Polytope of Type {86,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {86,8}*1376
Also Known As : {86,8|2}. if this polytope has another name.
Group : SmallGroup(1376,155)
Rank : 3
Schlafli Type : {86,8}
Number of vertices, edges, etc : 86, 344, 8
Order of s0s1s2 : 344
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 : {86,4}*688
4-fold quotients : {86,2}*344
8-fold quotients : {43,2}*172
43-fold quotients : {2,8}*32
86-fold quotients : {2,4}*16
172-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,173)( 2,215)( 3,214)( 4,213)( 5,212)( 6,211)( 7,210)( 8,209)
( 9,208)( 10,207)( 11,206)( 12,205)( 13,204)( 14,203)( 15,202)( 16,201)
( 17,200)( 18,199)( 19,198)( 20,197)( 21,196)( 22,195)( 23,194)( 24,193)
( 25,192)( 26,191)( 27,190)( 28,189)( 29,188)( 30,187)( 31,186)( 32,185)
( 33,184)( 34,183)( 35,182)( 36,181)( 37,180)( 38,179)( 39,178)( 40,177)
( 41,176)( 42,175)( 43,174)( 44,216)( 45,258)( 46,257)( 47,256)( 48,255)
( 49,254)( 50,253)( 51,252)( 52,251)( 53,250)( 54,249)( 55,248)( 56,247)
( 57,246)( 58,245)( 59,244)( 60,243)( 61,242)( 62,241)( 63,240)( 64,239)
( 65,238)( 66,237)( 67,236)( 68,235)( 69,234)( 70,233)( 71,232)( 72,231)
( 73,230)( 74,229)( 75,228)( 76,227)( 77,226)( 78,225)( 79,224)( 80,223)
( 81,222)( 82,221)( 83,220)( 84,219)( 85,218)( 86,217)( 87,259)( 88,301)
( 89,300)( 90,299)( 91,298)( 92,297)( 93,296)( 94,295)( 95,294)( 96,293)
( 97,292)( 98,291)( 99,290)(100,289)(101,288)(102,287)(103,286)(104,285)
(105,284)(106,283)(107,282)(108,281)(109,280)(110,279)(111,278)(112,277)
(113,276)(114,275)(115,274)(116,273)(117,272)(118,271)(119,270)(120,269)
(121,268)(122,267)(123,266)(124,265)(125,264)(126,263)(127,262)(128,261)
(129,260)(130,302)(131,344)(132,343)(133,342)(134,341)(135,340)(136,339)
(137,338)(138,337)(139,336)(140,335)(141,334)(142,333)(143,332)(144,331)
(145,330)(146,329)(147,328)(148,327)(149,326)(150,325)(151,324)(152,323)
(153,322)(154,321)(155,320)(156,319)(157,318)(158,317)(159,316)(160,315)
(161,314)(162,313)(163,312)(164,311)(165,310)(166,309)(167,308)(168,307)
(169,306)(170,305)(171,304)(172,303)(345,517)(346,559)(347,558)(348,557)
(349,556)(350,555)(351,554)(352,553)(353,552)(354,551)(355,550)(356,549)
(357,548)(358,547)(359,546)(360,545)(361,544)(362,543)(363,542)(364,541)
(365,540)(366,539)(367,538)(368,537)(369,536)(370,535)(371,534)(372,533)
(373,532)(374,531)(375,530)(376,529)(377,528)(378,527)(379,526)(380,525)
(381,524)(382,523)(383,522)(384,521)(385,520)(386,519)(387,518)(388,560)
(389,602)(390,601)(391,600)(392,599)(393,598)(394,597)(395,596)(396,595)
(397,594)(398,593)(399,592)(400,591)(401,590)(402,589)(403,588)(404,587)
(405,586)(406,585)(407,584)(408,583)(409,582)(410,581)(411,580)(412,579)
(413,578)(414,577)(415,576)(416,575)(417,574)(418,573)(419,572)(420,571)
(421,570)(422,569)(423,568)(424,567)(425,566)(426,565)(427,564)(428,563)
(429,562)(430,561)(431,603)(432,645)(433,644)(434,643)(435,642)(436,641)
(437,640)(438,639)(439,638)(440,637)(441,636)(442,635)(443,634)(444,633)
(445,632)(446,631)(447,630)(448,629)(449,628)(450,627)(451,626)(452,625)
(453,624)(454,623)(455,622)(456,621)(457,620)(458,619)(459,618)(460,617)
(461,616)(462,615)(463,614)(464,613)(465,612)(466,611)(467,610)(468,609)
(469,608)(470,607)(471,606)(472,605)(473,604)(474,646)(475,688)(476,687)
(477,686)(478,685)(479,684)(480,683)(481,682)(482,681)(483,680)(484,679)
(485,678)(486,677)(487,676)(488,675)(489,674)(490,673)(491,672)(492,671)
(493,670)(494,669)(495,668)(496,667)(497,666)(498,665)(499,664)(500,663)
(501,662)(502,661)(503,660)(504,659)(505,658)(506,657)(507,656)(508,655)
(509,654)(510,653)(511,652)(512,651)(513,650)(514,649)(515,648)(516,647);;
s1 := ( 1,174)( 2,173)( 3,215)( 4,214)( 5,213)( 6,212)( 7,211)( 8,210)
( 9,209)( 10,208)( 11,207)( 12,206)( 13,205)( 14,204)( 15,203)( 16,202)
( 17,201)( 18,200)( 19,199)( 20,198)( 21,197)( 22,196)( 23,195)( 24,194)
( 25,193)( 26,192)( 27,191)( 28,190)( 29,189)( 30,188)( 31,187)( 32,186)
( 33,185)( 34,184)( 35,183)( 36,182)( 37,181)( 38,180)( 39,179)( 40,178)
( 41,177)( 42,176)( 43,175)( 44,217)( 45,216)( 46,258)( 47,257)( 48,256)
( 49,255)( 50,254)( 51,253)( 52,252)( 53,251)( 54,250)( 55,249)( 56,248)
( 57,247)( 58,246)( 59,245)( 60,244)( 61,243)( 62,242)( 63,241)( 64,240)
( 65,239)( 66,238)( 67,237)( 68,236)( 69,235)( 70,234)( 71,233)( 72,232)
( 73,231)( 74,230)( 75,229)( 76,228)( 77,227)( 78,226)( 79,225)( 80,224)
( 81,223)( 82,222)( 83,221)( 84,220)( 85,219)( 86,218)( 87,303)( 88,302)
( 89,344)( 90,343)( 91,342)( 92,341)( 93,340)( 94,339)( 95,338)( 96,337)
( 97,336)( 98,335)( 99,334)(100,333)(101,332)(102,331)(103,330)(104,329)
(105,328)(106,327)(107,326)(108,325)(109,324)(110,323)(111,322)(112,321)
(113,320)(114,319)(115,318)(116,317)(117,316)(118,315)(119,314)(120,313)
(121,312)(122,311)(123,310)(124,309)(125,308)(126,307)(127,306)(128,305)
(129,304)(130,260)(131,259)(132,301)(133,300)(134,299)(135,298)(136,297)
(137,296)(138,295)(139,294)(140,293)(141,292)(142,291)(143,290)(144,289)
(145,288)(146,287)(147,286)(148,285)(149,284)(150,283)(151,282)(152,281)
(153,280)(154,279)(155,278)(156,277)(157,276)(158,275)(159,274)(160,273)
(161,272)(162,271)(163,270)(164,269)(165,268)(166,267)(167,266)(168,265)
(169,264)(170,263)(171,262)(172,261)(345,604)(346,603)(347,645)(348,644)
(349,643)(350,642)(351,641)(352,640)(353,639)(354,638)(355,637)(356,636)
(357,635)(358,634)(359,633)(360,632)(361,631)(362,630)(363,629)(364,628)
(365,627)(366,626)(367,625)(368,624)(369,623)(370,622)(371,621)(372,620)
(373,619)(374,618)(375,617)(376,616)(377,615)(378,614)(379,613)(380,612)
(381,611)(382,610)(383,609)(384,608)(385,607)(386,606)(387,605)(388,647)
(389,646)(390,688)(391,687)(392,686)(393,685)(394,684)(395,683)(396,682)
(397,681)(398,680)(399,679)(400,678)(401,677)(402,676)(403,675)(404,674)
(405,673)(406,672)(407,671)(408,670)(409,669)(410,668)(411,667)(412,666)
(413,665)(414,664)(415,663)(416,662)(417,661)(418,660)(419,659)(420,658)
(421,657)(422,656)(423,655)(424,654)(425,653)(426,652)(427,651)(428,650)
(429,649)(430,648)(431,518)(432,517)(433,559)(434,558)(435,557)(436,556)
(437,555)(438,554)(439,553)(440,552)(441,551)(442,550)(443,549)(444,548)
(445,547)(446,546)(447,545)(448,544)(449,543)(450,542)(451,541)(452,540)
(453,539)(454,538)(455,537)(456,536)(457,535)(458,534)(459,533)(460,532)
(461,531)(462,530)(463,529)(464,528)(465,527)(466,526)(467,525)(468,524)
(469,523)(470,522)(471,521)(472,520)(473,519)(474,561)(475,560)(476,602)
(477,601)(478,600)(479,599)(480,598)(481,597)(482,596)(483,595)(484,594)
(485,593)(486,592)(487,591)(488,590)(489,589)(490,588)(491,587)(492,586)
(493,585)(494,584)(495,583)(496,582)(497,581)(498,580)(499,579)(500,578)
(501,577)(502,576)(503,575)(504,574)(505,573)(506,572)(507,571)(508,570)
(509,569)(510,568)(511,567)(512,566)(513,565)(514,564)(515,563)(516,562);;
s2 := ( 1,345)( 2,346)( 3,347)( 4,348)( 5,349)( 6,350)( 7,351)( 8,352)
( 9,353)( 10,354)( 11,355)( 12,356)( 13,357)( 14,358)( 15,359)( 16,360)
( 17,361)( 18,362)( 19,363)( 20,364)( 21,365)( 22,366)( 23,367)( 24,368)
( 25,369)( 26,370)( 27,371)( 28,372)( 29,373)( 30,374)( 31,375)( 32,376)
( 33,377)( 34,378)( 35,379)( 36,380)( 37,381)( 38,382)( 39,383)( 40,384)
( 41,385)( 42,386)( 43,387)( 44,388)( 45,389)( 46,390)( 47,391)( 48,392)
( 49,393)( 50,394)( 51,395)( 52,396)( 53,397)( 54,398)( 55,399)( 56,400)
( 57,401)( 58,402)( 59,403)( 60,404)( 61,405)( 62,406)( 63,407)( 64,408)
( 65,409)( 66,410)( 67,411)( 68,412)( 69,413)( 70,414)( 71,415)( 72,416)
( 73,417)( 74,418)( 75,419)( 76,420)( 77,421)( 78,422)( 79,423)( 80,424)
( 81,425)( 82,426)( 83,427)( 84,428)( 85,429)( 86,430)( 87,474)( 88,475)
( 89,476)( 90,477)( 91,478)( 92,479)( 93,480)( 94,481)( 95,482)( 96,483)
( 97,484)( 98,485)( 99,486)(100,487)(101,488)(102,489)(103,490)(104,491)
(105,492)(106,493)(107,494)(108,495)(109,496)(110,497)(111,498)(112,499)
(113,500)(114,501)(115,502)(116,503)(117,504)(118,505)(119,506)(120,507)
(121,508)(122,509)(123,510)(124,511)(125,512)(126,513)(127,514)(128,515)
(129,516)(130,431)(131,432)(132,433)(133,434)(134,435)(135,436)(136,437)
(137,438)(138,439)(139,440)(140,441)(141,442)(142,443)(143,444)(144,445)
(145,446)(146,447)(147,448)(148,449)(149,450)(150,451)(151,452)(152,453)
(153,454)(154,455)(155,456)(156,457)(157,458)(158,459)(159,460)(160,461)
(161,462)(162,463)(163,464)(164,465)(165,466)(166,467)(167,468)(168,469)
(169,470)(170,471)(171,472)(172,473)(173,517)(174,518)(175,519)(176,520)
(177,521)(178,522)(179,523)(180,524)(181,525)(182,526)(183,527)(184,528)
(185,529)(186,530)(187,531)(188,532)(189,533)(190,534)(191,535)(192,536)
(193,537)(194,538)(195,539)(196,540)(197,541)(198,542)(199,543)(200,544)
(201,545)(202,546)(203,547)(204,548)(205,549)(206,550)(207,551)(208,552)
(209,553)(210,554)(211,555)(212,556)(213,557)(214,558)(215,559)(216,560)
(217,561)(218,562)(219,563)(220,564)(221,565)(222,566)(223,567)(224,568)
(225,569)(226,570)(227,571)(228,572)(229,573)(230,574)(231,575)(232,576)
(233,577)(234,578)(235,579)(236,580)(237,581)(238,582)(239,583)(240,584)
(241,585)(242,586)(243,587)(244,588)(245,589)(246,590)(247,591)(248,592)
(249,593)(250,594)(251,595)(252,596)(253,597)(254,598)(255,599)(256,600)
(257,601)(258,602)(259,646)(260,647)(261,648)(262,649)(263,650)(264,651)
(265,652)(266,653)(267,654)(268,655)(269,656)(270,657)(271,658)(272,659)
(273,660)(274,661)(275,662)(276,663)(277,664)(278,665)(279,666)(280,667)
(281,668)(282,669)(283,670)(284,671)(285,672)(286,673)(287,674)(288,675)
(289,676)(290,677)(291,678)(292,679)(293,680)(294,681)(295,682)(296,683)
(297,684)(298,685)(299,686)(300,687)(301,688)(302,603)(303,604)(304,605)
(305,606)(306,607)(307,608)(308,609)(309,610)(310,611)(311,612)(312,613)
(313,614)(314,615)(315,616)(316,617)(317,618)(318,619)(319,620)(320,621)
(321,622)(322,623)(323,624)(324,625)(325,626)(326,627)(327,628)(328,629)
(329,630)(330,631)(331,632)(332,633)(333,634)(334,635)(335,636)(336,637)
(337,638)(338,639)(339,640)(340,641)(341,642)(342,643)(343,644)(344,645);;
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(688)!( 1,173)( 2,215)( 3,214)( 4,213)( 5,212)( 6,211)( 7,210)
( 8,209)( 9,208)( 10,207)( 11,206)( 12,205)( 13,204)( 14,203)( 15,202)
( 16,201)( 17,200)( 18,199)( 19,198)( 20,197)( 21,196)( 22,195)( 23,194)
( 24,193)( 25,192)( 26,191)( 27,190)( 28,189)( 29,188)( 30,187)( 31,186)
( 32,185)( 33,184)( 34,183)( 35,182)( 36,181)( 37,180)( 38,179)( 39,178)
( 40,177)( 41,176)( 42,175)( 43,174)( 44,216)( 45,258)( 46,257)( 47,256)
( 48,255)( 49,254)( 50,253)( 51,252)( 52,251)( 53,250)( 54,249)( 55,248)
( 56,247)( 57,246)( 58,245)( 59,244)( 60,243)( 61,242)( 62,241)( 63,240)
( 64,239)( 65,238)( 66,237)( 67,236)( 68,235)( 69,234)( 70,233)( 71,232)
( 72,231)( 73,230)( 74,229)( 75,228)( 76,227)( 77,226)( 78,225)( 79,224)
( 80,223)( 81,222)( 82,221)( 83,220)( 84,219)( 85,218)( 86,217)( 87,259)
( 88,301)( 89,300)( 90,299)( 91,298)( 92,297)( 93,296)( 94,295)( 95,294)
( 96,293)( 97,292)( 98,291)( 99,290)(100,289)(101,288)(102,287)(103,286)
(104,285)(105,284)(106,283)(107,282)(108,281)(109,280)(110,279)(111,278)
(112,277)(113,276)(114,275)(115,274)(116,273)(117,272)(118,271)(119,270)
(120,269)(121,268)(122,267)(123,266)(124,265)(125,264)(126,263)(127,262)
(128,261)(129,260)(130,302)(131,344)(132,343)(133,342)(134,341)(135,340)
(136,339)(137,338)(138,337)(139,336)(140,335)(141,334)(142,333)(143,332)
(144,331)(145,330)(146,329)(147,328)(148,327)(149,326)(150,325)(151,324)
(152,323)(153,322)(154,321)(155,320)(156,319)(157,318)(158,317)(159,316)
(160,315)(161,314)(162,313)(163,312)(164,311)(165,310)(166,309)(167,308)
(168,307)(169,306)(170,305)(171,304)(172,303)(345,517)(346,559)(347,558)
(348,557)(349,556)(350,555)(351,554)(352,553)(353,552)(354,551)(355,550)
(356,549)(357,548)(358,547)(359,546)(360,545)(361,544)(362,543)(363,542)
(364,541)(365,540)(366,539)(367,538)(368,537)(369,536)(370,535)(371,534)
(372,533)(373,532)(374,531)(375,530)(376,529)(377,528)(378,527)(379,526)
(380,525)(381,524)(382,523)(383,522)(384,521)(385,520)(386,519)(387,518)
(388,560)(389,602)(390,601)(391,600)(392,599)(393,598)(394,597)(395,596)
(396,595)(397,594)(398,593)(399,592)(400,591)(401,590)(402,589)(403,588)
(404,587)(405,586)(406,585)(407,584)(408,583)(409,582)(410,581)(411,580)
(412,579)(413,578)(414,577)(415,576)(416,575)(417,574)(418,573)(419,572)
(420,571)(421,570)(422,569)(423,568)(424,567)(425,566)(426,565)(427,564)
(428,563)(429,562)(430,561)(431,603)(432,645)(433,644)(434,643)(435,642)
(436,641)(437,640)(438,639)(439,638)(440,637)(441,636)(442,635)(443,634)
(444,633)(445,632)(446,631)(447,630)(448,629)(449,628)(450,627)(451,626)
(452,625)(453,624)(454,623)(455,622)(456,621)(457,620)(458,619)(459,618)
(460,617)(461,616)(462,615)(463,614)(464,613)(465,612)(466,611)(467,610)
(468,609)(469,608)(470,607)(471,606)(472,605)(473,604)(474,646)(475,688)
(476,687)(477,686)(478,685)(479,684)(480,683)(481,682)(482,681)(483,680)
(484,679)(485,678)(486,677)(487,676)(488,675)(489,674)(490,673)(491,672)
(492,671)(493,670)(494,669)(495,668)(496,667)(497,666)(498,665)(499,664)
(500,663)(501,662)(502,661)(503,660)(504,659)(505,658)(506,657)(507,656)
(508,655)(509,654)(510,653)(511,652)(512,651)(513,650)(514,649)(515,648)
(516,647);
s1 := Sym(688)!( 1,174)( 2,173)( 3,215)( 4,214)( 5,213)( 6,212)( 7,211)
( 8,210)( 9,209)( 10,208)( 11,207)( 12,206)( 13,205)( 14,204)( 15,203)
( 16,202)( 17,201)( 18,200)( 19,199)( 20,198)( 21,197)( 22,196)( 23,195)
( 24,194)( 25,193)( 26,192)( 27,191)( 28,190)( 29,189)( 30,188)( 31,187)
( 32,186)( 33,185)( 34,184)( 35,183)( 36,182)( 37,181)( 38,180)( 39,179)
( 40,178)( 41,177)( 42,176)( 43,175)( 44,217)( 45,216)( 46,258)( 47,257)
( 48,256)( 49,255)( 50,254)( 51,253)( 52,252)( 53,251)( 54,250)( 55,249)
( 56,248)( 57,247)( 58,246)( 59,245)( 60,244)( 61,243)( 62,242)( 63,241)
( 64,240)( 65,239)( 66,238)( 67,237)( 68,236)( 69,235)( 70,234)( 71,233)
( 72,232)( 73,231)( 74,230)( 75,229)( 76,228)( 77,227)( 78,226)( 79,225)
( 80,224)( 81,223)( 82,222)( 83,221)( 84,220)( 85,219)( 86,218)( 87,303)
( 88,302)( 89,344)( 90,343)( 91,342)( 92,341)( 93,340)( 94,339)( 95,338)
( 96,337)( 97,336)( 98,335)( 99,334)(100,333)(101,332)(102,331)(103,330)
(104,329)(105,328)(106,327)(107,326)(108,325)(109,324)(110,323)(111,322)
(112,321)(113,320)(114,319)(115,318)(116,317)(117,316)(118,315)(119,314)
(120,313)(121,312)(122,311)(123,310)(124,309)(125,308)(126,307)(127,306)
(128,305)(129,304)(130,260)(131,259)(132,301)(133,300)(134,299)(135,298)
(136,297)(137,296)(138,295)(139,294)(140,293)(141,292)(142,291)(143,290)
(144,289)(145,288)(146,287)(147,286)(148,285)(149,284)(150,283)(151,282)
(152,281)(153,280)(154,279)(155,278)(156,277)(157,276)(158,275)(159,274)
(160,273)(161,272)(162,271)(163,270)(164,269)(165,268)(166,267)(167,266)
(168,265)(169,264)(170,263)(171,262)(172,261)(345,604)(346,603)(347,645)
(348,644)(349,643)(350,642)(351,641)(352,640)(353,639)(354,638)(355,637)
(356,636)(357,635)(358,634)(359,633)(360,632)(361,631)(362,630)(363,629)
(364,628)(365,627)(366,626)(367,625)(368,624)(369,623)(370,622)(371,621)
(372,620)(373,619)(374,618)(375,617)(376,616)(377,615)(378,614)(379,613)
(380,612)(381,611)(382,610)(383,609)(384,608)(385,607)(386,606)(387,605)
(388,647)(389,646)(390,688)(391,687)(392,686)(393,685)(394,684)(395,683)
(396,682)(397,681)(398,680)(399,679)(400,678)(401,677)(402,676)(403,675)
(404,674)(405,673)(406,672)(407,671)(408,670)(409,669)(410,668)(411,667)
(412,666)(413,665)(414,664)(415,663)(416,662)(417,661)(418,660)(419,659)
(420,658)(421,657)(422,656)(423,655)(424,654)(425,653)(426,652)(427,651)
(428,650)(429,649)(430,648)(431,518)(432,517)(433,559)(434,558)(435,557)
(436,556)(437,555)(438,554)(439,553)(440,552)(441,551)(442,550)(443,549)
(444,548)(445,547)(446,546)(447,545)(448,544)(449,543)(450,542)(451,541)
(452,540)(453,539)(454,538)(455,537)(456,536)(457,535)(458,534)(459,533)
(460,532)(461,531)(462,530)(463,529)(464,528)(465,527)(466,526)(467,525)
(468,524)(469,523)(470,522)(471,521)(472,520)(473,519)(474,561)(475,560)
(476,602)(477,601)(478,600)(479,599)(480,598)(481,597)(482,596)(483,595)
(484,594)(485,593)(486,592)(487,591)(488,590)(489,589)(490,588)(491,587)
(492,586)(493,585)(494,584)(495,583)(496,582)(497,581)(498,580)(499,579)
(500,578)(501,577)(502,576)(503,575)(504,574)(505,573)(506,572)(507,571)
(508,570)(509,569)(510,568)(511,567)(512,566)(513,565)(514,564)(515,563)
(516,562);
s2 := Sym(688)!( 1,345)( 2,346)( 3,347)( 4,348)( 5,349)( 6,350)( 7,351)
( 8,352)( 9,353)( 10,354)( 11,355)( 12,356)( 13,357)( 14,358)( 15,359)
( 16,360)( 17,361)( 18,362)( 19,363)( 20,364)( 21,365)( 22,366)( 23,367)
( 24,368)( 25,369)( 26,370)( 27,371)( 28,372)( 29,373)( 30,374)( 31,375)
( 32,376)( 33,377)( 34,378)( 35,379)( 36,380)( 37,381)( 38,382)( 39,383)
( 40,384)( 41,385)( 42,386)( 43,387)( 44,388)( 45,389)( 46,390)( 47,391)
( 48,392)( 49,393)( 50,394)( 51,395)( 52,396)( 53,397)( 54,398)( 55,399)
( 56,400)( 57,401)( 58,402)( 59,403)( 60,404)( 61,405)( 62,406)( 63,407)
( 64,408)( 65,409)( 66,410)( 67,411)( 68,412)( 69,413)( 70,414)( 71,415)
( 72,416)( 73,417)( 74,418)( 75,419)( 76,420)( 77,421)( 78,422)( 79,423)
( 80,424)( 81,425)( 82,426)( 83,427)( 84,428)( 85,429)( 86,430)( 87,474)
( 88,475)( 89,476)( 90,477)( 91,478)( 92,479)( 93,480)( 94,481)( 95,482)
( 96,483)( 97,484)( 98,485)( 99,486)(100,487)(101,488)(102,489)(103,490)
(104,491)(105,492)(106,493)(107,494)(108,495)(109,496)(110,497)(111,498)
(112,499)(113,500)(114,501)(115,502)(116,503)(117,504)(118,505)(119,506)
(120,507)(121,508)(122,509)(123,510)(124,511)(125,512)(126,513)(127,514)
(128,515)(129,516)(130,431)(131,432)(132,433)(133,434)(134,435)(135,436)
(136,437)(137,438)(138,439)(139,440)(140,441)(141,442)(142,443)(143,444)
(144,445)(145,446)(146,447)(147,448)(148,449)(149,450)(150,451)(151,452)
(152,453)(153,454)(154,455)(155,456)(156,457)(157,458)(158,459)(159,460)
(160,461)(161,462)(162,463)(163,464)(164,465)(165,466)(166,467)(167,468)
(168,469)(169,470)(170,471)(171,472)(172,473)(173,517)(174,518)(175,519)
(176,520)(177,521)(178,522)(179,523)(180,524)(181,525)(182,526)(183,527)
(184,528)(185,529)(186,530)(187,531)(188,532)(189,533)(190,534)(191,535)
(192,536)(193,537)(194,538)(195,539)(196,540)(197,541)(198,542)(199,543)
(200,544)(201,545)(202,546)(203,547)(204,548)(205,549)(206,550)(207,551)
(208,552)(209,553)(210,554)(211,555)(212,556)(213,557)(214,558)(215,559)
(216,560)(217,561)(218,562)(219,563)(220,564)(221,565)(222,566)(223,567)
(224,568)(225,569)(226,570)(227,571)(228,572)(229,573)(230,574)(231,575)
(232,576)(233,577)(234,578)(235,579)(236,580)(237,581)(238,582)(239,583)
(240,584)(241,585)(242,586)(243,587)(244,588)(245,589)(246,590)(247,591)
(248,592)(249,593)(250,594)(251,595)(252,596)(253,597)(254,598)(255,599)
(256,600)(257,601)(258,602)(259,646)(260,647)(261,648)(262,649)(263,650)
(264,651)(265,652)(266,653)(267,654)(268,655)(269,656)(270,657)(271,658)
(272,659)(273,660)(274,661)(275,662)(276,663)(277,664)(278,665)(279,666)
(280,667)(281,668)(282,669)(283,670)(284,671)(285,672)(286,673)(287,674)
(288,675)(289,676)(290,677)(291,678)(292,679)(293,680)(294,681)(295,682)
(296,683)(297,684)(298,685)(299,686)(300,687)(301,688)(302,603)(303,604)
(304,605)(305,606)(306,607)(307,608)(308,609)(309,610)(310,611)(311,612)
(312,613)(313,614)(314,615)(315,616)(316,617)(317,618)(318,619)(319,620)
(320,621)(321,622)(322,623)(323,624)(324,625)(325,626)(326,627)(327,628)
(328,629)(329,630)(330,631)(331,632)(332,633)(333,634)(334,635)(335,636)
(336,637)(337,638)(338,639)(339,640)(340,641)(341,642)(342,643)(343,644)
(344,645);
poly := sub<Sym(688)|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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope