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