Polytope of Type {82,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {82,8}*1312
Also Known As : {82,8|2}. if this polytope has another name.
Group : SmallGroup(1312,155)
Rank : 3
Schlafli Type : {82,8}
Number of vertices, edges, etc : 82, 328, 8
Order of s₀s₁s₂ : 328
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {82,4}*656
   4-fold quotients : {82,2}*328
   8-fold quotients : {41,2}*164
   41-fold quotients : {2,8}*32
   82-fold quotients : {2,4}*16
   164-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,165)(  2,205)(  3,204)(  4,203)(  5,202)(  6,201)(  7,200)(  8,199)
(  9,198)( 10,197)( 11,196)( 12,195)( 13,194)( 14,193)( 15,192)( 16,191)
( 17,190)( 18,189)( 19,188)( 20,187)( 21,186)( 22,185)( 23,184)( 24,183)
( 25,182)( 26,181)( 27,180)( 28,179)( 29,178)( 30,177)( 31,176)( 32,175)
( 33,174)( 34,173)( 35,172)( 36,171)( 37,170)( 38,169)( 39,168)( 40,167)
( 41,166)( 42,206)( 43,246)( 44,245)( 45,244)( 46,243)( 47,242)( 48,241)
( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)( 56,233)
( 57,232)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)( 64,225)
( 65,224)( 66,223)( 67,222)( 68,221)( 69,220)( 70,219)( 71,218)( 72,217)
( 73,216)( 74,215)( 75,214)( 76,213)( 77,212)( 78,211)( 79,210)( 80,209)
( 81,208)( 82,207)( 83,247)( 84,287)( 85,286)( 86,285)( 87,284)( 88,283)
( 89,282)( 90,281)( 91,280)( 92,279)( 93,278)( 94,277)( 95,276)( 96,275)
( 97,274)( 98,273)( 99,272)(100,271)(101,270)(102,269)(103,268)(104,267)
(105,266)(106,265)(107,264)(108,263)(109,262)(110,261)(111,260)(112,259)
(113,258)(114,257)(115,256)(116,255)(117,254)(118,253)(119,252)(120,251)
(121,250)(122,249)(123,248)(124,288)(125,328)(126,327)(127,326)(128,325)
(129,324)(130,323)(131,322)(132,321)(133,320)(134,319)(135,318)(136,317)
(137,316)(138,315)(139,314)(140,313)(141,312)(142,311)(143,310)(144,309)
(145,308)(146,307)(147,306)(148,305)(149,304)(150,303)(151,302)(152,301)
(153,300)(154,299)(155,298)(156,297)(157,296)(158,295)(159,294)(160,293)
(161,292)(162,291)(163,290)(164,289)(329,493)(330,533)(331,532)(332,531)
(333,530)(334,529)(335,528)(336,527)(337,526)(338,525)(339,524)(340,523)
(341,522)(342,521)(343,520)(344,519)(345,518)(346,517)(347,516)(348,515)
(349,514)(350,513)(351,512)(352,511)(353,510)(354,509)(355,508)(356,507)
(357,506)(358,505)(359,504)(360,503)(361,502)(362,501)(363,500)(364,499)
(365,498)(366,497)(367,496)(368,495)(369,494)(370,534)(371,574)(372,573)
(373,572)(374,571)(375,570)(376,569)(377,568)(378,567)(379,566)(380,565)
(381,564)(382,563)(383,562)(384,561)(385,560)(386,559)(387,558)(388,557)
(389,556)(390,555)(391,554)(392,553)(393,552)(394,551)(395,550)(396,549)
(397,548)(398,547)(399,546)(400,545)(401,544)(402,543)(403,542)(404,541)
(405,540)(406,539)(407,538)(408,537)(409,536)(410,535)(411,575)(412,615)
(413,614)(414,613)(415,612)(416,611)(417,610)(418,609)(419,608)(420,607)
(421,606)(422,605)(423,604)(424,603)(425,602)(426,601)(427,600)(428,599)
(429,598)(430,597)(431,596)(432,595)(433,594)(434,593)(435,592)(436,591)
(437,590)(438,589)(439,588)(440,587)(441,586)(442,585)(443,584)(444,583)
(445,582)(446,581)(447,580)(448,579)(449,578)(450,577)(451,576)(452,616)
(453,656)(454,655)(455,654)(456,653)(457,652)(458,651)(459,650)(460,649)
(461,648)(462,647)(463,646)(464,645)(465,644)(466,643)(467,642)(468,641)
(469,640)(470,639)(471,638)(472,637)(473,636)(474,635)(475,634)(476,633)
(477,632)(478,631)(479,630)(480,629)(481,628)(482,627)(483,626)(484,625)
(485,624)(486,623)(487,622)(488,621)(489,620)(490,619)(491,618)(492,617);;
s1 := (  1,166)(  2,165)(  3,205)(  4,204)(  5,203)(  6,202)(  7,201)(  8,200)
(  9,199)( 10,198)( 11,197)( 12,196)( 13,195)( 14,194)( 15,193)( 16,192)
( 17,191)( 18,190)( 19,189)( 20,188)( 21,187)( 22,186)( 23,185)( 24,184)
( 25,183)( 26,182)( 27,181)( 28,180)( 29,179)( 30,178)( 31,177)( 32,176)
( 33,175)( 34,174)( 35,173)( 36,172)( 37,171)( 38,170)( 39,169)( 40,168)
( 41,167)( 42,207)( 43,206)( 44,246)( 45,245)( 46,244)( 47,243)( 48,242)
( 49,241)( 50,240)( 51,239)( 52,238)( 53,237)( 54,236)( 55,235)( 56,234)
( 57,233)( 58,232)( 59,231)( 60,230)( 61,229)( 62,228)( 63,227)( 64,226)
( 65,225)( 66,224)( 67,223)( 68,222)( 69,221)( 70,220)( 71,219)( 72,218)
( 73,217)( 74,216)( 75,215)( 76,214)( 77,213)( 78,212)( 79,211)( 80,210)
( 81,209)( 82,208)( 83,289)( 84,288)( 85,328)( 86,327)( 87,326)( 88,325)
( 89,324)( 90,323)( 91,322)( 92,321)( 93,320)( 94,319)( 95,318)( 96,317)
( 97,316)( 98,315)( 99,314)(100,313)(101,312)(102,311)(103,310)(104,309)
(105,308)(106,307)(107,306)(108,305)(109,304)(110,303)(111,302)(112,301)
(113,300)(114,299)(115,298)(116,297)(117,296)(118,295)(119,294)(120,293)
(121,292)(122,291)(123,290)(124,248)(125,247)(126,287)(127,286)(128,285)
(129,284)(130,283)(131,282)(132,281)(133,280)(134,279)(135,278)(136,277)
(137,276)(138,275)(139,274)(140,273)(141,272)(142,271)(143,270)(144,269)
(145,268)(146,267)(147,266)(148,265)(149,264)(150,263)(151,262)(152,261)
(153,260)(154,259)(155,258)(156,257)(157,256)(158,255)(159,254)(160,253)
(161,252)(162,251)(163,250)(164,249)(329,576)(330,575)(331,615)(332,614)
(333,613)(334,612)(335,611)(336,610)(337,609)(338,608)(339,607)(340,606)
(341,605)(342,604)(343,603)(344,602)(345,601)(346,600)(347,599)(348,598)
(349,597)(350,596)(351,595)(352,594)(353,593)(354,592)(355,591)(356,590)
(357,589)(358,588)(359,587)(360,586)(361,585)(362,584)(363,583)(364,582)
(365,581)(366,580)(367,579)(368,578)(369,577)(370,617)(371,616)(372,656)
(373,655)(374,654)(375,653)(376,652)(377,651)(378,650)(379,649)(380,648)
(381,647)(382,646)(383,645)(384,644)(385,643)(386,642)(387,641)(388,640)
(389,639)(390,638)(391,637)(392,636)(393,635)(394,634)(395,633)(396,632)
(397,631)(398,630)(399,629)(400,628)(401,627)(402,626)(403,625)(404,624)
(405,623)(406,622)(407,621)(408,620)(409,619)(410,618)(411,494)(412,493)
(413,533)(414,532)(415,531)(416,530)(417,529)(418,528)(419,527)(420,526)
(421,525)(422,524)(423,523)(424,522)(425,521)(426,520)(427,519)(428,518)
(429,517)(430,516)(431,515)(432,514)(433,513)(434,512)(435,511)(436,510)
(437,509)(438,508)(439,507)(440,506)(441,505)(442,504)(443,503)(444,502)
(445,501)(446,500)(447,499)(448,498)(449,497)(450,496)(451,495)(452,535)
(453,534)(454,574)(455,573)(456,572)(457,571)(458,570)(459,569)(460,568)
(461,567)(462,566)(463,565)(464,564)(465,563)(466,562)(467,561)(468,560)
(469,559)(470,558)(471,557)(472,556)(473,555)(474,554)(475,553)(476,552)
(477,551)(478,550)(479,549)(480,548)(481,547)(482,546)(483,545)(484,544)
(485,543)(486,542)(487,541)(488,540)(489,539)(490,538)(491,537)(492,536);;
s2 := (  1,329)(  2,330)(  3,331)(  4,332)(  5,333)(  6,334)(  7,335)(  8,336)
(  9,337)( 10,338)( 11,339)( 12,340)( 13,341)( 14,342)( 15,343)( 16,344)
( 17,345)( 18,346)( 19,347)( 20,348)( 21,349)( 22,350)( 23,351)( 24,352)
( 25,353)( 26,354)( 27,355)( 28,356)( 29,357)( 30,358)( 31,359)( 32,360)
( 33,361)( 34,362)( 35,363)( 36,364)( 37,365)( 38,366)( 39,367)( 40,368)
( 41,369)( 42,370)( 43,371)( 44,372)( 45,373)( 46,374)( 47,375)( 48,376)
( 49,377)( 50,378)( 51,379)( 52,380)( 53,381)( 54,382)( 55,383)( 56,384)
( 57,385)( 58,386)( 59,387)( 60,388)( 61,389)( 62,390)( 63,391)( 64,392)
( 65,393)( 66,394)( 67,395)( 68,396)( 69,397)( 70,398)( 71,399)( 72,400)
( 73,401)( 74,402)( 75,403)( 76,404)( 77,405)( 78,406)( 79,407)( 80,408)
( 81,409)( 82,410)( 83,452)( 84,453)( 85,454)( 86,455)( 87,456)( 88,457)
( 89,458)( 90,459)( 91,460)( 92,461)( 93,462)( 94,463)( 95,464)( 96,465)
( 97,466)( 98,467)( 99,468)(100,469)(101,470)(102,471)(103,472)(104,473)
(105,474)(106,475)(107,476)(108,477)(109,478)(110,479)(111,480)(112,481)
(113,482)(114,483)(115,484)(116,485)(117,486)(118,487)(119,488)(120,489)
(121,490)(122,491)(123,492)(124,411)(125,412)(126,413)(127,414)(128,415)
(129,416)(130,417)(131,418)(132,419)(133,420)(134,421)(135,422)(136,423)
(137,424)(138,425)(139,426)(140,427)(141,428)(142,429)(143,430)(144,431)
(145,432)(146,433)(147,434)(148,435)(149,436)(150,437)(151,438)(152,439)
(153,440)(154,441)(155,442)(156,443)(157,444)(158,445)(159,446)(160,447)
(161,448)(162,449)(163,450)(164,451)(165,493)(166,494)(167,495)(168,496)
(169,497)(170,498)(171,499)(172,500)(173,501)(174,502)(175,503)(176,504)
(177,505)(178,506)(179,507)(180,508)(181,509)(182,510)(183,511)(184,512)
(185,513)(186,514)(187,515)(188,516)(189,517)(190,518)(191,519)(192,520)
(193,521)(194,522)(195,523)(196,524)(197,525)(198,526)(199,527)(200,528)
(201,529)(202,530)(203,531)(204,532)(205,533)(206,534)(207,535)(208,536)
(209,537)(210,538)(211,539)(212,540)(213,541)(214,542)(215,543)(216,544)
(217,545)(218,546)(219,547)(220,548)(221,549)(222,550)(223,551)(224,552)
(225,553)(226,554)(227,555)(228,556)(229,557)(230,558)(231,559)(232,560)
(233,561)(234,562)(235,563)(236,564)(237,565)(238,566)(239,567)(240,568)
(241,569)(242,570)(243,571)(244,572)(245,573)(246,574)(247,616)(248,617)
(249,618)(250,619)(251,620)(252,621)(253,622)(254,623)(255,624)(256,625)
(257,626)(258,627)(259,628)(260,629)(261,630)(262,631)(263,632)(264,633)
(265,634)(266,635)(267,636)(268,637)(269,638)(270,639)(271,640)(272,641)
(273,642)(274,643)(275,644)(276,645)(277,646)(278,647)(279,648)(280,649)
(281,650)(282,651)(283,652)(284,653)(285,654)(286,655)(287,656)(288,575)
(289,576)(290,577)(291,578)(292,579)(293,580)(294,581)(295,582)(296,583)
(297,584)(298,585)(299,586)(300,587)(301,588)(302,589)(303,590)(304,591)
(305,592)(306,593)(307,594)(308,595)(309,596)(310,597)(311,598)(312,599)
(313,600)(314,601)(315,602)(316,603)(317,604)(318,605)(319,606)(320,607)
(321,608)(322,609)(323,610)(324,611)(325,612)(326,613)(327,614)(328,615);;
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*s2*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*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*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(656)!(  1,165)(  2,205)(  3,204)(  4,203)(  5,202)(  6,201)(  7,200)
(  8,199)(  9,198)( 10,197)( 11,196)( 12,195)( 13,194)( 14,193)( 15,192)
( 16,191)( 17,190)( 18,189)( 19,188)( 20,187)( 21,186)( 22,185)( 23,184)
( 24,183)( 25,182)( 26,181)( 27,180)( 28,179)( 29,178)( 30,177)( 31,176)
( 32,175)( 33,174)( 34,173)( 35,172)( 36,171)( 37,170)( 38,169)( 39,168)
( 40,167)( 41,166)( 42,206)( 43,246)( 44,245)( 45,244)( 46,243)( 47,242)
( 48,241)( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)
( 56,233)( 57,232)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)
( 64,225)( 65,224)( 66,223)( 67,222)( 68,221)( 69,220)( 70,219)( 71,218)
( 72,217)( 73,216)( 74,215)( 75,214)( 76,213)( 77,212)( 78,211)( 79,210)
( 80,209)( 81,208)( 82,207)( 83,247)( 84,287)( 85,286)( 86,285)( 87,284)
( 88,283)( 89,282)( 90,281)( 91,280)( 92,279)( 93,278)( 94,277)( 95,276)
( 96,275)( 97,274)( 98,273)( 99,272)(100,271)(101,270)(102,269)(103,268)
(104,267)(105,266)(106,265)(107,264)(108,263)(109,262)(110,261)(111,260)
(112,259)(113,258)(114,257)(115,256)(116,255)(117,254)(118,253)(119,252)
(120,251)(121,250)(122,249)(123,248)(124,288)(125,328)(126,327)(127,326)
(128,325)(129,324)(130,323)(131,322)(132,321)(133,320)(134,319)(135,318)
(136,317)(137,316)(138,315)(139,314)(140,313)(141,312)(142,311)(143,310)
(144,309)(145,308)(146,307)(147,306)(148,305)(149,304)(150,303)(151,302)
(152,301)(153,300)(154,299)(155,298)(156,297)(157,296)(158,295)(159,294)
(160,293)(161,292)(162,291)(163,290)(164,289)(329,493)(330,533)(331,532)
(332,531)(333,530)(334,529)(335,528)(336,527)(337,526)(338,525)(339,524)
(340,523)(341,522)(342,521)(343,520)(344,519)(345,518)(346,517)(347,516)
(348,515)(349,514)(350,513)(351,512)(352,511)(353,510)(354,509)(355,508)
(356,507)(357,506)(358,505)(359,504)(360,503)(361,502)(362,501)(363,500)
(364,499)(365,498)(366,497)(367,496)(368,495)(369,494)(370,534)(371,574)
(372,573)(373,572)(374,571)(375,570)(376,569)(377,568)(378,567)(379,566)
(380,565)(381,564)(382,563)(383,562)(384,561)(385,560)(386,559)(387,558)
(388,557)(389,556)(390,555)(391,554)(392,553)(393,552)(394,551)(395,550)
(396,549)(397,548)(398,547)(399,546)(400,545)(401,544)(402,543)(403,542)
(404,541)(405,540)(406,539)(407,538)(408,537)(409,536)(410,535)(411,575)
(412,615)(413,614)(414,613)(415,612)(416,611)(417,610)(418,609)(419,608)
(420,607)(421,606)(422,605)(423,604)(424,603)(425,602)(426,601)(427,600)
(428,599)(429,598)(430,597)(431,596)(432,595)(433,594)(434,593)(435,592)
(436,591)(437,590)(438,589)(439,588)(440,587)(441,586)(442,585)(443,584)
(444,583)(445,582)(446,581)(447,580)(448,579)(449,578)(450,577)(451,576)
(452,616)(453,656)(454,655)(455,654)(456,653)(457,652)(458,651)(459,650)
(460,649)(461,648)(462,647)(463,646)(464,645)(465,644)(466,643)(467,642)
(468,641)(469,640)(470,639)(471,638)(472,637)(473,636)(474,635)(475,634)
(476,633)(477,632)(478,631)(479,630)(480,629)(481,628)(482,627)(483,626)
(484,625)(485,624)(486,623)(487,622)(488,621)(489,620)(490,619)(491,618)
(492,617);
s1 := Sym(656)!(  1,166)(  2,165)(  3,205)(  4,204)(  5,203)(  6,202)(  7,201)
(  8,200)(  9,199)( 10,198)( 11,197)( 12,196)( 13,195)( 14,194)( 15,193)
( 16,192)( 17,191)( 18,190)( 19,189)( 20,188)( 21,187)( 22,186)( 23,185)
( 24,184)( 25,183)( 26,182)( 27,181)( 28,180)( 29,179)( 30,178)( 31,177)
( 32,176)( 33,175)( 34,174)( 35,173)( 36,172)( 37,171)( 38,170)( 39,169)
( 40,168)( 41,167)( 42,207)( 43,206)( 44,246)( 45,245)( 46,244)( 47,243)
( 48,242)( 49,241)( 50,240)( 51,239)( 52,238)( 53,237)( 54,236)( 55,235)
( 56,234)( 57,233)( 58,232)( 59,231)( 60,230)( 61,229)( 62,228)( 63,227)
( 64,226)( 65,225)( 66,224)( 67,223)( 68,222)( 69,221)( 70,220)( 71,219)
( 72,218)( 73,217)( 74,216)( 75,215)( 76,214)( 77,213)( 78,212)( 79,211)
( 80,210)( 81,209)( 82,208)( 83,289)( 84,288)( 85,328)( 86,327)( 87,326)
( 88,325)( 89,324)( 90,323)( 91,322)( 92,321)( 93,320)( 94,319)( 95,318)
( 96,317)( 97,316)( 98,315)( 99,314)(100,313)(101,312)(102,311)(103,310)
(104,309)(105,308)(106,307)(107,306)(108,305)(109,304)(110,303)(111,302)
(112,301)(113,300)(114,299)(115,298)(116,297)(117,296)(118,295)(119,294)
(120,293)(121,292)(122,291)(123,290)(124,248)(125,247)(126,287)(127,286)
(128,285)(129,284)(130,283)(131,282)(132,281)(133,280)(134,279)(135,278)
(136,277)(137,276)(138,275)(139,274)(140,273)(141,272)(142,271)(143,270)
(144,269)(145,268)(146,267)(147,266)(148,265)(149,264)(150,263)(151,262)
(152,261)(153,260)(154,259)(155,258)(156,257)(157,256)(158,255)(159,254)
(160,253)(161,252)(162,251)(163,250)(164,249)(329,576)(330,575)(331,615)
(332,614)(333,613)(334,612)(335,611)(336,610)(337,609)(338,608)(339,607)
(340,606)(341,605)(342,604)(343,603)(344,602)(345,601)(346,600)(347,599)
(348,598)(349,597)(350,596)(351,595)(352,594)(353,593)(354,592)(355,591)
(356,590)(357,589)(358,588)(359,587)(360,586)(361,585)(362,584)(363,583)
(364,582)(365,581)(366,580)(367,579)(368,578)(369,577)(370,617)(371,616)
(372,656)(373,655)(374,654)(375,653)(376,652)(377,651)(378,650)(379,649)
(380,648)(381,647)(382,646)(383,645)(384,644)(385,643)(386,642)(387,641)
(388,640)(389,639)(390,638)(391,637)(392,636)(393,635)(394,634)(395,633)
(396,632)(397,631)(398,630)(399,629)(400,628)(401,627)(402,626)(403,625)
(404,624)(405,623)(406,622)(407,621)(408,620)(409,619)(410,618)(411,494)
(412,493)(413,533)(414,532)(415,531)(416,530)(417,529)(418,528)(419,527)
(420,526)(421,525)(422,524)(423,523)(424,522)(425,521)(426,520)(427,519)
(428,518)(429,517)(430,516)(431,515)(432,514)(433,513)(434,512)(435,511)
(436,510)(437,509)(438,508)(439,507)(440,506)(441,505)(442,504)(443,503)
(444,502)(445,501)(446,500)(447,499)(448,498)(449,497)(450,496)(451,495)
(452,535)(453,534)(454,574)(455,573)(456,572)(457,571)(458,570)(459,569)
(460,568)(461,567)(462,566)(463,565)(464,564)(465,563)(466,562)(467,561)
(468,560)(469,559)(470,558)(471,557)(472,556)(473,555)(474,554)(475,553)
(476,552)(477,551)(478,550)(479,549)(480,548)(481,547)(482,546)(483,545)
(484,544)(485,543)(486,542)(487,541)(488,540)(489,539)(490,538)(491,537)
(492,536);
s2 := Sym(656)!(  1,329)(  2,330)(  3,331)(  4,332)(  5,333)(  6,334)(  7,335)
(  8,336)(  9,337)( 10,338)( 11,339)( 12,340)( 13,341)( 14,342)( 15,343)
( 16,344)( 17,345)( 18,346)( 19,347)( 20,348)( 21,349)( 22,350)( 23,351)
( 24,352)( 25,353)( 26,354)( 27,355)( 28,356)( 29,357)( 30,358)( 31,359)
( 32,360)( 33,361)( 34,362)( 35,363)( 36,364)( 37,365)( 38,366)( 39,367)
( 40,368)( 41,369)( 42,370)( 43,371)( 44,372)( 45,373)( 46,374)( 47,375)
( 48,376)( 49,377)( 50,378)( 51,379)( 52,380)( 53,381)( 54,382)( 55,383)
( 56,384)( 57,385)( 58,386)( 59,387)( 60,388)( 61,389)( 62,390)( 63,391)
( 64,392)( 65,393)( 66,394)( 67,395)( 68,396)( 69,397)( 70,398)( 71,399)
( 72,400)( 73,401)( 74,402)( 75,403)( 76,404)( 77,405)( 78,406)( 79,407)
( 80,408)( 81,409)( 82,410)( 83,452)( 84,453)( 85,454)( 86,455)( 87,456)
( 88,457)( 89,458)( 90,459)( 91,460)( 92,461)( 93,462)( 94,463)( 95,464)
( 96,465)( 97,466)( 98,467)( 99,468)(100,469)(101,470)(102,471)(103,472)
(104,473)(105,474)(106,475)(107,476)(108,477)(109,478)(110,479)(111,480)
(112,481)(113,482)(114,483)(115,484)(116,485)(117,486)(118,487)(119,488)
(120,489)(121,490)(122,491)(123,492)(124,411)(125,412)(126,413)(127,414)
(128,415)(129,416)(130,417)(131,418)(132,419)(133,420)(134,421)(135,422)
(136,423)(137,424)(138,425)(139,426)(140,427)(141,428)(142,429)(143,430)
(144,431)(145,432)(146,433)(147,434)(148,435)(149,436)(150,437)(151,438)
(152,439)(153,440)(154,441)(155,442)(156,443)(157,444)(158,445)(159,446)
(160,447)(161,448)(162,449)(163,450)(164,451)(165,493)(166,494)(167,495)
(168,496)(169,497)(170,498)(171,499)(172,500)(173,501)(174,502)(175,503)
(176,504)(177,505)(178,506)(179,507)(180,508)(181,509)(182,510)(183,511)
(184,512)(185,513)(186,514)(187,515)(188,516)(189,517)(190,518)(191,519)
(192,520)(193,521)(194,522)(195,523)(196,524)(197,525)(198,526)(199,527)
(200,528)(201,529)(202,530)(203,531)(204,532)(205,533)(206,534)(207,535)
(208,536)(209,537)(210,538)(211,539)(212,540)(213,541)(214,542)(215,543)
(216,544)(217,545)(218,546)(219,547)(220,548)(221,549)(222,550)(223,551)
(224,552)(225,553)(226,554)(227,555)(228,556)(229,557)(230,558)(231,559)
(232,560)(233,561)(234,562)(235,563)(236,564)(237,565)(238,566)(239,567)
(240,568)(241,569)(242,570)(243,571)(244,572)(245,573)(246,574)(247,616)
(248,617)(249,618)(250,619)(251,620)(252,621)(253,622)(254,623)(255,624)
(256,625)(257,626)(258,627)(259,628)(260,629)(261,630)(262,631)(263,632)
(264,633)(265,634)(266,635)(267,636)(268,637)(269,638)(270,639)(271,640)
(272,641)(273,642)(274,643)(275,644)(276,645)(277,646)(278,647)(279,648)
(280,649)(281,650)(282,651)(283,652)(284,653)(285,654)(286,655)(287,656)
(288,575)(289,576)(290,577)(291,578)(292,579)(293,580)(294,581)(295,582)
(296,583)(297,584)(298,585)(299,586)(300,587)(301,588)(302,589)(303,590)
(304,591)(305,592)(306,593)(307,594)(308,595)(309,596)(310,597)(311,598)
(312,599)(313,600)(314,601)(315,602)(316,603)(317,604)(318,605)(319,606)
(320,607)(321,608)(322,609)(323,610)(324,611)(325,612)(326,613)(327,614)
(328,615);
poly := sub<Sym(656)|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*s2*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*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*s0*s1*s0*s1 >;

References : None.
to this polytope