Polytope of Type {14,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,8}*1568a
if this polytope has a name.
Group : SmallGroup(1568,805)
Rank : 3
Schlafli Type : {14,8}
Number of vertices, edges, etc : 98, 392, 56
Order of s0s1s2 : 8
Order of s0s1s2s1 : 14
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 : {14,4}*784
4-fold quotients : {14,4}*392
49-fold quotients : {2,8}*32
98-fold quotients : {2,4}*16
196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,295)( 2,301)( 3,300)( 4,299)( 5,298)( 6,297)( 7,296)( 8,337)
( 9,343)( 10,342)( 11,341)( 12,340)( 13,339)( 14,338)( 15,330)( 16,336)
( 17,335)( 18,334)( 19,333)( 20,332)( 21,331)( 22,323)( 23,329)( 24,328)
( 25,327)( 26,326)( 27,325)( 28,324)( 29,316)( 30,322)( 31,321)( 32,320)
( 33,319)( 34,318)( 35,317)( 36,309)( 37,315)( 38,314)( 39,313)( 40,312)
( 41,311)( 42,310)( 43,302)( 44,308)( 45,307)( 46,306)( 47,305)( 48,304)
( 49,303)( 50,344)( 51,350)( 52,349)( 53,348)( 54,347)( 55,346)( 56,345)
( 57,386)( 58,392)( 59,391)( 60,390)( 61,389)( 62,388)( 63,387)( 64,379)
( 65,385)( 66,384)( 67,383)( 68,382)( 69,381)( 70,380)( 71,372)( 72,378)
( 73,377)( 74,376)( 75,375)( 76,374)( 77,373)( 78,365)( 79,371)( 80,370)
( 81,369)( 82,368)( 83,367)( 84,366)( 85,358)( 86,364)( 87,363)( 88,362)
( 89,361)( 90,360)( 91,359)( 92,351)( 93,357)( 94,356)( 95,355)( 96,354)
( 97,353)( 98,352)( 99,246)(100,252)(101,251)(102,250)(103,249)(104,248)
(105,247)(106,288)(107,294)(108,293)(109,292)(110,291)(111,290)(112,289)
(113,281)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)(120,274)
(121,280)(122,279)(123,278)(124,277)(125,276)(126,275)(127,267)(128,273)
(129,272)(130,271)(131,270)(132,269)(133,268)(134,260)(135,266)(136,265)
(137,264)(138,263)(139,262)(140,261)(141,253)(142,259)(143,258)(144,257)
(145,256)(146,255)(147,254)(148,197)(149,203)(150,202)(151,201)(152,200)
(153,199)(154,198)(155,239)(156,245)(157,244)(158,243)(159,242)(160,241)
(161,240)(162,232)(163,238)(164,237)(165,236)(166,235)(167,234)(168,233)
(169,225)(170,231)(171,230)(172,229)(173,228)(174,227)(175,226)(176,218)
(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)(183,211)(184,217)
(185,216)(186,215)(187,214)(188,213)(189,212)(190,204)(191,210)(192,209)
(193,208)(194,207)(195,206)(196,205)(393,687)(394,693)(395,692)(396,691)
(397,690)(398,689)(399,688)(400,729)(401,735)(402,734)(403,733)(404,732)
(405,731)(406,730)(407,722)(408,728)(409,727)(410,726)(411,725)(412,724)
(413,723)(414,715)(415,721)(416,720)(417,719)(418,718)(419,717)(420,716)
(421,708)(422,714)(423,713)(424,712)(425,711)(426,710)(427,709)(428,701)
(429,707)(430,706)(431,705)(432,704)(433,703)(434,702)(435,694)(436,700)
(437,699)(438,698)(439,697)(440,696)(441,695)(442,736)(443,742)(444,741)
(445,740)(446,739)(447,738)(448,737)(449,778)(450,784)(451,783)(452,782)
(453,781)(454,780)(455,779)(456,771)(457,777)(458,776)(459,775)(460,774)
(461,773)(462,772)(463,764)(464,770)(465,769)(466,768)(467,767)(468,766)
(469,765)(470,757)(471,763)(472,762)(473,761)(474,760)(475,759)(476,758)
(477,750)(478,756)(479,755)(480,754)(481,753)(482,752)(483,751)(484,743)
(485,749)(486,748)(487,747)(488,746)(489,745)(490,744)(491,638)(492,644)
(493,643)(494,642)(495,641)(496,640)(497,639)(498,680)(499,686)(500,685)
(501,684)(502,683)(503,682)(504,681)(505,673)(506,679)(507,678)(508,677)
(509,676)(510,675)(511,674)(512,666)(513,672)(514,671)(515,670)(516,669)
(517,668)(518,667)(519,659)(520,665)(521,664)(522,663)(523,662)(524,661)
(525,660)(526,652)(527,658)(528,657)(529,656)(530,655)(531,654)(532,653)
(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)(540,589)
(541,595)(542,594)(543,593)(544,592)(545,591)(546,590)(547,631)(548,637)
(549,636)(550,635)(551,634)(552,633)(553,632)(554,624)(555,630)(556,629)
(557,628)(558,627)(559,626)(560,625)(561,617)(562,623)(563,622)(564,621)
(565,620)(566,619)(567,618)(568,610)(569,616)(570,615)(571,614)(572,613)
(573,612)(574,611)(575,603)(576,609)(577,608)(578,607)(579,606)(580,605)
(581,604)(582,596)(583,602)(584,601)(585,600)(586,599)(587,598)(588,597);;
s1 := ( 1, 8)( 3, 45)( 4, 39)( 5, 33)( 6, 27)( 7, 21)( 9, 44)( 10, 38)
( 11, 32)( 12, 26)( 13, 20)( 15, 43)( 16, 37)( 17, 31)( 18, 25)( 22, 36)
( 23, 30)( 28, 49)( 34, 48)( 35, 42)( 40, 47)( 50, 57)( 52, 94)( 53, 88)
( 54, 82)( 55, 76)( 56, 70)( 58, 93)( 59, 87)( 60, 81)( 61, 75)( 62, 69)
( 64, 92)( 65, 86)( 66, 80)( 67, 74)( 71, 85)( 72, 79)( 77, 98)( 83, 97)
( 84, 91)( 89, 96)( 99,155)(100,149)(101,192)(102,186)(103,180)(104,174)
(105,168)(106,148)(107,191)(108,185)(109,179)(110,173)(111,167)(112,161)
(113,190)(114,184)(115,178)(116,172)(117,166)(118,160)(119,154)(120,183)
(121,177)(122,171)(123,165)(124,159)(125,153)(126,196)(127,176)(128,170)
(129,164)(130,158)(131,152)(132,195)(133,189)(134,169)(135,163)(136,157)
(137,151)(138,194)(139,188)(140,182)(141,162)(142,156)(143,150)(144,193)
(145,187)(146,181)(147,175)(197,253)(198,247)(199,290)(200,284)(201,278)
(202,272)(203,266)(204,246)(205,289)(206,283)(207,277)(208,271)(209,265)
(210,259)(211,288)(212,282)(213,276)(214,270)(215,264)(216,258)(217,252)
(218,281)(219,275)(220,269)(221,263)(222,257)(223,251)(224,294)(225,274)
(226,268)(227,262)(228,256)(229,250)(230,293)(231,287)(232,267)(233,261)
(234,255)(235,249)(236,292)(237,286)(238,280)(239,260)(240,254)(241,248)
(242,291)(243,285)(244,279)(245,273)(295,302)(297,339)(298,333)(299,327)
(300,321)(301,315)(303,338)(304,332)(305,326)(306,320)(307,314)(309,337)
(310,331)(311,325)(312,319)(316,330)(317,324)(322,343)(328,342)(329,336)
(334,341)(344,351)(346,388)(347,382)(348,376)(349,370)(350,364)(352,387)
(353,381)(354,375)(355,369)(356,363)(358,386)(359,380)(360,374)(361,368)
(365,379)(366,373)(371,392)(377,391)(378,385)(383,390)(393,498)(394,492)
(395,535)(396,529)(397,523)(398,517)(399,511)(400,491)(401,534)(402,528)
(403,522)(404,516)(405,510)(406,504)(407,533)(408,527)(409,521)(410,515)
(411,509)(412,503)(413,497)(414,526)(415,520)(416,514)(417,508)(418,502)
(419,496)(420,539)(421,519)(422,513)(423,507)(424,501)(425,495)(426,538)
(427,532)(428,512)(429,506)(430,500)(431,494)(432,537)(433,531)(434,525)
(435,505)(436,499)(437,493)(438,536)(439,530)(440,524)(441,518)(442,547)
(443,541)(444,584)(445,578)(446,572)(447,566)(448,560)(449,540)(450,583)
(451,577)(452,571)(453,565)(454,559)(455,553)(456,582)(457,576)(458,570)
(459,564)(460,558)(461,552)(462,546)(463,575)(464,569)(465,563)(466,557)
(467,551)(468,545)(469,588)(470,568)(471,562)(472,556)(473,550)(474,544)
(475,587)(476,581)(477,561)(478,555)(479,549)(480,543)(481,586)(482,580)
(483,574)(484,554)(485,548)(486,542)(487,585)(488,579)(489,573)(490,567)
(589,743)(590,737)(591,780)(592,774)(593,768)(594,762)(595,756)(596,736)
(597,779)(598,773)(599,767)(600,761)(601,755)(602,749)(603,778)(604,772)
(605,766)(606,760)(607,754)(608,748)(609,742)(610,771)(611,765)(612,759)
(613,753)(614,747)(615,741)(616,784)(617,764)(618,758)(619,752)(620,746)
(621,740)(622,783)(623,777)(624,757)(625,751)(626,745)(627,739)(628,782)
(629,776)(630,770)(631,750)(632,744)(633,738)(634,781)(635,775)(636,769)
(637,763)(638,694)(639,688)(640,731)(641,725)(642,719)(643,713)(644,707)
(645,687)(646,730)(647,724)(648,718)(649,712)(650,706)(651,700)(652,729)
(653,723)(654,717)(655,711)(656,705)(657,699)(658,693)(659,722)(660,716)
(661,710)(662,704)(663,698)(664,692)(665,735)(666,715)(667,709)(668,703)
(669,697)(670,691)(671,734)(672,728)(673,708)(674,702)(675,696)(676,690)
(677,733)(678,727)(679,721)(680,701)(681,695)(682,689)(683,732)(684,726)
(685,720)(686,714);;
s2 := ( 1,393)( 2,394)( 3,395)( 4,396)( 5,397)( 6,398)( 7,399)( 8,437)
( 9,438)( 10,439)( 11,440)( 12,441)( 13,435)( 14,436)( 15,432)( 16,433)
( 17,434)( 18,428)( 19,429)( 20,430)( 21,431)( 22,427)( 23,421)( 24,422)
( 25,423)( 26,424)( 27,425)( 28,426)( 29,415)( 30,416)( 31,417)( 32,418)
( 33,419)( 34,420)( 35,414)( 36,410)( 37,411)( 38,412)( 39,413)( 40,407)
( 41,408)( 42,409)( 43,405)( 44,406)( 45,400)( 46,401)( 47,402)( 48,403)
( 49,404)( 50,442)( 51,443)( 52,444)( 53,445)( 54,446)( 55,447)( 56,448)
( 57,486)( 58,487)( 59,488)( 60,489)( 61,490)( 62,484)( 63,485)( 64,481)
( 65,482)( 66,483)( 67,477)( 68,478)( 69,479)( 70,480)( 71,476)( 72,470)
( 73,471)( 74,472)( 75,473)( 76,474)( 77,475)( 78,464)( 79,465)( 80,466)
( 81,467)( 82,468)( 83,469)( 84,463)( 85,459)( 86,460)( 87,461)( 88,462)
( 89,456)( 90,457)( 91,458)( 92,454)( 93,455)( 94,449)( 95,450)( 96,451)
( 97,452)( 98,453)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)
(105,546)(106,584)(107,585)(108,586)(109,587)(110,588)(111,582)(112,583)
(113,579)(114,580)(115,581)(116,575)(117,576)(118,577)(119,578)(120,574)
(121,568)(122,569)(123,570)(124,571)(125,572)(126,573)(127,562)(128,563)
(129,564)(130,565)(131,566)(132,567)(133,561)(134,557)(135,558)(136,559)
(137,560)(138,554)(139,555)(140,556)(141,552)(142,553)(143,547)(144,548)
(145,549)(146,550)(147,551)(148,491)(149,492)(150,493)(151,494)(152,495)
(153,496)(154,497)(155,535)(156,536)(157,537)(158,538)(159,539)(160,533)
(161,534)(162,530)(163,531)(164,532)(165,526)(166,527)(167,528)(168,529)
(169,525)(170,519)(171,520)(172,521)(173,522)(174,523)(175,524)(176,513)
(177,514)(178,515)(179,516)(180,517)(181,518)(182,512)(183,508)(184,509)
(185,510)(186,511)(187,505)(188,506)(189,507)(190,503)(191,504)(192,498)
(193,499)(194,500)(195,501)(196,502)(197,638)(198,639)(199,640)(200,641)
(201,642)(202,643)(203,644)(204,682)(205,683)(206,684)(207,685)(208,686)
(209,680)(210,681)(211,677)(212,678)(213,679)(214,673)(215,674)(216,675)
(217,676)(218,672)(219,666)(220,667)(221,668)(222,669)(223,670)(224,671)
(225,660)(226,661)(227,662)(228,663)(229,664)(230,665)(231,659)(232,655)
(233,656)(234,657)(235,658)(236,652)(237,653)(238,654)(239,650)(240,651)
(241,645)(242,646)(243,647)(244,648)(245,649)(246,589)(247,590)(248,591)
(249,592)(250,593)(251,594)(252,595)(253,633)(254,634)(255,635)(256,636)
(257,637)(258,631)(259,632)(260,628)(261,629)(262,630)(263,624)(264,625)
(265,626)(266,627)(267,623)(268,617)(269,618)(270,619)(271,620)(272,621)
(273,622)(274,611)(275,612)(276,613)(277,614)(278,615)(279,616)(280,610)
(281,606)(282,607)(283,608)(284,609)(285,603)(286,604)(287,605)(288,601)
(289,602)(290,596)(291,597)(292,598)(293,599)(294,600)(295,687)(296,688)
(297,689)(298,690)(299,691)(300,692)(301,693)(302,731)(303,732)(304,733)
(305,734)(306,735)(307,729)(308,730)(309,726)(310,727)(311,728)(312,722)
(313,723)(314,724)(315,725)(316,721)(317,715)(318,716)(319,717)(320,718)
(321,719)(322,720)(323,709)(324,710)(325,711)(326,712)(327,713)(328,714)
(329,708)(330,704)(331,705)(332,706)(333,707)(334,701)(335,702)(336,703)
(337,699)(338,700)(339,694)(340,695)(341,696)(342,697)(343,698)(344,736)
(345,737)(346,738)(347,739)(348,740)(349,741)(350,742)(351,780)(352,781)
(353,782)(354,783)(355,784)(356,778)(357,779)(358,775)(359,776)(360,777)
(361,771)(362,772)(363,773)(364,774)(365,770)(366,764)(367,765)(368,766)
(369,767)(370,768)(371,769)(372,758)(373,759)(374,760)(375,761)(376,762)
(377,763)(378,757)(379,753)(380,754)(381,755)(382,756)(383,750)(384,751)
(385,752)(386,748)(387,749)(388,743)(389,744)(390,745)(391,746)(392,747);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(784)!( 1,295)( 2,301)( 3,300)( 4,299)( 5,298)( 6,297)( 7,296)
( 8,337)( 9,343)( 10,342)( 11,341)( 12,340)( 13,339)( 14,338)( 15,330)
( 16,336)( 17,335)( 18,334)( 19,333)( 20,332)( 21,331)( 22,323)( 23,329)
( 24,328)( 25,327)( 26,326)( 27,325)( 28,324)( 29,316)( 30,322)( 31,321)
( 32,320)( 33,319)( 34,318)( 35,317)( 36,309)( 37,315)( 38,314)( 39,313)
( 40,312)( 41,311)( 42,310)( 43,302)( 44,308)( 45,307)( 46,306)( 47,305)
( 48,304)( 49,303)( 50,344)( 51,350)( 52,349)( 53,348)( 54,347)( 55,346)
( 56,345)( 57,386)( 58,392)( 59,391)( 60,390)( 61,389)( 62,388)( 63,387)
( 64,379)( 65,385)( 66,384)( 67,383)( 68,382)( 69,381)( 70,380)( 71,372)
( 72,378)( 73,377)( 74,376)( 75,375)( 76,374)( 77,373)( 78,365)( 79,371)
( 80,370)( 81,369)( 82,368)( 83,367)( 84,366)( 85,358)( 86,364)( 87,363)
( 88,362)( 89,361)( 90,360)( 91,359)( 92,351)( 93,357)( 94,356)( 95,355)
( 96,354)( 97,353)( 98,352)( 99,246)(100,252)(101,251)(102,250)(103,249)
(104,248)(105,247)(106,288)(107,294)(108,293)(109,292)(110,291)(111,290)
(112,289)(113,281)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)
(120,274)(121,280)(122,279)(123,278)(124,277)(125,276)(126,275)(127,267)
(128,273)(129,272)(130,271)(131,270)(132,269)(133,268)(134,260)(135,266)
(136,265)(137,264)(138,263)(139,262)(140,261)(141,253)(142,259)(143,258)
(144,257)(145,256)(146,255)(147,254)(148,197)(149,203)(150,202)(151,201)
(152,200)(153,199)(154,198)(155,239)(156,245)(157,244)(158,243)(159,242)
(160,241)(161,240)(162,232)(163,238)(164,237)(165,236)(166,235)(167,234)
(168,233)(169,225)(170,231)(171,230)(172,229)(173,228)(174,227)(175,226)
(176,218)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)(183,211)
(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)(190,204)(191,210)
(192,209)(193,208)(194,207)(195,206)(196,205)(393,687)(394,693)(395,692)
(396,691)(397,690)(398,689)(399,688)(400,729)(401,735)(402,734)(403,733)
(404,732)(405,731)(406,730)(407,722)(408,728)(409,727)(410,726)(411,725)
(412,724)(413,723)(414,715)(415,721)(416,720)(417,719)(418,718)(419,717)
(420,716)(421,708)(422,714)(423,713)(424,712)(425,711)(426,710)(427,709)
(428,701)(429,707)(430,706)(431,705)(432,704)(433,703)(434,702)(435,694)
(436,700)(437,699)(438,698)(439,697)(440,696)(441,695)(442,736)(443,742)
(444,741)(445,740)(446,739)(447,738)(448,737)(449,778)(450,784)(451,783)
(452,782)(453,781)(454,780)(455,779)(456,771)(457,777)(458,776)(459,775)
(460,774)(461,773)(462,772)(463,764)(464,770)(465,769)(466,768)(467,767)
(468,766)(469,765)(470,757)(471,763)(472,762)(473,761)(474,760)(475,759)
(476,758)(477,750)(478,756)(479,755)(480,754)(481,753)(482,752)(483,751)
(484,743)(485,749)(486,748)(487,747)(488,746)(489,745)(490,744)(491,638)
(492,644)(493,643)(494,642)(495,641)(496,640)(497,639)(498,680)(499,686)
(500,685)(501,684)(502,683)(503,682)(504,681)(505,673)(506,679)(507,678)
(508,677)(509,676)(510,675)(511,674)(512,666)(513,672)(514,671)(515,670)
(516,669)(517,668)(518,667)(519,659)(520,665)(521,664)(522,663)(523,662)
(524,661)(525,660)(526,652)(527,658)(528,657)(529,656)(530,655)(531,654)
(532,653)(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)
(540,589)(541,595)(542,594)(543,593)(544,592)(545,591)(546,590)(547,631)
(548,637)(549,636)(550,635)(551,634)(552,633)(553,632)(554,624)(555,630)
(556,629)(557,628)(558,627)(559,626)(560,625)(561,617)(562,623)(563,622)
(564,621)(565,620)(566,619)(567,618)(568,610)(569,616)(570,615)(571,614)
(572,613)(573,612)(574,611)(575,603)(576,609)(577,608)(578,607)(579,606)
(580,605)(581,604)(582,596)(583,602)(584,601)(585,600)(586,599)(587,598)
(588,597);
s1 := Sym(784)!( 1, 8)( 3, 45)( 4, 39)( 5, 33)( 6, 27)( 7, 21)( 9, 44)
( 10, 38)( 11, 32)( 12, 26)( 13, 20)( 15, 43)( 16, 37)( 17, 31)( 18, 25)
( 22, 36)( 23, 30)( 28, 49)( 34, 48)( 35, 42)( 40, 47)( 50, 57)( 52, 94)
( 53, 88)( 54, 82)( 55, 76)( 56, 70)( 58, 93)( 59, 87)( 60, 81)( 61, 75)
( 62, 69)( 64, 92)( 65, 86)( 66, 80)( 67, 74)( 71, 85)( 72, 79)( 77, 98)
( 83, 97)( 84, 91)( 89, 96)( 99,155)(100,149)(101,192)(102,186)(103,180)
(104,174)(105,168)(106,148)(107,191)(108,185)(109,179)(110,173)(111,167)
(112,161)(113,190)(114,184)(115,178)(116,172)(117,166)(118,160)(119,154)
(120,183)(121,177)(122,171)(123,165)(124,159)(125,153)(126,196)(127,176)
(128,170)(129,164)(130,158)(131,152)(132,195)(133,189)(134,169)(135,163)
(136,157)(137,151)(138,194)(139,188)(140,182)(141,162)(142,156)(143,150)
(144,193)(145,187)(146,181)(147,175)(197,253)(198,247)(199,290)(200,284)
(201,278)(202,272)(203,266)(204,246)(205,289)(206,283)(207,277)(208,271)
(209,265)(210,259)(211,288)(212,282)(213,276)(214,270)(215,264)(216,258)
(217,252)(218,281)(219,275)(220,269)(221,263)(222,257)(223,251)(224,294)
(225,274)(226,268)(227,262)(228,256)(229,250)(230,293)(231,287)(232,267)
(233,261)(234,255)(235,249)(236,292)(237,286)(238,280)(239,260)(240,254)
(241,248)(242,291)(243,285)(244,279)(245,273)(295,302)(297,339)(298,333)
(299,327)(300,321)(301,315)(303,338)(304,332)(305,326)(306,320)(307,314)
(309,337)(310,331)(311,325)(312,319)(316,330)(317,324)(322,343)(328,342)
(329,336)(334,341)(344,351)(346,388)(347,382)(348,376)(349,370)(350,364)
(352,387)(353,381)(354,375)(355,369)(356,363)(358,386)(359,380)(360,374)
(361,368)(365,379)(366,373)(371,392)(377,391)(378,385)(383,390)(393,498)
(394,492)(395,535)(396,529)(397,523)(398,517)(399,511)(400,491)(401,534)
(402,528)(403,522)(404,516)(405,510)(406,504)(407,533)(408,527)(409,521)
(410,515)(411,509)(412,503)(413,497)(414,526)(415,520)(416,514)(417,508)
(418,502)(419,496)(420,539)(421,519)(422,513)(423,507)(424,501)(425,495)
(426,538)(427,532)(428,512)(429,506)(430,500)(431,494)(432,537)(433,531)
(434,525)(435,505)(436,499)(437,493)(438,536)(439,530)(440,524)(441,518)
(442,547)(443,541)(444,584)(445,578)(446,572)(447,566)(448,560)(449,540)
(450,583)(451,577)(452,571)(453,565)(454,559)(455,553)(456,582)(457,576)
(458,570)(459,564)(460,558)(461,552)(462,546)(463,575)(464,569)(465,563)
(466,557)(467,551)(468,545)(469,588)(470,568)(471,562)(472,556)(473,550)
(474,544)(475,587)(476,581)(477,561)(478,555)(479,549)(480,543)(481,586)
(482,580)(483,574)(484,554)(485,548)(486,542)(487,585)(488,579)(489,573)
(490,567)(589,743)(590,737)(591,780)(592,774)(593,768)(594,762)(595,756)
(596,736)(597,779)(598,773)(599,767)(600,761)(601,755)(602,749)(603,778)
(604,772)(605,766)(606,760)(607,754)(608,748)(609,742)(610,771)(611,765)
(612,759)(613,753)(614,747)(615,741)(616,784)(617,764)(618,758)(619,752)
(620,746)(621,740)(622,783)(623,777)(624,757)(625,751)(626,745)(627,739)
(628,782)(629,776)(630,770)(631,750)(632,744)(633,738)(634,781)(635,775)
(636,769)(637,763)(638,694)(639,688)(640,731)(641,725)(642,719)(643,713)
(644,707)(645,687)(646,730)(647,724)(648,718)(649,712)(650,706)(651,700)
(652,729)(653,723)(654,717)(655,711)(656,705)(657,699)(658,693)(659,722)
(660,716)(661,710)(662,704)(663,698)(664,692)(665,735)(666,715)(667,709)
(668,703)(669,697)(670,691)(671,734)(672,728)(673,708)(674,702)(675,696)
(676,690)(677,733)(678,727)(679,721)(680,701)(681,695)(682,689)(683,732)
(684,726)(685,720)(686,714);
s2 := Sym(784)!( 1,393)( 2,394)( 3,395)( 4,396)( 5,397)( 6,398)( 7,399)
( 8,437)( 9,438)( 10,439)( 11,440)( 12,441)( 13,435)( 14,436)( 15,432)
( 16,433)( 17,434)( 18,428)( 19,429)( 20,430)( 21,431)( 22,427)( 23,421)
( 24,422)( 25,423)( 26,424)( 27,425)( 28,426)( 29,415)( 30,416)( 31,417)
( 32,418)( 33,419)( 34,420)( 35,414)( 36,410)( 37,411)( 38,412)( 39,413)
( 40,407)( 41,408)( 42,409)( 43,405)( 44,406)( 45,400)( 46,401)( 47,402)
( 48,403)( 49,404)( 50,442)( 51,443)( 52,444)( 53,445)( 54,446)( 55,447)
( 56,448)( 57,486)( 58,487)( 59,488)( 60,489)( 61,490)( 62,484)( 63,485)
( 64,481)( 65,482)( 66,483)( 67,477)( 68,478)( 69,479)( 70,480)( 71,476)
( 72,470)( 73,471)( 74,472)( 75,473)( 76,474)( 77,475)( 78,464)( 79,465)
( 80,466)( 81,467)( 82,468)( 83,469)( 84,463)( 85,459)( 86,460)( 87,461)
( 88,462)( 89,456)( 90,457)( 91,458)( 92,454)( 93,455)( 94,449)( 95,450)
( 96,451)( 97,452)( 98,453)( 99,540)(100,541)(101,542)(102,543)(103,544)
(104,545)(105,546)(106,584)(107,585)(108,586)(109,587)(110,588)(111,582)
(112,583)(113,579)(114,580)(115,581)(116,575)(117,576)(118,577)(119,578)
(120,574)(121,568)(122,569)(123,570)(124,571)(125,572)(126,573)(127,562)
(128,563)(129,564)(130,565)(131,566)(132,567)(133,561)(134,557)(135,558)
(136,559)(137,560)(138,554)(139,555)(140,556)(141,552)(142,553)(143,547)
(144,548)(145,549)(146,550)(147,551)(148,491)(149,492)(150,493)(151,494)
(152,495)(153,496)(154,497)(155,535)(156,536)(157,537)(158,538)(159,539)
(160,533)(161,534)(162,530)(163,531)(164,532)(165,526)(166,527)(167,528)
(168,529)(169,525)(170,519)(171,520)(172,521)(173,522)(174,523)(175,524)
(176,513)(177,514)(178,515)(179,516)(180,517)(181,518)(182,512)(183,508)
(184,509)(185,510)(186,511)(187,505)(188,506)(189,507)(190,503)(191,504)
(192,498)(193,499)(194,500)(195,501)(196,502)(197,638)(198,639)(199,640)
(200,641)(201,642)(202,643)(203,644)(204,682)(205,683)(206,684)(207,685)
(208,686)(209,680)(210,681)(211,677)(212,678)(213,679)(214,673)(215,674)
(216,675)(217,676)(218,672)(219,666)(220,667)(221,668)(222,669)(223,670)
(224,671)(225,660)(226,661)(227,662)(228,663)(229,664)(230,665)(231,659)
(232,655)(233,656)(234,657)(235,658)(236,652)(237,653)(238,654)(239,650)
(240,651)(241,645)(242,646)(243,647)(244,648)(245,649)(246,589)(247,590)
(248,591)(249,592)(250,593)(251,594)(252,595)(253,633)(254,634)(255,635)
(256,636)(257,637)(258,631)(259,632)(260,628)(261,629)(262,630)(263,624)
(264,625)(265,626)(266,627)(267,623)(268,617)(269,618)(270,619)(271,620)
(272,621)(273,622)(274,611)(275,612)(276,613)(277,614)(278,615)(279,616)
(280,610)(281,606)(282,607)(283,608)(284,609)(285,603)(286,604)(287,605)
(288,601)(289,602)(290,596)(291,597)(292,598)(293,599)(294,600)(295,687)
(296,688)(297,689)(298,690)(299,691)(300,692)(301,693)(302,731)(303,732)
(304,733)(305,734)(306,735)(307,729)(308,730)(309,726)(310,727)(311,728)
(312,722)(313,723)(314,724)(315,725)(316,721)(317,715)(318,716)(319,717)
(320,718)(321,719)(322,720)(323,709)(324,710)(325,711)(326,712)(327,713)
(328,714)(329,708)(330,704)(331,705)(332,706)(333,707)(334,701)(335,702)
(336,703)(337,699)(338,700)(339,694)(340,695)(341,696)(342,697)(343,698)
(344,736)(345,737)(346,738)(347,739)(348,740)(349,741)(350,742)(351,780)
(352,781)(353,782)(354,783)(355,784)(356,778)(357,779)(358,775)(359,776)
(360,777)(361,771)(362,772)(363,773)(364,774)(365,770)(366,764)(367,765)
(368,766)(369,767)(370,768)(371,769)(372,758)(373,759)(374,760)(375,761)
(376,762)(377,763)(378,757)(379,753)(380,754)(381,755)(382,756)(383,750)
(384,751)(385,752)(386,748)(387,749)(388,743)(389,744)(390,745)(391,746)
(392,747);
poly := sub<Sym(784)|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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*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 >;
References : None.
to this polytope