Polytope of Type {198,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {198,4}*1584c
if this polytope has a name.
Group : SmallGroup(1584,366)
Rank : 3
Schlafli Type : {198,4}
Number of vertices, edges, etc : 198, 396, 4
Order of s0s1s2 : 99
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {99,4}*792
3-fold quotients : {66,4}*528c
6-fold quotients : {33,4}*264
11-fold quotients : {18,4}*144c
22-fold quotients : {9,4}*72
33-fold quotients : {6,4}*48b
66-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13,121)( 14,122)( 15,124)
( 16,123)( 17,129)( 18,130)( 19,132)( 20,131)( 21,125)( 22,126)( 23,128)
( 24,127)( 25,109)( 26,110)( 27,112)( 28,111)( 29,117)( 30,118)( 31,120)
( 32,119)( 33,113)( 34,114)( 35,116)( 36,115)( 37, 97)( 38, 98)( 39,100)
( 40, 99)( 41,105)( 42,106)( 43,108)( 44,107)( 45,101)( 46,102)( 47,104)
( 48,103)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)( 54, 94)( 55, 96)
( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 73)( 62, 74)( 63, 76)
( 64, 75)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 77)( 70, 78)( 71, 80)
( 72, 79)(133,273)(134,274)(135,276)(136,275)(137,269)(138,270)(139,272)
(140,271)(141,265)(142,266)(143,268)(144,267)(145,393)(146,394)(147,396)
(148,395)(149,389)(150,390)(151,392)(152,391)(153,385)(154,386)(155,388)
(156,387)(157,381)(158,382)(159,384)(160,383)(161,377)(162,378)(163,380)
(164,379)(165,373)(166,374)(167,376)(168,375)(169,369)(170,370)(171,372)
(172,371)(173,365)(174,366)(175,368)(176,367)(177,361)(178,362)(179,364)
(180,363)(181,357)(182,358)(183,360)(184,359)(185,353)(186,354)(187,356)
(188,355)(189,349)(190,350)(191,352)(192,351)(193,345)(194,346)(195,348)
(196,347)(197,341)(198,342)(199,344)(200,343)(201,337)(202,338)(203,340)
(204,339)(205,333)(206,334)(207,336)(208,335)(209,329)(210,330)(211,332)
(212,331)(213,325)(214,326)(215,328)(216,327)(217,321)(218,322)(219,324)
(220,323)(221,317)(222,318)(223,320)(224,319)(225,313)(226,314)(227,316)
(228,315)(229,309)(230,310)(231,312)(232,311)(233,305)(234,306)(235,308)
(236,307)(237,301)(238,302)(239,304)(240,303)(241,297)(242,298)(243,300)
(244,299)(245,293)(246,294)(247,296)(248,295)(249,289)(250,290)(251,292)
(252,291)(253,285)(254,286)(255,288)(256,287)(257,281)(258,282)(259,284)
(260,283)(261,277)(262,278)(263,280)(264,279)(399,400)(401,405)(402,406)
(403,408)(404,407)(409,517)(410,518)(411,520)(412,519)(413,525)(414,526)
(415,528)(416,527)(417,521)(418,522)(419,524)(420,523)(421,505)(422,506)
(423,508)(424,507)(425,513)(426,514)(427,516)(428,515)(429,509)(430,510)
(431,512)(432,511)(433,493)(434,494)(435,496)(436,495)(437,501)(438,502)
(439,504)(440,503)(441,497)(442,498)(443,500)(444,499)(445,481)(446,482)
(447,484)(448,483)(449,489)(450,490)(451,492)(452,491)(453,485)(454,486)
(455,488)(456,487)(457,469)(458,470)(459,472)(460,471)(461,477)(462,478)
(463,480)(464,479)(465,473)(466,474)(467,476)(468,475)(529,669)(530,670)
(531,672)(532,671)(533,665)(534,666)(535,668)(536,667)(537,661)(538,662)
(539,664)(540,663)(541,789)(542,790)(543,792)(544,791)(545,785)(546,786)
(547,788)(548,787)(549,781)(550,782)(551,784)(552,783)(553,777)(554,778)
(555,780)(556,779)(557,773)(558,774)(559,776)(560,775)(561,769)(562,770)
(563,772)(564,771)(565,765)(566,766)(567,768)(568,767)(569,761)(570,762)
(571,764)(572,763)(573,757)(574,758)(575,760)(576,759)(577,753)(578,754)
(579,756)(580,755)(581,749)(582,750)(583,752)(584,751)(585,745)(586,746)
(587,748)(588,747)(589,741)(590,742)(591,744)(592,743)(593,737)(594,738)
(595,740)(596,739)(597,733)(598,734)(599,736)(600,735)(601,729)(602,730)
(603,732)(604,731)(605,725)(606,726)(607,728)(608,727)(609,721)(610,722)
(611,724)(612,723)(613,717)(614,718)(615,720)(616,719)(617,713)(618,714)
(619,716)(620,715)(621,709)(622,710)(623,712)(624,711)(625,705)(626,706)
(627,708)(628,707)(629,701)(630,702)(631,704)(632,703)(633,697)(634,698)
(635,700)(636,699)(637,693)(638,694)(639,696)(640,695)(641,689)(642,690)
(643,692)(644,691)(645,685)(646,686)(647,688)(648,687)(649,681)(650,682)
(651,684)(652,683)(653,677)(654,678)(655,680)(656,679)(657,673)(658,674)
(659,676)(660,675);;
s1 := ( 1,541)( 2,544)( 3,543)( 4,542)( 5,549)( 6,552)( 7,551)( 8,550)
( 9,545)( 10,548)( 11,547)( 12,546)( 13,529)( 14,532)( 15,531)( 16,530)
( 17,537)( 18,540)( 19,539)( 20,538)( 21,533)( 22,536)( 23,535)( 24,534)
( 25,649)( 26,652)( 27,651)( 28,650)( 29,657)( 30,660)( 31,659)( 32,658)
( 33,653)( 34,656)( 35,655)( 36,654)( 37,637)( 38,640)( 39,639)( 40,638)
( 41,645)( 42,648)( 43,647)( 44,646)( 45,641)( 46,644)( 47,643)( 48,642)
( 49,625)( 50,628)( 51,627)( 52,626)( 53,633)( 54,636)( 55,635)( 56,634)
( 57,629)( 58,632)( 59,631)( 60,630)( 61,613)( 62,616)( 63,615)( 64,614)
( 65,621)( 66,624)( 67,623)( 68,622)( 69,617)( 70,620)( 71,619)( 72,618)
( 73,601)( 74,604)( 75,603)( 76,602)( 77,609)( 78,612)( 79,611)( 80,610)
( 81,605)( 82,608)( 83,607)( 84,606)( 85,589)( 86,592)( 87,591)( 88,590)
( 89,597)( 90,600)( 91,599)( 92,598)( 93,593)( 94,596)( 95,595)( 96,594)
( 97,577)( 98,580)( 99,579)(100,578)(101,585)(102,588)(103,587)(104,586)
(105,581)(106,584)(107,583)(108,582)(109,565)(110,568)(111,567)(112,566)
(113,573)(114,576)(115,575)(116,574)(117,569)(118,572)(119,571)(120,570)
(121,553)(122,556)(123,555)(124,554)(125,561)(126,564)(127,563)(128,562)
(129,557)(130,560)(131,559)(132,558)(133,409)(134,412)(135,411)(136,410)
(137,417)(138,420)(139,419)(140,418)(141,413)(142,416)(143,415)(144,414)
(145,397)(146,400)(147,399)(148,398)(149,405)(150,408)(151,407)(152,406)
(153,401)(154,404)(155,403)(156,402)(157,517)(158,520)(159,519)(160,518)
(161,525)(162,528)(163,527)(164,526)(165,521)(166,524)(167,523)(168,522)
(169,505)(170,508)(171,507)(172,506)(173,513)(174,516)(175,515)(176,514)
(177,509)(178,512)(179,511)(180,510)(181,493)(182,496)(183,495)(184,494)
(185,501)(186,504)(187,503)(188,502)(189,497)(190,500)(191,499)(192,498)
(193,481)(194,484)(195,483)(196,482)(197,489)(198,492)(199,491)(200,490)
(201,485)(202,488)(203,487)(204,486)(205,469)(206,472)(207,471)(208,470)
(209,477)(210,480)(211,479)(212,478)(213,473)(214,476)(215,475)(216,474)
(217,457)(218,460)(219,459)(220,458)(221,465)(222,468)(223,467)(224,466)
(225,461)(226,464)(227,463)(228,462)(229,445)(230,448)(231,447)(232,446)
(233,453)(234,456)(235,455)(236,454)(237,449)(238,452)(239,451)(240,450)
(241,433)(242,436)(243,435)(244,434)(245,441)(246,444)(247,443)(248,442)
(249,437)(250,440)(251,439)(252,438)(253,421)(254,424)(255,423)(256,422)
(257,429)(258,432)(259,431)(260,430)(261,425)(262,428)(263,427)(264,426)
(265,681)(266,684)(267,683)(268,682)(269,677)(270,680)(271,679)(272,678)
(273,673)(274,676)(275,675)(276,674)(277,669)(278,672)(279,671)(280,670)
(281,665)(282,668)(283,667)(284,666)(285,661)(286,664)(287,663)(288,662)
(289,789)(290,792)(291,791)(292,790)(293,785)(294,788)(295,787)(296,786)
(297,781)(298,784)(299,783)(300,782)(301,777)(302,780)(303,779)(304,778)
(305,773)(306,776)(307,775)(308,774)(309,769)(310,772)(311,771)(312,770)
(313,765)(314,768)(315,767)(316,766)(317,761)(318,764)(319,763)(320,762)
(321,757)(322,760)(323,759)(324,758)(325,753)(326,756)(327,755)(328,754)
(329,749)(330,752)(331,751)(332,750)(333,745)(334,748)(335,747)(336,746)
(337,741)(338,744)(339,743)(340,742)(341,737)(342,740)(343,739)(344,738)
(345,733)(346,736)(347,735)(348,734)(349,729)(350,732)(351,731)(352,730)
(353,725)(354,728)(355,727)(356,726)(357,721)(358,724)(359,723)(360,722)
(361,717)(362,720)(363,719)(364,718)(365,713)(366,716)(367,715)(368,714)
(369,709)(370,712)(371,711)(372,710)(373,705)(374,708)(375,707)(376,706)
(377,701)(378,704)(379,703)(380,702)(381,697)(382,700)(383,699)(384,698)
(385,693)(386,696)(387,695)(388,694)(389,689)(390,692)(391,691)(392,690)
(393,685)(394,688)(395,687)(396,686);;
s2 := ( 1,398)( 2,397)( 3,400)( 4,399)( 5,402)( 6,401)( 7,404)( 8,403)
( 9,406)( 10,405)( 11,408)( 12,407)( 13,410)( 14,409)( 15,412)( 16,411)
( 17,414)( 18,413)( 19,416)( 20,415)( 21,418)( 22,417)( 23,420)( 24,419)
( 25,422)( 26,421)( 27,424)( 28,423)( 29,426)( 30,425)( 31,428)( 32,427)
( 33,430)( 34,429)( 35,432)( 36,431)( 37,434)( 38,433)( 39,436)( 40,435)
( 41,438)( 42,437)( 43,440)( 44,439)( 45,442)( 46,441)( 47,444)( 48,443)
( 49,446)( 50,445)( 51,448)( 52,447)( 53,450)( 54,449)( 55,452)( 56,451)
( 57,454)( 58,453)( 59,456)( 60,455)( 61,458)( 62,457)( 63,460)( 64,459)
( 65,462)( 66,461)( 67,464)( 68,463)( 69,466)( 70,465)( 71,468)( 72,467)
( 73,470)( 74,469)( 75,472)( 76,471)( 77,474)( 78,473)( 79,476)( 80,475)
( 81,478)( 82,477)( 83,480)( 84,479)( 85,482)( 86,481)( 87,484)( 88,483)
( 89,486)( 90,485)( 91,488)( 92,487)( 93,490)( 94,489)( 95,492)( 96,491)
( 97,494)( 98,493)( 99,496)(100,495)(101,498)(102,497)(103,500)(104,499)
(105,502)(106,501)(107,504)(108,503)(109,506)(110,505)(111,508)(112,507)
(113,510)(114,509)(115,512)(116,511)(117,514)(118,513)(119,516)(120,515)
(121,518)(122,517)(123,520)(124,519)(125,522)(126,521)(127,524)(128,523)
(129,526)(130,525)(131,528)(132,527)(133,530)(134,529)(135,532)(136,531)
(137,534)(138,533)(139,536)(140,535)(141,538)(142,537)(143,540)(144,539)
(145,542)(146,541)(147,544)(148,543)(149,546)(150,545)(151,548)(152,547)
(153,550)(154,549)(155,552)(156,551)(157,554)(158,553)(159,556)(160,555)
(161,558)(162,557)(163,560)(164,559)(165,562)(166,561)(167,564)(168,563)
(169,566)(170,565)(171,568)(172,567)(173,570)(174,569)(175,572)(176,571)
(177,574)(178,573)(179,576)(180,575)(181,578)(182,577)(183,580)(184,579)
(185,582)(186,581)(187,584)(188,583)(189,586)(190,585)(191,588)(192,587)
(193,590)(194,589)(195,592)(196,591)(197,594)(198,593)(199,596)(200,595)
(201,598)(202,597)(203,600)(204,599)(205,602)(206,601)(207,604)(208,603)
(209,606)(210,605)(211,608)(212,607)(213,610)(214,609)(215,612)(216,611)
(217,614)(218,613)(219,616)(220,615)(221,618)(222,617)(223,620)(224,619)
(225,622)(226,621)(227,624)(228,623)(229,626)(230,625)(231,628)(232,627)
(233,630)(234,629)(235,632)(236,631)(237,634)(238,633)(239,636)(240,635)
(241,638)(242,637)(243,640)(244,639)(245,642)(246,641)(247,644)(248,643)
(249,646)(250,645)(251,648)(252,647)(253,650)(254,649)(255,652)(256,651)
(257,654)(258,653)(259,656)(260,655)(261,658)(262,657)(263,660)(264,659)
(265,662)(266,661)(267,664)(268,663)(269,666)(270,665)(271,668)(272,667)
(273,670)(274,669)(275,672)(276,671)(277,674)(278,673)(279,676)(280,675)
(281,678)(282,677)(283,680)(284,679)(285,682)(286,681)(287,684)(288,683)
(289,686)(290,685)(291,688)(292,687)(293,690)(294,689)(295,692)(296,691)
(297,694)(298,693)(299,696)(300,695)(301,698)(302,697)(303,700)(304,699)
(305,702)(306,701)(307,704)(308,703)(309,706)(310,705)(311,708)(312,707)
(313,710)(314,709)(315,712)(316,711)(317,714)(318,713)(319,716)(320,715)
(321,718)(322,717)(323,720)(324,719)(325,722)(326,721)(327,724)(328,723)
(329,726)(330,725)(331,728)(332,727)(333,730)(334,729)(335,732)(336,731)
(337,734)(338,733)(339,736)(340,735)(341,738)(342,737)(343,740)(344,739)
(345,742)(346,741)(347,744)(348,743)(349,746)(350,745)(351,748)(352,747)
(353,750)(354,749)(355,752)(356,751)(357,754)(358,753)(359,756)(360,755)
(361,758)(362,757)(363,760)(364,759)(365,762)(366,761)(367,764)(368,763)
(369,766)(370,765)(371,768)(372,767)(373,770)(374,769)(375,772)(376,771)
(377,774)(378,773)(379,776)(380,775)(381,778)(382,777)(383,780)(384,779)
(385,782)(386,781)(387,784)(388,783)(389,786)(390,785)(391,788)(392,787)
(393,790)(394,789)(395,792)(396,791);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(792)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13,121)( 14,122)
( 15,124)( 16,123)( 17,129)( 18,130)( 19,132)( 20,131)( 21,125)( 22,126)
( 23,128)( 24,127)( 25,109)( 26,110)( 27,112)( 28,111)( 29,117)( 30,118)
( 31,120)( 32,119)( 33,113)( 34,114)( 35,116)( 36,115)( 37, 97)( 38, 98)
( 39,100)( 40, 99)( 41,105)( 42,106)( 43,108)( 44,107)( 45,101)( 46,102)
( 47,104)( 48,103)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)( 54, 94)
( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 73)( 62, 74)
( 63, 76)( 64, 75)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 77)( 70, 78)
( 71, 80)( 72, 79)(133,273)(134,274)(135,276)(136,275)(137,269)(138,270)
(139,272)(140,271)(141,265)(142,266)(143,268)(144,267)(145,393)(146,394)
(147,396)(148,395)(149,389)(150,390)(151,392)(152,391)(153,385)(154,386)
(155,388)(156,387)(157,381)(158,382)(159,384)(160,383)(161,377)(162,378)
(163,380)(164,379)(165,373)(166,374)(167,376)(168,375)(169,369)(170,370)
(171,372)(172,371)(173,365)(174,366)(175,368)(176,367)(177,361)(178,362)
(179,364)(180,363)(181,357)(182,358)(183,360)(184,359)(185,353)(186,354)
(187,356)(188,355)(189,349)(190,350)(191,352)(192,351)(193,345)(194,346)
(195,348)(196,347)(197,341)(198,342)(199,344)(200,343)(201,337)(202,338)
(203,340)(204,339)(205,333)(206,334)(207,336)(208,335)(209,329)(210,330)
(211,332)(212,331)(213,325)(214,326)(215,328)(216,327)(217,321)(218,322)
(219,324)(220,323)(221,317)(222,318)(223,320)(224,319)(225,313)(226,314)
(227,316)(228,315)(229,309)(230,310)(231,312)(232,311)(233,305)(234,306)
(235,308)(236,307)(237,301)(238,302)(239,304)(240,303)(241,297)(242,298)
(243,300)(244,299)(245,293)(246,294)(247,296)(248,295)(249,289)(250,290)
(251,292)(252,291)(253,285)(254,286)(255,288)(256,287)(257,281)(258,282)
(259,284)(260,283)(261,277)(262,278)(263,280)(264,279)(399,400)(401,405)
(402,406)(403,408)(404,407)(409,517)(410,518)(411,520)(412,519)(413,525)
(414,526)(415,528)(416,527)(417,521)(418,522)(419,524)(420,523)(421,505)
(422,506)(423,508)(424,507)(425,513)(426,514)(427,516)(428,515)(429,509)
(430,510)(431,512)(432,511)(433,493)(434,494)(435,496)(436,495)(437,501)
(438,502)(439,504)(440,503)(441,497)(442,498)(443,500)(444,499)(445,481)
(446,482)(447,484)(448,483)(449,489)(450,490)(451,492)(452,491)(453,485)
(454,486)(455,488)(456,487)(457,469)(458,470)(459,472)(460,471)(461,477)
(462,478)(463,480)(464,479)(465,473)(466,474)(467,476)(468,475)(529,669)
(530,670)(531,672)(532,671)(533,665)(534,666)(535,668)(536,667)(537,661)
(538,662)(539,664)(540,663)(541,789)(542,790)(543,792)(544,791)(545,785)
(546,786)(547,788)(548,787)(549,781)(550,782)(551,784)(552,783)(553,777)
(554,778)(555,780)(556,779)(557,773)(558,774)(559,776)(560,775)(561,769)
(562,770)(563,772)(564,771)(565,765)(566,766)(567,768)(568,767)(569,761)
(570,762)(571,764)(572,763)(573,757)(574,758)(575,760)(576,759)(577,753)
(578,754)(579,756)(580,755)(581,749)(582,750)(583,752)(584,751)(585,745)
(586,746)(587,748)(588,747)(589,741)(590,742)(591,744)(592,743)(593,737)
(594,738)(595,740)(596,739)(597,733)(598,734)(599,736)(600,735)(601,729)
(602,730)(603,732)(604,731)(605,725)(606,726)(607,728)(608,727)(609,721)
(610,722)(611,724)(612,723)(613,717)(614,718)(615,720)(616,719)(617,713)
(618,714)(619,716)(620,715)(621,709)(622,710)(623,712)(624,711)(625,705)
(626,706)(627,708)(628,707)(629,701)(630,702)(631,704)(632,703)(633,697)
(634,698)(635,700)(636,699)(637,693)(638,694)(639,696)(640,695)(641,689)
(642,690)(643,692)(644,691)(645,685)(646,686)(647,688)(648,687)(649,681)
(650,682)(651,684)(652,683)(653,677)(654,678)(655,680)(656,679)(657,673)
(658,674)(659,676)(660,675);
s1 := Sym(792)!( 1,541)( 2,544)( 3,543)( 4,542)( 5,549)( 6,552)( 7,551)
( 8,550)( 9,545)( 10,548)( 11,547)( 12,546)( 13,529)( 14,532)( 15,531)
( 16,530)( 17,537)( 18,540)( 19,539)( 20,538)( 21,533)( 22,536)( 23,535)
( 24,534)( 25,649)( 26,652)( 27,651)( 28,650)( 29,657)( 30,660)( 31,659)
( 32,658)( 33,653)( 34,656)( 35,655)( 36,654)( 37,637)( 38,640)( 39,639)
( 40,638)( 41,645)( 42,648)( 43,647)( 44,646)( 45,641)( 46,644)( 47,643)
( 48,642)( 49,625)( 50,628)( 51,627)( 52,626)( 53,633)( 54,636)( 55,635)
( 56,634)( 57,629)( 58,632)( 59,631)( 60,630)( 61,613)( 62,616)( 63,615)
( 64,614)( 65,621)( 66,624)( 67,623)( 68,622)( 69,617)( 70,620)( 71,619)
( 72,618)( 73,601)( 74,604)( 75,603)( 76,602)( 77,609)( 78,612)( 79,611)
( 80,610)( 81,605)( 82,608)( 83,607)( 84,606)( 85,589)( 86,592)( 87,591)
( 88,590)( 89,597)( 90,600)( 91,599)( 92,598)( 93,593)( 94,596)( 95,595)
( 96,594)( 97,577)( 98,580)( 99,579)(100,578)(101,585)(102,588)(103,587)
(104,586)(105,581)(106,584)(107,583)(108,582)(109,565)(110,568)(111,567)
(112,566)(113,573)(114,576)(115,575)(116,574)(117,569)(118,572)(119,571)
(120,570)(121,553)(122,556)(123,555)(124,554)(125,561)(126,564)(127,563)
(128,562)(129,557)(130,560)(131,559)(132,558)(133,409)(134,412)(135,411)
(136,410)(137,417)(138,420)(139,419)(140,418)(141,413)(142,416)(143,415)
(144,414)(145,397)(146,400)(147,399)(148,398)(149,405)(150,408)(151,407)
(152,406)(153,401)(154,404)(155,403)(156,402)(157,517)(158,520)(159,519)
(160,518)(161,525)(162,528)(163,527)(164,526)(165,521)(166,524)(167,523)
(168,522)(169,505)(170,508)(171,507)(172,506)(173,513)(174,516)(175,515)
(176,514)(177,509)(178,512)(179,511)(180,510)(181,493)(182,496)(183,495)
(184,494)(185,501)(186,504)(187,503)(188,502)(189,497)(190,500)(191,499)
(192,498)(193,481)(194,484)(195,483)(196,482)(197,489)(198,492)(199,491)
(200,490)(201,485)(202,488)(203,487)(204,486)(205,469)(206,472)(207,471)
(208,470)(209,477)(210,480)(211,479)(212,478)(213,473)(214,476)(215,475)
(216,474)(217,457)(218,460)(219,459)(220,458)(221,465)(222,468)(223,467)
(224,466)(225,461)(226,464)(227,463)(228,462)(229,445)(230,448)(231,447)
(232,446)(233,453)(234,456)(235,455)(236,454)(237,449)(238,452)(239,451)
(240,450)(241,433)(242,436)(243,435)(244,434)(245,441)(246,444)(247,443)
(248,442)(249,437)(250,440)(251,439)(252,438)(253,421)(254,424)(255,423)
(256,422)(257,429)(258,432)(259,431)(260,430)(261,425)(262,428)(263,427)
(264,426)(265,681)(266,684)(267,683)(268,682)(269,677)(270,680)(271,679)
(272,678)(273,673)(274,676)(275,675)(276,674)(277,669)(278,672)(279,671)
(280,670)(281,665)(282,668)(283,667)(284,666)(285,661)(286,664)(287,663)
(288,662)(289,789)(290,792)(291,791)(292,790)(293,785)(294,788)(295,787)
(296,786)(297,781)(298,784)(299,783)(300,782)(301,777)(302,780)(303,779)
(304,778)(305,773)(306,776)(307,775)(308,774)(309,769)(310,772)(311,771)
(312,770)(313,765)(314,768)(315,767)(316,766)(317,761)(318,764)(319,763)
(320,762)(321,757)(322,760)(323,759)(324,758)(325,753)(326,756)(327,755)
(328,754)(329,749)(330,752)(331,751)(332,750)(333,745)(334,748)(335,747)
(336,746)(337,741)(338,744)(339,743)(340,742)(341,737)(342,740)(343,739)
(344,738)(345,733)(346,736)(347,735)(348,734)(349,729)(350,732)(351,731)
(352,730)(353,725)(354,728)(355,727)(356,726)(357,721)(358,724)(359,723)
(360,722)(361,717)(362,720)(363,719)(364,718)(365,713)(366,716)(367,715)
(368,714)(369,709)(370,712)(371,711)(372,710)(373,705)(374,708)(375,707)
(376,706)(377,701)(378,704)(379,703)(380,702)(381,697)(382,700)(383,699)
(384,698)(385,693)(386,696)(387,695)(388,694)(389,689)(390,692)(391,691)
(392,690)(393,685)(394,688)(395,687)(396,686);
s2 := Sym(792)!( 1,398)( 2,397)( 3,400)( 4,399)( 5,402)( 6,401)( 7,404)
( 8,403)( 9,406)( 10,405)( 11,408)( 12,407)( 13,410)( 14,409)( 15,412)
( 16,411)( 17,414)( 18,413)( 19,416)( 20,415)( 21,418)( 22,417)( 23,420)
( 24,419)( 25,422)( 26,421)( 27,424)( 28,423)( 29,426)( 30,425)( 31,428)
( 32,427)( 33,430)( 34,429)( 35,432)( 36,431)( 37,434)( 38,433)( 39,436)
( 40,435)( 41,438)( 42,437)( 43,440)( 44,439)( 45,442)( 46,441)( 47,444)
( 48,443)( 49,446)( 50,445)( 51,448)( 52,447)( 53,450)( 54,449)( 55,452)
( 56,451)( 57,454)( 58,453)( 59,456)( 60,455)( 61,458)( 62,457)( 63,460)
( 64,459)( 65,462)( 66,461)( 67,464)( 68,463)( 69,466)( 70,465)( 71,468)
( 72,467)( 73,470)( 74,469)( 75,472)( 76,471)( 77,474)( 78,473)( 79,476)
( 80,475)( 81,478)( 82,477)( 83,480)( 84,479)( 85,482)( 86,481)( 87,484)
( 88,483)( 89,486)( 90,485)( 91,488)( 92,487)( 93,490)( 94,489)( 95,492)
( 96,491)( 97,494)( 98,493)( 99,496)(100,495)(101,498)(102,497)(103,500)
(104,499)(105,502)(106,501)(107,504)(108,503)(109,506)(110,505)(111,508)
(112,507)(113,510)(114,509)(115,512)(116,511)(117,514)(118,513)(119,516)
(120,515)(121,518)(122,517)(123,520)(124,519)(125,522)(126,521)(127,524)
(128,523)(129,526)(130,525)(131,528)(132,527)(133,530)(134,529)(135,532)
(136,531)(137,534)(138,533)(139,536)(140,535)(141,538)(142,537)(143,540)
(144,539)(145,542)(146,541)(147,544)(148,543)(149,546)(150,545)(151,548)
(152,547)(153,550)(154,549)(155,552)(156,551)(157,554)(158,553)(159,556)
(160,555)(161,558)(162,557)(163,560)(164,559)(165,562)(166,561)(167,564)
(168,563)(169,566)(170,565)(171,568)(172,567)(173,570)(174,569)(175,572)
(176,571)(177,574)(178,573)(179,576)(180,575)(181,578)(182,577)(183,580)
(184,579)(185,582)(186,581)(187,584)(188,583)(189,586)(190,585)(191,588)
(192,587)(193,590)(194,589)(195,592)(196,591)(197,594)(198,593)(199,596)
(200,595)(201,598)(202,597)(203,600)(204,599)(205,602)(206,601)(207,604)
(208,603)(209,606)(210,605)(211,608)(212,607)(213,610)(214,609)(215,612)
(216,611)(217,614)(218,613)(219,616)(220,615)(221,618)(222,617)(223,620)
(224,619)(225,622)(226,621)(227,624)(228,623)(229,626)(230,625)(231,628)
(232,627)(233,630)(234,629)(235,632)(236,631)(237,634)(238,633)(239,636)
(240,635)(241,638)(242,637)(243,640)(244,639)(245,642)(246,641)(247,644)
(248,643)(249,646)(250,645)(251,648)(252,647)(253,650)(254,649)(255,652)
(256,651)(257,654)(258,653)(259,656)(260,655)(261,658)(262,657)(263,660)
(264,659)(265,662)(266,661)(267,664)(268,663)(269,666)(270,665)(271,668)
(272,667)(273,670)(274,669)(275,672)(276,671)(277,674)(278,673)(279,676)
(280,675)(281,678)(282,677)(283,680)(284,679)(285,682)(286,681)(287,684)
(288,683)(289,686)(290,685)(291,688)(292,687)(293,690)(294,689)(295,692)
(296,691)(297,694)(298,693)(299,696)(300,695)(301,698)(302,697)(303,700)
(304,699)(305,702)(306,701)(307,704)(308,703)(309,706)(310,705)(311,708)
(312,707)(313,710)(314,709)(315,712)(316,711)(317,714)(318,713)(319,716)
(320,715)(321,718)(322,717)(323,720)(324,719)(325,722)(326,721)(327,724)
(328,723)(329,726)(330,725)(331,728)(332,727)(333,730)(334,729)(335,732)
(336,731)(337,734)(338,733)(339,736)(340,735)(341,738)(342,737)(343,740)
(344,739)(345,742)(346,741)(347,744)(348,743)(349,746)(350,745)(351,748)
(352,747)(353,750)(354,749)(355,752)(356,751)(357,754)(358,753)(359,756)
(360,755)(361,758)(362,757)(363,760)(364,759)(365,762)(366,761)(367,764)
(368,763)(369,766)(370,765)(371,768)(372,767)(373,770)(374,769)(375,772)
(376,771)(377,774)(378,773)(379,776)(380,775)(381,778)(382,777)(383,780)
(384,779)(385,782)(386,781)(387,784)(388,783)(389,786)(390,785)(391,788)
(392,787)(393,790)(394,789)(395,792)(396,791);
poly := sub<Sym(792)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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