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Polytope of Type {4,4,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,46}*1472
Also Known As : {{4,4|2},{4,46|2}}. if this polytope has another name.
Group : SmallGroup(1472,1033)
Rank : 4
Schlafli Type : {4,4,46}
Number of vertices, edges, etc : 4, 8, 92, 46
Order of s0s1s2s3 : 92
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {2,4,46}*736, {4,2,46}*736
   4-fold quotients : {4,2,23}*368, {2,2,46}*368
   8-fold quotients : {2,2,23}*184
   23-fold quotients : {4,4,2}*64
   46-fold quotients : {2,4,2}*32, {4,2,2}*32
   92-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,369)(  2,370)(  3,371)(  4,372)(  5,373)(  6,374)(  7,375)(  8,376)
(  9,377)( 10,378)( 11,379)( 12,380)( 13,381)( 14,382)( 15,383)( 16,384)
( 17,385)( 18,386)( 19,387)( 20,388)( 21,389)( 22,390)( 23,391)( 24,392)
( 25,393)( 26,394)( 27,395)( 28,396)( 29,397)( 30,398)( 31,399)( 32,400)
( 33,401)( 34,402)( 35,403)( 36,404)( 37,405)( 38,406)( 39,407)( 40,408)
( 41,409)( 42,410)( 43,411)( 44,412)( 45,413)( 46,414)( 47,415)( 48,416)
( 49,417)( 50,418)( 51,419)( 52,420)( 53,421)( 54,422)( 55,423)( 56,424)
( 57,425)( 58,426)( 59,427)( 60,428)( 61,429)( 62,430)( 63,431)( 64,432)
( 65,433)( 66,434)( 67,435)( 68,436)( 69,437)( 70,438)( 71,439)( 72,440)
( 73,441)( 74,442)( 75,443)( 76,444)( 77,445)( 78,446)( 79,447)( 80,448)
( 81,449)( 82,450)( 83,451)( 84,452)( 85,453)( 86,454)( 87,455)( 88,456)
( 89,457)( 90,458)( 91,459)( 92,460)( 93,461)( 94,462)( 95,463)( 96,464)
( 97,465)( 98,466)( 99,467)(100,468)(101,469)(102,470)(103,471)(104,472)
(105,473)(106,474)(107,475)(108,476)(109,477)(110,478)(111,479)(112,480)
(113,481)(114,482)(115,483)(116,484)(117,485)(118,486)(119,487)(120,488)
(121,489)(122,490)(123,491)(124,492)(125,493)(126,494)(127,495)(128,496)
(129,497)(130,498)(131,499)(132,500)(133,501)(134,502)(135,503)(136,504)
(137,505)(138,506)(139,507)(140,508)(141,509)(142,510)(143,511)(144,512)
(145,513)(146,514)(147,515)(148,516)(149,517)(150,518)(151,519)(152,520)
(153,521)(154,522)(155,523)(156,524)(157,525)(158,526)(159,527)(160,528)
(161,529)(162,530)(163,531)(164,532)(165,533)(166,534)(167,535)(168,536)
(169,537)(170,538)(171,539)(172,540)(173,541)(174,542)(175,543)(176,544)
(177,545)(178,546)(179,547)(180,548)(181,549)(182,550)(183,551)(184,552)
(185,553)(186,554)(187,555)(188,556)(189,557)(190,558)(191,559)(192,560)
(193,561)(194,562)(195,563)(196,564)(197,565)(198,566)(199,567)(200,568)
(201,569)(202,570)(203,571)(204,572)(205,573)(206,574)(207,575)(208,576)
(209,577)(210,578)(211,579)(212,580)(213,581)(214,582)(215,583)(216,584)
(217,585)(218,586)(219,587)(220,588)(221,589)(222,590)(223,591)(224,592)
(225,593)(226,594)(227,595)(228,596)(229,597)(230,598)(231,599)(232,600)
(233,601)(234,602)(235,603)(236,604)(237,605)(238,606)(239,607)(240,608)
(241,609)(242,610)(243,611)(244,612)(245,613)(246,614)(247,615)(248,616)
(249,617)(250,618)(251,619)(252,620)(253,621)(254,622)(255,623)(256,624)
(257,625)(258,626)(259,627)(260,628)(261,629)(262,630)(263,631)(264,632)
(265,633)(266,634)(267,635)(268,636)(269,637)(270,638)(271,639)(272,640)
(273,641)(274,642)(275,643)(276,644)(277,645)(278,646)(279,647)(280,648)
(281,649)(282,650)(283,651)(284,652)(285,653)(286,654)(287,655)(288,656)
(289,657)(290,658)(291,659)(292,660)(293,661)(294,662)(295,663)(296,664)
(297,665)(298,666)(299,667)(300,668)(301,669)(302,670)(303,671)(304,672)
(305,673)(306,674)(307,675)(308,676)(309,677)(310,678)(311,679)(312,680)
(313,681)(314,682)(315,683)(316,684)(317,685)(318,686)(319,687)(320,688)
(321,689)(322,690)(323,691)(324,692)(325,693)(326,694)(327,695)(328,696)
(329,697)(330,698)(331,699)(332,700)(333,701)(334,702)(335,703)(336,704)
(337,705)(338,706)(339,707)(340,708)(341,709)(342,710)(343,711)(344,712)
(345,713)(346,714)(347,715)(348,716)(349,717)(350,718)(351,719)(352,720)
(353,721)(354,722)(355,723)(356,724)(357,725)(358,726)(359,727)(360,728)
(361,729)(362,730)(363,731)(364,732)(365,733)(366,734)(367,735)(368,736);;
s1 := (185,208)(186,209)(187,210)(188,211)(189,212)(190,213)(191,214)(192,215)
(193,216)(194,217)(195,218)(196,219)(197,220)(198,221)(199,222)(200,223)
(201,224)(202,225)(203,226)(204,227)(205,228)(206,229)(207,230)(231,254)
(232,255)(233,256)(234,257)(235,258)(236,259)(237,260)(238,261)(239,262)
(240,263)(241,264)(242,265)(243,266)(244,267)(245,268)(246,269)(247,270)
(248,271)(249,272)(250,273)(251,274)(252,275)(253,276)(277,300)(278,301)
(279,302)(280,303)(281,304)(282,305)(283,306)(284,307)(285,308)(286,309)
(287,310)(288,311)(289,312)(290,313)(291,314)(292,315)(293,316)(294,317)
(295,318)(296,319)(297,320)(298,321)(299,322)(323,346)(324,347)(325,348)
(326,349)(327,350)(328,351)(329,352)(330,353)(331,354)(332,355)(333,356)
(334,357)(335,358)(336,359)(337,360)(338,361)(339,362)(340,363)(341,364)
(342,365)(343,366)(344,367)(345,368)(369,415)(370,416)(371,417)(372,418)
(373,419)(374,420)(375,421)(376,422)(377,423)(378,424)(379,425)(380,426)
(381,427)(382,428)(383,429)(384,430)(385,431)(386,432)(387,433)(388,434)
(389,435)(390,436)(391,437)(392,438)(393,439)(394,440)(395,441)(396,442)
(397,443)(398,444)(399,445)(400,446)(401,447)(402,448)(403,449)(404,450)
(405,451)(406,452)(407,453)(408,454)(409,455)(410,456)(411,457)(412,458)
(413,459)(414,460)(461,507)(462,508)(463,509)(464,510)(465,511)(466,512)
(467,513)(468,514)(469,515)(470,516)(471,517)(472,518)(473,519)(474,520)
(475,521)(476,522)(477,523)(478,524)(479,525)(480,526)(481,527)(482,528)
(483,529)(484,530)(485,531)(486,532)(487,533)(488,534)(489,535)(490,536)
(491,537)(492,538)(493,539)(494,540)(495,541)(496,542)(497,543)(498,544)
(499,545)(500,546)(501,547)(502,548)(503,549)(504,550)(505,551)(506,552)
(553,622)(554,623)(555,624)(556,625)(557,626)(558,627)(559,628)(560,629)
(561,630)(562,631)(563,632)(564,633)(565,634)(566,635)(567,636)(568,637)
(569,638)(570,639)(571,640)(572,641)(573,642)(574,643)(575,644)(576,599)
(577,600)(578,601)(579,602)(580,603)(581,604)(582,605)(583,606)(584,607)
(585,608)(586,609)(587,610)(588,611)(589,612)(590,613)(591,614)(592,615)
(593,616)(594,617)(595,618)(596,619)(597,620)(598,621)(645,714)(646,715)
(647,716)(648,717)(649,718)(650,719)(651,720)(652,721)(653,722)(654,723)
(655,724)(656,725)(657,726)(658,727)(659,728)(660,729)(661,730)(662,731)
(663,732)(664,733)(665,734)(666,735)(667,736)(668,691)(669,692)(670,693)
(671,694)(672,695)(673,696)(674,697)(675,698)(676,699)(677,700)(678,701)
(679,702)(680,703)(681,704)(682,705)(683,706)(684,707)(685,708)(686,709)
(687,710)(688,711)(689,712)(690,713);;
s2 := (  1,277)(  2,299)(  3,298)(  4,297)(  5,296)(  6,295)(  7,294)(  8,293)
(  9,292)( 10,291)( 11,290)( 12,289)( 13,288)( 14,287)( 15,286)( 16,285)
( 17,284)( 18,283)( 19,282)( 20,281)( 21,280)( 22,279)( 23,278)( 24,300)
( 25,322)( 26,321)( 27,320)( 28,319)( 29,318)( 30,317)( 31,316)( 32,315)
( 33,314)( 34,313)( 35,312)( 36,311)( 37,310)( 38,309)( 39,308)( 40,307)
( 41,306)( 42,305)( 43,304)( 44,303)( 45,302)( 46,301)( 47,323)( 48,345)
( 49,344)( 50,343)( 51,342)( 52,341)( 53,340)( 54,339)( 55,338)( 56,337)
( 57,336)( 58,335)( 59,334)( 60,333)( 61,332)( 62,331)( 63,330)( 64,329)
( 65,328)( 66,327)( 67,326)( 68,325)( 69,324)( 70,346)( 71,368)( 72,367)
( 73,366)( 74,365)( 75,364)( 76,363)( 77,362)( 78,361)( 79,360)( 80,359)
( 81,358)( 82,357)( 83,356)( 84,355)( 85,354)( 86,353)( 87,352)( 88,351)
( 89,350)( 90,349)( 91,348)( 92,347)( 93,185)( 94,207)( 95,206)( 96,205)
( 97,204)( 98,203)( 99,202)(100,201)(101,200)(102,199)(103,198)(104,197)
(105,196)(106,195)(107,194)(108,193)(109,192)(110,191)(111,190)(112,189)
(113,188)(114,187)(115,186)(116,208)(117,230)(118,229)(119,228)(120,227)
(121,226)(122,225)(123,224)(124,223)(125,222)(126,221)(127,220)(128,219)
(129,218)(130,217)(131,216)(132,215)(133,214)(134,213)(135,212)(136,211)
(137,210)(138,209)(139,231)(140,253)(141,252)(142,251)(143,250)(144,249)
(145,248)(146,247)(147,246)(148,245)(149,244)(150,243)(151,242)(152,241)
(153,240)(154,239)(155,238)(156,237)(157,236)(158,235)(159,234)(160,233)
(161,232)(162,254)(163,276)(164,275)(165,274)(166,273)(167,272)(168,271)
(169,270)(170,269)(171,268)(172,267)(173,266)(174,265)(175,264)(176,263)
(177,262)(178,261)(179,260)(180,259)(181,258)(182,257)(183,256)(184,255)
(369,645)(370,667)(371,666)(372,665)(373,664)(374,663)(375,662)(376,661)
(377,660)(378,659)(379,658)(380,657)(381,656)(382,655)(383,654)(384,653)
(385,652)(386,651)(387,650)(388,649)(389,648)(390,647)(391,646)(392,668)
(393,690)(394,689)(395,688)(396,687)(397,686)(398,685)(399,684)(400,683)
(401,682)(402,681)(403,680)(404,679)(405,678)(406,677)(407,676)(408,675)
(409,674)(410,673)(411,672)(412,671)(413,670)(414,669)(415,691)(416,713)
(417,712)(418,711)(419,710)(420,709)(421,708)(422,707)(423,706)(424,705)
(425,704)(426,703)(427,702)(428,701)(429,700)(430,699)(431,698)(432,697)
(433,696)(434,695)(435,694)(436,693)(437,692)(438,714)(439,736)(440,735)
(441,734)(442,733)(443,732)(444,731)(445,730)(446,729)(447,728)(448,727)
(449,726)(450,725)(451,724)(452,723)(453,722)(454,721)(455,720)(456,719)
(457,718)(458,717)(459,716)(460,715)(461,553)(462,575)(463,574)(464,573)
(465,572)(466,571)(467,570)(468,569)(469,568)(470,567)(471,566)(472,565)
(473,564)(474,563)(475,562)(476,561)(477,560)(478,559)(479,558)(480,557)
(481,556)(482,555)(483,554)(484,576)(485,598)(486,597)(487,596)(488,595)
(489,594)(490,593)(491,592)(492,591)(493,590)(494,589)(495,588)(496,587)
(497,586)(498,585)(499,584)(500,583)(501,582)(502,581)(503,580)(504,579)
(505,578)(506,577)(507,599)(508,621)(509,620)(510,619)(511,618)(512,617)
(513,616)(514,615)(515,614)(516,613)(517,612)(518,611)(519,610)(520,609)
(521,608)(522,607)(523,606)(524,605)(525,604)(526,603)(527,602)(528,601)
(529,600)(530,622)(531,644)(532,643)(533,642)(534,641)(535,640)(536,639)
(537,638)(538,637)(539,636)(540,635)(541,634)(542,633)(543,632)(544,631)
(545,630)(546,629)(547,628)(548,627)(549,626)(550,625)(551,624)(552,623);;
s3 := (  1, 94)(  2, 93)(  3,115)(  4,114)(  5,113)(  6,112)(  7,111)(  8,110)
(  9,109)( 10,108)( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)( 16,102)
( 17,101)( 18,100)( 19, 99)( 20, 98)( 21, 97)( 22, 96)( 23, 95)( 24,117)
( 25,116)( 26,138)( 27,137)( 28,136)( 29,135)( 30,134)( 31,133)( 32,132)
( 33,131)( 34,130)( 35,129)( 36,128)( 37,127)( 38,126)( 39,125)( 40,124)
( 41,123)( 42,122)( 43,121)( 44,120)( 45,119)( 46,118)( 47,140)( 48,139)
( 49,161)( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)( 56,154)
( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)( 64,146)
( 65,145)( 66,144)( 67,143)( 68,142)( 69,141)( 70,163)( 71,162)( 72,184)
( 73,183)( 74,182)( 75,181)( 76,180)( 77,179)( 78,178)( 79,177)( 80,176)
( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)( 88,168)
( 89,167)( 90,166)( 91,165)( 92,164)(185,278)(186,277)(187,299)(188,298)
(189,297)(190,296)(191,295)(192,294)(193,293)(194,292)(195,291)(196,290)
(197,289)(198,288)(199,287)(200,286)(201,285)(202,284)(203,283)(204,282)
(205,281)(206,280)(207,279)(208,301)(209,300)(210,322)(211,321)(212,320)
(213,319)(214,318)(215,317)(216,316)(217,315)(218,314)(219,313)(220,312)
(221,311)(222,310)(223,309)(224,308)(225,307)(226,306)(227,305)(228,304)
(229,303)(230,302)(231,324)(232,323)(233,345)(234,344)(235,343)(236,342)
(237,341)(238,340)(239,339)(240,338)(241,337)(242,336)(243,335)(244,334)
(245,333)(246,332)(247,331)(248,330)(249,329)(250,328)(251,327)(252,326)
(253,325)(254,347)(255,346)(256,368)(257,367)(258,366)(259,365)(260,364)
(261,363)(262,362)(263,361)(264,360)(265,359)(266,358)(267,357)(268,356)
(269,355)(270,354)(271,353)(272,352)(273,351)(274,350)(275,349)(276,348)
(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)(553,646)(554,645)(555,667)(556,666)
(557,665)(558,664)(559,663)(560,662)(561,661)(562,660)(563,659)(564,658)
(565,657)(566,656)(567,655)(568,654)(569,653)(570,652)(571,651)(572,650)
(573,649)(574,648)(575,647)(576,669)(577,668)(578,690)(579,689)(580,688)
(581,687)(582,686)(583,685)(584,684)(585,683)(586,682)(587,681)(588,680)
(589,679)(590,678)(591,677)(592,676)(593,675)(594,674)(595,673)(596,672)
(597,671)(598,670)(599,692)(600,691)(601,713)(602,712)(603,711)(604,710)
(605,709)(606,708)(607,707)(608,706)(609,705)(610,704)(611,703)(612,702)
(613,701)(614,700)(615,699)(616,698)(617,697)(618,696)(619,695)(620,694)
(621,693)(622,715)(623,714)(624,736)(625,735)(626,734)(627,733)(628,732)
(629,731)(630,730)(631,729)(632,728)(633,727)(634,726)(635,725)(636,724)
(637,723)(638,722)(639,721)(640,720)(641,719)(642,718)(643,717)(644,716);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(736)!(  1,369)(  2,370)(  3,371)(  4,372)(  5,373)(  6,374)(  7,375)
(  8,376)(  9,377)( 10,378)( 11,379)( 12,380)( 13,381)( 14,382)( 15,383)
( 16,384)( 17,385)( 18,386)( 19,387)( 20,388)( 21,389)( 22,390)( 23,391)
( 24,392)( 25,393)( 26,394)( 27,395)( 28,396)( 29,397)( 30,398)( 31,399)
( 32,400)( 33,401)( 34,402)( 35,403)( 36,404)( 37,405)( 38,406)( 39,407)
( 40,408)( 41,409)( 42,410)( 43,411)( 44,412)( 45,413)( 46,414)( 47,415)
( 48,416)( 49,417)( 50,418)( 51,419)( 52,420)( 53,421)( 54,422)( 55,423)
( 56,424)( 57,425)( 58,426)( 59,427)( 60,428)( 61,429)( 62,430)( 63,431)
( 64,432)( 65,433)( 66,434)( 67,435)( 68,436)( 69,437)( 70,438)( 71,439)
( 72,440)( 73,441)( 74,442)( 75,443)( 76,444)( 77,445)( 78,446)( 79,447)
( 80,448)( 81,449)( 82,450)( 83,451)( 84,452)( 85,453)( 86,454)( 87,455)
( 88,456)( 89,457)( 90,458)( 91,459)( 92,460)( 93,461)( 94,462)( 95,463)
( 96,464)( 97,465)( 98,466)( 99,467)(100,468)(101,469)(102,470)(103,471)
(104,472)(105,473)(106,474)(107,475)(108,476)(109,477)(110,478)(111,479)
(112,480)(113,481)(114,482)(115,483)(116,484)(117,485)(118,486)(119,487)
(120,488)(121,489)(122,490)(123,491)(124,492)(125,493)(126,494)(127,495)
(128,496)(129,497)(130,498)(131,499)(132,500)(133,501)(134,502)(135,503)
(136,504)(137,505)(138,506)(139,507)(140,508)(141,509)(142,510)(143,511)
(144,512)(145,513)(146,514)(147,515)(148,516)(149,517)(150,518)(151,519)
(152,520)(153,521)(154,522)(155,523)(156,524)(157,525)(158,526)(159,527)
(160,528)(161,529)(162,530)(163,531)(164,532)(165,533)(166,534)(167,535)
(168,536)(169,537)(170,538)(171,539)(172,540)(173,541)(174,542)(175,543)
(176,544)(177,545)(178,546)(179,547)(180,548)(181,549)(182,550)(183,551)
(184,552)(185,553)(186,554)(187,555)(188,556)(189,557)(190,558)(191,559)
(192,560)(193,561)(194,562)(195,563)(196,564)(197,565)(198,566)(199,567)
(200,568)(201,569)(202,570)(203,571)(204,572)(205,573)(206,574)(207,575)
(208,576)(209,577)(210,578)(211,579)(212,580)(213,581)(214,582)(215,583)
(216,584)(217,585)(218,586)(219,587)(220,588)(221,589)(222,590)(223,591)
(224,592)(225,593)(226,594)(227,595)(228,596)(229,597)(230,598)(231,599)
(232,600)(233,601)(234,602)(235,603)(236,604)(237,605)(238,606)(239,607)
(240,608)(241,609)(242,610)(243,611)(244,612)(245,613)(246,614)(247,615)
(248,616)(249,617)(250,618)(251,619)(252,620)(253,621)(254,622)(255,623)
(256,624)(257,625)(258,626)(259,627)(260,628)(261,629)(262,630)(263,631)
(264,632)(265,633)(266,634)(267,635)(268,636)(269,637)(270,638)(271,639)
(272,640)(273,641)(274,642)(275,643)(276,644)(277,645)(278,646)(279,647)
(280,648)(281,649)(282,650)(283,651)(284,652)(285,653)(286,654)(287,655)
(288,656)(289,657)(290,658)(291,659)(292,660)(293,661)(294,662)(295,663)
(296,664)(297,665)(298,666)(299,667)(300,668)(301,669)(302,670)(303,671)
(304,672)(305,673)(306,674)(307,675)(308,676)(309,677)(310,678)(311,679)
(312,680)(313,681)(314,682)(315,683)(316,684)(317,685)(318,686)(319,687)
(320,688)(321,689)(322,690)(323,691)(324,692)(325,693)(326,694)(327,695)
(328,696)(329,697)(330,698)(331,699)(332,700)(333,701)(334,702)(335,703)
(336,704)(337,705)(338,706)(339,707)(340,708)(341,709)(342,710)(343,711)
(344,712)(345,713)(346,714)(347,715)(348,716)(349,717)(350,718)(351,719)
(352,720)(353,721)(354,722)(355,723)(356,724)(357,725)(358,726)(359,727)
(360,728)(361,729)(362,730)(363,731)(364,732)(365,733)(366,734)(367,735)
(368,736);
s1 := Sym(736)!(185,208)(186,209)(187,210)(188,211)(189,212)(190,213)(191,214)
(192,215)(193,216)(194,217)(195,218)(196,219)(197,220)(198,221)(199,222)
(200,223)(201,224)(202,225)(203,226)(204,227)(205,228)(206,229)(207,230)
(231,254)(232,255)(233,256)(234,257)(235,258)(236,259)(237,260)(238,261)
(239,262)(240,263)(241,264)(242,265)(243,266)(244,267)(245,268)(246,269)
(247,270)(248,271)(249,272)(250,273)(251,274)(252,275)(253,276)(277,300)
(278,301)(279,302)(280,303)(281,304)(282,305)(283,306)(284,307)(285,308)
(286,309)(287,310)(288,311)(289,312)(290,313)(291,314)(292,315)(293,316)
(294,317)(295,318)(296,319)(297,320)(298,321)(299,322)(323,346)(324,347)
(325,348)(326,349)(327,350)(328,351)(329,352)(330,353)(331,354)(332,355)
(333,356)(334,357)(335,358)(336,359)(337,360)(338,361)(339,362)(340,363)
(341,364)(342,365)(343,366)(344,367)(345,368)(369,415)(370,416)(371,417)
(372,418)(373,419)(374,420)(375,421)(376,422)(377,423)(378,424)(379,425)
(380,426)(381,427)(382,428)(383,429)(384,430)(385,431)(386,432)(387,433)
(388,434)(389,435)(390,436)(391,437)(392,438)(393,439)(394,440)(395,441)
(396,442)(397,443)(398,444)(399,445)(400,446)(401,447)(402,448)(403,449)
(404,450)(405,451)(406,452)(407,453)(408,454)(409,455)(410,456)(411,457)
(412,458)(413,459)(414,460)(461,507)(462,508)(463,509)(464,510)(465,511)
(466,512)(467,513)(468,514)(469,515)(470,516)(471,517)(472,518)(473,519)
(474,520)(475,521)(476,522)(477,523)(478,524)(479,525)(480,526)(481,527)
(482,528)(483,529)(484,530)(485,531)(486,532)(487,533)(488,534)(489,535)
(490,536)(491,537)(492,538)(493,539)(494,540)(495,541)(496,542)(497,543)
(498,544)(499,545)(500,546)(501,547)(502,548)(503,549)(504,550)(505,551)
(506,552)(553,622)(554,623)(555,624)(556,625)(557,626)(558,627)(559,628)
(560,629)(561,630)(562,631)(563,632)(564,633)(565,634)(566,635)(567,636)
(568,637)(569,638)(570,639)(571,640)(572,641)(573,642)(574,643)(575,644)
(576,599)(577,600)(578,601)(579,602)(580,603)(581,604)(582,605)(583,606)
(584,607)(585,608)(586,609)(587,610)(588,611)(589,612)(590,613)(591,614)
(592,615)(593,616)(594,617)(595,618)(596,619)(597,620)(598,621)(645,714)
(646,715)(647,716)(648,717)(649,718)(650,719)(651,720)(652,721)(653,722)
(654,723)(655,724)(656,725)(657,726)(658,727)(659,728)(660,729)(661,730)
(662,731)(663,732)(664,733)(665,734)(666,735)(667,736)(668,691)(669,692)
(670,693)(671,694)(672,695)(673,696)(674,697)(675,698)(676,699)(677,700)
(678,701)(679,702)(680,703)(681,704)(682,705)(683,706)(684,707)(685,708)
(686,709)(687,710)(688,711)(689,712)(690,713);
s2 := Sym(736)!(  1,277)(  2,299)(  3,298)(  4,297)(  5,296)(  6,295)(  7,294)
(  8,293)(  9,292)( 10,291)( 11,290)( 12,289)( 13,288)( 14,287)( 15,286)
( 16,285)( 17,284)( 18,283)( 19,282)( 20,281)( 21,280)( 22,279)( 23,278)
( 24,300)( 25,322)( 26,321)( 27,320)( 28,319)( 29,318)( 30,317)( 31,316)
( 32,315)( 33,314)( 34,313)( 35,312)( 36,311)( 37,310)( 38,309)( 39,308)
( 40,307)( 41,306)( 42,305)( 43,304)( 44,303)( 45,302)( 46,301)( 47,323)
( 48,345)( 49,344)( 50,343)( 51,342)( 52,341)( 53,340)( 54,339)( 55,338)
( 56,337)( 57,336)( 58,335)( 59,334)( 60,333)( 61,332)( 62,331)( 63,330)
( 64,329)( 65,328)( 66,327)( 67,326)( 68,325)( 69,324)( 70,346)( 71,368)
( 72,367)( 73,366)( 74,365)( 75,364)( 76,363)( 77,362)( 78,361)( 79,360)
( 80,359)( 81,358)( 82,357)( 83,356)( 84,355)( 85,354)( 86,353)( 87,352)
( 88,351)( 89,350)( 90,349)( 91,348)( 92,347)( 93,185)( 94,207)( 95,206)
( 96,205)( 97,204)( 98,203)( 99,202)(100,201)(101,200)(102,199)(103,198)
(104,197)(105,196)(106,195)(107,194)(108,193)(109,192)(110,191)(111,190)
(112,189)(113,188)(114,187)(115,186)(116,208)(117,230)(118,229)(119,228)
(120,227)(121,226)(122,225)(123,224)(124,223)(125,222)(126,221)(127,220)
(128,219)(129,218)(130,217)(131,216)(132,215)(133,214)(134,213)(135,212)
(136,211)(137,210)(138,209)(139,231)(140,253)(141,252)(142,251)(143,250)
(144,249)(145,248)(146,247)(147,246)(148,245)(149,244)(150,243)(151,242)
(152,241)(153,240)(154,239)(155,238)(156,237)(157,236)(158,235)(159,234)
(160,233)(161,232)(162,254)(163,276)(164,275)(165,274)(166,273)(167,272)
(168,271)(169,270)(170,269)(171,268)(172,267)(173,266)(174,265)(175,264)
(176,263)(177,262)(178,261)(179,260)(180,259)(181,258)(182,257)(183,256)
(184,255)(369,645)(370,667)(371,666)(372,665)(373,664)(374,663)(375,662)
(376,661)(377,660)(378,659)(379,658)(380,657)(381,656)(382,655)(383,654)
(384,653)(385,652)(386,651)(387,650)(388,649)(389,648)(390,647)(391,646)
(392,668)(393,690)(394,689)(395,688)(396,687)(397,686)(398,685)(399,684)
(400,683)(401,682)(402,681)(403,680)(404,679)(405,678)(406,677)(407,676)
(408,675)(409,674)(410,673)(411,672)(412,671)(413,670)(414,669)(415,691)
(416,713)(417,712)(418,711)(419,710)(420,709)(421,708)(422,707)(423,706)
(424,705)(425,704)(426,703)(427,702)(428,701)(429,700)(430,699)(431,698)
(432,697)(433,696)(434,695)(435,694)(436,693)(437,692)(438,714)(439,736)
(440,735)(441,734)(442,733)(443,732)(444,731)(445,730)(446,729)(447,728)
(448,727)(449,726)(450,725)(451,724)(452,723)(453,722)(454,721)(455,720)
(456,719)(457,718)(458,717)(459,716)(460,715)(461,553)(462,575)(463,574)
(464,573)(465,572)(466,571)(467,570)(468,569)(469,568)(470,567)(471,566)
(472,565)(473,564)(474,563)(475,562)(476,561)(477,560)(478,559)(479,558)
(480,557)(481,556)(482,555)(483,554)(484,576)(485,598)(486,597)(487,596)
(488,595)(489,594)(490,593)(491,592)(492,591)(493,590)(494,589)(495,588)
(496,587)(497,586)(498,585)(499,584)(500,583)(501,582)(502,581)(503,580)
(504,579)(505,578)(506,577)(507,599)(508,621)(509,620)(510,619)(511,618)
(512,617)(513,616)(514,615)(515,614)(516,613)(517,612)(518,611)(519,610)
(520,609)(521,608)(522,607)(523,606)(524,605)(525,604)(526,603)(527,602)
(528,601)(529,600)(530,622)(531,644)(532,643)(533,642)(534,641)(535,640)
(536,639)(537,638)(538,637)(539,636)(540,635)(541,634)(542,633)(543,632)
(544,631)(545,630)(546,629)(547,628)(548,627)(549,626)(550,625)(551,624)
(552,623);
s3 := Sym(736)!(  1, 94)(  2, 93)(  3,115)(  4,114)(  5,113)(  6,112)(  7,111)
(  8,110)(  9,109)( 10,108)( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)
( 16,102)( 17,101)( 18,100)( 19, 99)( 20, 98)( 21, 97)( 22, 96)( 23, 95)
( 24,117)( 25,116)( 26,138)( 27,137)( 28,136)( 29,135)( 30,134)( 31,133)
( 32,132)( 33,131)( 34,130)( 35,129)( 36,128)( 37,127)( 38,126)( 39,125)
( 40,124)( 41,123)( 42,122)( 43,121)( 44,120)( 45,119)( 46,118)( 47,140)
( 48,139)( 49,161)( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)
( 56,154)( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)
( 64,146)( 65,145)( 66,144)( 67,143)( 68,142)( 69,141)( 70,163)( 71,162)
( 72,184)( 73,183)( 74,182)( 75,181)( 76,180)( 77,179)( 78,178)( 79,177)
( 80,176)( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)
( 88,168)( 89,167)( 90,166)( 91,165)( 92,164)(185,278)(186,277)(187,299)
(188,298)(189,297)(190,296)(191,295)(192,294)(193,293)(194,292)(195,291)
(196,290)(197,289)(198,288)(199,287)(200,286)(201,285)(202,284)(203,283)
(204,282)(205,281)(206,280)(207,279)(208,301)(209,300)(210,322)(211,321)
(212,320)(213,319)(214,318)(215,317)(216,316)(217,315)(218,314)(219,313)
(220,312)(221,311)(222,310)(223,309)(224,308)(225,307)(226,306)(227,305)
(228,304)(229,303)(230,302)(231,324)(232,323)(233,345)(234,344)(235,343)
(236,342)(237,341)(238,340)(239,339)(240,338)(241,337)(242,336)(243,335)
(244,334)(245,333)(246,332)(247,331)(248,330)(249,329)(250,328)(251,327)
(252,326)(253,325)(254,347)(255,346)(256,368)(257,367)(258,366)(259,365)
(260,364)(261,363)(262,362)(263,361)(264,360)(265,359)(266,358)(267,357)
(268,356)(269,355)(270,354)(271,353)(272,352)(273,351)(274,350)(275,349)
(276,348)(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)(553,646)(554,645)(555,667)
(556,666)(557,665)(558,664)(559,663)(560,662)(561,661)(562,660)(563,659)
(564,658)(565,657)(566,656)(567,655)(568,654)(569,653)(570,652)(571,651)
(572,650)(573,649)(574,648)(575,647)(576,669)(577,668)(578,690)(579,689)
(580,688)(581,687)(582,686)(583,685)(584,684)(585,683)(586,682)(587,681)
(588,680)(589,679)(590,678)(591,677)(592,676)(593,675)(594,674)(595,673)
(596,672)(597,671)(598,670)(599,692)(600,691)(601,713)(602,712)(603,711)
(604,710)(605,709)(606,708)(607,707)(608,706)(609,705)(610,704)(611,703)
(612,702)(613,701)(614,700)(615,699)(616,698)(617,697)(618,696)(619,695)
(620,694)(621,693)(622,715)(623,714)(624,736)(625,735)(626,734)(627,733)
(628,732)(629,731)(630,730)(631,729)(632,728)(633,727)(634,726)(635,725)
(636,724)(637,723)(638,722)(639,721)(640,720)(641,719)(642,718)(643,717)
(644,716);
poly := sub<Sym(736)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope