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Polytope of Type {20,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,16}*1280b
if this polytope has a name.
Group : SmallGroup(1280,81734)
Rank : 3
Schlafli Type : {20,16}
Number of vertices, edges, etc : 40, 320, 32
Order of s0s1s2 : 80
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
   4-fold quotients : {20,4}*320, {20,8}*320a, {20,8}*320b
   5-fold quotients : {4,16}*256b
   8-fold quotients : {20,4}*160, {10,8}*160
   10-fold quotients : {4,8}*128a
   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)
( 41,201)( 42,205)( 43,204)( 44,203)( 45,202)( 46,206)( 47,210)( 48,209)
( 49,208)( 50,207)( 51,211)( 52,215)( 53,214)( 54,213)( 55,212)( 56,216)
( 57,220)( 58,219)( 59,218)( 60,217)( 61,221)( 62,225)( 63,224)( 64,223)
( 65,222)( 66,226)( 67,230)( 68,229)( 69,228)( 70,227)( 71,231)( 72,235)
( 73,234)( 74,233)( 75,232)( 76,236)( 77,240)( 78,239)( 79,238)( 80,237)
( 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)
(121,291)(122,295)(123,294)(124,293)(125,292)(126,296)(127,300)(128,299)
(129,298)(130,297)(131,281)(132,285)(133,284)(134,283)(135,282)(136,286)
(137,290)(138,289)(139,288)(140,287)(141,311)(142,315)(143,314)(144,313)
(145,312)(146,316)(147,320)(148,319)(149,318)(150,317)(151,301)(152,305)
(153,304)(154,303)(155,302)(156,306)(157,310)(158,309)(159,308)(160,307)
(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)
(361,521)(362,525)(363,524)(364,523)(365,522)(366,526)(367,530)(368,529)
(369,528)(370,527)(371,531)(372,535)(373,534)(374,533)(375,532)(376,536)
(377,540)(378,539)(379,538)(380,537)(381,541)(382,545)(383,544)(384,543)
(385,542)(386,546)(387,550)(388,549)(389,548)(390,547)(391,551)(392,555)
(393,554)(394,553)(395,552)(396,556)(397,560)(398,559)(399,558)(400,557)
(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)
(441,611)(442,615)(443,614)(444,613)(445,612)(446,616)(447,620)(448,619)
(449,618)(450,617)(451,601)(452,605)(453,604)(454,603)(455,602)(456,606)
(457,610)(458,609)(459,608)(460,607)(461,631)(462,635)(463,634)(464,633)
(465,632)(466,636)(467,640)(468,639)(469,638)(470,637)(471,621)(472,625)
(473,624)(474,623)(475,622)(476,626)(477,630)(478,629)(479,628)(480,627);;
s1 := (  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 18)( 12, 17)( 13, 16)( 14, 20)
( 15, 19)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 33)( 34, 35)
( 36, 38)( 39, 40)( 41, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 58)( 52, 57)
( 53, 56)( 54, 60)( 55, 59)( 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)
(121,143)(122,142)(123,141)(124,145)(125,144)(126,148)(127,147)(128,146)
(129,150)(130,149)(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)(171,218)(172,217)
(173,216)(174,220)(175,219)(176,213)(177,212)(178,211)(179,215)(180,214)
(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)(187,222)(188,221)
(189,225)(190,224)(191,233)(192,232)(193,231)(194,235)(195,234)(196,238)
(197,237)(198,236)(199,240)(200,239)(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)
(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)(347,422)(348,421)
(349,425)(350,424)(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)(371,458)(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)(391,473)(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)
(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)(507,632)(508,631)
(509,635)(510,634)(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)(531,568)(532,567)
(533,566)(534,570)(535,569)(536,563)(537,562)(538,561)(539,565)(540,564)
(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)(547,592)(548,591)
(549,595)(550,594)(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)( 21,346)( 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)
( 41,376)( 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)( 61,391)( 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)
(121,476)(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)(181,506)(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)
(201,536)(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)(221,551)(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)
(281,636)(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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*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 ];;
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)( 41,201)( 42,205)( 43,204)( 44,203)( 45,202)( 46,206)( 47,210)
( 48,209)( 49,208)( 50,207)( 51,211)( 52,215)( 53,214)( 54,213)( 55,212)
( 56,216)( 57,220)( 58,219)( 59,218)( 60,217)( 61,221)( 62,225)( 63,224)
( 64,223)( 65,222)( 66,226)( 67,230)( 68,229)( 69,228)( 70,227)( 71,231)
( 72,235)( 73,234)( 74,233)( 75,232)( 76,236)( 77,240)( 78,239)( 79,238)
( 80,237)( 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)(121,291)(122,295)(123,294)(124,293)(125,292)(126,296)(127,300)
(128,299)(129,298)(130,297)(131,281)(132,285)(133,284)(134,283)(135,282)
(136,286)(137,290)(138,289)(139,288)(140,287)(141,311)(142,315)(143,314)
(144,313)(145,312)(146,316)(147,320)(148,319)(149,318)(150,317)(151,301)
(152,305)(153,304)(154,303)(155,302)(156,306)(157,310)(158,309)(159,308)
(160,307)(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)(361,521)(362,525)(363,524)(364,523)(365,522)(366,526)(367,530)
(368,529)(369,528)(370,527)(371,531)(372,535)(373,534)(374,533)(375,532)
(376,536)(377,540)(378,539)(379,538)(380,537)(381,541)(382,545)(383,544)
(384,543)(385,542)(386,546)(387,550)(388,549)(389,548)(390,547)(391,551)
(392,555)(393,554)(394,553)(395,552)(396,556)(397,560)(398,559)(399,558)
(400,557)(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)(441,611)(442,615)(443,614)(444,613)(445,612)(446,616)(447,620)
(448,619)(449,618)(450,617)(451,601)(452,605)(453,604)(454,603)(455,602)
(456,606)(457,610)(458,609)(459,608)(460,607)(461,631)(462,635)(463,634)
(464,633)(465,632)(466,636)(467,640)(468,639)(469,638)(470,637)(471,621)
(472,625)(473,624)(474,623)(475,622)(476,626)(477,630)(478,629)(479,628)
(480,627);
s1 := Sym(640)!(  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 18)( 12, 17)( 13, 16)
( 14, 20)( 15, 19)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 33)
( 34, 35)( 36, 38)( 39, 40)( 41, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 58)
( 52, 57)( 53, 56)( 54, 60)( 55, 59)( 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)(121,143)(122,142)(123,141)(124,145)(125,144)(126,148)(127,147)
(128,146)(129,150)(130,149)(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)(171,218)
(172,217)(173,216)(174,220)(175,219)(176,213)(177,212)(178,211)(179,215)
(180,214)(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)(187,222)
(188,221)(189,225)(190,224)(191,233)(192,232)(193,231)(194,235)(195,234)
(196,238)(197,237)(198,236)(199,240)(200,239)(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)(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)(347,422)
(348,421)(349,425)(350,424)(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)(371,458)
(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)(391,473)(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)(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)(507,632)
(508,631)(509,635)(510,634)(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)(531,568)
(532,567)(533,566)(534,570)(535,569)(536,563)(537,562)(538,561)(539,565)
(540,564)(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)(547,592)
(548,591)(549,595)(550,594)(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)( 21,346)( 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)( 41,376)( 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)( 61,391)( 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)(121,476)(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)(181,506)(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)(201,536)(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)(221,551)(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)(281,636)(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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*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 >; 
 
References : None.
to this polytope