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Polytope of Type {184,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {184,4}*1472b
if this polytope has a name.
Group : SmallGroup(1472,719)
Rank : 3
Schlafli Type : {184,4}
Number of vertices, edges, etc : 184, 368, 4
Order of s0s1s2 : 184
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   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 : {92,4}*736
   4-fold quotients : {92,2}*368, {46,4}*368
   8-fold quotients : {46,2}*184
   16-fold quotients : {23,2}*92
   23-fold quotients : {8,4}*64b
   46-fold quotients : {4,4}*32
   92-fold quotients : {2,4}*16, {4,2}*16
   184-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,369)(  2,391)(  3,390)(  4,389)(  5,388)(  6,387)(  7,386)(  8,385)
(  9,384)( 10,383)( 11,382)( 12,381)( 13,380)( 14,379)( 15,378)( 16,377)
( 17,376)( 18,375)( 19,374)( 20,373)( 21,372)( 22,371)( 23,370)( 24,392)
( 25,414)( 26,413)( 27,412)( 28,411)( 29,410)( 30,409)( 31,408)( 32,407)
( 33,406)( 34,405)( 35,404)( 36,403)( 37,402)( 38,401)( 39,400)( 40,399)
( 41,398)( 42,397)( 43,396)( 44,395)( 45,394)( 46,393)( 47,438)( 48,460)
( 49,459)( 50,458)( 51,457)( 52,456)( 53,455)( 54,454)( 55,453)( 56,452)
( 57,451)( 58,450)( 59,449)( 60,448)( 61,447)( 62,446)( 63,445)( 64,444)
( 65,443)( 66,442)( 67,441)( 68,440)( 69,439)( 70,415)( 71,437)( 72,436)
( 73,435)( 74,434)( 75,433)( 76,432)( 77,431)( 78,430)( 79,429)( 80,428)
( 81,427)( 82,426)( 83,425)( 84,424)( 85,423)( 86,422)( 87,421)( 88,420)
( 89,419)( 90,418)( 91,417)( 92,416)( 93,484)( 94,506)( 95,505)( 96,504)
( 97,503)( 98,502)( 99,501)(100,500)(101,499)(102,498)(103,497)(104,496)
(105,495)(106,494)(107,493)(108,492)(109,491)(110,490)(111,489)(112,488)
(113,487)(114,486)(115,485)(116,461)(117,483)(118,482)(119,481)(120,480)
(121,479)(122,478)(123,477)(124,476)(125,475)(126,474)(127,473)(128,472)
(129,471)(130,470)(131,469)(132,468)(133,467)(134,466)(135,465)(136,464)
(137,463)(138,462)(139,507)(140,529)(141,528)(142,527)(143,526)(144,525)
(145,524)(146,523)(147,522)(148,521)(149,520)(150,519)(151,518)(152,517)
(153,516)(154,515)(155,514)(156,513)(157,512)(158,511)(159,510)(160,509)
(161,508)(162,530)(163,552)(164,551)(165,550)(166,549)(167,548)(168,547)
(169,546)(170,545)(171,544)(172,543)(173,542)(174,541)(175,540)(176,539)
(177,538)(178,537)(179,536)(180,535)(181,534)(182,533)(183,532)(184,531)
(185,553)(186,575)(187,574)(188,573)(189,572)(190,571)(191,570)(192,569)
(193,568)(194,567)(195,566)(196,565)(197,564)(198,563)(199,562)(200,561)
(201,560)(202,559)(203,558)(204,557)(205,556)(206,555)(207,554)(208,576)
(209,598)(210,597)(211,596)(212,595)(213,594)(214,593)(215,592)(216,591)
(217,590)(218,589)(219,588)(220,587)(221,586)(222,585)(223,584)(224,583)
(225,582)(226,581)(227,580)(228,579)(229,578)(230,577)(231,622)(232,644)
(233,643)(234,642)(235,641)(236,640)(237,639)(238,638)(239,637)(240,636)
(241,635)(242,634)(243,633)(244,632)(245,631)(246,630)(247,629)(248,628)
(249,627)(250,626)(251,625)(252,624)(253,623)(254,599)(255,621)(256,620)
(257,619)(258,618)(259,617)(260,616)(261,615)(262,614)(263,613)(264,612)
(265,611)(266,610)(267,609)(268,608)(269,607)(270,606)(271,605)(272,604)
(273,603)(274,602)(275,601)(276,600)(277,668)(278,690)(279,689)(280,688)
(281,687)(282,686)(283,685)(284,684)(285,683)(286,682)(287,681)(288,680)
(289,679)(290,678)(291,677)(292,676)(293,675)(294,674)(295,673)(296,672)
(297,671)(298,670)(299,669)(300,645)(301,667)(302,666)(303,665)(304,664)
(305,663)(306,662)(307,661)(308,660)(309,659)(310,658)(311,657)(312,656)
(313,655)(314,654)(315,653)(316,652)(317,651)(318,650)(319,649)(320,648)
(321,647)(322,646)(323,691)(324,713)(325,712)(326,711)(327,710)(328,709)
(329,708)(330,707)(331,706)(332,705)(333,704)(334,703)(335,702)(336,701)
(337,700)(338,699)(339,698)(340,697)(341,696)(342,695)(343,694)(344,693)
(345,692)(346,714)(347,736)(348,735)(349,734)(350,733)(351,732)(352,731)
(353,730)(354,729)(355,728)(356,727)(357,726)(358,725)(359,724)(360,723)
(361,722)(362,721)(363,720)(364,719)(365,718)(366,717)(367,716)(368,715);;
s1 := (  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)
( 10, 16)( 11, 15)( 12, 14)( 24, 25)( 26, 46)( 27, 45)( 28, 44)( 29, 43)
( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 48)( 49, 69)
( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)
( 58, 60)( 70, 71)( 72, 92)( 73, 91)( 74, 90)( 75, 89)( 76, 88)( 77, 87)
( 78, 86)( 79, 85)( 80, 84)( 81, 83)( 93,117)( 94,116)( 95,138)( 96,137)
( 97,136)( 98,135)( 99,134)(100,133)(101,132)(102,131)(103,130)(104,129)
(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)(111,122)(112,121)
(113,120)(114,119)(115,118)(139,163)(140,162)(141,184)(142,183)(143,182)
(144,181)(145,180)(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)
(152,173)(153,172)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)
(160,165)(161,164)(185,232)(186,231)(187,253)(188,252)(189,251)(190,250)
(191,249)(192,248)(193,247)(194,246)(195,245)(196,244)(197,243)(198,242)
(199,241)(200,240)(201,239)(202,238)(203,237)(204,236)(205,235)(206,234)
(207,233)(208,255)(209,254)(210,276)(211,275)(212,274)(213,273)(214,272)
(215,271)(216,270)(217,269)(218,268)(219,267)(220,266)(221,265)(222,264)
(223,263)(224,262)(225,261)(226,260)(227,259)(228,258)(229,257)(230,256)
(277,347)(278,346)(279,368)(280,367)(281,366)(282,365)(283,364)(284,363)
(285,362)(286,361)(287,360)(288,359)(289,358)(290,357)(291,356)(292,355)
(293,354)(294,353)(295,352)(296,351)(297,350)(298,349)(299,348)(300,324)
(301,323)(302,345)(303,344)(304,343)(305,342)(306,341)(307,340)(308,339)
(309,338)(310,337)(311,336)(312,335)(313,334)(314,333)(315,332)(316,331)
(317,330)(318,329)(319,328)(320,327)(321,326)(322,325)(369,462)(370,461)
(371,483)(372,482)(373,481)(374,480)(375,479)(376,478)(377,477)(378,476)
(379,475)(380,474)(381,473)(382,472)(383,471)(384,470)(385,469)(386,468)
(387,467)(388,466)(389,465)(390,464)(391,463)(392,485)(393,484)(394,506)
(395,505)(396,504)(397,503)(398,502)(399,501)(400,500)(401,499)(402,498)
(403,497)(404,496)(405,495)(406,494)(407,493)(408,492)(409,491)(410,490)
(411,489)(412,488)(413,487)(414,486)(415,508)(416,507)(417,529)(418,528)
(419,527)(420,526)(421,525)(422,524)(423,523)(424,522)(425,521)(426,520)
(427,519)(428,518)(429,517)(430,516)(431,515)(432,514)(433,513)(434,512)
(435,511)(436,510)(437,509)(438,531)(439,530)(440,552)(441,551)(442,550)
(443,549)(444,548)(445,547)(446,546)(447,545)(448,544)(449,543)(450,542)
(451,541)(452,540)(453,539)(454,538)(455,537)(456,536)(457,535)(458,534)
(459,533)(460,532)(553,715)(554,714)(555,736)(556,735)(557,734)(558,733)
(559,732)(560,731)(561,730)(562,729)(563,728)(564,727)(565,726)(566,725)
(567,724)(568,723)(569,722)(570,721)(571,720)(572,719)(573,718)(574,717)
(575,716)(576,692)(577,691)(578,713)(579,712)(580,711)(581,710)(582,709)
(583,708)(584,707)(585,706)(586,705)(587,704)(588,703)(589,702)(590,701)
(591,700)(592,699)(593,698)(594,697)(595,696)(596,695)(597,694)(598,693)
(599,669)(600,668)(601,690)(602,689)(603,688)(604,687)(605,686)(606,685)
(607,684)(608,683)(609,682)(610,681)(611,680)(612,679)(613,678)(614,677)
(615,676)(616,675)(617,674)(618,673)(619,672)(620,671)(621,670)(622,646)
(623,645)(624,667)(625,666)(626,665)(627,664)(628,663)(629,662)(630,661)
(631,660)(632,659)(633,658)(634,657)(635,656)(636,655)(637,654)(638,653)
(639,652)(640,651)(641,650)(642,649)(643,648)(644,647);;
s2 := (  1,185)(  2,186)(  3,187)(  4,188)(  5,189)(  6,190)(  7,191)(  8,192)
(  9,193)( 10,194)( 11,195)( 12,196)( 13,197)( 14,198)( 15,199)( 16,200)
( 17,201)( 18,202)( 19,203)( 20,204)( 21,205)( 22,206)( 23,207)( 24,208)
( 25,209)( 26,210)( 27,211)( 28,212)( 29,213)( 30,214)( 31,215)( 32,216)
( 33,217)( 34,218)( 35,219)( 36,220)( 37,221)( 38,222)( 39,223)( 40,224)
( 41,225)( 42,226)( 43,227)( 44,228)( 45,229)( 46,230)( 47,231)( 48,232)
( 49,233)( 50,234)( 51,235)( 52,236)( 53,237)( 54,238)( 55,239)( 56,240)
( 57,241)( 58,242)( 59,243)( 60,244)( 61,245)( 62,246)( 63,247)( 64,248)
( 65,249)( 66,250)( 67,251)( 68,252)( 69,253)( 70,254)( 71,255)( 72,256)
( 73,257)( 74,258)( 75,259)( 76,260)( 77,261)( 78,262)( 79,263)( 80,264)
( 81,265)( 82,266)( 83,267)( 84,268)( 85,269)( 86,270)( 87,271)( 88,272)
( 89,273)( 90,274)( 91,275)( 92,276)( 93,300)( 94,301)( 95,302)( 96,303)
( 97,304)( 98,305)( 99,306)(100,307)(101,308)(102,309)(103,310)(104,311)
(105,312)(106,313)(107,314)(108,315)(109,316)(110,317)(111,318)(112,319)
(113,320)(114,321)(115,322)(116,277)(117,278)(118,279)(119,280)(120,281)
(121,282)(122,283)(123,284)(124,285)(125,286)(126,287)(127,288)(128,289)
(129,290)(130,291)(131,292)(132,293)(133,294)(134,295)(135,296)(136,297)
(137,298)(138,299)(139,346)(140,347)(141,348)(142,349)(143,350)(144,351)
(145,352)(146,353)(147,354)(148,355)(149,356)(150,357)(151,358)(152,359)
(153,360)(154,361)(155,362)(156,363)(157,364)(158,365)(159,366)(160,367)
(161,368)(162,323)(163,324)(164,325)(165,326)(166,327)(167,328)(168,329)
(169,330)(170,331)(171,332)(172,333)(173,334)(174,335)(175,336)(176,337)
(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,344)(184,345)
(369,553)(370,554)(371,555)(372,556)(373,557)(374,558)(375,559)(376,560)
(377,561)(378,562)(379,563)(380,564)(381,565)(382,566)(383,567)(384,568)
(385,569)(386,570)(387,571)(388,572)(389,573)(390,574)(391,575)(392,576)
(393,577)(394,578)(395,579)(396,580)(397,581)(398,582)(399,583)(400,584)
(401,585)(402,586)(403,587)(404,588)(405,589)(406,590)(407,591)(408,592)
(409,593)(410,594)(411,595)(412,596)(413,597)(414,598)(415,599)(416,600)
(417,601)(418,602)(419,603)(420,604)(421,605)(422,606)(423,607)(424,608)
(425,609)(426,610)(427,611)(428,612)(429,613)(430,614)(431,615)(432,616)
(433,617)(434,618)(435,619)(436,620)(437,621)(438,622)(439,623)(440,624)
(441,625)(442,626)(443,627)(444,628)(445,629)(446,630)(447,631)(448,632)
(449,633)(450,634)(451,635)(452,636)(453,637)(454,638)(455,639)(456,640)
(457,641)(458,642)(459,643)(460,644)(461,668)(462,669)(463,670)(464,671)
(465,672)(466,673)(467,674)(468,675)(469,676)(470,677)(471,678)(472,679)
(473,680)(474,681)(475,682)(476,683)(477,684)(478,685)(479,686)(480,687)
(481,688)(482,689)(483,690)(484,645)(485,646)(486,647)(487,648)(488,649)
(489,650)(490,651)(491,652)(492,653)(493,654)(494,655)(495,656)(496,657)
(497,658)(498,659)(499,660)(500,661)(501,662)(502,663)(503,664)(504,665)
(505,666)(506,667)(507,714)(508,715)(509,716)(510,717)(511,718)(512,719)
(513,720)(514,721)(515,722)(516,723)(517,724)(518,725)(519,726)(520,727)
(521,728)(522,729)(523,730)(524,731)(525,732)(526,733)(527,734)(528,735)
(529,736)(530,691)(531,692)(532,693)(533,694)(534,695)(535,696)(536,697)
(537,698)(538,699)(539,700)(540,701)(541,702)(542,703)(543,704)(544,705)
(545,706)(546,707)(547,708)(548,709)(549,710)(550,711)(551,712)(552,713);;
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*s2*s1*s2*s1*s0*s1*s0*s2*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(736)!(  1,369)(  2,391)(  3,390)(  4,389)(  5,388)(  6,387)(  7,386)
(  8,385)(  9,384)( 10,383)( 11,382)( 12,381)( 13,380)( 14,379)( 15,378)
( 16,377)( 17,376)( 18,375)( 19,374)( 20,373)( 21,372)( 22,371)( 23,370)
( 24,392)( 25,414)( 26,413)( 27,412)( 28,411)( 29,410)( 30,409)( 31,408)
( 32,407)( 33,406)( 34,405)( 35,404)( 36,403)( 37,402)( 38,401)( 39,400)
( 40,399)( 41,398)( 42,397)( 43,396)( 44,395)( 45,394)( 46,393)( 47,438)
( 48,460)( 49,459)( 50,458)( 51,457)( 52,456)( 53,455)( 54,454)( 55,453)
( 56,452)( 57,451)( 58,450)( 59,449)( 60,448)( 61,447)( 62,446)( 63,445)
( 64,444)( 65,443)( 66,442)( 67,441)( 68,440)( 69,439)( 70,415)( 71,437)
( 72,436)( 73,435)( 74,434)( 75,433)( 76,432)( 77,431)( 78,430)( 79,429)
( 80,428)( 81,427)( 82,426)( 83,425)( 84,424)( 85,423)( 86,422)( 87,421)
( 88,420)( 89,419)( 90,418)( 91,417)( 92,416)( 93,484)( 94,506)( 95,505)
( 96,504)( 97,503)( 98,502)( 99,501)(100,500)(101,499)(102,498)(103,497)
(104,496)(105,495)(106,494)(107,493)(108,492)(109,491)(110,490)(111,489)
(112,488)(113,487)(114,486)(115,485)(116,461)(117,483)(118,482)(119,481)
(120,480)(121,479)(122,478)(123,477)(124,476)(125,475)(126,474)(127,473)
(128,472)(129,471)(130,470)(131,469)(132,468)(133,467)(134,466)(135,465)
(136,464)(137,463)(138,462)(139,507)(140,529)(141,528)(142,527)(143,526)
(144,525)(145,524)(146,523)(147,522)(148,521)(149,520)(150,519)(151,518)
(152,517)(153,516)(154,515)(155,514)(156,513)(157,512)(158,511)(159,510)
(160,509)(161,508)(162,530)(163,552)(164,551)(165,550)(166,549)(167,548)
(168,547)(169,546)(170,545)(171,544)(172,543)(173,542)(174,541)(175,540)
(176,539)(177,538)(178,537)(179,536)(180,535)(181,534)(182,533)(183,532)
(184,531)(185,553)(186,575)(187,574)(188,573)(189,572)(190,571)(191,570)
(192,569)(193,568)(194,567)(195,566)(196,565)(197,564)(198,563)(199,562)
(200,561)(201,560)(202,559)(203,558)(204,557)(205,556)(206,555)(207,554)
(208,576)(209,598)(210,597)(211,596)(212,595)(213,594)(214,593)(215,592)
(216,591)(217,590)(218,589)(219,588)(220,587)(221,586)(222,585)(223,584)
(224,583)(225,582)(226,581)(227,580)(228,579)(229,578)(230,577)(231,622)
(232,644)(233,643)(234,642)(235,641)(236,640)(237,639)(238,638)(239,637)
(240,636)(241,635)(242,634)(243,633)(244,632)(245,631)(246,630)(247,629)
(248,628)(249,627)(250,626)(251,625)(252,624)(253,623)(254,599)(255,621)
(256,620)(257,619)(258,618)(259,617)(260,616)(261,615)(262,614)(263,613)
(264,612)(265,611)(266,610)(267,609)(268,608)(269,607)(270,606)(271,605)
(272,604)(273,603)(274,602)(275,601)(276,600)(277,668)(278,690)(279,689)
(280,688)(281,687)(282,686)(283,685)(284,684)(285,683)(286,682)(287,681)
(288,680)(289,679)(290,678)(291,677)(292,676)(293,675)(294,674)(295,673)
(296,672)(297,671)(298,670)(299,669)(300,645)(301,667)(302,666)(303,665)
(304,664)(305,663)(306,662)(307,661)(308,660)(309,659)(310,658)(311,657)
(312,656)(313,655)(314,654)(315,653)(316,652)(317,651)(318,650)(319,649)
(320,648)(321,647)(322,646)(323,691)(324,713)(325,712)(326,711)(327,710)
(328,709)(329,708)(330,707)(331,706)(332,705)(333,704)(334,703)(335,702)
(336,701)(337,700)(338,699)(339,698)(340,697)(341,696)(342,695)(343,694)
(344,693)(345,692)(346,714)(347,736)(348,735)(349,734)(350,733)(351,732)
(352,731)(353,730)(354,729)(355,728)(356,727)(357,726)(358,725)(359,724)
(360,723)(361,722)(362,721)(363,720)(364,719)(365,718)(366,717)(367,716)
(368,715);
s1 := Sym(736)!(  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)
(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 24, 25)( 26, 46)( 27, 45)( 28, 44)
( 29, 43)( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 48)
( 49, 69)( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)( 56, 62)
( 57, 61)( 58, 60)( 70, 71)( 72, 92)( 73, 91)( 74, 90)( 75, 89)( 76, 88)
( 77, 87)( 78, 86)( 79, 85)( 80, 84)( 81, 83)( 93,117)( 94,116)( 95,138)
( 96,137)( 97,136)( 98,135)( 99,134)(100,133)(101,132)(102,131)(103,130)
(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)(111,122)
(112,121)(113,120)(114,119)(115,118)(139,163)(140,162)(141,184)(142,183)
(143,182)(144,181)(145,180)(146,179)(147,178)(148,177)(149,176)(150,175)
(151,174)(152,173)(153,172)(154,171)(155,170)(156,169)(157,168)(158,167)
(159,166)(160,165)(161,164)(185,232)(186,231)(187,253)(188,252)(189,251)
(190,250)(191,249)(192,248)(193,247)(194,246)(195,245)(196,244)(197,243)
(198,242)(199,241)(200,240)(201,239)(202,238)(203,237)(204,236)(205,235)
(206,234)(207,233)(208,255)(209,254)(210,276)(211,275)(212,274)(213,273)
(214,272)(215,271)(216,270)(217,269)(218,268)(219,267)(220,266)(221,265)
(222,264)(223,263)(224,262)(225,261)(226,260)(227,259)(228,258)(229,257)
(230,256)(277,347)(278,346)(279,368)(280,367)(281,366)(282,365)(283,364)
(284,363)(285,362)(286,361)(287,360)(288,359)(289,358)(290,357)(291,356)
(292,355)(293,354)(294,353)(295,352)(296,351)(297,350)(298,349)(299,348)
(300,324)(301,323)(302,345)(303,344)(304,343)(305,342)(306,341)(307,340)
(308,339)(309,338)(310,337)(311,336)(312,335)(313,334)(314,333)(315,332)
(316,331)(317,330)(318,329)(319,328)(320,327)(321,326)(322,325)(369,462)
(370,461)(371,483)(372,482)(373,481)(374,480)(375,479)(376,478)(377,477)
(378,476)(379,475)(380,474)(381,473)(382,472)(383,471)(384,470)(385,469)
(386,468)(387,467)(388,466)(389,465)(390,464)(391,463)(392,485)(393,484)
(394,506)(395,505)(396,504)(397,503)(398,502)(399,501)(400,500)(401,499)
(402,498)(403,497)(404,496)(405,495)(406,494)(407,493)(408,492)(409,491)
(410,490)(411,489)(412,488)(413,487)(414,486)(415,508)(416,507)(417,529)
(418,528)(419,527)(420,526)(421,525)(422,524)(423,523)(424,522)(425,521)
(426,520)(427,519)(428,518)(429,517)(430,516)(431,515)(432,514)(433,513)
(434,512)(435,511)(436,510)(437,509)(438,531)(439,530)(440,552)(441,551)
(442,550)(443,549)(444,548)(445,547)(446,546)(447,545)(448,544)(449,543)
(450,542)(451,541)(452,540)(453,539)(454,538)(455,537)(456,536)(457,535)
(458,534)(459,533)(460,532)(553,715)(554,714)(555,736)(556,735)(557,734)
(558,733)(559,732)(560,731)(561,730)(562,729)(563,728)(564,727)(565,726)
(566,725)(567,724)(568,723)(569,722)(570,721)(571,720)(572,719)(573,718)
(574,717)(575,716)(576,692)(577,691)(578,713)(579,712)(580,711)(581,710)
(582,709)(583,708)(584,707)(585,706)(586,705)(587,704)(588,703)(589,702)
(590,701)(591,700)(592,699)(593,698)(594,697)(595,696)(596,695)(597,694)
(598,693)(599,669)(600,668)(601,690)(602,689)(603,688)(604,687)(605,686)
(606,685)(607,684)(608,683)(609,682)(610,681)(611,680)(612,679)(613,678)
(614,677)(615,676)(616,675)(617,674)(618,673)(619,672)(620,671)(621,670)
(622,646)(623,645)(624,667)(625,666)(626,665)(627,664)(628,663)(629,662)
(630,661)(631,660)(632,659)(633,658)(634,657)(635,656)(636,655)(637,654)
(638,653)(639,652)(640,651)(641,650)(642,649)(643,648)(644,647);
s2 := Sym(736)!(  1,185)(  2,186)(  3,187)(  4,188)(  5,189)(  6,190)(  7,191)
(  8,192)(  9,193)( 10,194)( 11,195)( 12,196)( 13,197)( 14,198)( 15,199)
( 16,200)( 17,201)( 18,202)( 19,203)( 20,204)( 21,205)( 22,206)( 23,207)
( 24,208)( 25,209)( 26,210)( 27,211)( 28,212)( 29,213)( 30,214)( 31,215)
( 32,216)( 33,217)( 34,218)( 35,219)( 36,220)( 37,221)( 38,222)( 39,223)
( 40,224)( 41,225)( 42,226)( 43,227)( 44,228)( 45,229)( 46,230)( 47,231)
( 48,232)( 49,233)( 50,234)( 51,235)( 52,236)( 53,237)( 54,238)( 55,239)
( 56,240)( 57,241)( 58,242)( 59,243)( 60,244)( 61,245)( 62,246)( 63,247)
( 64,248)( 65,249)( 66,250)( 67,251)( 68,252)( 69,253)( 70,254)( 71,255)
( 72,256)( 73,257)( 74,258)( 75,259)( 76,260)( 77,261)( 78,262)( 79,263)
( 80,264)( 81,265)( 82,266)( 83,267)( 84,268)( 85,269)( 86,270)( 87,271)
( 88,272)( 89,273)( 90,274)( 91,275)( 92,276)( 93,300)( 94,301)( 95,302)
( 96,303)( 97,304)( 98,305)( 99,306)(100,307)(101,308)(102,309)(103,310)
(104,311)(105,312)(106,313)(107,314)(108,315)(109,316)(110,317)(111,318)
(112,319)(113,320)(114,321)(115,322)(116,277)(117,278)(118,279)(119,280)
(120,281)(121,282)(122,283)(123,284)(124,285)(125,286)(126,287)(127,288)
(128,289)(129,290)(130,291)(131,292)(132,293)(133,294)(134,295)(135,296)
(136,297)(137,298)(138,299)(139,346)(140,347)(141,348)(142,349)(143,350)
(144,351)(145,352)(146,353)(147,354)(148,355)(149,356)(150,357)(151,358)
(152,359)(153,360)(154,361)(155,362)(156,363)(157,364)(158,365)(159,366)
(160,367)(161,368)(162,323)(163,324)(164,325)(165,326)(166,327)(167,328)
(168,329)(169,330)(170,331)(171,332)(172,333)(173,334)(174,335)(175,336)
(176,337)(177,338)(178,339)(179,340)(180,341)(181,342)(182,343)(183,344)
(184,345)(369,553)(370,554)(371,555)(372,556)(373,557)(374,558)(375,559)
(376,560)(377,561)(378,562)(379,563)(380,564)(381,565)(382,566)(383,567)
(384,568)(385,569)(386,570)(387,571)(388,572)(389,573)(390,574)(391,575)
(392,576)(393,577)(394,578)(395,579)(396,580)(397,581)(398,582)(399,583)
(400,584)(401,585)(402,586)(403,587)(404,588)(405,589)(406,590)(407,591)
(408,592)(409,593)(410,594)(411,595)(412,596)(413,597)(414,598)(415,599)
(416,600)(417,601)(418,602)(419,603)(420,604)(421,605)(422,606)(423,607)
(424,608)(425,609)(426,610)(427,611)(428,612)(429,613)(430,614)(431,615)
(432,616)(433,617)(434,618)(435,619)(436,620)(437,621)(438,622)(439,623)
(440,624)(441,625)(442,626)(443,627)(444,628)(445,629)(446,630)(447,631)
(448,632)(449,633)(450,634)(451,635)(452,636)(453,637)(454,638)(455,639)
(456,640)(457,641)(458,642)(459,643)(460,644)(461,668)(462,669)(463,670)
(464,671)(465,672)(466,673)(467,674)(468,675)(469,676)(470,677)(471,678)
(472,679)(473,680)(474,681)(475,682)(476,683)(477,684)(478,685)(479,686)
(480,687)(481,688)(482,689)(483,690)(484,645)(485,646)(486,647)(487,648)
(488,649)(489,650)(490,651)(491,652)(492,653)(493,654)(494,655)(495,656)
(496,657)(497,658)(498,659)(499,660)(500,661)(501,662)(502,663)(503,664)
(504,665)(505,666)(506,667)(507,714)(508,715)(509,716)(510,717)(511,718)
(512,719)(513,720)(514,721)(515,722)(516,723)(517,724)(518,725)(519,726)
(520,727)(521,728)(522,729)(523,730)(524,731)(525,732)(526,733)(527,734)
(528,735)(529,736)(530,691)(531,692)(532,693)(533,694)(534,695)(535,696)
(536,697)(537,698)(538,699)(539,700)(540,701)(541,702)(542,703)(543,704)
(544,705)(545,706)(546,707)(547,708)(548,709)(549,710)(550,711)(551,712)
(552,713);
poly := sub<Sym(736)|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*s2*s1*s2*s1*s0*s1*s0*s2*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*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 >; 
 
References : None.
to this polytope