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Polytope of Type {46,4,4}

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