129,614)(130,615)(131,606)(132,607)(133,608)(134,609)(135,610)
(136,601)(137,602)(138,603)(139,604)(140,605)(141,636)(142,637)(143,638)
(144,639)(145,640)(146,631)(147,632)(148,633)(149,634)(150,635)(151,626)
(152,627)(153,628)(154,629)(155,630)(156,621)(157,622)(158,623)(159,624)
(160,625)(161,321)(162,322)(163,323)(164,324)(165,325)(166,326)(167,327)
(168,328)(169,329)(170,330)(171,331)(172,332)(173,333)(174,334)(175,335)
(176,336)(177,337)(178,338)(179,339)(180,340)(181,341)(182,342)(183,343)
(184,344)(185,345)(186,346)(187,347)(188,348)(189,349)(190,350)(191,351)
(192,352)(193,353)(194,354)(195,355)(196,356)(197,357)(198,358)(199,359)
(200,360)(201,376)(202,377)(203,378)(204,379)(205,380)(206,371)(207,372)
(208,373)(209,374)(210,375)(211,366)(212,367)(213,368)(214,369)(215,370)
(216,361)(217,362)(218,363)(219,364)(220,365)(221,396)(222,397)(223,398)
(224,399)(225,400)(226,391)(227,392)(228,393)(229,394)(230,395)(231,386)
(232,387)(233,388)(234,389)(235,390)(236,381)(237,382)(238,383)(239,384)
(240,385)(241,401)(242,402)(243,403)(244,404)(245,405)(246,406)(247,407)
(248,408)(249,409)(250,410)(251,411)(252,412)(253,413)(254,414)(255,415)
(256,416)(257,417)(258,418)(259,419)(260,420)(261,421)(262,422)(263,423)
(264,424)(265,425)(266,426)(267,427)(268,428)(269,429)(270,430)(271,431)
(272,432)(273,433)(274,434)(275,435)(276,436)(277,437)(278,438)(279,439)
(280,440)(281,456)(282,457)(283,458)(284,459)(285,460)(286,451)(287,452)
(288,453)(289,454)(290,455)(291,446)(292,447)(293,448)(294,449)(295,450)
(296,441)(297,442)(298,443)(299,444)(300,445)(301,476)(302,477)(303,478)
(304,479)(305,480)(306,471)(307,472)(308,473)(309,474)(310,475)(311,466)
(312,467)(313,468)(314,469)(315,470)(316,461)(317,462)(318,463)(319,464)
(320,465);
poly := sub<Sym(640)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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