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