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Polytope of Type {40,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,8}*1280c
if this polytope has a name.
Group : SmallGroup(1280,81632)
Rank : 3
Schlafli Type : {40,8}
Number of vertices, edges, etc : 80, 320, 16
Order of s0s1s2 : 40
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,8}*640a, {40,4}*640b
   4-fold quotients : {20,4}*320, {20,8}*320a, {20,8}*320b
   5-fold quotients : {8,8}*256c
   8-fold quotients : {20,4}*160, {10,8}*160
   10-fold quotients : {4,8}*128a, {8,4}*128b
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32, {2,8}*32
   64-fold quotients : {5,2}*20
   80-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,161)(  2,165)(  3,164)(  4,163)(  5,162)(  6,166)(  7,170)(  8,169)
(  9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)( 16,176)
( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)( 24,183)
( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)( 32,195)
( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)( 40,197)
( 41,206)( 42,210)( 43,209)( 44,208)( 45,207)( 46,201)( 47,205)( 48,204)
( 49,203)( 50,202)( 51,216)( 52,220)( 53,219)( 54,218)( 55,217)( 56,211)
( 57,215)( 58,214)( 59,213)( 60,212)( 61,226)( 62,230)( 63,229)( 64,228)
( 65,227)( 66,221)( 67,225)( 68,224)( 69,223)( 70,222)( 71,236)( 72,240)
( 73,239)( 74,238)( 75,237)( 76,231)( 77,235)( 78,234)( 79,233)( 80,232)
( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,256)( 87,260)( 88,259)
( 89,258)( 90,257)( 91,241)( 92,245)( 93,244)( 94,243)( 95,242)( 96,246)
( 97,250)( 98,249)( 99,248)(100,247)(101,271)(102,275)(103,274)(104,273)
(105,272)(106,276)(107,280)(108,279)(109,278)(110,277)(111,261)(112,265)
(113,264)(114,263)(115,262)(116,266)(117,270)(118,269)(119,268)(120,267)
(121,296)(122,300)(123,299)(124,298)(125,297)(126,291)(127,295)(128,294)
(129,293)(130,292)(131,286)(132,290)(133,289)(134,288)(135,287)(136,281)
(137,285)(138,284)(139,283)(140,282)(141,316)(142,320)(143,319)(144,318)
(145,317)(146,311)(147,315)(148,314)(149,313)(150,312)(151,306)(152,310)
(153,309)(154,308)(155,307)(156,301)(157,305)(158,304)(159,303)(160,302)
(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)(328,489)
(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)(336,496)
(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)(344,503)
(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)(352,515)
(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)(360,517)
(361,526)(362,530)(363,529)(364,528)(365,527)(366,521)(367,525)(368,524)
(369,523)(370,522)(371,536)(372,540)(373,539)(374,538)(375,537)(376,531)
(377,535)(378,534)(379,533)(380,532)(381,546)(382,550)(383,549)(384,548)
(385,547)(386,541)(387,545)(388,544)(389,543)(390,542)(391,556)(392,560)
(393,559)(394,558)(395,557)(396,551)(397,555)(398,554)(399,553)(400,552)
(401,571)(402,575)(403,574)(404,573)(405,572)(406,576)(407,580)(408,579)
(409,578)(410,577)(411,561)(412,565)(413,564)(414,563)(415,562)(416,566)
(417,570)(418,569)(419,568)(420,567)(421,591)(422,595)(423,594)(424,593)
(425,592)(426,596)(427,600)(428,599)(429,598)(430,597)(431,581)(432,585)
(433,584)(434,583)(435,582)(436,586)(437,590)(438,589)(439,588)(440,587)
(441,616)(442,620)(443,619)(444,618)(445,617)(446,611)(447,615)(448,614)
(449,613)(450,612)(451,606)(452,610)(453,609)(454,608)(455,607)(456,601)
(457,605)(458,604)(459,603)(460,602)(461,636)(462,640)(463,639)(464,638)
(465,637)(466,631)(467,635)(468,634)(469,633)(470,632)(471,626)(472,630)
(473,629)(474,628)(475,627)(476,621)(477,625)(478,624)(479,623)(480,622);;
s1 := (  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 18)( 12, 17)( 13, 16)( 14, 20)
( 15, 19)( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 38)( 32, 37)( 33, 36)
( 34, 40)( 35, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 53)
( 54, 55)( 56, 58)( 59, 60)( 61, 68)( 62, 67)( 63, 66)( 64, 70)( 65, 69)
( 71, 73)( 74, 75)( 76, 78)( 79, 80)( 81,103)( 82,102)( 83,101)( 84,105)
( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,118)( 92,117)
( 93,116)( 94,120)( 95,119)( 96,113)( 97,112)( 98,111)( 99,115)(100,114)
(121,148)(122,147)(123,146)(124,150)(125,149)(126,143)(127,142)(128,141)
(129,145)(130,144)(131,153)(132,152)(133,151)(134,155)(135,154)(136,158)
(137,157)(138,156)(139,160)(140,159)(161,203)(162,202)(163,201)(164,205)
(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,218)(172,217)
(173,216)(174,220)(175,219)(176,213)(177,212)(178,211)(179,215)(180,214)
(181,223)(182,222)(183,221)(184,225)(185,224)(186,228)(187,227)(188,226)
(189,230)(190,229)(191,238)(192,237)(193,236)(194,240)(195,239)(196,233)
(197,232)(198,231)(199,235)(200,234)(241,308)(242,307)(243,306)(244,310)
(245,309)(246,303)(247,302)(248,301)(249,305)(250,304)(251,313)(252,312)
(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)
(261,288)(262,287)(263,286)(264,290)(265,289)(266,283)(267,282)(268,281)
(269,285)(270,284)(271,293)(272,292)(273,291)(274,295)(275,294)(276,298)
(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)(323,401)(324,405)
(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)(331,418)(332,417)
(333,416)(334,420)(335,419)(336,413)(337,412)(338,411)(339,415)(340,414)
(341,423)(342,422)(343,421)(344,425)(345,424)(346,428)(347,427)(348,426)
(349,430)(350,429)(351,438)(352,437)(353,436)(354,440)(355,439)(356,433)
(357,432)(358,431)(359,435)(360,434)(361,448)(362,447)(363,446)(364,450)
(365,449)(366,443)(367,442)(368,441)(369,445)(370,444)(371,453)(372,452)
(373,451)(374,455)(375,454)(376,458)(377,457)(378,456)(379,460)(380,459)
(381,468)(382,467)(383,466)(384,470)(385,469)(386,463)(387,462)(388,461)
(389,465)(390,464)(391,473)(392,472)(393,471)(394,475)(395,474)(396,478)
(397,477)(398,476)(399,480)(400,479)(481,613)(482,612)(483,611)(484,615)
(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,608)(492,607)
(493,606)(494,610)(495,609)(496,603)(497,602)(498,601)(499,605)(500,604)
(501,633)(502,632)(503,631)(504,635)(505,634)(506,638)(507,637)(508,636)
(509,640)(510,639)(511,628)(512,627)(513,626)(514,630)(515,629)(516,623)
(517,622)(518,621)(519,625)(520,624)(521,573)(522,572)(523,571)(524,575)
(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,568)(532,567)
(533,566)(534,570)(535,569)(536,563)(537,562)(538,561)(539,565)(540,564)
(541,593)(542,592)(543,591)(544,595)(545,594)(546,598)(547,597)(548,596)
(549,600)(550,599)(551,588)(552,587)(553,586)(554,590)(555,589)(556,583)
(557,582)(558,581)(559,585)(560,584);;
s2 := (  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)( 21,341)( 22,342)( 23,343)( 24,344)
( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)( 32,352)
( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)( 40,360)
( 41,376)( 42,377)( 43,378)( 44,379)( 45,380)( 46,371)( 47,372)( 48,373)
( 49,374)( 50,375)( 51,366)( 52,367)( 53,368)( 54,369)( 55,370)( 56,361)
( 57,362)( 58,363)( 59,364)( 60,365)( 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)
( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)( 88,428)
( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)( 96,436)
( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)(104,404)
(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)(112,412)
(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)(120,420)
(121,476)(122,477)(123,478)(124,479)(125,480)(126,471)(127,472)(128,473)
(129,474)(130,475)(131,466)(132,467)(133,468)(134,469)(135,470)(136,461)
(137,462)(138,463)(139,464)(140,465)(141,456)(142,457)(143,458)(144,459)
(145,460)(146,451)(147,452)(148,453)(149,454)(150,455)(151,446)(152,447)
(153,448)(154,449)(155,450)(156,441)(157,442)(158,443)(159,444)(160,445)
(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)(181,501)(182,502)(183,503)(184,504)
(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,511)(192,512)
(193,513)(194,514)(195,515)(196,516)(197,517)(198,518)(199,519)(200,520)
(201,536)(202,537)(203,538)(204,539)(205,540)(206,531)(207,532)(208,533)
(209,534)(210,535)(211,526)(212,527)(213,528)(214,529)(215,530)(216,521)
(217,522)(218,523)(219,524)(220,525)(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)
(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)(248,588)
(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)(256,596)
(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)(264,564)
(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)(272,572)
(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)(280,580)
(281,636)(282,637)(283,638)(284,639)(285,640)(286,631)(287,632)(288,633)
(289,634)(290,635)(291,626)(292,627)(293,628)(294,629)(295,630)(296,621)
(297,622)(298,623)(299,624)(300,625)(301,616)(302,617)(303,618)(304,619)
(305,620)(306,611)(307,612)(308,613)(309,614)(310,615)(311,606)(312,607)
(313,608)(314,609)(315,610)(316,601)(317,602)(318,603)(319,604)(320,605);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(640)!(  1,161)(  2,165)(  3,164)(  4,163)(  5,162)(  6,166)(  7,170)
(  8,169)(  9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)
( 16,176)( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)
( 24,183)( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)
( 32,195)( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)
( 40,197)( 41,206)( 42,210)( 43,209)( 44,208)( 45,207)( 46,201)( 47,205)
( 48,204)( 49,203)( 50,202)( 51,216)( 52,220)( 53,219)( 54,218)( 55,217)
( 56,211)( 57,215)( 58,214)( 59,213)( 60,212)( 61,226)( 62,230)( 63,229)
( 64,228)( 65,227)( 66,221)( 67,225)( 68,224)( 69,223)( 70,222)( 71,236)
( 72,240)( 73,239)( 74,238)( 75,237)( 76,231)( 77,235)( 78,234)( 79,233)
( 80,232)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,256)( 87,260)
( 88,259)( 89,258)( 90,257)( 91,241)( 92,245)( 93,244)( 94,243)( 95,242)
( 96,246)( 97,250)( 98,249)( 99,248)(100,247)(101,271)(102,275)(103,274)
(104,273)(105,272)(106,276)(107,280)(108,279)(109,278)(110,277)(111,261)
(112,265)(113,264)(114,263)(115,262)(116,266)(117,270)(118,269)(119,268)
(120,267)(121,296)(122,300)(123,299)(124,298)(125,297)(126,291)(127,295)
(128,294)(129,293)(130,292)(131,286)(132,290)(133,289)(134,288)(135,287)
(136,281)(137,285)(138,284)(139,283)(140,282)(141,316)(142,320)(143,319)
(144,318)(145,317)(146,311)(147,315)(148,314)(149,313)(150,312)(151,306)
(152,310)(153,309)(154,308)(155,307)(156,301)(157,305)(158,304)(159,303)
(160,302)(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)
(328,489)(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)
(336,496)(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)
(344,503)(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)
(352,515)(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)
(360,517)(361,526)(362,530)(363,529)(364,528)(365,527)(366,521)(367,525)
(368,524)(369,523)(370,522)(371,536)(372,540)(373,539)(374,538)(375,537)
(376,531)(377,535)(378,534)(379,533)(380,532)(381,546)(382,550)(383,549)
(384,548)(385,547)(386,541)(387,545)(388,544)(389,543)(390,542)(391,556)
(392,560)(393,559)(394,558)(395,557)(396,551)(397,555)(398,554)(399,553)
(400,552)(401,571)(402,575)(403,574)(404,573)(405,572)(406,576)(407,580)
(408,579)(409,578)(410,577)(411,561)(412,565)(413,564)(414,563)(415,562)
(416,566)(417,570)(418,569)(419,568)(420,567)(421,591)(422,595)(423,594)
(424,593)(425,592)(426,596)(427,600)(428,599)(429,598)(430,597)(431,581)
(432,585)(433,584)(434,583)(435,582)(436,586)(437,590)(438,589)(439,588)
(440,587)(441,616)(442,620)(443,619)(444,618)(445,617)(446,611)(447,615)
(448,614)(449,613)(450,612)(451,606)(452,610)(453,609)(454,608)(455,607)
(456,601)(457,605)(458,604)(459,603)(460,602)(461,636)(462,640)(463,639)
(464,638)(465,637)(466,631)(467,635)(468,634)(469,633)(470,632)(471,626)
(472,630)(473,629)(474,628)(475,627)(476,621)(477,625)(478,624)(479,623)
(480,622);
s1 := Sym(640)!(  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 18)( 12, 17)( 13, 16)
( 14, 20)( 15, 19)( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 38)( 32, 37)
( 33, 36)( 34, 40)( 35, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)
( 51, 53)( 54, 55)( 56, 58)( 59, 60)( 61, 68)( 62, 67)( 63, 66)( 64, 70)
( 65, 69)( 71, 73)( 74, 75)( 76, 78)( 79, 80)( 81,103)( 82,102)( 83,101)
( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,118)
( 92,117)( 93,116)( 94,120)( 95,119)( 96,113)( 97,112)( 98,111)( 99,115)
(100,114)(121,148)(122,147)(123,146)(124,150)(125,149)(126,143)(127,142)
(128,141)(129,145)(130,144)(131,153)(132,152)(133,151)(134,155)(135,154)
(136,158)(137,157)(138,156)(139,160)(140,159)(161,203)(162,202)(163,201)
(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,218)
(172,217)(173,216)(174,220)(175,219)(176,213)(177,212)(178,211)(179,215)
(180,214)(181,223)(182,222)(183,221)(184,225)(185,224)(186,228)(187,227)
(188,226)(189,230)(190,229)(191,238)(192,237)(193,236)(194,240)(195,239)
(196,233)(197,232)(198,231)(199,235)(200,234)(241,308)(242,307)(243,306)
(244,310)(245,309)(246,303)(247,302)(248,301)(249,305)(250,304)(251,313)
(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)
(260,319)(261,288)(262,287)(263,286)(264,290)(265,289)(266,283)(267,282)
(268,281)(269,285)(270,284)(271,293)(272,292)(273,291)(274,295)(275,294)
(276,298)(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)(323,401)
(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)(331,418)
(332,417)(333,416)(334,420)(335,419)(336,413)(337,412)(338,411)(339,415)
(340,414)(341,423)(342,422)(343,421)(344,425)(345,424)(346,428)(347,427)
(348,426)(349,430)(350,429)(351,438)(352,437)(353,436)(354,440)(355,439)
(356,433)(357,432)(358,431)(359,435)(360,434)(361,448)(362,447)(363,446)
(364,450)(365,449)(366,443)(367,442)(368,441)(369,445)(370,444)(371,453)
(372,452)(373,451)(374,455)(375,454)(376,458)(377,457)(378,456)(379,460)
(380,459)(381,468)(382,467)(383,466)(384,470)(385,469)(386,463)(387,462)
(388,461)(389,465)(390,464)(391,473)(392,472)(393,471)(394,475)(395,474)
(396,478)(397,477)(398,476)(399,480)(400,479)(481,613)(482,612)(483,611)
(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,608)
(492,607)(493,606)(494,610)(495,609)(496,603)(497,602)(498,601)(499,605)
(500,604)(501,633)(502,632)(503,631)(504,635)(505,634)(506,638)(507,637)
(508,636)(509,640)(510,639)(511,628)(512,627)(513,626)(514,630)(515,629)
(516,623)(517,622)(518,621)(519,625)(520,624)(521,573)(522,572)(523,571)
(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,568)
(532,567)(533,566)(534,570)(535,569)(536,563)(537,562)(538,561)(539,565)
(540,564)(541,593)(542,592)(543,591)(544,595)(545,594)(546,598)(547,597)
(548,596)(549,600)(550,599)(551,588)(552,587)(553,586)(554,590)(555,589)
(556,583)(557,582)(558,581)(559,585)(560,584);
s2 := 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)( 21,341)( 22,342)( 23,343)
( 24,344)( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)
( 32,352)( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)
( 40,360)( 41,376)( 42,377)( 43,378)( 44,379)( 45,380)( 46,371)( 47,372)
( 48,373)( 49,374)( 50,375)( 51,366)( 52,367)( 53,368)( 54,369)( 55,370)
( 56,361)( 57,362)( 58,363)( 59,364)( 60,365)( 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)( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)
( 88,428)( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)
( 96,436)( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)
(104,404)(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)
(112,412)(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)
(120,420)(121,476)(122,477)(123,478)(124,479)(125,480)(126,471)(127,472)
(128,473)(129,474)(130,475)(131,466)(132,467)(133,468)(134,469)(135,470)
(136,461)(137,462)(138,463)(139,464)(140,465)(141,456)(142,457)(143,458)
(144,459)(145,460)(146,451)(147,452)(148,453)(149,454)(150,455)(151,446)
(152,447)(153,448)(154,449)(155,450)(156,441)(157,442)(158,443)(159,444)
(160,445)(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)(181,501)(182,502)(183,503)
(184,504)(185,505)(186,506)(187,507)(188,508)(189,509)(190,510)(191,511)
(192,512)(193,513)(194,514)(195,515)(196,516)(197,517)(198,518)(199,519)
(200,520)(201,536)(202,537)(203,538)(204,539)(205,540)(206,531)(207,532)
(208,533)(209,534)(210,535)(211,526)(212,527)(213,528)(214,529)(215,530)
(216,521)(217,522)(218,523)(219,524)(220,525)(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)(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)
(248,588)(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)
(256,596)(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)
(264,564)(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)
(272,572)(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)
(280,580)(281,636)(282,637)(283,638)(284,639)(285,640)(286,631)(287,632)
(288,633)(289,634)(290,635)(291,626)(292,627)(293,628)(294,629)(295,630)
(296,621)(297,622)(298,623)(299,624)(300,625)(301,616)(302,617)(303,618)
(304,619)(305,620)(306,611)(307,612)(308,613)(309,614)(310,615)(311,606)
(312,607)(313,608)(314,609)(315,610)(316,601)(317,602)(318,603)(319,604)
(320,605);
poly := sub<Sym(640)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope