Polytope of Type {94,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {94,8}*1504
Also Known As : {94,8|2}. if this polytope has another name.
Group : SmallGroup(1504,155)
Rank : 3
Schlafli Type : {94,8}
Number of vertices, edges, etc : 94, 376, 8
Order of s0s1s2 : 376
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 : {94,4}*752
4-fold quotients : {94,2}*376
8-fold quotients : {47,2}*188
47-fold quotients : {2,8}*32
94-fold quotients : {2,4}*16
188-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,189)( 2,235)( 3,234)( 4,233)( 5,232)( 6,231)( 7,230)( 8,229)
( 9,228)( 10,227)( 11,226)( 12,225)( 13,224)( 14,223)( 15,222)( 16,221)
( 17,220)( 18,219)( 19,218)( 20,217)( 21,216)( 22,215)( 23,214)( 24,213)
( 25,212)( 26,211)( 27,210)( 28,209)( 29,208)( 30,207)( 31,206)( 32,205)
( 33,204)( 34,203)( 35,202)( 36,201)( 37,200)( 38,199)( 39,198)( 40,197)
( 41,196)( 42,195)( 43,194)( 44,193)( 45,192)( 46,191)( 47,190)( 48,236)
( 49,282)( 50,281)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)( 56,275)
( 57,274)( 58,273)( 59,272)( 60,271)( 61,270)( 62,269)( 63,268)( 64,267)
( 65,266)( 66,265)( 67,264)( 68,263)( 69,262)( 70,261)( 71,260)( 72,259)
( 73,258)( 74,257)( 75,256)( 76,255)( 77,254)( 78,253)( 79,252)( 80,251)
( 81,250)( 82,249)( 83,248)( 84,247)( 85,246)( 86,245)( 87,244)( 88,243)
( 89,242)( 90,241)( 91,240)( 92,239)( 93,238)( 94,237)( 95,283)( 96,329)
( 97,328)( 98,327)( 99,326)(100,325)(101,324)(102,323)(103,322)(104,321)
(105,320)(106,319)(107,318)(108,317)(109,316)(110,315)(111,314)(112,313)
(113,312)(114,311)(115,310)(116,309)(117,308)(118,307)(119,306)(120,305)
(121,304)(122,303)(123,302)(124,301)(125,300)(126,299)(127,298)(128,297)
(129,296)(130,295)(131,294)(132,293)(133,292)(134,291)(135,290)(136,289)
(137,288)(138,287)(139,286)(140,285)(141,284)(142,330)(143,376)(144,375)
(145,374)(146,373)(147,372)(148,371)(149,370)(150,369)(151,368)(152,367)
(153,366)(154,365)(155,364)(156,363)(157,362)(158,361)(159,360)(160,359)
(161,358)(162,357)(163,356)(164,355)(165,354)(166,353)(167,352)(168,351)
(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)(176,343)
(177,342)(178,341)(179,340)(180,339)(181,338)(182,337)(183,336)(184,335)
(185,334)(186,333)(187,332)(188,331)(377,565)(378,611)(379,610)(380,609)
(381,608)(382,607)(383,606)(384,605)(385,604)(386,603)(387,602)(388,601)
(389,600)(390,599)(391,598)(392,597)(393,596)(394,595)(395,594)(396,593)
(397,592)(398,591)(399,590)(400,589)(401,588)(402,587)(403,586)(404,585)
(405,584)(406,583)(407,582)(408,581)(409,580)(410,579)(411,578)(412,577)
(413,576)(414,575)(415,574)(416,573)(417,572)(418,571)(419,570)(420,569)
(421,568)(422,567)(423,566)(424,612)(425,658)(426,657)(427,656)(428,655)
(429,654)(430,653)(431,652)(432,651)(433,650)(434,649)(435,648)(436,647)
(437,646)(438,645)(439,644)(440,643)(441,642)(442,641)(443,640)(444,639)
(445,638)(446,637)(447,636)(448,635)(449,634)(450,633)(451,632)(452,631)
(453,630)(454,629)(455,628)(456,627)(457,626)(458,625)(459,624)(460,623)
(461,622)(462,621)(463,620)(464,619)(465,618)(466,617)(467,616)(468,615)
(469,614)(470,613)(471,659)(472,705)(473,704)(474,703)(475,702)(476,701)
(477,700)(478,699)(479,698)(480,697)(481,696)(482,695)(483,694)(484,693)
(485,692)(486,691)(487,690)(488,689)(489,688)(490,687)(491,686)(492,685)
(493,684)(494,683)(495,682)(496,681)(497,680)(498,679)(499,678)(500,677)
(501,676)(502,675)(503,674)(504,673)(505,672)(506,671)(507,670)(508,669)
(509,668)(510,667)(511,666)(512,665)(513,664)(514,663)(515,662)(516,661)
(517,660)(518,706)(519,752)(520,751)(521,750)(522,749)(523,748)(524,747)
(525,746)(526,745)(527,744)(528,743)(529,742)(530,741)(531,740)(532,739)
(533,738)(534,737)(535,736)(536,735)(537,734)(538,733)(539,732)(540,731)
(541,730)(542,729)(543,728)(544,727)(545,726)(546,725)(547,724)(548,723)
(549,722)(550,721)(551,720)(552,719)(553,718)(554,717)(555,716)(556,715)
(557,714)(558,713)(559,712)(560,711)(561,710)(562,709)(563,708)(564,707);;
s1 := ( 1,190)( 2,189)( 3,235)( 4,234)( 5,233)( 6,232)( 7,231)( 8,230)
( 9,229)( 10,228)( 11,227)( 12,226)( 13,225)( 14,224)( 15,223)( 16,222)
( 17,221)( 18,220)( 19,219)( 20,218)( 21,217)( 22,216)( 23,215)( 24,214)
( 25,213)( 26,212)( 27,211)( 28,210)( 29,209)( 30,208)( 31,207)( 32,206)
( 33,205)( 34,204)( 35,203)( 36,202)( 37,201)( 38,200)( 39,199)( 40,198)
( 41,197)( 42,196)( 43,195)( 44,194)( 45,193)( 46,192)( 47,191)( 48,237)
( 49,236)( 50,282)( 51,281)( 52,280)( 53,279)( 54,278)( 55,277)( 56,276)
( 57,275)( 58,274)( 59,273)( 60,272)( 61,271)( 62,270)( 63,269)( 64,268)
( 65,267)( 66,266)( 67,265)( 68,264)( 69,263)( 70,262)( 71,261)( 72,260)
( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,254)( 79,253)( 80,252)
( 81,251)( 82,250)( 83,249)( 84,248)( 85,247)( 86,246)( 87,245)( 88,244)
( 89,243)( 90,242)( 91,241)( 92,240)( 93,239)( 94,238)( 95,331)( 96,330)
( 97,376)( 98,375)( 99,374)(100,373)(101,372)(102,371)(103,370)(104,369)
(105,368)(106,367)(107,366)(108,365)(109,364)(110,363)(111,362)(112,361)
(113,360)(114,359)(115,358)(116,357)(117,356)(118,355)(119,354)(120,353)
(121,352)(122,351)(123,350)(124,349)(125,348)(126,347)(127,346)(128,345)
(129,344)(130,343)(131,342)(132,341)(133,340)(134,339)(135,338)(136,337)
(137,336)(138,335)(139,334)(140,333)(141,332)(142,284)(143,283)(144,329)
(145,328)(146,327)(147,326)(148,325)(149,324)(150,323)(151,322)(152,321)
(153,320)(154,319)(155,318)(156,317)(157,316)(158,315)(159,314)(160,313)
(161,312)(162,311)(163,310)(164,309)(165,308)(166,307)(167,306)(168,305)
(169,304)(170,303)(171,302)(172,301)(173,300)(174,299)(175,298)(176,297)
(177,296)(178,295)(179,294)(180,293)(181,292)(182,291)(183,290)(184,289)
(185,288)(186,287)(187,286)(188,285)(377,660)(378,659)(379,705)(380,704)
(381,703)(382,702)(383,701)(384,700)(385,699)(386,698)(387,697)(388,696)
(389,695)(390,694)(391,693)(392,692)(393,691)(394,690)(395,689)(396,688)
(397,687)(398,686)(399,685)(400,684)(401,683)(402,682)(403,681)(404,680)
(405,679)(406,678)(407,677)(408,676)(409,675)(410,674)(411,673)(412,672)
(413,671)(414,670)(415,669)(416,668)(417,667)(418,666)(419,665)(420,664)
(421,663)(422,662)(423,661)(424,707)(425,706)(426,752)(427,751)(428,750)
(429,749)(430,748)(431,747)(432,746)(433,745)(434,744)(435,743)(436,742)
(437,741)(438,740)(439,739)(440,738)(441,737)(442,736)(443,735)(444,734)
(445,733)(446,732)(447,731)(448,730)(449,729)(450,728)(451,727)(452,726)
(453,725)(454,724)(455,723)(456,722)(457,721)(458,720)(459,719)(460,718)
(461,717)(462,716)(463,715)(464,714)(465,713)(466,712)(467,711)(468,710)
(469,709)(470,708)(471,566)(472,565)(473,611)(474,610)(475,609)(476,608)
(477,607)(478,606)(479,605)(480,604)(481,603)(482,602)(483,601)(484,600)
(485,599)(486,598)(487,597)(488,596)(489,595)(490,594)(491,593)(492,592)
(493,591)(494,590)(495,589)(496,588)(497,587)(498,586)(499,585)(500,584)
(501,583)(502,582)(503,581)(504,580)(505,579)(506,578)(507,577)(508,576)
(509,575)(510,574)(511,573)(512,572)(513,571)(514,570)(515,569)(516,568)
(517,567)(518,613)(519,612)(520,658)(521,657)(522,656)(523,655)(524,654)
(525,653)(526,652)(527,651)(528,650)(529,649)(530,648)(531,647)(532,646)
(533,645)(534,644)(535,643)(536,642)(537,641)(538,640)(539,639)(540,638)
(541,637)(542,636)(543,635)(544,634)(545,633)(546,632)(547,631)(548,630)
(549,629)(550,628)(551,627)(552,626)(553,625)(554,624)(555,623)(556,622)
(557,621)(558,620)(559,619)(560,618)(561,617)(562,616)(563,615)(564,614);;
s2 := ( 1,377)( 2,378)( 3,379)( 4,380)( 5,381)( 6,382)( 7,383)( 8,384)
( 9,385)( 10,386)( 11,387)( 12,388)( 13,389)( 14,390)( 15,391)( 16,392)
( 17,393)( 18,394)( 19,395)( 20,396)( 21,397)( 22,398)( 23,399)( 24,400)
( 25,401)( 26,402)( 27,403)( 28,404)( 29,405)( 30,406)( 31,407)( 32,408)
( 33,409)( 34,410)( 35,411)( 36,412)( 37,413)( 38,414)( 39,415)( 40,416)
( 41,417)( 42,418)( 43,419)( 44,420)( 45,421)( 46,422)( 47,423)( 48,424)
( 49,425)( 50,426)( 51,427)( 52,428)( 53,429)( 54,430)( 55,431)( 56,432)
( 57,433)( 58,434)( 59,435)( 60,436)( 61,437)( 62,438)( 63,439)( 64,440)
( 65,441)( 66,442)( 67,443)( 68,444)( 69,445)( 70,446)( 71,447)( 72,448)
( 73,449)( 74,450)( 75,451)( 76,452)( 77,453)( 78,454)( 79,455)( 80,456)
( 81,457)( 82,458)( 83,459)( 84,460)( 85,461)( 86,462)( 87,463)( 88,464)
( 89,465)( 90,466)( 91,467)( 92,468)( 93,469)( 94,470)( 95,518)( 96,519)
( 97,520)( 98,521)( 99,522)(100,523)(101,524)(102,525)(103,526)(104,527)
(105,528)(106,529)(107,530)(108,531)(109,532)(110,533)(111,534)(112,535)
(113,536)(114,537)(115,538)(116,539)(117,540)(118,541)(119,542)(120,543)
(121,544)(122,545)(123,546)(124,547)(125,548)(126,549)(127,550)(128,551)
(129,552)(130,553)(131,554)(132,555)(133,556)(134,557)(135,558)(136,559)
(137,560)(138,561)(139,562)(140,563)(141,564)(142,471)(143,472)(144,473)
(145,474)(146,475)(147,476)(148,477)(149,478)(150,479)(151,480)(152,481)
(153,482)(154,483)(155,484)(156,485)(157,486)(158,487)(159,488)(160,489)
(161,490)(162,491)(163,492)(164,493)(165,494)(166,495)(167,496)(168,497)
(169,498)(170,499)(171,500)(172,501)(173,502)(174,503)(175,504)(176,505)
(177,506)(178,507)(179,508)(180,509)(181,510)(182,511)(183,512)(184,513)
(185,514)(186,515)(187,516)(188,517)(189,565)(190,566)(191,567)(192,568)
(193,569)(194,570)(195,571)(196,572)(197,573)(198,574)(199,575)(200,576)
(201,577)(202,578)(203,579)(204,580)(205,581)(206,582)(207,583)(208,584)
(209,585)(210,586)(211,587)(212,588)(213,589)(214,590)(215,591)(216,592)
(217,593)(218,594)(219,595)(220,596)(221,597)(222,598)(223,599)(224,600)
(225,601)(226,602)(227,603)(228,604)(229,605)(230,606)(231,607)(232,608)
(233,609)(234,610)(235,611)(236,612)(237,613)(238,614)(239,615)(240,616)
(241,617)(242,618)(243,619)(244,620)(245,621)(246,622)(247,623)(248,624)
(249,625)(250,626)(251,627)(252,628)(253,629)(254,630)(255,631)(256,632)
(257,633)(258,634)(259,635)(260,636)(261,637)(262,638)(263,639)(264,640)
(265,641)(266,642)(267,643)(268,644)(269,645)(270,646)(271,647)(272,648)
(273,649)(274,650)(275,651)(276,652)(277,653)(278,654)(279,655)(280,656)
(281,657)(282,658)(283,706)(284,707)(285,708)(286,709)(287,710)(288,711)
(289,712)(290,713)(291,714)(292,715)(293,716)(294,717)(295,718)(296,719)
(297,720)(298,721)(299,722)(300,723)(301,724)(302,725)(303,726)(304,727)
(305,728)(306,729)(307,730)(308,731)(309,732)(310,733)(311,734)(312,735)
(313,736)(314,737)(315,738)(316,739)(317,740)(318,741)(319,742)(320,743)
(321,744)(322,745)(323,746)(324,747)(325,748)(326,749)(327,750)(328,751)
(329,752)(330,659)(331,660)(332,661)(333,662)(334,663)(335,664)(336,665)
(337,666)(338,667)(339,668)(340,669)(341,670)(342,671)(343,672)(344,673)
(345,674)(346,675)(347,676)(348,677)(349,678)(350,679)(351,680)(352,681)
(353,682)(354,683)(355,684)(356,685)(357,686)(358,687)(359,688)(360,689)
(361,690)(362,691)(363,692)(364,693)(365,694)(366,695)(367,696)(368,697)
(369,698)(370,699)(371,700)(372,701)(373,702)(374,703)(375,704)(376,705);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(752)!( 1,189)( 2,235)( 3,234)( 4,233)( 5,232)( 6,231)( 7,230)
( 8,229)( 9,228)( 10,227)( 11,226)( 12,225)( 13,224)( 14,223)( 15,222)
( 16,221)( 17,220)( 18,219)( 19,218)( 20,217)( 21,216)( 22,215)( 23,214)
( 24,213)( 25,212)( 26,211)( 27,210)( 28,209)( 29,208)( 30,207)( 31,206)
( 32,205)( 33,204)( 34,203)( 35,202)( 36,201)( 37,200)( 38,199)( 39,198)
( 40,197)( 41,196)( 42,195)( 43,194)( 44,193)( 45,192)( 46,191)( 47,190)
( 48,236)( 49,282)( 50,281)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)
( 56,275)( 57,274)( 58,273)( 59,272)( 60,271)( 61,270)( 62,269)( 63,268)
( 64,267)( 65,266)( 66,265)( 67,264)( 68,263)( 69,262)( 70,261)( 71,260)
( 72,259)( 73,258)( 74,257)( 75,256)( 76,255)( 77,254)( 78,253)( 79,252)
( 80,251)( 81,250)( 82,249)( 83,248)( 84,247)( 85,246)( 86,245)( 87,244)
( 88,243)( 89,242)( 90,241)( 91,240)( 92,239)( 93,238)( 94,237)( 95,283)
( 96,329)( 97,328)( 98,327)( 99,326)(100,325)(101,324)(102,323)(103,322)
(104,321)(105,320)(106,319)(107,318)(108,317)(109,316)(110,315)(111,314)
(112,313)(113,312)(114,311)(115,310)(116,309)(117,308)(118,307)(119,306)
(120,305)(121,304)(122,303)(123,302)(124,301)(125,300)(126,299)(127,298)
(128,297)(129,296)(130,295)(131,294)(132,293)(133,292)(134,291)(135,290)
(136,289)(137,288)(138,287)(139,286)(140,285)(141,284)(142,330)(143,376)
(144,375)(145,374)(146,373)(147,372)(148,371)(149,370)(150,369)(151,368)
(152,367)(153,366)(154,365)(155,364)(156,363)(157,362)(158,361)(159,360)
(160,359)(161,358)(162,357)(163,356)(164,355)(165,354)(166,353)(167,352)
(168,351)(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)
(176,343)(177,342)(178,341)(179,340)(180,339)(181,338)(182,337)(183,336)
(184,335)(185,334)(186,333)(187,332)(188,331)(377,565)(378,611)(379,610)
(380,609)(381,608)(382,607)(383,606)(384,605)(385,604)(386,603)(387,602)
(388,601)(389,600)(390,599)(391,598)(392,597)(393,596)(394,595)(395,594)
(396,593)(397,592)(398,591)(399,590)(400,589)(401,588)(402,587)(403,586)
(404,585)(405,584)(406,583)(407,582)(408,581)(409,580)(410,579)(411,578)
(412,577)(413,576)(414,575)(415,574)(416,573)(417,572)(418,571)(419,570)
(420,569)(421,568)(422,567)(423,566)(424,612)(425,658)(426,657)(427,656)
(428,655)(429,654)(430,653)(431,652)(432,651)(433,650)(434,649)(435,648)
(436,647)(437,646)(438,645)(439,644)(440,643)(441,642)(442,641)(443,640)
(444,639)(445,638)(446,637)(447,636)(448,635)(449,634)(450,633)(451,632)
(452,631)(453,630)(454,629)(455,628)(456,627)(457,626)(458,625)(459,624)
(460,623)(461,622)(462,621)(463,620)(464,619)(465,618)(466,617)(467,616)
(468,615)(469,614)(470,613)(471,659)(472,705)(473,704)(474,703)(475,702)
(476,701)(477,700)(478,699)(479,698)(480,697)(481,696)(482,695)(483,694)
(484,693)(485,692)(486,691)(487,690)(488,689)(489,688)(490,687)(491,686)
(492,685)(493,684)(494,683)(495,682)(496,681)(497,680)(498,679)(499,678)
(500,677)(501,676)(502,675)(503,674)(504,673)(505,672)(506,671)(507,670)
(508,669)(509,668)(510,667)(511,666)(512,665)(513,664)(514,663)(515,662)
(516,661)(517,660)(518,706)(519,752)(520,751)(521,750)(522,749)(523,748)
(524,747)(525,746)(526,745)(527,744)(528,743)(529,742)(530,741)(531,740)
(532,739)(533,738)(534,737)(535,736)(536,735)(537,734)(538,733)(539,732)
(540,731)(541,730)(542,729)(543,728)(544,727)(545,726)(546,725)(547,724)
(548,723)(549,722)(550,721)(551,720)(552,719)(553,718)(554,717)(555,716)
(556,715)(557,714)(558,713)(559,712)(560,711)(561,710)(562,709)(563,708)
(564,707);
s1 := Sym(752)!( 1,190)( 2,189)( 3,235)( 4,234)( 5,233)( 6,232)( 7,231)
( 8,230)( 9,229)( 10,228)( 11,227)( 12,226)( 13,225)( 14,224)( 15,223)
( 16,222)( 17,221)( 18,220)( 19,219)( 20,218)( 21,217)( 22,216)( 23,215)
( 24,214)( 25,213)( 26,212)( 27,211)( 28,210)( 29,209)( 30,208)( 31,207)
( 32,206)( 33,205)( 34,204)( 35,203)( 36,202)( 37,201)( 38,200)( 39,199)
( 40,198)( 41,197)( 42,196)( 43,195)( 44,194)( 45,193)( 46,192)( 47,191)
( 48,237)( 49,236)( 50,282)( 51,281)( 52,280)( 53,279)( 54,278)( 55,277)
( 56,276)( 57,275)( 58,274)( 59,273)( 60,272)( 61,271)( 62,270)( 63,269)
( 64,268)( 65,267)( 66,266)( 67,265)( 68,264)( 69,263)( 70,262)( 71,261)
( 72,260)( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,254)( 79,253)
( 80,252)( 81,251)( 82,250)( 83,249)( 84,248)( 85,247)( 86,246)( 87,245)
( 88,244)( 89,243)( 90,242)( 91,241)( 92,240)( 93,239)( 94,238)( 95,331)
( 96,330)( 97,376)( 98,375)( 99,374)(100,373)(101,372)(102,371)(103,370)
(104,369)(105,368)(106,367)(107,366)(108,365)(109,364)(110,363)(111,362)
(112,361)(113,360)(114,359)(115,358)(116,357)(117,356)(118,355)(119,354)
(120,353)(121,352)(122,351)(123,350)(124,349)(125,348)(126,347)(127,346)
(128,345)(129,344)(130,343)(131,342)(132,341)(133,340)(134,339)(135,338)
(136,337)(137,336)(138,335)(139,334)(140,333)(141,332)(142,284)(143,283)
(144,329)(145,328)(146,327)(147,326)(148,325)(149,324)(150,323)(151,322)
(152,321)(153,320)(154,319)(155,318)(156,317)(157,316)(158,315)(159,314)
(160,313)(161,312)(162,311)(163,310)(164,309)(165,308)(166,307)(167,306)
(168,305)(169,304)(170,303)(171,302)(172,301)(173,300)(174,299)(175,298)
(176,297)(177,296)(178,295)(179,294)(180,293)(181,292)(182,291)(183,290)
(184,289)(185,288)(186,287)(187,286)(188,285)(377,660)(378,659)(379,705)
(380,704)(381,703)(382,702)(383,701)(384,700)(385,699)(386,698)(387,697)
(388,696)(389,695)(390,694)(391,693)(392,692)(393,691)(394,690)(395,689)
(396,688)(397,687)(398,686)(399,685)(400,684)(401,683)(402,682)(403,681)
(404,680)(405,679)(406,678)(407,677)(408,676)(409,675)(410,674)(411,673)
(412,672)(413,671)(414,670)(415,669)(416,668)(417,667)(418,666)(419,665)
(420,664)(421,663)(422,662)(423,661)(424,707)(425,706)(426,752)(427,751)
(428,750)(429,749)(430,748)(431,747)(432,746)(433,745)(434,744)(435,743)
(436,742)(437,741)(438,740)(439,739)(440,738)(441,737)(442,736)(443,735)
(444,734)(445,733)(446,732)(447,731)(448,730)(449,729)(450,728)(451,727)
(452,726)(453,725)(454,724)(455,723)(456,722)(457,721)(458,720)(459,719)
(460,718)(461,717)(462,716)(463,715)(464,714)(465,713)(466,712)(467,711)
(468,710)(469,709)(470,708)(471,566)(472,565)(473,611)(474,610)(475,609)
(476,608)(477,607)(478,606)(479,605)(480,604)(481,603)(482,602)(483,601)
(484,600)(485,599)(486,598)(487,597)(488,596)(489,595)(490,594)(491,593)
(492,592)(493,591)(494,590)(495,589)(496,588)(497,587)(498,586)(499,585)
(500,584)(501,583)(502,582)(503,581)(504,580)(505,579)(506,578)(507,577)
(508,576)(509,575)(510,574)(511,573)(512,572)(513,571)(514,570)(515,569)
(516,568)(517,567)(518,613)(519,612)(520,658)(521,657)(522,656)(523,655)
(524,654)(525,653)(526,652)(527,651)(528,650)(529,649)(530,648)(531,647)
(532,646)(533,645)(534,644)(535,643)(536,642)(537,641)(538,640)(539,639)
(540,638)(541,637)(542,636)(543,635)(544,634)(545,633)(546,632)(547,631)
(548,630)(549,629)(550,628)(551,627)(552,626)(553,625)(554,624)(555,623)
(556,622)(557,621)(558,620)(559,619)(560,618)(561,617)(562,616)(563,615)
(564,614);
s2 := Sym(752)!( 1,377)( 2,378)( 3,379)( 4,380)( 5,381)( 6,382)( 7,383)
( 8,384)( 9,385)( 10,386)( 11,387)( 12,388)( 13,389)( 14,390)( 15,391)
( 16,392)( 17,393)( 18,394)( 19,395)( 20,396)( 21,397)( 22,398)( 23,399)
( 24,400)( 25,401)( 26,402)( 27,403)( 28,404)( 29,405)( 30,406)( 31,407)
( 32,408)( 33,409)( 34,410)( 35,411)( 36,412)( 37,413)( 38,414)( 39,415)
( 40,416)( 41,417)( 42,418)( 43,419)( 44,420)( 45,421)( 46,422)( 47,423)
( 48,424)( 49,425)( 50,426)( 51,427)( 52,428)( 53,429)( 54,430)( 55,431)
( 56,432)( 57,433)( 58,434)( 59,435)( 60,436)( 61,437)( 62,438)( 63,439)
( 64,440)( 65,441)( 66,442)( 67,443)( 68,444)( 69,445)( 70,446)( 71,447)
( 72,448)( 73,449)( 74,450)( 75,451)( 76,452)( 77,453)( 78,454)( 79,455)
( 80,456)( 81,457)( 82,458)( 83,459)( 84,460)( 85,461)( 86,462)( 87,463)
( 88,464)( 89,465)( 90,466)( 91,467)( 92,468)( 93,469)( 94,470)( 95,518)
( 96,519)( 97,520)( 98,521)( 99,522)(100,523)(101,524)(102,525)(103,526)
(104,527)(105,528)(106,529)(107,530)(108,531)(109,532)(110,533)(111,534)
(112,535)(113,536)(114,537)(115,538)(116,539)(117,540)(118,541)(119,542)
(120,543)(121,544)(122,545)(123,546)(124,547)(125,548)(126,549)(127,550)
(128,551)(129,552)(130,553)(131,554)(132,555)(133,556)(134,557)(135,558)
(136,559)(137,560)(138,561)(139,562)(140,563)(141,564)(142,471)(143,472)
(144,473)(145,474)(146,475)(147,476)(148,477)(149,478)(150,479)(151,480)
(152,481)(153,482)(154,483)(155,484)(156,485)(157,486)(158,487)(159,488)
(160,489)(161,490)(162,491)(163,492)(164,493)(165,494)(166,495)(167,496)
(168,497)(169,498)(170,499)(171,500)(172,501)(173,502)(174,503)(175,504)
(176,505)(177,506)(178,507)(179,508)(180,509)(181,510)(182,511)(183,512)
(184,513)(185,514)(186,515)(187,516)(188,517)(189,565)(190,566)(191,567)
(192,568)(193,569)(194,570)(195,571)(196,572)(197,573)(198,574)(199,575)
(200,576)(201,577)(202,578)(203,579)(204,580)(205,581)(206,582)(207,583)
(208,584)(209,585)(210,586)(211,587)(212,588)(213,589)(214,590)(215,591)
(216,592)(217,593)(218,594)(219,595)(220,596)(221,597)(222,598)(223,599)
(224,600)(225,601)(226,602)(227,603)(228,604)(229,605)(230,606)(231,607)
(232,608)(233,609)(234,610)(235,611)(236,612)(237,613)(238,614)(239,615)
(240,616)(241,617)(242,618)(243,619)(244,620)(245,621)(246,622)(247,623)
(248,624)(249,625)(250,626)(251,627)(252,628)(253,629)(254,630)(255,631)
(256,632)(257,633)(258,634)(259,635)(260,636)(261,637)(262,638)(263,639)
(264,640)(265,641)(266,642)(267,643)(268,644)(269,645)(270,646)(271,647)
(272,648)(273,649)(274,650)(275,651)(276,652)(277,653)(278,654)(279,655)
(280,656)(281,657)(282,658)(283,706)(284,707)(285,708)(286,709)(287,710)
(288,711)(289,712)(290,713)(291,714)(292,715)(293,716)(294,717)(295,718)
(296,719)(297,720)(298,721)(299,722)(300,723)(301,724)(302,725)(303,726)
(304,727)(305,728)(306,729)(307,730)(308,731)(309,732)(310,733)(311,734)
(312,735)(313,736)(314,737)(315,738)(316,739)(317,740)(318,741)(319,742)
(320,743)(321,744)(322,745)(323,746)(324,747)(325,748)(326,749)(327,750)
(328,751)(329,752)(330,659)(331,660)(332,661)(333,662)(334,663)(335,664)
(336,665)(337,666)(338,667)(339,668)(340,669)(341,670)(342,671)(343,672)
(344,673)(345,674)(346,675)(347,676)(348,677)(349,678)(350,679)(351,680)
(352,681)(353,682)(354,683)(355,684)(356,685)(357,686)(358,687)(359,688)
(360,689)(361,690)(362,691)(363,692)(364,693)(365,694)(366,695)(367,696)
(368,697)(369,698)(370,699)(371,700)(372,701)(373,702)(374,703)(375,704)
(376,705);
poly := sub<Sym(752)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope