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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}*1472a
Also Known As : {184,4|2}. if this polytope has another name.
Group : SmallGroup(1472,685)
Rank : 3
Schlafli Type : {184,4}
Number of vertices, edges, etc : 184, 368, 4
Order of s0s1s2 : 184
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
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 : {92,4}*736, {184,2}*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}*64a
   46-fold quotients : {4,4}*32, {8,2}*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)( 47,415)( 48,437)
( 49,436)( 50,435)( 51,434)( 52,433)( 53,432)( 54,431)( 55,430)( 56,429)
( 57,428)( 58,427)( 59,426)( 60,425)( 61,424)( 62,423)( 63,422)( 64,421)
( 65,420)( 66,419)( 67,418)( 68,417)( 69,416)( 70,438)( 71,460)( 72,459)
( 73,458)( 74,457)( 75,456)( 76,455)( 77,454)( 78,453)( 79,452)( 80,451)
( 81,450)( 82,449)( 83,448)( 84,447)( 85,446)( 86,445)( 87,444)( 88,443)
( 89,442)( 90,441)( 91,440)( 92,439)( 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)(139,530)(140,552)(141,551)(142,550)(143,549)(144,548)
(145,547)(146,546)(147,545)(148,544)(149,543)(150,542)(151,541)(152,540)
(153,539)(154,538)(155,537)(156,536)(157,535)(158,534)(159,533)(160,532)
(161,531)(162,507)(163,529)(164,528)(165,527)(166,526)(167,525)(168,524)
(169,523)(170,522)(171,521)(172,520)(173,519)(174,518)(175,517)(176,516)
(177,515)(178,514)(179,513)(180,512)(181,511)(182,510)(183,509)(184,508)
(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)(231,599)(232,621)
(233,620)(234,619)(235,618)(236,617)(237,616)(238,615)(239,614)(240,613)
(241,612)(242,611)(243,610)(244,609)(245,608)(246,607)(247,606)(248,605)
(249,604)(250,603)(251,602)(252,601)(253,600)(254,622)(255,644)(256,643)
(257,642)(258,641)(259,640)(260,639)(261,638)(262,637)(263,636)(264,635)
(265,634)(266,633)(267,632)(268,631)(269,630)(270,629)(271,628)(272,627)
(273,626)(274,625)(275,624)(276,623)(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)(323,714)(324,736)(325,735)(326,734)(327,733)(328,732)
(329,731)(330,730)(331,729)(332,728)(333,727)(334,726)(335,725)(336,724)
(337,723)(338,722)(339,721)(340,720)(341,719)(342,718)(343,717)(344,716)
(345,715)(346,691)(347,713)(348,712)(349,711)(350,710)(351,709)(352,708)
(353,707)(354,706)(355,705)(356,704)(357,703)(358,702)(359,701)(360,700)
(361,699)(362,698)(363,697)(364,696)(365,695)(366,694)(367,693)(368,692);;
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)(553,692)(554,691)(555,713)(556,712)(557,711)(558,710)
(559,709)(560,708)(561,707)(562,706)(563,705)(564,704)(565,703)(566,702)
(567,701)(568,700)(569,699)(570,698)(571,697)(572,696)(573,695)(574,694)
(575,693)(576,715)(577,714)(578,736)(579,735)(580,734)(581,733)(582,732)
(583,731)(584,730)(585,729)(586,728)(587,727)(588,726)(589,725)(590,724)
(591,723)(592,722)(593,721)(594,720)(595,719)(596,718)(597,717)(598,716)
(599,646)(600,645)(601,667)(602,666)(603,665)(604,664)(605,663)(606,662)
(607,661)(608,660)(609,659)(610,658)(611,657)(612,656)(613,655)(614,654)
(615,653)(616,652)(617,651)(618,650)(619,649)(620,648)(621,647)(622,669)
(623,668)(624,690)(625,689)(626,688)(627,687)(628,686)(629,685)(630,684)
(631,683)(632,682)(633,681)(634,680)(635,679)(636,678)(637,677)(638,676)
(639,675)(640,674)(641,673)(642,672)(643,671)(644,670);;
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)( 93,277)( 94,278)( 95,279)( 96,280)
( 97,281)( 98,282)( 99,283)(100,284)(101,285)(102,286)(103,287)(104,288)
(105,289)(106,290)(107,291)(108,292)(109,293)(110,294)(111,295)(112,296)
(113,297)(114,298)(115,299)(116,300)(117,301)(118,302)(119,303)(120,304)
(121,305)(122,306)(123,307)(124,308)(125,309)(126,310)(127,311)(128,312)
(129,313)(130,314)(131,315)(132,316)(133,317)(134,318)(135,319)(136,320)
(137,321)(138,322)(139,323)(140,324)(141,325)(142,326)(143,327)(144,328)
(145,329)(146,330)(147,331)(148,332)(149,333)(150,334)(151,335)(152,336)
(153,337)(154,338)(155,339)(156,340)(157,341)(158,342)(159,343)(160,344)
(161,345)(162,346)(163,347)(164,348)(165,349)(166,350)(167,351)(168,352)
(169,353)(170,354)(171,355)(172,356)(173,357)(174,358)(175,359)(176,360)
(177,361)(178,362)(179,363)(180,364)(181,365)(182,366)(183,367)(184,368)
(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)(461,645)(462,646)(463,647)(464,648)
(465,649)(466,650)(467,651)(468,652)(469,653)(470,654)(471,655)(472,656)
(473,657)(474,658)(475,659)(476,660)(477,661)(478,662)(479,663)(480,664)
(481,665)(482,666)(483,667)(484,668)(485,669)(486,670)(487,671)(488,672)
(489,673)(490,674)(491,675)(492,676)(493,677)(494,678)(495,679)(496,680)
(497,681)(498,682)(499,683)(500,684)(501,685)(502,686)(503,687)(504,688)
(505,689)(506,690)(507,691)(508,692)(509,693)(510,694)(511,695)(512,696)
(513,697)(514,698)(515,699)(516,700)(517,701)(518,702)(519,703)(520,704)
(521,705)(522,706)(523,707)(524,708)(525,709)(526,710)(527,711)(528,712)
(529,713)(530,714)(531,715)(532,716)(533,717)(534,718)(535,719)(536,720)
(537,721)(538,722)(539,723)(540,724)(541,725)(542,726)(543,727)(544,728)
(545,729)(546,730)(547,731)(548,732)(549,733)(550,734)(551,735)(552,736);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 47,415)
( 48,437)( 49,436)( 50,435)( 51,434)( 52,433)( 53,432)( 54,431)( 55,430)
( 56,429)( 57,428)( 58,427)( 59,426)( 60,425)( 61,424)( 62,423)( 63,422)
( 64,421)( 65,420)( 66,419)( 67,418)( 68,417)( 69,416)( 70,438)( 71,460)
( 72,459)( 73,458)( 74,457)( 75,456)( 76,455)( 77,454)( 78,453)( 79,452)
( 80,451)( 81,450)( 82,449)( 83,448)( 84,447)( 85,446)( 86,445)( 87,444)
( 88,443)( 89,442)( 90,441)( 91,440)( 92,439)( 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)(139,530)(140,552)(141,551)(142,550)(143,549)
(144,548)(145,547)(146,546)(147,545)(148,544)(149,543)(150,542)(151,541)
(152,540)(153,539)(154,538)(155,537)(156,536)(157,535)(158,534)(159,533)
(160,532)(161,531)(162,507)(163,529)(164,528)(165,527)(166,526)(167,525)
(168,524)(169,523)(170,522)(171,521)(172,520)(173,519)(174,518)(175,517)
(176,516)(177,515)(178,514)(179,513)(180,512)(181,511)(182,510)(183,509)
(184,508)(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)(231,599)
(232,621)(233,620)(234,619)(235,618)(236,617)(237,616)(238,615)(239,614)
(240,613)(241,612)(242,611)(243,610)(244,609)(245,608)(246,607)(247,606)
(248,605)(249,604)(250,603)(251,602)(252,601)(253,600)(254,622)(255,644)
(256,643)(257,642)(258,641)(259,640)(260,639)(261,638)(262,637)(263,636)
(264,635)(265,634)(266,633)(267,632)(268,631)(269,630)(270,629)(271,628)
(272,627)(273,626)(274,625)(275,624)(276,623)(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)(323,714)(324,736)(325,735)(326,734)(327,733)
(328,732)(329,731)(330,730)(331,729)(332,728)(333,727)(334,726)(335,725)
(336,724)(337,723)(338,722)(339,721)(340,720)(341,719)(342,718)(343,717)
(344,716)(345,715)(346,691)(347,713)(348,712)(349,711)(350,710)(351,709)
(352,708)(353,707)(354,706)(355,705)(356,704)(357,703)(358,702)(359,701)
(360,700)(361,699)(362,698)(363,697)(364,696)(365,695)(366,694)(367,693)
(368,692);
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)(553,692)(554,691)(555,713)(556,712)(557,711)
(558,710)(559,709)(560,708)(561,707)(562,706)(563,705)(564,704)(565,703)
(566,702)(567,701)(568,700)(569,699)(570,698)(571,697)(572,696)(573,695)
(574,694)(575,693)(576,715)(577,714)(578,736)(579,735)(580,734)(581,733)
(582,732)(583,731)(584,730)(585,729)(586,728)(587,727)(588,726)(589,725)
(590,724)(591,723)(592,722)(593,721)(594,720)(595,719)(596,718)(597,717)
(598,716)(599,646)(600,645)(601,667)(602,666)(603,665)(604,664)(605,663)
(606,662)(607,661)(608,660)(609,659)(610,658)(611,657)(612,656)(613,655)
(614,654)(615,653)(616,652)(617,651)(618,650)(619,649)(620,648)(621,647)
(622,669)(623,668)(624,690)(625,689)(626,688)(627,687)(628,686)(629,685)
(630,684)(631,683)(632,682)(633,681)(634,680)(635,679)(636,678)(637,677)
(638,676)(639,675)(640,674)(641,673)(642,672)(643,671)(644,670);
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)( 93,277)( 94,278)( 95,279)
( 96,280)( 97,281)( 98,282)( 99,283)(100,284)(101,285)(102,286)(103,287)
(104,288)(105,289)(106,290)(107,291)(108,292)(109,293)(110,294)(111,295)
(112,296)(113,297)(114,298)(115,299)(116,300)(117,301)(118,302)(119,303)
(120,304)(121,305)(122,306)(123,307)(124,308)(125,309)(126,310)(127,311)
(128,312)(129,313)(130,314)(131,315)(132,316)(133,317)(134,318)(135,319)
(136,320)(137,321)(138,322)(139,323)(140,324)(141,325)(142,326)(143,327)
(144,328)(145,329)(146,330)(147,331)(148,332)(149,333)(150,334)(151,335)
(152,336)(153,337)(154,338)(155,339)(156,340)(157,341)(158,342)(159,343)
(160,344)(161,345)(162,346)(163,347)(164,348)(165,349)(166,350)(167,351)
(168,352)(169,353)(170,354)(171,355)(172,356)(173,357)(174,358)(175,359)
(176,360)(177,361)(178,362)(179,363)(180,364)(181,365)(182,366)(183,367)
(184,368)(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)(461,645)(462,646)(463,647)
(464,648)(465,649)(466,650)(467,651)(468,652)(469,653)(470,654)(471,655)
(472,656)(473,657)(474,658)(475,659)(476,660)(477,661)(478,662)(479,663)
(480,664)(481,665)(482,666)(483,667)(484,668)(485,669)(486,670)(487,671)
(488,672)(489,673)(490,674)(491,675)(492,676)(493,677)(494,678)(495,679)
(496,680)(497,681)(498,682)(499,683)(500,684)(501,685)(502,686)(503,687)
(504,688)(505,689)(506,690)(507,691)(508,692)(509,693)(510,694)(511,695)
(512,696)(513,697)(514,698)(515,699)(516,700)(517,701)(518,702)(519,703)
(520,704)(521,705)(522,706)(523,707)(524,708)(525,709)(526,710)(527,711)
(528,712)(529,713)(530,714)(531,715)(532,716)(533,717)(534,718)(535,719)
(536,720)(537,721)(538,722)(539,723)(540,724)(541,725)(542,726)(543,727)
(544,728)(545,729)(546,730)(547,731)(548,732)(549,733)(550,734)(551,735)
(552,736);
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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