Polytope of Type {4,198}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,198}*1584b
if this polytope has a name.
Group : SmallGroup(1584,366)
Rank : 3
Schlafli Type : {4,198}
Number of vertices, edges, etc : 4, 396, 198
Order of s₀s₁s₂ : 198
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,99}*792
   3-fold quotients : {4,66}*528b
   6-fold quotients : {4,33}*264
   11-fold quotients : {4,18}*144b
   22-fold quotients : {4,9}*72
   33-fold quotients : {4,6}*48c
   66-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)
(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)
(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)
(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480)
(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)(494,496)
(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)(510,512)
(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)(526,528)
(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)(542,544)
(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)(558,560)
(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)(574,576)
(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)(590,592)
(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)(606,608)
(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)(622,624)
(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)(638,640)
(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)(654,656)
(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)(670,672)
(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)(686,688)
(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)(702,704)
(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)(718,720)
(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)(734,736)
(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)(750,752)
(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)(766,768)
(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)(782,784)
(785,787)(786,788)(789,791)(790,792);;
s1 := (  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);;
s2 := (  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);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(792)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)
(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)
(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)
(478,480)(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)
(494,496)(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)
(510,512)(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)
(526,528)(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)
(542,544)(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)
(558,560)(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)
(574,576)(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)
(590,592)(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)
(606,608)(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)
(622,624)(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)
(638,640)(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)
(654,656)(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)
(670,672)(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)
(686,688)(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)
(702,704)(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)
(718,720)(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)
(734,736)(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)
(750,752)(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)
(766,768)(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)
(782,784)(785,787)(786,788)(789,791)(790,792);
s1 := 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);
s2 := 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);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*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*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*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*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*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*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*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*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*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*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*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*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*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*s1*s2*s1*s2 >;

References : None.
to this polytope