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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}*1280a
if this polytope has a name.
Group : SmallGroup(1280,58267)
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
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {40,4}*640a, {40,8}*640a, {40,8}*640b, {20,8}*640a, {40,8}*640c, {40,8}*640d
   4-fold quotients : {40,4}*320a, {20,4}*320, {40,4}*320b, {20,8}*320a, {20,8}*320b
   5-fold quotients : {8,8}*256a
   8-fold quotients : {20,4}*160, {40,2}*160, {10,8}*160
   10-fold quotients : {4,8}*128a, {8,4}*128a, {8,8}*128a, {8,8}*128b, {8,8}*128c, {8,8}*128d
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {4,8}*64a, {8,4}*64a, {4,8}*64b, {8,4}*64b, {4,4}*64
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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, 13)( 14, 15)( 16, 18)( 19, 20)
( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 33)( 34, 35)( 36, 38)( 39, 40)
( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 58)( 52, 57)( 53, 56)
( 54, 60)( 55, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 70)( 65, 69)( 71, 78)
( 72, 77)( 73, 76)( 74, 80)( 75, 79)( 81,103)( 82,102)( 83,101)( 84,105)
( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,113)( 92,112)
( 93,111)( 94,115)( 95,114)( 96,118)( 97,117)( 98,116)( 99,120)(100,119)
(121,148)(122,147)(123,146)(124,150)(125,149)(126,143)(127,142)(128,141)
(129,145)(130,144)(131,158)(132,157)(133,156)(134,160)(135,159)(136,153)
(137,152)(138,151)(139,155)(140,154)(161,203)(162,202)(163,201)(164,205)
(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,213)(172,212)
(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)(179,220)(180,219)
(181,223)(182,222)(183,221)(184,225)(185,224)(186,228)(187,227)(188,226)
(189,230)(190,229)(191,233)(192,232)(193,231)(194,235)(195,234)(196,238)
(197,237)(198,236)(199,240)(200,239)(241,303)(242,302)(243,301)(244,305)
(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)(252,312)
(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)
(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)(268,286)
(269,290)(270,289)(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)(331,413)(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)(361,448)(362,447)(363,446)(364,450)
(365,449)(366,443)(367,442)(368,441)(369,445)(370,444)(371,458)(372,457)
(373,456)(374,460)(375,459)(376,453)(377,452)(378,451)(379,455)(380,454)
(381,468)(382,467)(383,466)(384,470)(385,469)(386,463)(387,462)(388,461)
(389,465)(390,464)(391,478)(392,477)(393,476)(394,480)(395,479)(396,473)
(397,472)(398,471)(399,475)(400,474)(481,613)(482,612)(483,611)(484,615)
(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,603)(492,602)
(493,601)(494,605)(495,604)(496,608)(497,607)(498,606)(499,610)(500,609)
(501,633)(502,632)(503,631)(504,635)(505,634)(506,638)(507,637)(508,636)
(509,640)(510,639)(511,623)(512,622)(513,621)(514,625)(515,624)(516,628)
(517,627)(518,626)(519,630)(520,629)(521,573)(522,572)(523,571)(524,575)
(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,563)(532,562)
(533,561)(534,565)(535,564)(536,568)(537,567)(538,566)(539,570)(540,569)
(541,593)(542,592)(543,591)(544,595)(545,594)(546,598)(547,597)(548,596)
(549,600)(550,599)(551,583)(552,582)(553,581)(554,585)(555,584)(556,588)
(557,587)(558,586)(559,590)(560,589);;
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)
( 41,371)( 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)( 61,391)( 62,392)( 63,393)( 64,394)
( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)( 72,382)
( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)( 80,390)
( 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)
(121,471)(122,472)(123,473)(124,474)(125,475)(126,476)(127,477)(128,478)
(129,479)(130,480)(131,461)(132,462)(133,463)(134,464)(135,465)(136,466)
(137,467)(138,468)(139,469)(140,470)(141,451)(142,452)(143,453)(144,454)
(145,455)(146,456)(147,457)(148,458)(149,459)(150,460)(151,441)(152,442)
(153,443)(154,444)(155,445)(156,446)(157,447)(158,448)(159,449)(160,450)
(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)
(201,531)(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)(221,551)(222,552)(223,553)(224,554)
(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)(232,542)
(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)(240,550)
(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)
(281,631)(282,632)(283,633)(284,634)(285,635)(286,636)(287,637)(288,638)
(289,639)(290,640)(291,621)(292,622)(293,623)(294,624)(295,625)(296,626)
(297,627)(298,628)(299,629)(300,630)(301,611)(302,612)(303,613)(304,614)
(305,615)(306,616)(307,617)(308,618)(309,619)(310,620)(311,601)(312,602)
(313,603)(314,604)(315,605)(316,606)(317,607)(318,608)(319,609)(320,610);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*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*s0*s1*s0*s1*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)!(  1,161)(  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, 13)( 14, 15)( 16, 18)
( 19, 20)( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 33)( 34, 35)( 36, 38)
( 39, 40)( 41, 48)( 42, 47)( 43, 46)( 44, 50)( 45, 49)( 51, 58)( 52, 57)
( 53, 56)( 54, 60)( 55, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 70)( 65, 69)
( 71, 78)( 72, 77)( 73, 76)( 74, 80)( 75, 79)( 81,103)( 82,102)( 83,101)
( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,113)
( 92,112)( 93,111)( 94,115)( 95,114)( 96,118)( 97,117)( 98,116)( 99,120)
(100,119)(121,148)(122,147)(123,146)(124,150)(125,149)(126,143)(127,142)
(128,141)(129,145)(130,144)(131,158)(132,157)(133,156)(134,160)(135,159)
(136,153)(137,152)(138,151)(139,155)(140,154)(161,203)(162,202)(163,201)
(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,213)
(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)(179,220)
(180,219)(181,223)(182,222)(183,221)(184,225)(185,224)(186,228)(187,227)
(188,226)(189,230)(190,229)(191,233)(192,232)(193,231)(194,235)(195,234)
(196,238)(197,237)(198,236)(199,240)(200,239)(241,303)(242,302)(243,301)
(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)
(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)
(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)
(268,286)(269,290)(270,289)(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)(331,413)
(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)(361,448)(362,447)(363,446)
(364,450)(365,449)(366,443)(367,442)(368,441)(369,445)(370,444)(371,458)
(372,457)(373,456)(374,460)(375,459)(376,453)(377,452)(378,451)(379,455)
(380,454)(381,468)(382,467)(383,466)(384,470)(385,469)(386,463)(387,462)
(388,461)(389,465)(390,464)(391,478)(392,477)(393,476)(394,480)(395,479)
(396,473)(397,472)(398,471)(399,475)(400,474)(481,613)(482,612)(483,611)
(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,603)
(492,602)(493,601)(494,605)(495,604)(496,608)(497,607)(498,606)(499,610)
(500,609)(501,633)(502,632)(503,631)(504,635)(505,634)(506,638)(507,637)
(508,636)(509,640)(510,639)(511,623)(512,622)(513,621)(514,625)(515,624)
(516,628)(517,627)(518,626)(519,630)(520,629)(521,573)(522,572)(523,571)
(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,563)
(532,562)(533,561)(534,565)(535,564)(536,568)(537,567)(538,566)(539,570)
(540,569)(541,593)(542,592)(543,591)(544,595)(545,594)(546,598)(547,597)
(548,596)(549,600)(550,599)(551,583)(552,582)(553,581)(554,585)(555,584)
(556,588)(557,587)(558,586)(559,590)(560,589);
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)( 41,371)( 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)( 61,391)( 62,392)( 63,393)
( 64,394)( 65,395)( 66,396)( 67,397)( 68,398)( 69,399)( 70,400)( 71,381)
( 72,382)( 73,383)( 74,384)( 75,385)( 76,386)( 77,387)( 78,388)( 79,389)
( 80,390)( 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)(121,471)(122,472)(123,473)(124,474)(125,475)(126,476)(127,477)
(128,478)(129,479)(130,480)(131,461)(132,462)(133,463)(134,464)(135,465)
(136,466)(137,467)(138,468)(139,469)(140,470)(141,451)(142,452)(143,453)
(144,454)(145,455)(146,456)(147,457)(148,458)(149,459)(150,460)(151,441)
(152,442)(153,443)(154,444)(155,445)(156,446)(157,447)(158,448)(159,449)
(160,450)(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)(201,531)(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)(221,551)(222,552)(223,553)
(224,554)(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,541)
(232,542)(233,543)(234,544)(235,545)(236,546)(237,547)(238,548)(239,549)
(240,550)(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)(281,631)(282,632)(283,633)(284,634)(285,635)(286,636)(287,637)
(288,638)(289,639)(290,640)(291,621)(292,622)(293,623)(294,624)(295,625)
(296,626)(297,627)(298,628)(299,629)(300,630)(301,611)(302,612)(303,613)
(304,614)(305,615)(306,616)(307,617)(308,618)(309,619)(310,620)(311,601)
(312,602)(313,603)(314,604)(315,605)(316,606)(317,607)(318,608)(319,609)
(320,610);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*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*s0*s1*s0*s1*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