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