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.
Irregular Quotients (of which this is a minimal cover):
None.
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