Polytope of Type {4,4,44}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,44}*1408
Also Known As : {{4,4|2},{4,44|2}}. if this polytope has another name.
Group : SmallGroup(1408,7822)
Rank : 4
Schlafli Type : {4,4,44}
Number of vertices, edges, etc : 4, 8, 88, 44
Order of s0s1s2s3 : 44
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 : {2,4,44}*704, {4,2,44}*704, {4,4,22}*704
4-fold quotients : {2,2,44}*352, {2,4,22}*352, {4,2,22}*352
8-fold quotients : {4,2,11}*176, {2,2,22}*176
11-fold quotients : {4,4,4}*128
16-fold quotients : {2,2,11}*88
22-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
44-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
88-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 89)( 2, 90)( 3, 91)( 4, 92)( 5, 93)( 6, 94)( 7, 95)( 8, 96)
( 9, 97)( 10, 98)( 11, 99)( 12,100)( 13,101)( 14,102)( 15,103)( 16,104)
( 17,105)( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)( 24,112)
( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)( 30,118)( 31,119)( 32,120)
( 33,121)( 34,122)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)( 40,128)
( 41,129)( 42,130)( 43,131)( 44,132)( 45,133)( 46,134)( 47,135)( 48,136)
( 49,137)( 50,138)( 51,139)( 52,140)( 53,141)( 54,142)( 55,143)( 56,144)
( 57,145)( 58,146)( 59,147)( 60,148)( 61,149)( 62,150)( 63,151)( 64,152)
( 65,153)( 66,154)( 67,155)( 68,156)( 69,157)( 70,158)( 71,159)( 72,160)
( 73,161)( 74,162)( 75,163)( 76,164)( 77,165)( 78,166)( 79,167)( 80,168)
( 81,169)( 82,170)( 83,171)( 84,172)( 85,173)( 86,174)( 87,175)( 88,176)
(177,265)(178,266)(179,267)(180,268)(181,269)(182,270)(183,271)(184,272)
(185,273)(186,274)(187,275)(188,276)(189,277)(190,278)(191,279)(192,280)
(193,281)(194,282)(195,283)(196,284)(197,285)(198,286)(199,287)(200,288)
(201,289)(202,290)(203,291)(204,292)(205,293)(206,294)(207,295)(208,296)
(209,297)(210,298)(211,299)(212,300)(213,301)(214,302)(215,303)(216,304)
(217,305)(218,306)(219,307)(220,308)(221,309)(222,310)(223,311)(224,312)
(225,313)(226,314)(227,315)(228,316)(229,317)(230,318)(231,319)(232,320)
(233,321)(234,322)(235,323)(236,324)(237,325)(238,326)(239,327)(240,328)
(241,329)(242,330)(243,331)(244,332)(245,333)(246,334)(247,335)(248,336)
(249,337)(250,338)(251,339)(252,340)(253,341)(254,342)(255,343)(256,344)
(257,345)(258,346)(259,347)(260,348)(261,349)(262,350)(263,351)(264,352)
(353,441)(354,442)(355,443)(356,444)(357,445)(358,446)(359,447)(360,448)
(361,449)(362,450)(363,451)(364,452)(365,453)(366,454)(367,455)(368,456)
(369,457)(370,458)(371,459)(372,460)(373,461)(374,462)(375,463)(376,464)
(377,465)(378,466)(379,467)(380,468)(381,469)(382,470)(383,471)(384,472)
(385,473)(386,474)(387,475)(388,476)(389,477)(390,478)(391,479)(392,480)
(393,481)(394,482)(395,483)(396,484)(397,485)(398,486)(399,487)(400,488)
(401,489)(402,490)(403,491)(404,492)(405,493)(406,494)(407,495)(408,496)
(409,497)(410,498)(411,499)(412,500)(413,501)(414,502)(415,503)(416,504)
(417,505)(418,506)(419,507)(420,508)(421,509)(422,510)(423,511)(424,512)
(425,513)(426,514)(427,515)(428,516)(429,517)(430,518)(431,519)(432,520)
(433,521)(434,522)(435,523)(436,524)(437,525)(438,526)(439,527)(440,528)
(529,617)(530,618)(531,619)(532,620)(533,621)(534,622)(535,623)(536,624)
(537,625)(538,626)(539,627)(540,628)(541,629)(542,630)(543,631)(544,632)
(545,633)(546,634)(547,635)(548,636)(549,637)(550,638)(551,639)(552,640)
(553,641)(554,642)(555,643)(556,644)(557,645)(558,646)(559,647)(560,648)
(561,649)(562,650)(563,651)(564,652)(565,653)(566,654)(567,655)(568,656)
(569,657)(570,658)(571,659)(572,660)(573,661)(574,662)(575,663)(576,664)
(577,665)(578,666)(579,667)(580,668)(581,669)(582,670)(583,671)(584,672)
(585,673)(586,674)(587,675)(588,676)(589,677)(590,678)(591,679)(592,680)
(593,681)(594,682)(595,683)(596,684)(597,685)(598,686)(599,687)(600,688)
(601,689)(602,690)(603,691)(604,692)(605,693)(606,694)(607,695)(608,696)
(609,697)(610,698)(611,699)(612,700)(613,701)(614,702)(615,703)(616,704);;
s1 := ( 89,133)( 90,134)( 91,135)( 92,136)( 93,137)( 94,138)( 95,139)( 96,140)
( 97,141)( 98,142)( 99,143)(100,144)(101,145)(102,146)(103,147)(104,148)
(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,155)(112,156)
(113,157)(114,158)(115,159)(116,160)(117,161)(118,162)(119,163)(120,164)
(121,165)(122,166)(123,167)(124,168)(125,169)(126,170)(127,171)(128,172)
(129,173)(130,174)(131,175)(132,176)(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)(221,243)(222,244)(223,245)(224,246)(225,247)(226,248)
(227,249)(228,250)(229,251)(230,252)(231,253)(232,254)(233,255)(234,256)
(235,257)(236,258)(237,259)(238,260)(239,261)(240,262)(241,263)(242,264)
(265,331)(266,332)(267,333)(268,334)(269,335)(270,336)(271,337)(272,338)
(273,339)(274,340)(275,341)(276,342)(277,343)(278,344)(279,345)(280,346)
(281,347)(282,348)(283,349)(284,350)(285,351)(286,352)(287,309)(288,310)
(289,311)(290,312)(291,313)(292,314)(293,315)(294,316)(295,317)(296,318)
(297,319)(298,320)(299,321)(300,322)(301,323)(302,324)(303,325)(304,326)
(305,327)(306,328)(307,329)(308,330)(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)
(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)(617,639)(618,640)(619,641)(620,642)
(621,643)(622,644)(623,645)(624,646)(625,647)(626,648)(627,649)(628,650)
(629,651)(630,652)(631,653)(632,654)(633,655)(634,656)(635,657)(636,658)
(637,659)(638,660)(661,683)(662,684)(663,685)(664,686)(665,687)(666,688)
(667,689)(668,690)(669,691)(670,692)(671,693)(672,694)(673,695)(674,696)
(675,697)(676,698)(677,699)(678,700)(679,701)(680,702)(681,703)(682,704);;
s2 := ( 1,177)( 2,187)( 3,186)( 4,185)( 5,184)( 6,183)( 7,182)( 8,181)
( 9,180)( 10,179)( 11,178)( 12,188)( 13,198)( 14,197)( 15,196)( 16,195)
( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,199)( 24,209)
( 25,208)( 26,207)( 27,206)( 28,205)( 29,204)( 30,203)( 31,202)( 32,201)
( 33,200)( 34,210)( 35,220)( 36,219)( 37,218)( 38,217)( 39,216)( 40,215)
( 41,214)( 42,213)( 43,212)( 44,211)( 45,221)( 46,231)( 47,230)( 48,229)
( 49,228)( 50,227)( 51,226)( 52,225)( 53,224)( 54,223)( 55,222)( 56,232)
( 57,242)( 58,241)( 59,240)( 60,239)( 61,238)( 62,237)( 63,236)( 64,235)
( 65,234)( 66,233)( 67,243)( 68,253)( 69,252)( 70,251)( 71,250)( 72,249)
( 73,248)( 74,247)( 75,246)( 76,245)( 77,244)( 78,254)( 79,264)( 80,263)
( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,257)( 87,256)( 88,255)
( 89,265)( 90,275)( 91,274)( 92,273)( 93,272)( 94,271)( 95,270)( 96,269)
( 97,268)( 98,267)( 99,266)(100,276)(101,286)(102,285)(103,284)(104,283)
(105,282)(106,281)(107,280)(108,279)(109,278)(110,277)(111,287)(112,297)
(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)(120,289)
(121,288)(122,298)(123,308)(124,307)(125,306)(126,305)(127,304)(128,303)
(129,302)(130,301)(131,300)(132,299)(133,309)(134,319)(135,318)(136,317)
(137,316)(138,315)(139,314)(140,313)(141,312)(142,311)(143,310)(144,320)
(145,330)(146,329)(147,328)(148,327)(149,326)(150,325)(151,324)(152,323)
(153,322)(154,321)(155,331)(156,341)(157,340)(158,339)(159,338)(160,337)
(161,336)(162,335)(163,334)(164,333)(165,332)(166,342)(167,352)(168,351)
(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)(176,343)
(353,529)(354,539)(355,538)(356,537)(357,536)(358,535)(359,534)(360,533)
(361,532)(362,531)(363,530)(364,540)(365,550)(366,549)(367,548)(368,547)
(369,546)(370,545)(371,544)(372,543)(373,542)(374,541)(375,551)(376,561)
(377,560)(378,559)(379,558)(380,557)(381,556)(382,555)(383,554)(384,553)
(385,552)(386,562)(387,572)(388,571)(389,570)(390,569)(391,568)(392,567)
(393,566)(394,565)(395,564)(396,563)(397,573)(398,583)(399,582)(400,581)
(401,580)(402,579)(403,578)(404,577)(405,576)(406,575)(407,574)(408,584)
(409,594)(410,593)(411,592)(412,591)(413,590)(414,589)(415,588)(416,587)
(417,586)(418,585)(419,595)(420,605)(421,604)(422,603)(423,602)(424,601)
(425,600)(426,599)(427,598)(428,597)(429,596)(430,606)(431,616)(432,615)
(433,614)(434,613)(435,612)(436,611)(437,610)(438,609)(439,608)(440,607)
(441,617)(442,627)(443,626)(444,625)(445,624)(446,623)(447,622)(448,621)
(449,620)(450,619)(451,618)(452,628)(453,638)(454,637)(455,636)(456,635)
(457,634)(458,633)(459,632)(460,631)(461,630)(462,629)(463,639)(464,649)
(465,648)(466,647)(467,646)(468,645)(469,644)(470,643)(471,642)(472,641)
(473,640)(474,650)(475,660)(476,659)(477,658)(478,657)(479,656)(480,655)
(481,654)(482,653)(483,652)(484,651)(485,661)(486,671)(487,670)(488,669)
(489,668)(490,667)(491,666)(492,665)(493,664)(494,663)(495,662)(496,672)
(497,682)(498,681)(499,680)(500,679)(501,678)(502,677)(503,676)(504,675)
(505,674)(506,673)(507,683)(508,693)(509,692)(510,691)(511,690)(512,689)
(513,688)(514,687)(515,686)(516,685)(517,684)(518,694)(519,704)(520,703)
(521,702)(522,701)(523,700)(524,699)(525,698)(526,697)(527,696)(528,695);;
s3 := ( 1,442)( 2,441)( 3,451)( 4,450)( 5,449)( 6,448)( 7,447)( 8,446)
( 9,445)( 10,444)( 11,443)( 12,453)( 13,452)( 14,462)( 15,461)( 16,460)
( 17,459)( 18,458)( 19,457)( 20,456)( 21,455)( 22,454)( 23,464)( 24,463)
( 25,473)( 26,472)( 27,471)( 28,470)( 29,469)( 30,468)( 31,467)( 32,466)
( 33,465)( 34,475)( 35,474)( 36,484)( 37,483)( 38,482)( 39,481)( 40,480)
( 41,479)( 42,478)( 43,477)( 44,476)( 45,486)( 46,485)( 47,495)( 48,494)
( 49,493)( 50,492)( 51,491)( 52,490)( 53,489)( 54,488)( 55,487)( 56,497)
( 57,496)( 58,506)( 59,505)( 60,504)( 61,503)( 62,502)( 63,501)( 64,500)
( 65,499)( 66,498)( 67,508)( 68,507)( 69,517)( 70,516)( 71,515)( 72,514)
( 73,513)( 74,512)( 75,511)( 76,510)( 77,509)( 78,519)( 79,518)( 80,528)
( 81,527)( 82,526)( 83,525)( 84,524)( 85,523)( 86,522)( 87,521)( 88,520)
( 89,354)( 90,353)( 91,363)( 92,362)( 93,361)( 94,360)( 95,359)( 96,358)
( 97,357)( 98,356)( 99,355)(100,365)(101,364)(102,374)(103,373)(104,372)
(105,371)(106,370)(107,369)(108,368)(109,367)(110,366)(111,376)(112,375)
(113,385)(114,384)(115,383)(116,382)(117,381)(118,380)(119,379)(120,378)
(121,377)(122,387)(123,386)(124,396)(125,395)(126,394)(127,393)(128,392)
(129,391)(130,390)(131,389)(132,388)(133,398)(134,397)(135,407)(136,406)
(137,405)(138,404)(139,403)(140,402)(141,401)(142,400)(143,399)(144,409)
(145,408)(146,418)(147,417)(148,416)(149,415)(150,414)(151,413)(152,412)
(153,411)(154,410)(155,420)(156,419)(157,429)(158,428)(159,427)(160,426)
(161,425)(162,424)(163,423)(164,422)(165,421)(166,431)(167,430)(168,440)
(169,439)(170,438)(171,437)(172,436)(173,435)(174,434)(175,433)(176,432)
(177,629)(178,628)(179,638)(180,637)(181,636)(182,635)(183,634)(184,633)
(185,632)(186,631)(187,630)(188,618)(189,617)(190,627)(191,626)(192,625)
(193,624)(194,623)(195,622)(196,621)(197,620)(198,619)(199,651)(200,650)
(201,660)(202,659)(203,658)(204,657)(205,656)(206,655)(207,654)(208,653)
(209,652)(210,640)(211,639)(212,649)(213,648)(214,647)(215,646)(216,645)
(217,644)(218,643)(219,642)(220,641)(221,673)(222,672)(223,682)(224,681)
(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,662)
(233,661)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)(240,665)
(241,664)(242,663)(243,695)(244,694)(245,704)(246,703)(247,702)(248,701)
(249,700)(250,699)(251,698)(252,697)(253,696)(254,684)(255,683)(256,693)
(257,692)(258,691)(259,690)(260,689)(261,688)(262,687)(263,686)(264,685)
(265,541)(266,540)(267,550)(268,549)(269,548)(270,547)(271,546)(272,545)
(273,544)(274,543)(275,542)(276,530)(277,529)(278,539)(279,538)(280,537)
(281,536)(282,535)(283,534)(284,533)(285,532)(286,531)(287,563)(288,562)
(289,572)(290,571)(291,570)(292,569)(293,568)(294,567)(295,566)(296,565)
(297,564)(298,552)(299,551)(300,561)(301,560)(302,559)(303,558)(304,557)
(305,556)(306,555)(307,554)(308,553)(309,585)(310,584)(311,594)(312,593)
(313,592)(314,591)(315,590)(316,589)(317,588)(318,587)(319,586)(320,574)
(321,573)(322,583)(323,582)(324,581)(325,580)(326,579)(327,578)(328,577)
(329,576)(330,575)(331,607)(332,606)(333,616)(334,615)(335,614)(336,613)
(337,612)(338,611)(339,610)(340,609)(341,608)(342,596)(343,595)(344,605)
(345,604)(346,603)(347,602)(348,601)(349,600)(350,599)(351,598)(352,597);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(704)!( 1, 89)( 2, 90)( 3, 91)( 4, 92)( 5, 93)( 6, 94)( 7, 95)
( 8, 96)( 9, 97)( 10, 98)( 11, 99)( 12,100)( 13,101)( 14,102)( 15,103)
( 16,104)( 17,105)( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)
( 24,112)( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)( 30,118)( 31,119)
( 32,120)( 33,121)( 34,122)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)
( 40,128)( 41,129)( 42,130)( 43,131)( 44,132)( 45,133)( 46,134)( 47,135)
( 48,136)( 49,137)( 50,138)( 51,139)( 52,140)( 53,141)( 54,142)( 55,143)
( 56,144)( 57,145)( 58,146)( 59,147)( 60,148)( 61,149)( 62,150)( 63,151)
( 64,152)( 65,153)( 66,154)( 67,155)( 68,156)( 69,157)( 70,158)( 71,159)
( 72,160)( 73,161)( 74,162)( 75,163)( 76,164)( 77,165)( 78,166)( 79,167)
( 80,168)( 81,169)( 82,170)( 83,171)( 84,172)( 85,173)( 86,174)( 87,175)
( 88,176)(177,265)(178,266)(179,267)(180,268)(181,269)(182,270)(183,271)
(184,272)(185,273)(186,274)(187,275)(188,276)(189,277)(190,278)(191,279)
(192,280)(193,281)(194,282)(195,283)(196,284)(197,285)(198,286)(199,287)
(200,288)(201,289)(202,290)(203,291)(204,292)(205,293)(206,294)(207,295)
(208,296)(209,297)(210,298)(211,299)(212,300)(213,301)(214,302)(215,303)
(216,304)(217,305)(218,306)(219,307)(220,308)(221,309)(222,310)(223,311)
(224,312)(225,313)(226,314)(227,315)(228,316)(229,317)(230,318)(231,319)
(232,320)(233,321)(234,322)(235,323)(236,324)(237,325)(238,326)(239,327)
(240,328)(241,329)(242,330)(243,331)(244,332)(245,333)(246,334)(247,335)
(248,336)(249,337)(250,338)(251,339)(252,340)(253,341)(254,342)(255,343)
(256,344)(257,345)(258,346)(259,347)(260,348)(261,349)(262,350)(263,351)
(264,352)(353,441)(354,442)(355,443)(356,444)(357,445)(358,446)(359,447)
(360,448)(361,449)(362,450)(363,451)(364,452)(365,453)(366,454)(367,455)
(368,456)(369,457)(370,458)(371,459)(372,460)(373,461)(374,462)(375,463)
(376,464)(377,465)(378,466)(379,467)(380,468)(381,469)(382,470)(383,471)
(384,472)(385,473)(386,474)(387,475)(388,476)(389,477)(390,478)(391,479)
(392,480)(393,481)(394,482)(395,483)(396,484)(397,485)(398,486)(399,487)
(400,488)(401,489)(402,490)(403,491)(404,492)(405,493)(406,494)(407,495)
(408,496)(409,497)(410,498)(411,499)(412,500)(413,501)(414,502)(415,503)
(416,504)(417,505)(418,506)(419,507)(420,508)(421,509)(422,510)(423,511)
(424,512)(425,513)(426,514)(427,515)(428,516)(429,517)(430,518)(431,519)
(432,520)(433,521)(434,522)(435,523)(436,524)(437,525)(438,526)(439,527)
(440,528)(529,617)(530,618)(531,619)(532,620)(533,621)(534,622)(535,623)
(536,624)(537,625)(538,626)(539,627)(540,628)(541,629)(542,630)(543,631)
(544,632)(545,633)(546,634)(547,635)(548,636)(549,637)(550,638)(551,639)
(552,640)(553,641)(554,642)(555,643)(556,644)(557,645)(558,646)(559,647)
(560,648)(561,649)(562,650)(563,651)(564,652)(565,653)(566,654)(567,655)
(568,656)(569,657)(570,658)(571,659)(572,660)(573,661)(574,662)(575,663)
(576,664)(577,665)(578,666)(579,667)(580,668)(581,669)(582,670)(583,671)
(584,672)(585,673)(586,674)(587,675)(588,676)(589,677)(590,678)(591,679)
(592,680)(593,681)(594,682)(595,683)(596,684)(597,685)(598,686)(599,687)
(600,688)(601,689)(602,690)(603,691)(604,692)(605,693)(606,694)(607,695)
(608,696)(609,697)(610,698)(611,699)(612,700)(613,701)(614,702)(615,703)
(616,704);
s1 := Sym(704)!( 89,133)( 90,134)( 91,135)( 92,136)( 93,137)( 94,138)( 95,139)
( 96,140)( 97,141)( 98,142)( 99,143)(100,144)(101,145)(102,146)(103,147)
(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,155)
(112,156)(113,157)(114,158)(115,159)(116,160)(117,161)(118,162)(119,163)
(120,164)(121,165)(122,166)(123,167)(124,168)(125,169)(126,170)(127,171)
(128,172)(129,173)(130,174)(131,175)(132,176)(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)(221,243)(222,244)(223,245)(224,246)(225,247)
(226,248)(227,249)(228,250)(229,251)(230,252)(231,253)(232,254)(233,255)
(234,256)(235,257)(236,258)(237,259)(238,260)(239,261)(240,262)(241,263)
(242,264)(265,331)(266,332)(267,333)(268,334)(269,335)(270,336)(271,337)
(272,338)(273,339)(274,340)(275,341)(276,342)(277,343)(278,344)(279,345)
(280,346)(281,347)(282,348)(283,349)(284,350)(285,351)(286,352)(287,309)
(288,310)(289,311)(290,312)(291,313)(292,314)(293,315)(294,316)(295,317)
(296,318)(297,319)(298,320)(299,321)(300,322)(301,323)(302,324)(303,325)
(304,326)(305,327)(306,328)(307,329)(308,330)(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)(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)(617,639)(618,640)(619,641)
(620,642)(621,643)(622,644)(623,645)(624,646)(625,647)(626,648)(627,649)
(628,650)(629,651)(630,652)(631,653)(632,654)(633,655)(634,656)(635,657)
(636,658)(637,659)(638,660)(661,683)(662,684)(663,685)(664,686)(665,687)
(666,688)(667,689)(668,690)(669,691)(670,692)(671,693)(672,694)(673,695)
(674,696)(675,697)(676,698)(677,699)(678,700)(679,701)(680,702)(681,703)
(682,704);
s2 := Sym(704)!( 1,177)( 2,187)( 3,186)( 4,185)( 5,184)( 6,183)( 7,182)
( 8,181)( 9,180)( 10,179)( 11,178)( 12,188)( 13,198)( 14,197)( 15,196)
( 16,195)( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,199)
( 24,209)( 25,208)( 26,207)( 27,206)( 28,205)( 29,204)( 30,203)( 31,202)
( 32,201)( 33,200)( 34,210)( 35,220)( 36,219)( 37,218)( 38,217)( 39,216)
( 40,215)( 41,214)( 42,213)( 43,212)( 44,211)( 45,221)( 46,231)( 47,230)
( 48,229)( 49,228)( 50,227)( 51,226)( 52,225)( 53,224)( 54,223)( 55,222)
( 56,232)( 57,242)( 58,241)( 59,240)( 60,239)( 61,238)( 62,237)( 63,236)
( 64,235)( 65,234)( 66,233)( 67,243)( 68,253)( 69,252)( 70,251)( 71,250)
( 72,249)( 73,248)( 74,247)( 75,246)( 76,245)( 77,244)( 78,254)( 79,264)
( 80,263)( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,257)( 87,256)
( 88,255)( 89,265)( 90,275)( 91,274)( 92,273)( 93,272)( 94,271)( 95,270)
( 96,269)( 97,268)( 98,267)( 99,266)(100,276)(101,286)(102,285)(103,284)
(104,283)(105,282)(106,281)(107,280)(108,279)(109,278)(110,277)(111,287)
(112,297)(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)
(120,289)(121,288)(122,298)(123,308)(124,307)(125,306)(126,305)(127,304)
(128,303)(129,302)(130,301)(131,300)(132,299)(133,309)(134,319)(135,318)
(136,317)(137,316)(138,315)(139,314)(140,313)(141,312)(142,311)(143,310)
(144,320)(145,330)(146,329)(147,328)(148,327)(149,326)(150,325)(151,324)
(152,323)(153,322)(154,321)(155,331)(156,341)(157,340)(158,339)(159,338)
(160,337)(161,336)(162,335)(163,334)(164,333)(165,332)(166,342)(167,352)
(168,351)(169,350)(170,349)(171,348)(172,347)(173,346)(174,345)(175,344)
(176,343)(353,529)(354,539)(355,538)(356,537)(357,536)(358,535)(359,534)
(360,533)(361,532)(362,531)(363,530)(364,540)(365,550)(366,549)(367,548)
(368,547)(369,546)(370,545)(371,544)(372,543)(373,542)(374,541)(375,551)
(376,561)(377,560)(378,559)(379,558)(380,557)(381,556)(382,555)(383,554)
(384,553)(385,552)(386,562)(387,572)(388,571)(389,570)(390,569)(391,568)
(392,567)(393,566)(394,565)(395,564)(396,563)(397,573)(398,583)(399,582)
(400,581)(401,580)(402,579)(403,578)(404,577)(405,576)(406,575)(407,574)
(408,584)(409,594)(410,593)(411,592)(412,591)(413,590)(414,589)(415,588)
(416,587)(417,586)(418,585)(419,595)(420,605)(421,604)(422,603)(423,602)
(424,601)(425,600)(426,599)(427,598)(428,597)(429,596)(430,606)(431,616)
(432,615)(433,614)(434,613)(435,612)(436,611)(437,610)(438,609)(439,608)
(440,607)(441,617)(442,627)(443,626)(444,625)(445,624)(446,623)(447,622)
(448,621)(449,620)(450,619)(451,618)(452,628)(453,638)(454,637)(455,636)
(456,635)(457,634)(458,633)(459,632)(460,631)(461,630)(462,629)(463,639)
(464,649)(465,648)(466,647)(467,646)(468,645)(469,644)(470,643)(471,642)
(472,641)(473,640)(474,650)(475,660)(476,659)(477,658)(478,657)(479,656)
(480,655)(481,654)(482,653)(483,652)(484,651)(485,661)(486,671)(487,670)
(488,669)(489,668)(490,667)(491,666)(492,665)(493,664)(494,663)(495,662)
(496,672)(497,682)(498,681)(499,680)(500,679)(501,678)(502,677)(503,676)
(504,675)(505,674)(506,673)(507,683)(508,693)(509,692)(510,691)(511,690)
(512,689)(513,688)(514,687)(515,686)(516,685)(517,684)(518,694)(519,704)
(520,703)(521,702)(522,701)(523,700)(524,699)(525,698)(526,697)(527,696)
(528,695);
s3 := Sym(704)!( 1,442)( 2,441)( 3,451)( 4,450)( 5,449)( 6,448)( 7,447)
( 8,446)( 9,445)( 10,444)( 11,443)( 12,453)( 13,452)( 14,462)( 15,461)
( 16,460)( 17,459)( 18,458)( 19,457)( 20,456)( 21,455)( 22,454)( 23,464)
( 24,463)( 25,473)( 26,472)( 27,471)( 28,470)( 29,469)( 30,468)( 31,467)
( 32,466)( 33,465)( 34,475)( 35,474)( 36,484)( 37,483)( 38,482)( 39,481)
( 40,480)( 41,479)( 42,478)( 43,477)( 44,476)( 45,486)( 46,485)( 47,495)
( 48,494)( 49,493)( 50,492)( 51,491)( 52,490)( 53,489)( 54,488)( 55,487)
( 56,497)( 57,496)( 58,506)( 59,505)( 60,504)( 61,503)( 62,502)( 63,501)
( 64,500)( 65,499)( 66,498)( 67,508)( 68,507)( 69,517)( 70,516)( 71,515)
( 72,514)( 73,513)( 74,512)( 75,511)( 76,510)( 77,509)( 78,519)( 79,518)
( 80,528)( 81,527)( 82,526)( 83,525)( 84,524)( 85,523)( 86,522)( 87,521)
( 88,520)( 89,354)( 90,353)( 91,363)( 92,362)( 93,361)( 94,360)( 95,359)
( 96,358)( 97,357)( 98,356)( 99,355)(100,365)(101,364)(102,374)(103,373)
(104,372)(105,371)(106,370)(107,369)(108,368)(109,367)(110,366)(111,376)
(112,375)(113,385)(114,384)(115,383)(116,382)(117,381)(118,380)(119,379)
(120,378)(121,377)(122,387)(123,386)(124,396)(125,395)(126,394)(127,393)
(128,392)(129,391)(130,390)(131,389)(132,388)(133,398)(134,397)(135,407)
(136,406)(137,405)(138,404)(139,403)(140,402)(141,401)(142,400)(143,399)
(144,409)(145,408)(146,418)(147,417)(148,416)(149,415)(150,414)(151,413)
(152,412)(153,411)(154,410)(155,420)(156,419)(157,429)(158,428)(159,427)
(160,426)(161,425)(162,424)(163,423)(164,422)(165,421)(166,431)(167,430)
(168,440)(169,439)(170,438)(171,437)(172,436)(173,435)(174,434)(175,433)
(176,432)(177,629)(178,628)(179,638)(180,637)(181,636)(182,635)(183,634)
(184,633)(185,632)(186,631)(187,630)(188,618)(189,617)(190,627)(191,626)
(192,625)(193,624)(194,623)(195,622)(196,621)(197,620)(198,619)(199,651)
(200,650)(201,660)(202,659)(203,658)(204,657)(205,656)(206,655)(207,654)
(208,653)(209,652)(210,640)(211,639)(212,649)(213,648)(214,647)(215,646)
(216,645)(217,644)(218,643)(219,642)(220,641)(221,673)(222,672)(223,682)
(224,681)(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)
(232,662)(233,661)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)
(240,665)(241,664)(242,663)(243,695)(244,694)(245,704)(246,703)(247,702)
(248,701)(249,700)(250,699)(251,698)(252,697)(253,696)(254,684)(255,683)
(256,693)(257,692)(258,691)(259,690)(260,689)(261,688)(262,687)(263,686)
(264,685)(265,541)(266,540)(267,550)(268,549)(269,548)(270,547)(271,546)
(272,545)(273,544)(274,543)(275,542)(276,530)(277,529)(278,539)(279,538)
(280,537)(281,536)(282,535)(283,534)(284,533)(285,532)(286,531)(287,563)
(288,562)(289,572)(290,571)(291,570)(292,569)(293,568)(294,567)(295,566)
(296,565)(297,564)(298,552)(299,551)(300,561)(301,560)(302,559)(303,558)
(304,557)(305,556)(306,555)(307,554)(308,553)(309,585)(310,584)(311,594)
(312,593)(313,592)(314,591)(315,590)(316,589)(317,588)(318,587)(319,586)
(320,574)(321,573)(322,583)(323,582)(324,581)(325,580)(326,579)(327,578)
(328,577)(329,576)(330,575)(331,607)(332,606)(333,616)(334,615)(335,614)
(336,613)(337,612)(338,611)(339,610)(340,609)(341,608)(342,596)(343,595)
(344,605)(345,604)(346,603)(347,602)(348,601)(349,600)(350,599)(351,598)
(352,597);
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*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 >;
References : None.
to this polytope