Polytope of Type {8,8,10}

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