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