Polytope of Type {22,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,4,8}*1408a
Also Known As : {{22,4|2},{4,8|2}}. if this polytope has another name.
Group : SmallGroup(1408,13683)
Rank : 4
Schlafli Type : {22,4,8}
Number of vertices, edges, etc : 22, 44, 16, 8
Order of s0s1s2s3 : 88
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 : {22,4,4}*704, {22,2,8}*704
4-fold quotients : {11,2,8}*352, {22,2,4}*352, {22,4,2}*352
8-fold quotients : {11,2,4}*176, {22,2,2}*176
11-fold quotients : {2,4,8}*128a
16-fold quotients : {11,2,2}*88
22-fold quotients : {2,4,4}*64, {2,2,8}*64
44-fold quotients : {2,2,4}*32, {2,4,2}*32
88-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, 89)( 2, 99)( 3, 98)( 4, 97)( 5, 96)( 6, 95)( 7, 94)( 8, 93)( 9, 92)( 10, 91)( 11, 90)( 12,100)( 13,110)( 14,109)( 15,108)( 16,107)( 17,106)( 18,105)( 19,104)( 20,103)( 21,102)( 22,101)( 23,111)( 24,121)( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,122)( 35,132)( 36,131)( 37,130)( 38,129)( 39,128)( 40,127)( 41,126)( 42,125)( 43,124)( 44,123)( 45,133)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)( 56,144)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,145)( 67,155)( 68,165)( 69,164)( 70,163)( 71,162)( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)( 77,156)( 78,166)( 79,176)( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167)(177,265)(178,275)(179,274)(180,273)(181,272)(182,271)(183,270)(184,269)(185,268)(186,267)(187,266)(188,276)(189,286)(190,285)(191,284)(192,283)(193,282)(194,281)(195,280)(196,279)(197,278)(198,277)(199,287)(200,297)(201,296)(202,295)(203,294)(204,293)(205,292)(206,291)(207,290)(208,289)(209,288)(210,298)(211,308)(212,307)(213,306)(214,305)(215,304)(216,303)(217,302)(218,301)(219,300)(220,299)(221,309)(222,319)(223,318)(224,317)(225,316)(226,315)(227,314)(228,313)(229,312)(230,311)(231,310)(232,320)(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)(240,323)(241,322)(242,321)(243,331)(244,341)(245,340)(246,339)(247,338)(248,337)(249,336)(250,335)(251,334)(252,333)(253,332)(254,342)(255,352)(256,351)(257,350)(258,349)(259,348)(260,347)(261,346)(262,345)(263,344)(264,343)(353,441)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,463)(376,473)(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,485)(398,495)(399,494)(400,493)(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)(419,507)(420,517)(421,516)(422,515)(423,514)(424,513)(425,512)(426,511)(427,510)(428,509)(429,508)(430,518)(431,528)(432,527)(433,526)(434,525)(435,524)(436,523)(437,522)(438,521)(439,520)(440,519)(529,617)(530,627)(531,626)(532,625)(533,624)(534,623)(535,622)(536,621)(537,620)(538,619)(539,618)(540,628)(541,638)(542,637)(543,636)(544,635)(545,634)(546,633)(547,632)(548,631)(549,630)(550,629)(551,639)(552,649)(553,648)(554,647)(555,646)(556,645)(557,644)(558,643)(559,642)(560,641)(561,640)(562,650)(563,660)(564,659)(565,658)(566,657)(567,656)(568,655)(569,654)(570,653)(571,652)(572,651)(573,661)(574,671)(575,670)(576,669)(577,668)(578,667)(579,666)(580,665)(581,664)(582,663)(583,662)(584,672)(585,682)(586,681)(587,680)(588,679)(589,678)(590,677)(591,676)(592,675)(593,674)(594,673)(595,683)(596,693)(597,692)(598,691)(599,690)(600,689)(601,688)(602,687)(603,686)(604,685)(605,684)(606,694)(607,704)(608,703)(609,702)(610,701)(611,700)(612,699)(613,698)(614,697)(615,696)(616,695);;
s1 := ( 1,266)( 2,265)( 3,275)( 4,274)( 5,273)( 6,272)( 7,271)( 8,270)( 9,269)( 10,268)( 11,267)( 12,277)( 13,276)( 14,286)( 15,285)( 16,284)( 17,283)( 18,282)( 19,281)( 20,280)( 21,279)( 22,278)( 23,288)( 24,287)( 25,297)( 26,296)( 27,295)( 28,294)( 29,293)( 30,292)( 31,291)( 32,290)( 33,289)( 34,299)( 35,298)( 36,308)( 37,307)( 38,306)( 39,305)( 40,304)( 41,303)( 42,302)( 43,301)( 44,300)( 45,310)( 46,309)( 47,319)( 48,318)( 49,317)( 50,316)( 51,315)( 52,314)( 53,313)( 54,312)( 55,311)( 56,321)( 57,320)( 58,330)( 59,329)( 60,328)( 61,327)( 62,326)( 63,325)( 64,324)( 65,323)( 66,322)( 67,332)( 68,331)( 69,341)( 70,340)( 71,339)( 72,338)( 73,337)( 74,336)( 75,335)( 76,334)( 77,333)( 78,343)( 79,342)( 80,352)( 81,351)( 82,350)( 83,349)( 84,348)( 85,347)( 86,346)( 87,345)( 88,344)( 89,178)( 90,177)( 91,187)( 92,186)( 93,185)( 94,184)( 95,183)( 96,182)( 97,181)( 98,180)( 99,179)(100,189)(101,188)(102,198)(103,197)(104,196)(105,195)(106,194)(107,193)(108,192)(109,191)(110,190)(111,200)(112,199)(113,209)(114,208)(115,207)(116,206)(117,205)(118,204)(119,203)(120,202)(121,201)(122,211)(123,210)(124,220)(125,219)(126,218)(127,217)(128,216)(129,215)(130,214)(131,213)(132,212)(133,222)(134,221)(135,231)(136,230)(137,229)(138,228)(139,227)(140,226)(141,225)(142,224)(143,223)(144,233)(145,232)(146,242)(147,241)(148,240)(149,239)(150,238)(151,237)(152,236)(153,235)(154,234)(155,244)(156,243)(157,253)(158,252)(159,251)(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)(166,255)(167,254)(168,264)(169,263)(170,262)(171,261)(172,260)(173,259)(174,258)(175,257)(176,256)(353,618)(354,617)(355,627)(356,626)(357,625)(358,624)(359,623)(360,622)(361,621)(362,620)(363,619)(364,629)(365,628)(366,638)(367,637)(368,636)(369,635)(370,634)(371,633)(372,632)(373,631)(374,630)(375,640)(376,639)(377,649)(378,648)(379,647)(380,646)(381,645)(382,644)(383,643)(384,642)(385,641)(386,651)(387,650)(388,660)(389,659)(390,658)(391,657)(392,656)(393,655)(394,654)(395,653)(396,652)(397,662)(398,661)(399,671)(400,670)(401,669)(402,668)(403,667)(404,666)(405,665)(406,664)(407,663)(408,673)(409,672)(410,682)(411,681)(412,680)(413,679)(414,678)(415,677)(416,676)(417,675)(418,674)(419,684)(420,683)(421,693)(422,692)(423,691)(424,690)(425,689)(426,688)(427,687)(428,686)(429,685)(430,695)(431,694)(432,704)(433,703)(434,702)(435,701)(436,700)(437,699)(438,698)(439,697)(440,696)(441,530)(442,529)(443,539)(444,538)(445,537)(446,536)(447,535)(448,534)(449,533)(450,532)(451,531)(452,541)(453,540)(454,550)(455,549)(456,548)(457,547)(458,546)(459,545)(460,544)(461,543)(462,542)(463,552)(464,551)(465,561)(466,560)(467,559)(468,558)(469,557)(470,556)(471,555)(472,554)(473,553)(474,563)(475,562)(476,572)(477,571)(478,570)(479,569)(480,568)(481,567)(482,566)(483,565)(484,564)(485,574)(486,573)(487,583)(488,582)(489,581)(490,580)(491,579)(492,578)(493,577)(494,576)(495,575)(496,585)(497,584)(498,594)(499,593)(500,592)(501,591)(502,590)(503,589)(504,588)(505,587)(506,586)(507,596)(508,595)(509,605)(510,604)(511,603)(512,602)(513,601)(514,600)(515,599)(516,598)(517,597)(518,607)(519,606)(520,616)(521,615)(522,614)(523,613)(524,612)(525,611)(526,610)(527,609)(528,608);;
s2 := ( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176)(177,199)(178,200)(179,201)(180,202)(181,203)(182,204)(183,205)(184,206)(185,207)(186,208)(187,209)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)(221,254)(222,255)(223,256)(224,257)(225,258)(226,259)(227,260)(228,261)(229,262)(230,263)(231,264)(232,243)(233,244)(234,245)(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)(273,295)(274,296)(275,297)(276,298)(277,299)(278,300)(279,301)(280,302)(281,303)(282,304)(283,305)(284,306)(285,307)(286,308)(309,342)(310,343)(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)(318,351)(319,352)(320,331)(321,332)(322,333)(323,334)(324,335)(325,336)(326,337)(327,338)(328,339)(329,340)(330,341)(353,397)(354,398)(355,399)(356,400)(357,401)(358,402)(359,403)(360,404)(361,405)(362,406)(363,407)(364,408)(365,409)(366,410)(367,411)(368,412)(369,413)(370,414)(371,415)(372,416)(373,417)(374,418)(375,419)(376,420)(377,421)(378,422)(379,423)(380,424)(381,425)(382,426)(383,427)(384,428)(385,429)(386,430)(387,431)(388,432)(389,433)(390,434)(391,435)(392,436)(393,437)(394,438)(395,439)(396,440)(441,485)(442,486)(443,487)(444,488)(445,489)(446,490)(447,491)(448,492)(449,493)(450,494)(451,495)(452,496)(453,497)(454,498)(455,499)(456,500)(457,501)(458,502)(459,503)(460,504)(461,505)(462,506)(463,507)(464,508)(465,509)(466,510)(467,511)(468,512)(469,513)(470,514)(471,515)(472,516)(473,517)(474,518)(475,519)(476,520)(477,521)(478,522)(479,523)(480,524)(481,525)(482,526)(483,527)(484,528)(529,595)(530,596)(531,597)(532,598)(533,599)(534,600)(535,601)(536,602)(537,603)(538,604)(539,605)(540,606)(541,607)(542,608)(543,609)(544,610)(545,611)(546,612)(547,613)(548,614)(549,615)(550,616)(551,573)(552,574)(553,575)(554,576)(555,577)(556,578)(557,579)(558,580)(559,581)(560,582)(561,583)(562,584)(563,585)(564,586)(565,587)(566,588)(567,589)(568,590)(569,591)(570,592)(571,593)(572,594)(617,683)(618,684)(619,685)(620,686)(621,687)(622,688)(623,689)(624,690)(625,691)(626,692)(627,693)(628,694)(629,695)(630,696)(631,697)(632,698)(633,699)(634,700)(635,701)(636,702)(637,703)(638,704)(639,661)(640,662)(641,663)(642,664)(643,665)(644,666)(645,667)(646,668)(647,669)(648,670)(649,671)(650,672)(651,673)(652,674)(653,675)(654,676)(655,677)(656,678)(657,679)(658,680)(659,681)(660,682);;
s3 := ( 1,353)( 2,354)( 3,355)( 4,356)( 5,357)( 6,358)( 7,359)( 8,360)( 9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)( 16,368)( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,375)( 24,376)( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)( 32,384)( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)( 40,392)( 41,393)( 42,394)( 43,395)( 44,396)( 45,408)( 46,409)( 47,410)( 48,411)( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)( 56,397)( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)( 64,405)( 65,406)( 66,407)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)( 72,435)( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)( 80,421)( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)( 88,429)( 89,441)( 90,442)( 91,443)( 92,444)( 93,445)( 94,446)( 95,447)( 96,448)( 97,449)( 98,450)( 99,451)(100,452)(101,453)(102,454)(103,455)(104,456)(105,457)(106,458)(107,459)(108,460)(109,461)(110,462)(111,463)(112,464)(113,465)(114,466)(115,467)(116,468)(117,469)(118,470)(119,471)(120,472)(121,473)(122,474)(123,475)(124,476)(125,477)(126,478)(127,479)(128,480)(129,481)(130,482)(131,483)(132,484)(133,496)(134,497)(135,498)(136,499)(137,500)(138,501)(139,502)(140,503)(141,504)(142,505)(143,506)(144,485)(145,486)(146,487)(147,488)(148,489)(149,490)(150,491)(151,492)(152,493)(153,494)(154,495)(155,518)(156,519)(157,520)(158,521)(159,522)(160,523)(161,524)(162,525)(163,526)(164,527)(165,528)(166,507)(167,508)(168,509)(169,510)(170,511)(171,512)(172,513)(173,514)(174,515)(175,516)(176,517)(177,529)(178,530)(179,531)(180,532)(181,533)(182,534)(183,535)(184,536)(185,537)(186,538)(187,539)(188,540)(189,541)(190,542)(191,543)(192,544)(193,545)(194,546)(195,547)(196,548)(197,549)(198,550)(199,551)(200,552)(201,553)(202,554)(203,555)(204,556)(205,557)(206,558)(207,559)(208,560)(209,561)(210,562)(211,563)(212,564)(213,565)(214,566)(215,567)(216,568)(217,569)(218,570)(219,571)(220,572)(221,584)(222,585)(223,586)(224,587)(225,588)(226,589)(227,590)(228,591)(229,592)(230,593)(231,594)(232,573)(233,574)(234,575)(235,576)(236,577)(237,578)(238,579)(239,580)(240,581)(241,582)(242,583)(243,606)(244,607)(245,608)(246,609)(247,610)(248,611)(249,612)(250,613)(251,614)(252,615)(253,616)(254,595)(255,596)(256,597)(257,598)(258,599)(259,600)(260,601)(261,602)(262,603)(263,604)(264,605)(265,617)(266,618)(267,619)(268,620)(269,621)(270,622)(271,623)(272,624)(273,625)(274,626)(275,627)(276,628)(277,629)(278,630)(279,631)(280,632)(281,633)(282,634)(283,635)(284,636)(285,637)(286,638)(287,639)(288,640)(289,641)(290,642)(291,643)(292,644)(293,645)(294,646)(295,647)(296,648)(297,649)(298,650)(299,651)(300,652)(301,653)(302,654)(303,655)(304,656)(305,657)(306,658)(307,659)(308,660)(309,672)(310,673)(311,674)(312,675)(313,676)(314,677)(315,678)(316,679)(317,680)(318,681)(319,682)(320,661)(321,662)(322,663)(323,664)(324,665)(325,666)(326,667)(327,668)(328,669)(329,670)(330,671)(331,694)(332,695)(333,696)(334,697)(335,698)(336,699)(337,700)(338,701)(339,702)(340,703)(341,704)(342,683)(343,684)(344,685)(345,686)(346,687)(347,688)(348,689)(349,690)(350,691)(351,692)(352,693);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(704)!( 1, 89)( 2, 99)( 3, 98)( 4, 97)( 5, 96)( 6, 95)( 7, 94)( 8, 93)( 9, 92)( 10, 91)( 11, 90)( 12,100)( 13,110)( 14,109)( 15,108)( 16,107)( 17,106)( 18,105)( 19,104)( 20,103)( 21,102)( 22,101)( 23,111)( 24,121)( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,122)( 35,132)( 36,131)( 37,130)( 38,129)( 39,128)( 40,127)( 41,126)( 42,125)( 43,124)( 44,123)( 45,133)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)( 56,144)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,145)( 67,155)( 68,165)( 69,164)( 70,163)( 71,162)( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)( 77,156)( 78,166)( 79,176)( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167)(177,265)(178,275)(179,274)(180,273)(181,272)(182,271)(183,270)(184,269)(185,268)(186,267)(187,266)(188,276)(189,286)(190,285)(191,284)(192,283)(193,282)(194,281)(195,280)(196,279)(197,278)(198,277)(199,287)(200,297)(201,296)(202,295)(203,294)(204,293)(205,292)(206,291)(207,290)(208,289)(209,288)(210,298)(211,308)(212,307)(213,306)(214,305)(215,304)(216,303)(217,302)(218,301)(219,300)(220,299)(221,309)(222,319)(223,318)(224,317)(225,316)(226,315)(227,314)(228,313)(229,312)(230,311)(231,310)(232,320)(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)(240,323)(241,322)(242,321)(243,331)(244,341)(245,340)(246,339)(247,338)(248,337)(249,336)(250,335)(251,334)(252,333)(253,332)(254,342)(255,352)(256,351)(257,350)(258,349)(259,348)(260,347)(261,346)(262,345)(263,344)(264,343)(353,441)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,463)(376,473)(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,485)(398,495)(399,494)(400,493)(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)(419,507)(420,517)(421,516)(422,515)(423,514)(424,513)(425,512)(426,511)(427,510)(428,509)(429,508)(430,518)(431,528)(432,527)(433,526)(434,525)(435,524)(436,523)(437,522)(438,521)(439,520)(440,519)(529,617)(530,627)(531,626)(532,625)(533,624)(534,623)(535,622)(536,621)(537,620)(538,619)(539,618)(540,628)(541,638)(542,637)(543,636)(544,635)(545,634)(546,633)(547,632)(548,631)(549,630)(550,629)(551,639)(552,649)(553,648)(554,647)(555,646)(556,645)(557,644)(558,643)(559,642)(560,641)(561,640)(562,650)(563,660)(564,659)(565,658)(566,657)(567,656)(568,655)(569,654)(570,653)(571,652)(572,651)(573,661)(574,671)(575,670)(576,669)(577,668)(578,667)(579,666)(580,665)(581,664)(582,663)(583,662)(584,672)(585,682)(586,681)(587,680)(588,679)(589,678)(590,677)(591,676)(592,675)(593,674)(594,673)(595,683)(596,693)(597,692)(598,691)(599,690)(600,689)(601,688)(602,687)(603,686)(604,685)(605,684)(606,694)(607,704)(608,703)(609,702)(610,701)(611,700)(612,699)(613,698)(614,697)(615,696)(616,695);
s1 := Sym(704)!( 1,266)( 2,265)( 3,275)( 4,274)( 5,273)( 6,272)( 7,271)( 8,270)( 9,269)( 10,268)( 11,267)( 12,277)( 13,276)( 14,286)( 15,285)( 16,284)( 17,283)( 18,282)( 19,281)( 20,280)( 21,279)( 22,278)( 23,288)( 24,287)( 25,297)( 26,296)( 27,295)( 28,294)( 29,293)( 30,292)( 31,291)( 32,290)( 33,289)( 34,299)( 35,298)( 36,308)( 37,307)( 38,306)( 39,305)( 40,304)( 41,303)( 42,302)( 43,301)( 44,300)( 45,310)( 46,309)( 47,319)( 48,318)( 49,317)( 50,316)( 51,315)( 52,314)( 53,313)( 54,312)( 55,311)( 56,321)( 57,320)( 58,330)( 59,329)( 60,328)( 61,327)( 62,326)( 63,325)( 64,324)( 65,323)( 66,322)( 67,332)( 68,331)( 69,341)( 70,340)( 71,339)( 72,338)( 73,337)( 74,336)( 75,335)( 76,334)( 77,333)( 78,343)( 79,342)( 80,352)( 81,351)( 82,350)( 83,349)( 84,348)( 85,347)( 86,346)( 87,345)( 88,344)( 89,178)( 90,177)( 91,187)( 92,186)( 93,185)( 94,184)( 95,183)( 96,182)( 97,181)( 98,180)( 99,179)(100,189)(101,188)(102,198)(103,197)(104,196)(105,195)(106,194)(107,193)(108,192)(109,191)(110,190)(111,200)(112,199)(113,209)(114,208)(115,207)(116,206)(117,205)(118,204)(119,203)(120,202)(121,201)(122,211)(123,210)(124,220)(125,219)(126,218)(127,217)(128,216)(129,215)(130,214)(131,213)(132,212)(133,222)(134,221)(135,231)(136,230)(137,229)(138,228)(139,227)(140,226)(141,225)(142,224)(143,223)(144,233)(145,232)(146,242)(147,241)(148,240)(149,239)(150,238)(151,237)(152,236)(153,235)(154,234)(155,244)(156,243)(157,253)(158,252)(159,251)(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)(166,255)(167,254)(168,264)(169,263)(170,262)(171,261)(172,260)(173,259)(174,258)(175,257)(176,256)(353,618)(354,617)(355,627)(356,626)(357,625)(358,624)(359,623)(360,622)(361,621)(362,620)(363,619)(364,629)(365,628)(366,638)(367,637)(368,636)(369,635)(370,634)(371,633)(372,632)(373,631)(374,630)(375,640)(376,639)(377,649)(378,648)(379,647)(380,646)(381,645)(382,644)(383,643)(384,642)(385,641)(386,651)(387,650)(388,660)(389,659)(390,658)(391,657)(392,656)(393,655)(394,654)(395,653)(396,652)(397,662)(398,661)(399,671)(400,670)(401,669)(402,668)(403,667)(404,666)(405,665)(406,664)(407,663)(408,673)(409,672)(410,682)(411,681)(412,680)(413,679)(414,678)(415,677)(416,676)(417,675)(418,674)(419,684)(420,683)(421,693)(422,692)(423,691)(424,690)(425,689)(426,688)(427,687)(428,686)(429,685)(430,695)(431,694)(432,704)(433,703)(434,702)(435,701)(436,700)(437,699)(438,698)(439,697)(440,696)(441,530)(442,529)(443,539)(444,538)(445,537)(446,536)(447,535)(448,534)(449,533)(450,532)(451,531)(452,541)(453,540)(454,550)(455,549)(456,548)(457,547)(458,546)(459,545)(460,544)(461,543)(462,542)(463,552)(464,551)(465,561)(466,560)(467,559)(468,558)(469,557)(470,556)(471,555)(472,554)(473,553)(474,563)(475,562)(476,572)(477,571)(478,570)(479,569)(480,568)(481,567)(482,566)(483,565)(484,564)(485,574)(486,573)(487,583)(488,582)(489,581)(490,580)(491,579)(492,578)(493,577)(494,576)(495,575)(496,585)(497,584)(498,594)(499,593)(500,592)(501,591)(502,590)(503,589)(504,588)(505,587)(506,586)(507,596)(508,595)(509,605)(510,604)(511,603)(512,602)(513,601)(514,600)(515,599)(516,598)(517,597)(518,607)(519,606)(520,616)(521,615)(522,614)(523,613)(524,612)(525,611)(526,610)(527,609)(528,608);
s2 := Sym(704)!( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176)(177,199)(178,200)(179,201)(180,202)(181,203)(182,204)(183,205)(184,206)(185,207)(186,208)(187,209)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)(221,254)(222,255)(223,256)(224,257)(225,258)(226,259)(227,260)(228,261)(229,262)(230,263)(231,264)(232,243)(233,244)(234,245)(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)(273,295)(274,296)(275,297)(276,298)(277,299)(278,300)(279,301)(280,302)(281,303)(282,304)(283,305)(284,306)(285,307)(286,308)(309,342)(310,343)(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)(318,351)(319,352)(320,331)(321,332)(322,333)(323,334)(324,335)(325,336)(326,337)(327,338)(328,339)(329,340)(330,341)(353,397)(354,398)(355,399)(356,400)(357,401)(358,402)(359,403)(360,404)(361,405)(362,406)(363,407)(364,408)(365,409)(366,410)(367,411)(368,412)(369,413)(370,414)(371,415)(372,416)(373,417)(374,418)(375,419)(376,420)(377,421)(378,422)(379,423)(380,424)(381,425)(382,426)(383,427)(384,428)(385,429)(386,430)(387,431)(388,432)(389,433)(390,434)(391,435)(392,436)(393,437)(394,438)(395,439)(396,440)(441,485)(442,486)(443,487)(444,488)(445,489)(446,490)(447,491)(448,492)(449,493)(450,494)(451,495)(452,496)(453,497)(454,498)(455,499)(456,500)(457,501)(458,502)(459,503)(460,504)(461,505)(462,506)(463,507)(464,508)(465,509)(466,510)(467,511)(468,512)(469,513)(470,514)(471,515)(472,516)(473,517)(474,518)(475,519)(476,520)(477,521)(478,522)(479,523)(480,524)(481,525)(482,526)(483,527)(484,528)(529,595)(530,596)(531,597)(532,598)(533,599)(534,600)(535,601)(536,602)(537,603)(538,604)(539,605)(540,606)(541,607)(542,608)(543,609)(544,610)(545,611)(546,612)(547,613)(548,614)(549,615)(550,616)(551,573)(552,574)(553,575)(554,576)(555,577)(556,578)(557,579)(558,580)(559,581)(560,582)(561,583)(562,584)(563,585)(564,586)(565,587)(566,588)(567,589)(568,590)(569,591)(570,592)(571,593)(572,594)(617,683)(618,684)(619,685)(620,686)(621,687)(622,688)(623,689)(624,690)(625,691)(626,692)(627,693)(628,694)(629,695)(630,696)(631,697)(632,698)(633,699)(634,700)(635,701)(636,702)(637,703)(638,704)(639,661)(640,662)(641,663)(642,664)(643,665)(644,666)(645,667)(646,668)(647,669)(648,670)(649,671)(650,672)(651,673)(652,674)(653,675)(654,676)(655,677)(656,678)(657,679)(658,680)(659,681)(660,682);
s3 := Sym(704)!( 1,353)( 2,354)( 3,355)( 4,356)( 5,357)( 6,358)( 7,359)( 8,360)( 9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)( 16,368)( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,375)( 24,376)( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)( 32,384)( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)( 40,392)( 41,393)( 42,394)( 43,395)( 44,396)( 45,408)( 46,409)( 47,410)( 48,411)( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)( 56,397)( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)( 64,405)( 65,406)( 66,407)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)( 72,435)( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)( 80,421)( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)( 88,429)( 89,441)( 90,442)( 91,443)( 92,444)( 93,445)( 94,446)( 95,447)( 96,448)( 97,449)( 98,450)( 99,451)(100,452)(101,453)(102,454)(103,455)(104,456)(105,457)(106,458)(107,459)(108,460)(109,461)(110,462)(111,463)(112,464)(113,465)(114,466)(115,467)(116,468)(117,469)(118,470)(119,471)(120,472)(121,473)(122,474)(123,475)(124,476)(125,477)(126,478)(127,479)(128,480)(129,481)(130,482)(131,483)(132,484)(133,496)(134,497)(135,498)(136,499)(137,500)(138,501)(139,502)(140,503)(141,504)(142,505)(143,506)(144,485)(145,486)(146,487)(147,488)(148,489)(149,490)(150,491)(151,492)(152,493)(153,494)(154,495)(155,518)(156,519)(157,520)(158,521)(159,522)(160,523)(161,524)(162,525)(163,526)(164,527)(165,528)(166,507)(167,508)(168,509)(169,510)(170,511)(171,512)(172,513)(173,514)(174,515)(175,516)(176,517)(177,529)(178,530)(179,531)(180,532)(181,533)(182,534)(183,535)(184,536)(185,537)(186,538)(187,539)(188,540)(189,541)(190,542)(191,543)(192,544)(193,545)(194,546)(195,547)(196,548)(197,549)(198,550)(199,551)(200,552)(201,553)(202,554)(203,555)(204,556)(205,557)(206,558)(207,559)(208,560)(209,561)(210,562)(211,563)(212,564)(213,565)(214,566)(215,567)(216,568)(217,569)(218,570)(219,571)(220,572)(221,584)(222,585)(223,586)(224,587)(225,588)(226,589)(227,590)(228,591)(229,592)(230,593)(231,594)(232,573)(233,574)(234,575)(235,576)(236,577)(237,578)(238,579)(239,580)(240,581)(241,582)(242,583)(243,606)(244,607)(245,608)(246,609)(247,610)(248,611)(249,612)(250,613)(251,614)(252,615)(253,616)(254,595)(255,596)(256,597)(257,598)(258,599)(259,600)(260,601)(261,602)(262,603)(263,604)(264,605)(265,617)(266,618)(267,619)(268,620)(269,621)(270,622)(271,623)(272,624)(273,625)(274,626)(275,627)(276,628)(277,629)(278,630)(279,631)(280,632)(281,633)(282,634)(283,635)(284,636)(285,637)(286,638)(287,639)(288,640)(289,641)(290,642)(291,643)(292,644)(293,645)(294,646)(295,647)(296,648)(297,649)(298,650)(299,651)(300,652)(301,653)(302,654)(303,655)(304,656)(305,657)(306,658)(307,659)(308,660)(309,672)(310,673)(311,674)(312,675)(313,676)(314,677)(315,678)(316,679)(317,680)(318,681)(319,682)(320,661)(321,662)(322,663)(323,664)(324,665)(325,666)(326,667)(327,668)(328,669)(329,670)(330,671)(331,694)(332,695)(333,696)(334,697)(335,698)(336,699)(337,700)(338,701)(339,702)(340,703)(341,704)(342,683)(343,684)(344,685)(345,686)(346,687)(347,688)(348,689)(349,690)(350,691)(351,692)(352,693);
poly := sub<Sym(704)|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*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 >;
References : None.
to this polytope