Polytope of Type {4,80}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,80}*1280b
if this polytope has a name.
Group : SmallGroup(1280,81735)
Rank : 3
Schlafli Type : {4,80}
Number of vertices, edges, etc : 8, 320, 160
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 : {4,40}*640a
4-fold quotients : {4,40}*320a, {4,20}*320, {4,40}*320b
5-fold quotients : {4,16}*256b
8-fold quotients : {4,20}*160, {2,40}*160
10-fold quotients : {4,8}*128a
16-fold quotients : {2,20}*80, {4,10}*80
20-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
32-fold quotients : {2,10}*40
40-fold quotients : {4,4}*32, {2,8}*32
64-fold quotients : {2,5}*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)( 2,162)( 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)( 21,181)( 22,182)( 23,183)( 24,184)
( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,191)( 32,192)
( 33,193)( 34,194)( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)( 40,200)
( 41,201)( 42,202)( 43,203)( 44,204)( 45,205)( 46,206)( 47,207)( 48,208)
( 49,209)( 50,210)( 51,211)( 52,212)( 53,213)( 54,214)( 55,215)( 56,216)
( 57,217)( 58,218)( 59,219)( 60,220)( 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)
( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,256)( 87,257)( 88,258)
( 89,259)( 90,260)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,246)
( 97,247)( 98,248)( 99,249)(100,250)(101,271)(102,272)(103,273)(104,274)
(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,261)(112,262)
(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)
(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)(128,298)
(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,311)(142,312)(143,313)(144,314)
(145,315)(146,316)(147,317)(148,318)(149,319)(150,320)(151,301)(152,302)
(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)(160,310)
(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)(341,501)(342,502)(343,503)(344,504)
(345,505)(346,506)(347,507)(348,508)(349,509)(350,510)(351,511)(352,512)
(353,513)(354,514)(355,515)(356,516)(357,517)(358,518)(359,519)(360,520)
(361,521)(362,522)(363,523)(364,524)(365,525)(366,526)(367,527)(368,528)
(369,529)(370,530)(371,531)(372,532)(373,533)(374,534)(375,535)(376,536)
(377,537)(378,538)(379,539)(380,540)(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)
(401,571)(402,572)(403,573)(404,574)(405,575)(406,576)(407,577)(408,578)
(409,579)(410,580)(411,561)(412,562)(413,563)(414,564)(415,565)(416,566)
(417,567)(418,568)(419,569)(420,570)(421,591)(422,592)(423,593)(424,594)
(425,595)(426,596)(427,597)(428,598)(429,599)(430,600)(431,581)(432,582)
(433,583)(434,584)(435,585)(436,586)(437,587)(438,588)(439,589)(440,590)
(441,611)(442,612)(443,613)(444,614)(445,615)(446,616)(447,617)(448,618)
(449,619)(450,620)(451,601)(452,602)(453,603)(454,604)(455,605)(456,606)
(457,607)(458,608)(459,609)(460,610)(461,631)(462,632)(463,633)(464,634)
(465,635)(466,636)(467,637)(468,638)(469,639)(470,640)(471,621)(472,622)
(473,623)(474,624)(475,625)(476,626)(477,627)(478,628)(479,629)(480,630);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 11, 16)( 12, 20)( 13, 19)( 14, 18)
( 15, 17)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)
( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 56)( 52, 60)
( 53, 59)( 54, 58)( 55, 57)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)
( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 81,101)( 82,105)( 83,104)( 84,103)
( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,116)( 92,120)
( 93,119)( 94,118)( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)
(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)(128,149)
(129,148)(130,147)(131,156)(132,160)(133,159)(134,158)(135,157)(136,151)
(137,155)(138,154)(139,153)(140,152)(161,201)(162,205)(163,204)(164,203)
(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,216)(172,220)
(173,219)(174,218)(175,217)(176,211)(177,215)(178,214)(179,213)(180,212)
(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)(187,225)(188,224)
(189,223)(190,222)(191,231)(192,235)(193,234)(194,233)(195,232)(196,236)
(197,240)(198,239)(199,238)(200,237)(241,306)(242,310)(243,309)(244,308)
(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)(251,311)(252,315)
(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)(260,317)
(261,286)(262,290)(263,289)(264,288)(265,287)(266,281)(267,285)(268,284)
(269,283)(270,282)(271,291)(272,295)(273,294)(274,293)(275,292)(276,296)
(277,300)(278,299)(279,298)(280,297)(321,401)(322,405)(323,404)(324,403)
(325,402)(326,406)(327,410)(328,409)(329,408)(330,407)(331,416)(332,420)
(333,419)(334,418)(335,417)(336,411)(337,415)(338,414)(339,413)(340,412)
(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)(347,425)(348,424)
(349,423)(350,422)(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)(371,456)(372,460)
(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)(380,452)
(381,466)(382,470)(383,469)(384,468)(385,467)(386,461)(387,465)(388,464)
(389,463)(390,462)(391,471)(392,475)(393,474)(394,473)(395,472)(396,476)
(397,480)(398,479)(399,478)(400,477)(481,611)(482,615)(483,614)(484,613)
(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,606)(492,610)
(493,609)(494,608)(495,607)(496,601)(497,605)(498,604)(499,603)(500,602)
(501,636)(502,640)(503,639)(504,638)(505,637)(506,631)(507,635)(508,634)
(509,633)(510,632)(511,621)(512,625)(513,624)(514,623)(515,622)(516,626)
(517,630)(518,629)(519,628)(520,627)(521,571)(522,575)(523,574)(524,573)
(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,566)(532,570)
(533,569)(534,568)(535,567)(536,561)(537,565)(538,564)(539,563)(540,562)
(541,596)(542,600)(543,599)(544,598)(545,597)(546,591)(547,595)(548,594)
(549,593)(550,592)(551,581)(552,585)(553,584)(554,583)(555,582)(556,586)
(557,590)(558,589)(559,588)(560,587);;
s2 := ( 1,323)( 2,322)( 3,321)( 4,325)( 5,324)( 6,328)( 7,327)( 8,326)
( 9,330)( 10,329)( 11,333)( 12,332)( 13,331)( 14,335)( 15,334)( 16,338)
( 17,337)( 18,336)( 19,340)( 20,339)( 21,348)( 22,347)( 23,346)( 24,350)
( 25,349)( 26,343)( 27,342)( 28,341)( 29,345)( 30,344)( 31,358)( 32,357)
( 33,356)( 34,360)( 35,359)( 36,353)( 37,352)( 38,351)( 39,355)( 40,354)
( 41,378)( 42,377)( 43,376)( 44,380)( 45,379)( 46,373)( 47,372)( 48,371)
( 49,375)( 50,374)( 51,368)( 52,367)( 53,366)( 54,370)( 55,369)( 56,363)
( 57,362)( 58,361)( 59,365)( 60,364)( 61,393)( 62,392)( 63,391)( 64,395)
( 65,394)( 66,398)( 67,397)( 68,396)( 69,400)( 70,399)( 71,383)( 72,382)
( 73,381)( 74,385)( 75,384)( 76,388)( 77,387)( 78,386)( 79,390)( 80,389)
( 81,423)( 82,422)( 83,421)( 84,425)( 85,424)( 86,428)( 87,427)( 88,426)
( 89,430)( 90,429)( 91,433)( 92,432)( 93,431)( 94,435)( 95,434)( 96,438)
( 97,437)( 98,436)( 99,440)(100,439)(101,403)(102,402)(103,401)(104,405)
(105,404)(106,408)(107,407)(108,406)(109,410)(110,409)(111,413)(112,412)
(113,411)(114,415)(115,414)(116,418)(117,417)(118,416)(119,420)(120,419)
(121,478)(122,477)(123,476)(124,480)(125,479)(126,473)(127,472)(128,471)
(129,475)(130,474)(131,468)(132,467)(133,466)(134,470)(135,469)(136,463)
(137,462)(138,461)(139,465)(140,464)(141,458)(142,457)(143,456)(144,460)
(145,459)(146,453)(147,452)(148,451)(149,455)(150,454)(151,448)(152,447)
(153,446)(154,450)(155,449)(156,443)(157,442)(158,441)(159,445)(160,444)
(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)(168,486)
(169,490)(170,489)(171,493)(172,492)(173,491)(174,495)(175,494)(176,498)
(177,497)(178,496)(179,500)(180,499)(181,508)(182,507)(183,506)(184,510)
(185,509)(186,503)(187,502)(188,501)(189,505)(190,504)(191,518)(192,517)
(193,516)(194,520)(195,519)(196,513)(197,512)(198,511)(199,515)(200,514)
(201,538)(202,537)(203,536)(204,540)(205,539)(206,533)(207,532)(208,531)
(209,535)(210,534)(211,528)(212,527)(213,526)(214,530)(215,529)(216,523)
(217,522)(218,521)(219,525)(220,524)(221,553)(222,552)(223,551)(224,555)
(225,554)(226,558)(227,557)(228,556)(229,560)(230,559)(231,543)(232,542)
(233,541)(234,545)(235,544)(236,548)(237,547)(238,546)(239,550)(240,549)
(241,583)(242,582)(243,581)(244,585)(245,584)(246,588)(247,587)(248,586)
(249,590)(250,589)(251,593)(252,592)(253,591)(254,595)(255,594)(256,598)
(257,597)(258,596)(259,600)(260,599)(261,563)(262,562)(263,561)(264,565)
(265,564)(266,568)(267,567)(268,566)(269,570)(270,569)(271,573)(272,572)
(273,571)(274,575)(275,574)(276,578)(277,577)(278,576)(279,580)(280,579)
(281,638)(282,637)(283,636)(284,640)(285,639)(286,633)(287,632)(288,631)
(289,635)(290,634)(291,628)(292,627)(293,626)(294,630)(295,629)(296,623)
(297,622)(298,621)(299,625)(300,624)(301,618)(302,617)(303,616)(304,620)
(305,619)(306,613)(307,612)(308,611)(309,615)(310,614)(311,608)(312,607)
(313,606)(314,610)(315,609)(316,603)(317,602)(318,601)(319,605)(320,604);;
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*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
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)( 21,181)( 22,182)( 23,183)
( 24,184)( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,191)
( 32,192)( 33,193)( 34,194)( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)
( 40,200)( 41,201)( 42,202)( 43,203)( 44,204)( 45,205)( 46,206)( 47,207)
( 48,208)( 49,209)( 50,210)( 51,211)( 52,212)( 53,213)( 54,214)( 55,215)
( 56,216)( 57,217)( 58,218)( 59,219)( 60,220)( 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)( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,256)( 87,257)
( 88,258)( 89,259)( 90,260)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,246)( 97,247)( 98,248)( 99,249)(100,250)(101,271)(102,272)(103,273)
(104,274)(105,275)(106,276)(107,277)(108,278)(109,279)(110,280)(111,261)
(112,262)(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)
(120,270)(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)
(128,298)(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,311)(142,312)(143,313)
(144,314)(145,315)(146,316)(147,317)(148,318)(149,319)(150,320)(151,301)
(152,302)(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)
(160,310)(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)(341,501)(342,502)(343,503)
(344,504)(345,505)(346,506)(347,507)(348,508)(349,509)(350,510)(351,511)
(352,512)(353,513)(354,514)(355,515)(356,516)(357,517)(358,518)(359,519)
(360,520)(361,521)(362,522)(363,523)(364,524)(365,525)(366,526)(367,527)
(368,528)(369,529)(370,530)(371,531)(372,532)(373,533)(374,534)(375,535)
(376,536)(377,537)(378,538)(379,539)(380,540)(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)(401,571)(402,572)(403,573)(404,574)(405,575)(406,576)(407,577)
(408,578)(409,579)(410,580)(411,561)(412,562)(413,563)(414,564)(415,565)
(416,566)(417,567)(418,568)(419,569)(420,570)(421,591)(422,592)(423,593)
(424,594)(425,595)(426,596)(427,597)(428,598)(429,599)(430,600)(431,581)
(432,582)(433,583)(434,584)(435,585)(436,586)(437,587)(438,588)(439,589)
(440,590)(441,611)(442,612)(443,613)(444,614)(445,615)(446,616)(447,617)
(448,618)(449,619)(450,620)(451,601)(452,602)(453,603)(454,604)(455,605)
(456,606)(457,607)(458,608)(459,609)(460,610)(461,631)(462,632)(463,633)
(464,634)(465,635)(466,636)(467,637)(468,638)(469,639)(470,640)(471,621)
(472,622)(473,623)(474,624)(475,625)(476,626)(477,627)(478,628)(479,629)
(480,630);
s1 := Sym(640)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 11, 16)( 12, 20)( 13, 19)
( 14, 18)( 15, 17)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)
( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 66)( 62, 70)( 63, 69)( 64, 68)
( 65, 67)( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 81,101)( 82,105)( 83,104)
( 84,103)( 85,102)( 86,106)( 87,110)( 88,109)( 89,108)( 90,107)( 91,116)
( 92,120)( 93,119)( 94,118)( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)
(100,112)(121,141)(122,145)(123,144)(124,143)(125,142)(126,146)(127,150)
(128,149)(129,148)(130,147)(131,156)(132,160)(133,159)(134,158)(135,157)
(136,151)(137,155)(138,154)(139,153)(140,152)(161,201)(162,205)(163,204)
(164,203)(165,202)(166,206)(167,210)(168,209)(169,208)(170,207)(171,216)
(172,220)(173,219)(174,218)(175,217)(176,211)(177,215)(178,214)(179,213)
(180,212)(181,226)(182,230)(183,229)(184,228)(185,227)(186,221)(187,225)
(188,224)(189,223)(190,222)(191,231)(192,235)(193,234)(194,233)(195,232)
(196,236)(197,240)(198,239)(199,238)(200,237)(241,306)(242,310)(243,309)
(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)(251,311)
(252,315)(253,314)(254,313)(255,312)(256,316)(257,320)(258,319)(259,318)
(260,317)(261,286)(262,290)(263,289)(264,288)(265,287)(266,281)(267,285)
(268,284)(269,283)(270,282)(271,291)(272,295)(273,294)(274,293)(275,292)
(276,296)(277,300)(278,299)(279,298)(280,297)(321,401)(322,405)(323,404)
(324,403)(325,402)(326,406)(327,410)(328,409)(329,408)(330,407)(331,416)
(332,420)(333,419)(334,418)(335,417)(336,411)(337,415)(338,414)(339,413)
(340,412)(341,426)(342,430)(343,429)(344,428)(345,427)(346,421)(347,425)
(348,424)(349,423)(350,422)(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)(371,456)
(372,460)(373,459)(374,458)(375,457)(376,451)(377,455)(378,454)(379,453)
(380,452)(381,466)(382,470)(383,469)(384,468)(385,467)(386,461)(387,465)
(388,464)(389,463)(390,462)(391,471)(392,475)(393,474)(394,473)(395,472)
(396,476)(397,480)(398,479)(399,478)(400,477)(481,611)(482,615)(483,614)
(484,613)(485,612)(486,616)(487,620)(488,619)(489,618)(490,617)(491,606)
(492,610)(493,609)(494,608)(495,607)(496,601)(497,605)(498,604)(499,603)
(500,602)(501,636)(502,640)(503,639)(504,638)(505,637)(506,631)(507,635)
(508,634)(509,633)(510,632)(511,621)(512,625)(513,624)(514,623)(515,622)
(516,626)(517,630)(518,629)(519,628)(520,627)(521,571)(522,575)(523,574)
(524,573)(525,572)(526,576)(527,580)(528,579)(529,578)(530,577)(531,566)
(532,570)(533,569)(534,568)(535,567)(536,561)(537,565)(538,564)(539,563)
(540,562)(541,596)(542,600)(543,599)(544,598)(545,597)(546,591)(547,595)
(548,594)(549,593)(550,592)(551,581)(552,585)(553,584)(554,583)(555,582)
(556,586)(557,590)(558,589)(559,588)(560,587);
s2 := Sym(640)!( 1,323)( 2,322)( 3,321)( 4,325)( 5,324)( 6,328)( 7,327)
( 8,326)( 9,330)( 10,329)( 11,333)( 12,332)( 13,331)( 14,335)( 15,334)
( 16,338)( 17,337)( 18,336)( 19,340)( 20,339)( 21,348)( 22,347)( 23,346)
( 24,350)( 25,349)( 26,343)( 27,342)( 28,341)( 29,345)( 30,344)( 31,358)
( 32,357)( 33,356)( 34,360)( 35,359)( 36,353)( 37,352)( 38,351)( 39,355)
( 40,354)( 41,378)( 42,377)( 43,376)( 44,380)( 45,379)( 46,373)( 47,372)
( 48,371)( 49,375)( 50,374)( 51,368)( 52,367)( 53,366)( 54,370)( 55,369)
( 56,363)( 57,362)( 58,361)( 59,365)( 60,364)( 61,393)( 62,392)( 63,391)
( 64,395)( 65,394)( 66,398)( 67,397)( 68,396)( 69,400)( 70,399)( 71,383)
( 72,382)( 73,381)( 74,385)( 75,384)( 76,388)( 77,387)( 78,386)( 79,390)
( 80,389)( 81,423)( 82,422)( 83,421)( 84,425)( 85,424)( 86,428)( 87,427)
( 88,426)( 89,430)( 90,429)( 91,433)( 92,432)( 93,431)( 94,435)( 95,434)
( 96,438)( 97,437)( 98,436)( 99,440)(100,439)(101,403)(102,402)(103,401)
(104,405)(105,404)(106,408)(107,407)(108,406)(109,410)(110,409)(111,413)
(112,412)(113,411)(114,415)(115,414)(116,418)(117,417)(118,416)(119,420)
(120,419)(121,478)(122,477)(123,476)(124,480)(125,479)(126,473)(127,472)
(128,471)(129,475)(130,474)(131,468)(132,467)(133,466)(134,470)(135,469)
(136,463)(137,462)(138,461)(139,465)(140,464)(141,458)(142,457)(143,456)
(144,460)(145,459)(146,453)(147,452)(148,451)(149,455)(150,454)(151,448)
(152,447)(153,446)(154,450)(155,449)(156,443)(157,442)(158,441)(159,445)
(160,444)(161,483)(162,482)(163,481)(164,485)(165,484)(166,488)(167,487)
(168,486)(169,490)(170,489)(171,493)(172,492)(173,491)(174,495)(175,494)
(176,498)(177,497)(178,496)(179,500)(180,499)(181,508)(182,507)(183,506)
(184,510)(185,509)(186,503)(187,502)(188,501)(189,505)(190,504)(191,518)
(192,517)(193,516)(194,520)(195,519)(196,513)(197,512)(198,511)(199,515)
(200,514)(201,538)(202,537)(203,536)(204,540)(205,539)(206,533)(207,532)
(208,531)(209,535)(210,534)(211,528)(212,527)(213,526)(214,530)(215,529)
(216,523)(217,522)(218,521)(219,525)(220,524)(221,553)(222,552)(223,551)
(224,555)(225,554)(226,558)(227,557)(228,556)(229,560)(230,559)(231,543)
(232,542)(233,541)(234,545)(235,544)(236,548)(237,547)(238,546)(239,550)
(240,549)(241,583)(242,582)(243,581)(244,585)(245,584)(246,588)(247,587)
(248,586)(249,590)(250,589)(251,593)(252,592)(253,591)(254,595)(255,594)
(256,598)(257,597)(258,596)(259,600)(260,599)(261,563)(262,562)(263,561)
(264,565)(265,564)(266,568)(267,567)(268,566)(269,570)(270,569)(271,573)
(272,572)(273,571)(274,575)(275,574)(276,578)(277,577)(278,576)(279,580)
(280,579)(281,638)(282,637)(283,636)(284,640)(285,639)(286,633)(287,632)
(288,631)(289,635)(290,634)(291,628)(292,627)(293,626)(294,630)(295,629)
(296,623)(297,622)(298,621)(299,625)(300,624)(301,618)(302,617)(303,616)
(304,620)(305,619)(306,613)(307,612)(308,611)(309,615)(310,614)(311,608)
(312,607)(313,606)(314,610)(315,609)(316,603)(317,602)(318,601)(319,605)
(320,604);
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*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope