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Polytope of Type {4,44,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,44,4}*1408
Also Known As : {{4,44|2},{44,4|2}}. if this polytope has another name.
Group : SmallGroup(1408,7823)
Rank : 4
Schlafli Type : {4,44,4}
Number of vertices, edges, etc : 4, 88, 88, 4
Order of s0s1s2s3 : 44
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,44,4}*704, {4,44,2}*704, {4,22,4}*704
   4-fold quotients : {2,44,2}*352, {2,22,4}*352, {4,22,2}*352
   8-fold quotients : {2,22,2}*176
   11-fold quotients : {4,4,4}*128
   16-fold quotients : {2,11,2}*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 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)
( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)
( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)
( 89,133)( 90,143)( 91,142)( 92,141)( 93,140)( 94,139)( 95,138)( 96,137)
( 97,136)( 98,135)( 99,134)(100,144)(101,154)(102,153)(103,152)(104,151)
(105,150)(106,149)(107,148)(108,147)(109,146)(110,145)(111,155)(112,165)
(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)
(121,156)(122,166)(123,176)(124,175)(125,174)(126,173)(127,172)(128,171)
(129,170)(130,169)(131,168)(132,167)(177,199)(178,209)(179,208)(180,207)
(181,206)(182,205)(183,204)(184,203)(185,202)(186,201)(187,200)(188,210)
(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)
(197,212)(198,211)(221,243)(222,253)(223,252)(224,251)(225,250)(226,249)
(227,248)(228,247)(229,246)(230,245)(231,244)(232,254)(233,264)(234,263)
(235,262)(236,261)(237,260)(238,259)(239,258)(240,257)(241,256)(242,255)
(265,331)(266,341)(267,340)(268,339)(269,338)(270,337)(271,336)(272,335)
(273,334)(274,333)(275,332)(276,342)(277,352)(278,351)(279,350)(280,349)
(281,348)(282,347)(283,346)(284,345)(285,344)(286,343)(287,309)(288,319)
(289,318)(290,317)(291,316)(292,315)(293,314)(294,313)(295,312)(296,311)
(297,310)(298,320)(299,330)(300,329)(301,328)(302,327)(303,326)(304,325)
(305,324)(306,323)(307,322)(308,321)(353,397)(354,407)(355,406)(356,405)
(357,404)(358,403)(359,402)(360,401)(361,400)(362,399)(363,398)(364,408)
(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)
(373,410)(374,409)(375,419)(376,429)(377,428)(378,427)(379,426)(380,425)
(381,424)(382,423)(383,422)(384,421)(385,420)(386,430)(387,440)(388,439)
(389,438)(390,437)(391,436)(392,435)(393,434)(394,433)(395,432)(396,431)
(442,451)(443,450)(444,449)(445,448)(446,447)(453,462)(454,461)(455,460)
(456,459)(457,458)(464,473)(465,472)(466,471)(467,470)(468,469)(475,484)
(476,483)(477,482)(478,481)(479,480)(486,495)(487,494)(488,493)(489,492)
(490,491)(497,506)(498,505)(499,504)(500,503)(501,502)(508,517)(509,516)
(510,515)(511,514)(512,513)(519,528)(520,527)(521,526)(522,525)(523,524)
(529,595)(530,605)(531,604)(532,603)(533,602)(534,601)(535,600)(536,599)
(537,598)(538,597)(539,596)(540,606)(541,616)(542,615)(543,614)(544,613)
(545,612)(546,611)(547,610)(548,609)(549,608)(550,607)(551,573)(552,583)
(553,582)(554,581)(555,580)(556,579)(557,578)(558,577)(559,576)(560,575)
(561,574)(562,584)(563,594)(564,593)(565,592)(566,591)(567,590)(568,589)
(569,588)(570,587)(571,586)(572,585)(617,639)(618,649)(619,648)(620,647)
(621,646)(622,645)(623,644)(624,643)(625,642)(626,641)(627,640)(628,650)
(629,660)(630,659)(631,658)(632,657)(633,656)(634,655)(635,654)(636,653)
(637,652)(638,651)(661,683)(662,693)(663,692)(664,691)(665,690)(666,689)
(667,688)(668,687)(669,686)(670,685)(671,684)(672,694)(673,704)(674,703)
(675,702)(676,701)(677,700)(678,699)(679,698)(680,697)(681,696)(682,695);;
s2 := (  1,178)(  2,177)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)(  8,182)
(  9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)( 16,196)
( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,200)( 24,199)
( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,204)( 31,203)( 32,202)
( 33,201)( 34,211)( 35,210)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)
( 41,215)( 42,214)( 43,213)( 44,212)( 45,222)( 46,221)( 47,231)( 48,230)
( 49,229)( 50,228)( 51,227)( 52,226)( 53,225)( 54,224)( 55,223)( 56,233)
( 57,232)( 58,242)( 59,241)( 60,240)( 61,239)( 62,238)( 63,237)( 64,236)
( 65,235)( 66,234)( 67,244)( 68,243)( 69,253)( 70,252)( 71,251)( 72,250)
( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,255)( 79,254)( 80,264)
( 81,263)( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)( 88,256)
( 89,266)( 90,265)( 91,275)( 92,274)( 93,273)( 94,272)( 95,271)( 96,270)
( 97,269)( 98,268)( 99,267)(100,277)(101,276)(102,286)(103,285)(104,284)
(105,283)(106,282)(107,281)(108,280)(109,279)(110,278)(111,288)(112,287)
(113,297)(114,296)(115,295)(116,294)(117,293)(118,292)(119,291)(120,290)
(121,289)(122,299)(123,298)(124,308)(125,307)(126,306)(127,305)(128,304)
(129,303)(130,302)(131,301)(132,300)(133,310)(134,309)(135,319)(136,318)
(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)(144,321)
(145,320)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)(152,324)
(153,323)(154,322)(155,332)(156,331)(157,341)(158,340)(159,339)(160,338)
(161,337)(162,336)(163,335)(164,334)(165,333)(166,343)(167,342)(168,352)
(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,344)
(353,530)(354,529)(355,539)(356,538)(357,537)(358,536)(359,535)(360,534)
(361,533)(362,532)(363,531)(364,541)(365,540)(366,550)(367,549)(368,548)
(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)(375,552)(376,551)
(377,561)(378,560)(379,559)(380,558)(381,557)(382,556)(383,555)(384,554)
(385,553)(386,563)(387,562)(388,572)(389,571)(390,570)(391,569)(392,568)
(393,567)(394,566)(395,565)(396,564)(397,574)(398,573)(399,583)(400,582)
(401,581)(402,580)(403,579)(404,578)(405,577)(406,576)(407,575)(408,585)
(409,584)(410,594)(411,593)(412,592)(413,591)(414,590)(415,589)(416,588)
(417,587)(418,586)(419,596)(420,595)(421,605)(422,604)(423,603)(424,602)
(425,601)(426,600)(427,599)(428,598)(429,597)(430,607)(431,606)(432,616)
(433,615)(434,614)(435,613)(436,612)(437,611)(438,610)(439,609)(440,608)
(441,618)(442,617)(443,627)(444,626)(445,625)(446,624)(447,623)(448,622)
(449,621)(450,620)(451,619)(452,629)(453,628)(454,638)(455,637)(456,636)
(457,635)(458,634)(459,633)(460,632)(461,631)(462,630)(463,640)(464,639)
(465,649)(466,648)(467,647)(468,646)(469,645)(470,644)(471,643)(472,642)
(473,641)(474,651)(475,650)(476,660)(477,659)(478,658)(479,657)(480,656)
(481,655)(482,654)(483,653)(484,652)(485,662)(486,661)(487,671)(488,670)
(489,669)(490,668)(491,667)(492,666)(493,665)(494,664)(495,663)(496,673)
(497,672)(498,682)(499,681)(500,680)(501,679)(502,678)(503,677)(504,676)
(505,675)(506,674)(507,684)(508,683)(509,693)(510,692)(511,691)(512,690)
(513,689)(514,688)(515,687)(516,686)(517,685)(518,695)(519,694)(520,704)
(521,703)(522,702)(523,701)(524,700)(525,699)(526,698)(527,697)(528,696);;
s3 := (  1,441)(  2,442)(  3,443)(  4,444)(  5,445)(  6,446)(  7,447)(  8,448)
(  9,449)( 10,450)( 11,451)( 12,452)( 13,453)( 14,454)( 15,455)( 16,456)
( 17,457)( 18,458)( 19,459)( 20,460)( 21,461)( 22,462)( 23,463)( 24,464)
( 25,465)( 26,466)( 27,467)( 28,468)( 29,469)( 30,470)( 31,471)( 32,472)
( 33,473)( 34,474)( 35,475)( 36,476)( 37,477)( 38,478)( 39,479)( 40,480)
( 41,481)( 42,482)( 43,483)( 44,484)( 45,485)( 46,486)( 47,487)( 48,488)
( 49,489)( 50,490)( 51,491)( 52,492)( 53,493)( 54,494)( 55,495)( 56,496)
( 57,497)( 58,498)( 59,499)( 60,500)( 61,501)( 62,502)( 63,503)( 64,504)
( 65,505)( 66,506)( 67,507)( 68,508)( 69,509)( 70,510)( 71,511)( 72,512)
( 73,513)( 74,514)( 75,515)( 76,516)( 77,517)( 78,518)( 79,519)( 80,520)
( 81,521)( 82,522)( 83,523)( 84,524)( 85,525)( 86,526)( 87,527)( 88,528)
( 89,353)( 90,354)( 91,355)( 92,356)( 93,357)( 94,358)( 95,359)( 96,360)
( 97,361)( 98,362)( 99,363)(100,364)(101,365)(102,366)(103,367)(104,368)
(105,369)(106,370)(107,371)(108,372)(109,373)(110,374)(111,375)(112,376)
(113,377)(114,378)(115,379)(116,380)(117,381)(118,382)(119,383)(120,384)
(121,385)(122,386)(123,387)(124,388)(125,389)(126,390)(127,391)(128,392)
(129,393)(130,394)(131,395)(132,396)(133,397)(134,398)(135,399)(136,400)
(137,401)(138,402)(139,403)(140,404)(141,405)(142,406)(143,407)(144,408)
(145,409)(146,410)(147,411)(148,412)(149,413)(150,414)(151,415)(152,416)
(153,417)(154,418)(155,419)(156,420)(157,421)(158,422)(159,423)(160,424)
(161,425)(162,426)(163,427)(164,428)(165,429)(166,430)(167,431)(168,432)
(169,433)(170,434)(171,435)(172,436)(173,437)(174,438)(175,439)(176,440)
(177,628)(178,629)(179,630)(180,631)(181,632)(182,633)(183,634)(184,635)
(185,636)(186,637)(187,638)(188,617)(189,618)(190,619)(191,620)(192,621)
(193,622)(194,623)(195,624)(196,625)(197,626)(198,627)(199,650)(200,651)
(201,652)(202,653)(203,654)(204,655)(205,656)(206,657)(207,658)(208,659)
(209,660)(210,639)(211,640)(212,641)(213,642)(214,643)(215,644)(216,645)
(217,646)(218,647)(219,648)(220,649)(221,672)(222,673)(223,674)(224,675)
(225,676)(226,677)(227,678)(228,679)(229,680)(230,681)(231,682)(232,661)
(233,662)(234,663)(235,664)(236,665)(237,666)(238,667)(239,668)(240,669)
(241,670)(242,671)(243,694)(244,695)(245,696)(246,697)(247,698)(248,699)
(249,700)(250,701)(251,702)(252,703)(253,704)(254,683)(255,684)(256,685)
(257,686)(258,687)(259,688)(260,689)(261,690)(262,691)(263,692)(264,693)
(265,540)(266,541)(267,542)(268,543)(269,544)(270,545)(271,546)(272,547)
(273,548)(274,549)(275,550)(276,529)(277,530)(278,531)(279,532)(280,533)
(281,534)(282,535)(283,536)(284,537)(285,538)(286,539)(287,562)(288,563)
(289,564)(290,565)(291,566)(292,567)(293,568)(294,569)(295,570)(296,571)
(297,572)(298,551)(299,552)(300,553)(301,554)(302,555)(303,556)(304,557)
(305,558)(306,559)(307,560)(308,561)(309,584)(310,585)(311,586)(312,587)
(313,588)(314,589)(315,590)(316,591)(317,592)(318,593)(319,594)(320,573)
(321,574)(322,575)(323,576)(324,577)(325,578)(326,579)(327,580)(328,581)
(329,582)(330,583)(331,606)(332,607)(333,608)(334,609)(335,610)(336,611)
(337,612)(338,613)(339,614)(340,615)(341,616)(342,595)(343,596)(344,597)
(345,598)(346,599)(347,600)(348,601)(349,602)(350,603)(351,604)(352,605);;
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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)
( 83, 84)( 89,133)( 90,143)( 91,142)( 92,141)( 93,140)( 94,139)( 95,138)
( 96,137)( 97,136)( 98,135)( 99,134)(100,144)(101,154)(102,153)(103,152)
(104,151)(105,150)(106,149)(107,148)(108,147)(109,146)(110,145)(111,155)
(112,165)(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)
(120,157)(121,156)(122,166)(123,176)(124,175)(125,174)(126,173)(127,172)
(128,171)(129,170)(130,169)(131,168)(132,167)(177,199)(178,209)(179,208)
(180,207)(181,206)(182,205)(183,204)(184,203)(185,202)(186,201)(187,200)
(188,210)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)
(196,213)(197,212)(198,211)(221,243)(222,253)(223,252)(224,251)(225,250)
(226,249)(227,248)(228,247)(229,246)(230,245)(231,244)(232,254)(233,264)
(234,263)(235,262)(236,261)(237,260)(238,259)(239,258)(240,257)(241,256)
(242,255)(265,331)(266,341)(267,340)(268,339)(269,338)(270,337)(271,336)
(272,335)(273,334)(274,333)(275,332)(276,342)(277,352)(278,351)(279,350)
(280,349)(281,348)(282,347)(283,346)(284,345)(285,344)(286,343)(287,309)
(288,319)(289,318)(290,317)(291,316)(292,315)(293,314)(294,313)(295,312)
(296,311)(297,310)(298,320)(299,330)(300,329)(301,328)(302,327)(303,326)
(304,325)(305,324)(306,323)(307,322)(308,321)(353,397)(354,407)(355,406)
(356,405)(357,404)(358,403)(359,402)(360,401)(361,400)(362,399)(363,398)
(364,408)(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)
(372,411)(373,410)(374,409)(375,419)(376,429)(377,428)(378,427)(379,426)
(380,425)(381,424)(382,423)(383,422)(384,421)(385,420)(386,430)(387,440)
(388,439)(389,438)(390,437)(391,436)(392,435)(393,434)(394,433)(395,432)
(396,431)(442,451)(443,450)(444,449)(445,448)(446,447)(453,462)(454,461)
(455,460)(456,459)(457,458)(464,473)(465,472)(466,471)(467,470)(468,469)
(475,484)(476,483)(477,482)(478,481)(479,480)(486,495)(487,494)(488,493)
(489,492)(490,491)(497,506)(498,505)(499,504)(500,503)(501,502)(508,517)
(509,516)(510,515)(511,514)(512,513)(519,528)(520,527)(521,526)(522,525)
(523,524)(529,595)(530,605)(531,604)(532,603)(533,602)(534,601)(535,600)
(536,599)(537,598)(538,597)(539,596)(540,606)(541,616)(542,615)(543,614)
(544,613)(545,612)(546,611)(547,610)(548,609)(549,608)(550,607)(551,573)
(552,583)(553,582)(554,581)(555,580)(556,579)(557,578)(558,577)(559,576)
(560,575)(561,574)(562,584)(563,594)(564,593)(565,592)(566,591)(567,590)
(568,589)(569,588)(570,587)(571,586)(572,585)(617,639)(618,649)(619,648)
(620,647)(621,646)(622,645)(623,644)(624,643)(625,642)(626,641)(627,640)
(628,650)(629,660)(630,659)(631,658)(632,657)(633,656)(634,655)(635,654)
(636,653)(637,652)(638,651)(661,683)(662,693)(663,692)(664,691)(665,690)
(666,689)(667,688)(668,687)(669,686)(670,685)(671,684)(672,694)(673,704)
(674,703)(675,702)(676,701)(677,700)(678,699)(679,698)(680,697)(681,696)
(682,695);
s2 := Sym(704)!(  1,178)(  2,177)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)
(  8,182)(  9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)
( 16,196)( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,200)
( 24,199)( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,204)( 31,203)
( 32,202)( 33,201)( 34,211)( 35,210)( 36,220)( 37,219)( 38,218)( 39,217)
( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,222)( 46,221)( 47,231)
( 48,230)( 49,229)( 50,228)( 51,227)( 52,226)( 53,225)( 54,224)( 55,223)
( 56,233)( 57,232)( 58,242)( 59,241)( 60,240)( 61,239)( 62,238)( 63,237)
( 64,236)( 65,235)( 66,234)( 67,244)( 68,243)( 69,253)( 70,252)( 71,251)
( 72,250)( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,255)( 79,254)
( 80,264)( 81,263)( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)
( 88,256)( 89,266)( 90,265)( 91,275)( 92,274)( 93,273)( 94,272)( 95,271)
( 96,270)( 97,269)( 98,268)( 99,267)(100,277)(101,276)(102,286)(103,285)
(104,284)(105,283)(106,282)(107,281)(108,280)(109,279)(110,278)(111,288)
(112,287)(113,297)(114,296)(115,295)(116,294)(117,293)(118,292)(119,291)
(120,290)(121,289)(122,299)(123,298)(124,308)(125,307)(126,306)(127,305)
(128,304)(129,303)(130,302)(131,301)(132,300)(133,310)(134,309)(135,319)
(136,318)(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)
(144,321)(145,320)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)
(152,324)(153,323)(154,322)(155,332)(156,331)(157,341)(158,340)(159,339)
(160,338)(161,337)(162,336)(163,335)(164,334)(165,333)(166,343)(167,342)
(168,352)(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)
(176,344)(353,530)(354,529)(355,539)(356,538)(357,537)(358,536)(359,535)
(360,534)(361,533)(362,532)(363,531)(364,541)(365,540)(366,550)(367,549)
(368,548)(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)(375,552)
(376,551)(377,561)(378,560)(379,559)(380,558)(381,557)(382,556)(383,555)
(384,554)(385,553)(386,563)(387,562)(388,572)(389,571)(390,570)(391,569)
(392,568)(393,567)(394,566)(395,565)(396,564)(397,574)(398,573)(399,583)
(400,582)(401,581)(402,580)(403,579)(404,578)(405,577)(406,576)(407,575)
(408,585)(409,584)(410,594)(411,593)(412,592)(413,591)(414,590)(415,589)
(416,588)(417,587)(418,586)(419,596)(420,595)(421,605)(422,604)(423,603)
(424,602)(425,601)(426,600)(427,599)(428,598)(429,597)(430,607)(431,606)
(432,616)(433,615)(434,614)(435,613)(436,612)(437,611)(438,610)(439,609)
(440,608)(441,618)(442,617)(443,627)(444,626)(445,625)(446,624)(447,623)
(448,622)(449,621)(450,620)(451,619)(452,629)(453,628)(454,638)(455,637)
(456,636)(457,635)(458,634)(459,633)(460,632)(461,631)(462,630)(463,640)
(464,639)(465,649)(466,648)(467,647)(468,646)(469,645)(470,644)(471,643)
(472,642)(473,641)(474,651)(475,650)(476,660)(477,659)(478,658)(479,657)
(480,656)(481,655)(482,654)(483,653)(484,652)(485,662)(486,661)(487,671)
(488,670)(489,669)(490,668)(491,667)(492,666)(493,665)(494,664)(495,663)
(496,673)(497,672)(498,682)(499,681)(500,680)(501,679)(502,678)(503,677)
(504,676)(505,675)(506,674)(507,684)(508,683)(509,693)(510,692)(511,691)
(512,690)(513,689)(514,688)(515,687)(516,686)(517,685)(518,695)(519,694)
(520,704)(521,703)(522,702)(523,701)(524,700)(525,699)(526,698)(527,697)
(528,696);
s3 := Sym(704)!(  1,441)(  2,442)(  3,443)(  4,444)(  5,445)(  6,446)(  7,447)
(  8,448)(  9,449)( 10,450)( 11,451)( 12,452)( 13,453)( 14,454)( 15,455)
( 16,456)( 17,457)( 18,458)( 19,459)( 20,460)( 21,461)( 22,462)( 23,463)
( 24,464)( 25,465)( 26,466)( 27,467)( 28,468)( 29,469)( 30,470)( 31,471)
( 32,472)( 33,473)( 34,474)( 35,475)( 36,476)( 37,477)( 38,478)( 39,479)
( 40,480)( 41,481)( 42,482)( 43,483)( 44,484)( 45,485)( 46,486)( 47,487)
( 48,488)( 49,489)( 50,490)( 51,491)( 52,492)( 53,493)( 54,494)( 55,495)
( 56,496)( 57,497)( 58,498)( 59,499)( 60,500)( 61,501)( 62,502)( 63,503)
( 64,504)( 65,505)( 66,506)( 67,507)( 68,508)( 69,509)( 70,510)( 71,511)
( 72,512)( 73,513)( 74,514)( 75,515)( 76,516)( 77,517)( 78,518)( 79,519)
( 80,520)( 81,521)( 82,522)( 83,523)( 84,524)( 85,525)( 86,526)( 87,527)
( 88,528)( 89,353)( 90,354)( 91,355)( 92,356)( 93,357)( 94,358)( 95,359)
( 96,360)( 97,361)( 98,362)( 99,363)(100,364)(101,365)(102,366)(103,367)
(104,368)(105,369)(106,370)(107,371)(108,372)(109,373)(110,374)(111,375)
(112,376)(113,377)(114,378)(115,379)(116,380)(117,381)(118,382)(119,383)
(120,384)(121,385)(122,386)(123,387)(124,388)(125,389)(126,390)(127,391)
(128,392)(129,393)(130,394)(131,395)(132,396)(133,397)(134,398)(135,399)
(136,400)(137,401)(138,402)(139,403)(140,404)(141,405)(142,406)(143,407)
(144,408)(145,409)(146,410)(147,411)(148,412)(149,413)(150,414)(151,415)
(152,416)(153,417)(154,418)(155,419)(156,420)(157,421)(158,422)(159,423)
(160,424)(161,425)(162,426)(163,427)(164,428)(165,429)(166,430)(167,431)
(168,432)(169,433)(170,434)(171,435)(172,436)(173,437)(174,438)(175,439)
(176,440)(177,628)(178,629)(179,630)(180,631)(181,632)(182,633)(183,634)
(184,635)(185,636)(186,637)(187,638)(188,617)(189,618)(190,619)(191,620)
(192,621)(193,622)(194,623)(195,624)(196,625)(197,626)(198,627)(199,650)
(200,651)(201,652)(202,653)(203,654)(204,655)(205,656)(206,657)(207,658)
(208,659)(209,660)(210,639)(211,640)(212,641)(213,642)(214,643)(215,644)
(216,645)(217,646)(218,647)(219,648)(220,649)(221,672)(222,673)(223,674)
(224,675)(225,676)(226,677)(227,678)(228,679)(229,680)(230,681)(231,682)
(232,661)(233,662)(234,663)(235,664)(236,665)(237,666)(238,667)(239,668)
(240,669)(241,670)(242,671)(243,694)(244,695)(245,696)(246,697)(247,698)
(248,699)(249,700)(250,701)(251,702)(252,703)(253,704)(254,683)(255,684)
(256,685)(257,686)(258,687)(259,688)(260,689)(261,690)(262,691)(263,692)
(264,693)(265,540)(266,541)(267,542)(268,543)(269,544)(270,545)(271,546)
(272,547)(273,548)(274,549)(275,550)(276,529)(277,530)(278,531)(279,532)
(280,533)(281,534)(282,535)(283,536)(284,537)(285,538)(286,539)(287,562)
(288,563)(289,564)(290,565)(291,566)(292,567)(293,568)(294,569)(295,570)
(296,571)(297,572)(298,551)(299,552)(300,553)(301,554)(302,555)(303,556)
(304,557)(305,558)(306,559)(307,560)(308,561)(309,584)(310,585)(311,586)
(312,587)(313,588)(314,589)(315,590)(316,591)(317,592)(318,593)(319,594)
(320,573)(321,574)(322,575)(323,576)(324,577)(325,578)(326,579)(327,580)
(328,581)(329,582)(330,583)(331,606)(332,607)(333,608)(334,609)(335,610)
(336,611)(337,612)(338,613)(339,614)(340,615)(341,616)(342,595)(343,596)
(344,597)(345,598)(346,599)(347,600)(348,601)(349,602)(350,603)(351,604)
(352,605);
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope