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Polytope of Type {8,22,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,22,4}*1408
Also Known As : {{8,22|2},{22,4|2}}. if this polytope has another name.
Group : SmallGroup(1408,16180)
Rank : 4
Schlafli Type : {8,22,4}
Number of vertices, edges, etc : 8, 88, 44, 4
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 : {4,22,4}*704, {8,22,2}*704
   4-fold quotients : {2,22,4}*352, {4,22,2}*352
   8-fold quotients : {2,22,2}*176
   11-fold quotients : {8,2,4}*128
   16-fold quotients : {2,11,2}*88
   22-fold quotients : {4,2,4}*64, {8,2,2}*64
   44-fold quotients : {2,2,4}*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 := (  1,353)(  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)
( 89,485)( 90,486)( 91,487)( 92,488)( 93,489)( 94,490)( 95,491)( 96,492)
( 97,493)( 98,494)( 99,495)(100,496)(101,497)(102,498)(103,499)(104,500)
(105,501)(106,502)(107,503)(108,504)(109,505)(110,506)(111,507)(112,508)
(113,509)(114,510)(115,511)(116,512)(117,513)(118,514)(119,515)(120,516)
(121,517)(122,518)(123,519)(124,520)(125,521)(126,522)(127,523)(128,524)
(129,525)(130,526)(131,527)(132,528)(133,441)(134,442)(135,443)(136,444)
(137,445)(138,446)(139,447)(140,448)(141,449)(142,450)(143,451)(144,452)
(145,453)(146,454)(147,455)(148,456)(149,457)(150,458)(151,459)(152,460)
(153,461)(154,462)(155,463)(156,464)(157,465)(158,466)(159,467)(160,468)
(161,469)(162,470)(163,471)(164,472)(165,473)(166,474)(167,475)(168,476)
(169,477)(170,478)(171,479)(172,480)(173,481)(174,482)(175,483)(176,484)
(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)
(265,661)(266,662)(267,663)(268,664)(269,665)(270,666)(271,667)(272,668)
(273,669)(274,670)(275,671)(276,672)(277,673)(278,674)(279,675)(280,676)
(281,677)(282,678)(283,679)(284,680)(285,681)(286,682)(287,683)(288,684)
(289,685)(290,686)(291,687)(292,688)(293,689)(294,690)(295,691)(296,692)
(297,693)(298,694)(299,695)(300,696)(301,697)(302,698)(303,699)(304,700)
(305,701)(306,702)(307,703)(308,704)(309,617)(310,618)(311,619)(312,620)
(313,621)(314,622)(315,623)(316,624)(317,625)(318,626)(319,627)(320,628)
(321,629)(322,630)(323,631)(324,632)(325,633)(326,634)(327,635)(328,636)
(329,637)(330,638)(331,639)(332,640)(333,641)(334,642)(335,643)(336,644)
(337,645)(338,646)(339,647)(340,648)(341,649)(342,650)(343,651)(344,652)
(345,653)(346,654)(347,655)(348,656)(349,657)(350,658)(351,659)(352,660);;
s1 := (  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)( 45,144)( 46,154)( 47,153)( 48,152)
( 49,151)( 50,150)( 51,149)( 52,148)( 53,147)( 54,146)( 55,145)( 56,133)
( 57,143)( 58,142)( 59,141)( 60,140)( 61,139)( 62,138)( 63,137)( 64,136)
( 65,135)( 66,134)( 67,166)( 68,176)( 69,175)( 70,174)( 71,173)( 72,172)
( 73,171)( 74,170)( 75,169)( 76,168)( 77,167)( 78,155)( 79,165)( 80,164)
( 81,163)( 82,162)( 83,161)( 84,160)( 85,159)( 86,158)( 87,157)( 88,156)
(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)(221,320)(222,330)(223,329)(224,328)
(225,327)(226,326)(227,325)(228,324)(229,323)(230,322)(231,321)(232,309)
(233,319)(234,318)(235,317)(236,316)(237,315)(238,314)(239,313)(240,312)
(241,311)(242,310)(243,342)(244,352)(245,351)(246,350)(247,349)(248,348)
(249,347)(250,346)(251,345)(252,344)(253,343)(254,331)(255,341)(256,340)
(257,339)(258,338)(259,337)(260,336)(261,335)(262,334)(263,333)(264,332)
(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)(397,496)(398,506)(399,505)(400,504)
(401,503)(402,502)(403,501)(404,500)(405,499)(406,498)(407,497)(408,485)
(409,495)(410,494)(411,493)(412,492)(413,491)(414,490)(415,489)(416,488)
(417,487)(418,486)(419,518)(420,528)(421,527)(422,526)(423,525)(424,524)
(425,523)(426,522)(427,521)(428,520)(429,519)(430,507)(431,517)(432,516)
(433,515)(434,514)(435,513)(436,512)(437,511)(438,510)(439,509)(440,508)
(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)(573,672)(574,682)(575,681)(576,680)
(577,679)(578,678)(579,677)(580,676)(581,675)(582,674)(583,673)(584,661)
(585,671)(586,670)(587,669)(588,668)(589,667)(590,666)(591,665)(592,664)
(593,663)(594,662)(595,694)(596,704)(597,703)(598,702)(599,701)(600,700)
(601,699)(602,698)(603,697)(604,696)(605,695)(606,683)(607,693)(608,692)
(609,691)(610,690)(611,689)(612,688)(613,687)(614,686)(615,685)(616,684);;
s2 := (  1,134)(  2,133)(  3,143)(  4,142)(  5,141)(  6,140)(  7,139)(  8,138)
(  9,137)( 10,136)( 11,135)( 12,145)( 13,144)( 14,154)( 15,153)( 16,152)
( 17,151)( 18,150)( 19,149)( 20,148)( 21,147)( 22,146)( 23,156)( 24,155)
( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)
( 33,157)( 34,167)( 35,166)( 36,176)( 37,175)( 38,174)( 39,173)( 40,172)
( 41,171)( 42,170)( 43,169)( 44,168)( 45,101)( 46,100)( 47,110)( 48,109)
( 49,108)( 50,107)( 51,106)( 52,105)( 53,104)( 54,103)( 55,102)( 56, 90)
( 57, 89)( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95)( 63, 94)( 64, 93)
( 65, 92)( 66, 91)( 67,123)( 68,122)( 69,132)( 70,131)( 71,130)( 72,129)
( 73,128)( 74,127)( 75,126)( 76,125)( 77,124)( 78,112)( 79,111)( 80,121)
( 81,120)( 82,119)( 83,118)( 84,117)( 85,116)( 86,115)( 87,114)( 88,113)
(177,332)(178,331)(179,341)(180,340)(181,339)(182,338)(183,337)(184,336)
(185,335)(186,334)(187,333)(188,343)(189,342)(190,352)(191,351)(192,350)
(193,349)(194,348)(195,347)(196,346)(197,345)(198,344)(199,310)(200,309)
(201,319)(202,318)(203,317)(204,316)(205,315)(206,314)(207,313)(208,312)
(209,311)(210,321)(211,320)(212,330)(213,329)(214,328)(215,327)(216,326)
(217,325)(218,324)(219,323)(220,322)(221,299)(222,298)(223,308)(224,307)
(225,306)(226,305)(227,304)(228,303)(229,302)(230,301)(231,300)(232,288)
(233,287)(234,297)(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)
(241,290)(242,289)(243,277)(244,276)(245,286)(246,285)(247,284)(248,283)
(249,282)(250,281)(251,280)(252,279)(253,278)(254,266)(255,265)(256,275)
(257,274)(258,273)(259,272)(260,271)(261,270)(262,269)(263,268)(264,267)
(353,442)(354,441)(355,451)(356,450)(357,449)(358,448)(359,447)(360,446)
(361,445)(362,444)(363,443)(364,453)(365,452)(366,462)(367,461)(368,460)
(369,459)(370,458)(371,457)(372,456)(373,455)(374,454)(375,464)(376,463)
(377,473)(378,472)(379,471)(380,470)(381,469)(382,468)(383,467)(384,466)
(385,465)(386,475)(387,474)(388,484)(389,483)(390,482)(391,481)(392,480)
(393,479)(394,478)(395,477)(396,476)(397,486)(398,485)(399,495)(400,494)
(401,493)(402,492)(403,491)(404,490)(405,489)(406,488)(407,487)(408,497)
(409,496)(410,506)(411,505)(412,504)(413,503)(414,502)(415,501)(416,500)
(417,499)(418,498)(419,508)(420,507)(421,517)(422,516)(423,515)(424,514)
(425,513)(426,512)(427,511)(428,510)(429,509)(430,519)(431,518)(432,528)
(433,527)(434,526)(435,525)(436,524)(437,523)(438,522)(439,521)(440,520)
(529,640)(530,639)(531,649)(532,648)(533,647)(534,646)(535,645)(536,644)
(537,643)(538,642)(539,641)(540,651)(541,650)(542,660)(543,659)(544,658)
(545,657)(546,656)(547,655)(548,654)(549,653)(550,652)(551,618)(552,617)
(553,627)(554,626)(555,625)(556,624)(557,623)(558,622)(559,621)(560,620)
(561,619)(562,629)(563,628)(564,638)(565,637)(566,636)(567,635)(568,634)
(569,633)(570,632)(571,631)(572,630)(573,684)(574,683)(575,693)(576,692)
(577,691)(578,690)(579,689)(580,688)(581,687)(582,686)(583,685)(584,695)
(585,694)(586,704)(587,703)(588,702)(589,701)(590,700)(591,699)(592,698)
(593,697)(594,696)(595,662)(596,661)(597,671)(598,670)(599,669)(600,668)
(601,667)(602,666)(603,665)(604,664)(605,663)(606,673)(607,672)(608,682)
(609,681)(610,680)(611,679)(612,678)(613,677)(614,676)(615,675)(616,674);;
s3 := (  1,177)(  2,178)(  3,179)(  4,180)(  5,181)(  6,182)(  7,183)(  8,184)
(  9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)( 16,192)
( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)( 24,200)
( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)( 32,208)
( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)( 40,216)
( 41,217)( 42,218)( 43,219)( 44,220)( 45,221)( 46,222)( 47,223)( 48,224)
( 49,225)( 50,226)( 51,227)( 52,228)( 53,229)( 54,230)( 55,231)( 56,232)
( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)( 64,240)
( 65,241)( 66,242)( 67,243)( 68,244)( 69,245)( 70,246)( 71,247)( 72,248)
( 73,249)( 74,250)( 75,251)( 76,252)( 77,253)( 78,254)( 79,255)( 80,256)
( 81,257)( 82,258)( 83,259)( 84,260)( 85,261)( 86,262)( 87,263)( 88,264)
( 89,265)( 90,266)( 91,267)( 92,268)( 93,269)( 94,270)( 95,271)( 96,272)
( 97,273)( 98,274)( 99,275)(100,276)(101,277)(102,278)(103,279)(104,280)
(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)(112,288)
(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)(120,296)
(121,297)(122,298)(123,299)(124,300)(125,301)(126,302)(127,303)(128,304)
(129,305)(130,306)(131,307)(132,308)(133,309)(134,310)(135,311)(136,312)
(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)(144,320)
(145,321)(146,322)(147,323)(148,324)(149,325)(150,326)(151,327)(152,328)
(153,329)(154,330)(155,331)(156,332)(157,333)(158,334)(159,335)(160,336)
(161,337)(162,338)(163,339)(164,340)(165,341)(166,342)(167,343)(168,344)
(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)(176,352)
(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)(360,536)
(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)(368,544)
(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)(376,552)
(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)(384,560)
(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)(392,568)
(393,569)(394,570)(395,571)(396,572)(397,573)(398,574)(399,575)(400,576)
(401,577)(402,578)(403,579)(404,580)(405,581)(406,582)(407,583)(408,584)
(409,585)(410,586)(411,587)(412,588)(413,589)(414,590)(415,591)(416,592)
(417,593)(418,594)(419,595)(420,596)(421,597)(422,598)(423,599)(424,600)
(425,601)(426,602)(427,603)(428,604)(429,605)(430,606)(431,607)(432,608)
(433,609)(434,610)(435,611)(436,612)(437,613)(438,614)(439,615)(440,616)
(441,617)(442,618)(443,619)(444,620)(445,621)(446,622)(447,623)(448,624)
(449,625)(450,626)(451,627)(452,628)(453,629)(454,630)(455,631)(456,632)
(457,633)(458,634)(459,635)(460,636)(461,637)(462,638)(463,639)(464,640)
(465,641)(466,642)(467,643)(468,644)(469,645)(470,646)(471,647)(472,648)
(473,649)(474,650)(475,651)(476,652)(477,653)(478,654)(479,655)(480,656)
(481,657)(482,658)(483,659)(484,660)(485,661)(486,662)(487,663)(488,664)
(489,665)(490,666)(491,667)(492,668)(493,669)(494,670)(495,671)(496,672)
(497,673)(498,674)(499,675)(500,676)(501,677)(502,678)(503,679)(504,680)
(505,681)(506,682)(507,683)(508,684)(509,685)(510,686)(511,687)(512,688)
(513,689)(514,690)(515,691)(516,692)(517,693)(518,694)(519,695)(520,696)
(521,697)(522,698)(523,699)(524,700)(525,701)(526,702)(527,703)(528,704);;
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*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, 
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)!(  1,353)(  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)( 89,485)( 90,486)( 91,487)( 92,488)( 93,489)( 94,490)( 95,491)
( 96,492)( 97,493)( 98,494)( 99,495)(100,496)(101,497)(102,498)(103,499)
(104,500)(105,501)(106,502)(107,503)(108,504)(109,505)(110,506)(111,507)
(112,508)(113,509)(114,510)(115,511)(116,512)(117,513)(118,514)(119,515)
(120,516)(121,517)(122,518)(123,519)(124,520)(125,521)(126,522)(127,523)
(128,524)(129,525)(130,526)(131,527)(132,528)(133,441)(134,442)(135,443)
(136,444)(137,445)(138,446)(139,447)(140,448)(141,449)(142,450)(143,451)
(144,452)(145,453)(146,454)(147,455)(148,456)(149,457)(150,458)(151,459)
(152,460)(153,461)(154,462)(155,463)(156,464)(157,465)(158,466)(159,467)
(160,468)(161,469)(162,470)(163,471)(164,472)(165,473)(166,474)(167,475)
(168,476)(169,477)(170,478)(171,479)(172,480)(173,481)(174,482)(175,483)
(176,484)(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)(265,661)(266,662)(267,663)(268,664)(269,665)(270,666)(271,667)
(272,668)(273,669)(274,670)(275,671)(276,672)(277,673)(278,674)(279,675)
(280,676)(281,677)(282,678)(283,679)(284,680)(285,681)(286,682)(287,683)
(288,684)(289,685)(290,686)(291,687)(292,688)(293,689)(294,690)(295,691)
(296,692)(297,693)(298,694)(299,695)(300,696)(301,697)(302,698)(303,699)
(304,700)(305,701)(306,702)(307,703)(308,704)(309,617)(310,618)(311,619)
(312,620)(313,621)(314,622)(315,623)(316,624)(317,625)(318,626)(319,627)
(320,628)(321,629)(322,630)(323,631)(324,632)(325,633)(326,634)(327,635)
(328,636)(329,637)(330,638)(331,639)(332,640)(333,641)(334,642)(335,643)
(336,644)(337,645)(338,646)(339,647)(340,648)(341,649)(342,650)(343,651)
(344,652)(345,653)(346,654)(347,655)(348,656)(349,657)(350,658)(351,659)
(352,660);
s1 := 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)( 45,144)( 46,154)( 47,153)
( 48,152)( 49,151)( 50,150)( 51,149)( 52,148)( 53,147)( 54,146)( 55,145)
( 56,133)( 57,143)( 58,142)( 59,141)( 60,140)( 61,139)( 62,138)( 63,137)
( 64,136)( 65,135)( 66,134)( 67,166)( 68,176)( 69,175)( 70,174)( 71,173)
( 72,172)( 73,171)( 74,170)( 75,169)( 76,168)( 77,167)( 78,155)( 79,165)
( 80,164)( 81,163)( 82,162)( 83,161)( 84,160)( 85,159)( 86,158)( 87,157)
( 88,156)(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)(221,320)(222,330)(223,329)
(224,328)(225,327)(226,326)(227,325)(228,324)(229,323)(230,322)(231,321)
(232,309)(233,319)(234,318)(235,317)(236,316)(237,315)(238,314)(239,313)
(240,312)(241,311)(242,310)(243,342)(244,352)(245,351)(246,350)(247,349)
(248,348)(249,347)(250,346)(251,345)(252,344)(253,343)(254,331)(255,341)
(256,340)(257,339)(258,338)(259,337)(260,336)(261,335)(262,334)(263,333)
(264,332)(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)(397,496)(398,506)(399,505)
(400,504)(401,503)(402,502)(403,501)(404,500)(405,499)(406,498)(407,497)
(408,485)(409,495)(410,494)(411,493)(412,492)(413,491)(414,490)(415,489)
(416,488)(417,487)(418,486)(419,518)(420,528)(421,527)(422,526)(423,525)
(424,524)(425,523)(426,522)(427,521)(428,520)(429,519)(430,507)(431,517)
(432,516)(433,515)(434,514)(435,513)(436,512)(437,511)(438,510)(439,509)
(440,508)(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)(573,672)(574,682)(575,681)
(576,680)(577,679)(578,678)(579,677)(580,676)(581,675)(582,674)(583,673)
(584,661)(585,671)(586,670)(587,669)(588,668)(589,667)(590,666)(591,665)
(592,664)(593,663)(594,662)(595,694)(596,704)(597,703)(598,702)(599,701)
(600,700)(601,699)(602,698)(603,697)(604,696)(605,695)(606,683)(607,693)
(608,692)(609,691)(610,690)(611,689)(612,688)(613,687)(614,686)(615,685)
(616,684);
s2 := Sym(704)!(  1,134)(  2,133)(  3,143)(  4,142)(  5,141)(  6,140)(  7,139)
(  8,138)(  9,137)( 10,136)( 11,135)( 12,145)( 13,144)( 14,154)( 15,153)
( 16,152)( 17,151)( 18,150)( 19,149)( 20,148)( 21,147)( 22,146)( 23,156)
( 24,155)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)
( 32,158)( 33,157)( 34,167)( 35,166)( 36,176)( 37,175)( 38,174)( 39,173)
( 40,172)( 41,171)( 42,170)( 43,169)( 44,168)( 45,101)( 46,100)( 47,110)
( 48,109)( 49,108)( 50,107)( 51,106)( 52,105)( 53,104)( 54,103)( 55,102)
( 56, 90)( 57, 89)( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95)( 63, 94)
( 64, 93)( 65, 92)( 66, 91)( 67,123)( 68,122)( 69,132)( 70,131)( 71,130)
( 72,129)( 73,128)( 74,127)( 75,126)( 76,125)( 77,124)( 78,112)( 79,111)
( 80,121)( 81,120)( 82,119)( 83,118)( 84,117)( 85,116)( 86,115)( 87,114)
( 88,113)(177,332)(178,331)(179,341)(180,340)(181,339)(182,338)(183,337)
(184,336)(185,335)(186,334)(187,333)(188,343)(189,342)(190,352)(191,351)
(192,350)(193,349)(194,348)(195,347)(196,346)(197,345)(198,344)(199,310)
(200,309)(201,319)(202,318)(203,317)(204,316)(205,315)(206,314)(207,313)
(208,312)(209,311)(210,321)(211,320)(212,330)(213,329)(214,328)(215,327)
(216,326)(217,325)(218,324)(219,323)(220,322)(221,299)(222,298)(223,308)
(224,307)(225,306)(226,305)(227,304)(228,303)(229,302)(230,301)(231,300)
(232,288)(233,287)(234,297)(235,296)(236,295)(237,294)(238,293)(239,292)
(240,291)(241,290)(242,289)(243,277)(244,276)(245,286)(246,285)(247,284)
(248,283)(249,282)(250,281)(251,280)(252,279)(253,278)(254,266)(255,265)
(256,275)(257,274)(258,273)(259,272)(260,271)(261,270)(262,269)(263,268)
(264,267)(353,442)(354,441)(355,451)(356,450)(357,449)(358,448)(359,447)
(360,446)(361,445)(362,444)(363,443)(364,453)(365,452)(366,462)(367,461)
(368,460)(369,459)(370,458)(371,457)(372,456)(373,455)(374,454)(375,464)
(376,463)(377,473)(378,472)(379,471)(380,470)(381,469)(382,468)(383,467)
(384,466)(385,465)(386,475)(387,474)(388,484)(389,483)(390,482)(391,481)
(392,480)(393,479)(394,478)(395,477)(396,476)(397,486)(398,485)(399,495)
(400,494)(401,493)(402,492)(403,491)(404,490)(405,489)(406,488)(407,487)
(408,497)(409,496)(410,506)(411,505)(412,504)(413,503)(414,502)(415,501)
(416,500)(417,499)(418,498)(419,508)(420,507)(421,517)(422,516)(423,515)
(424,514)(425,513)(426,512)(427,511)(428,510)(429,509)(430,519)(431,518)
(432,528)(433,527)(434,526)(435,525)(436,524)(437,523)(438,522)(439,521)
(440,520)(529,640)(530,639)(531,649)(532,648)(533,647)(534,646)(535,645)
(536,644)(537,643)(538,642)(539,641)(540,651)(541,650)(542,660)(543,659)
(544,658)(545,657)(546,656)(547,655)(548,654)(549,653)(550,652)(551,618)
(552,617)(553,627)(554,626)(555,625)(556,624)(557,623)(558,622)(559,621)
(560,620)(561,619)(562,629)(563,628)(564,638)(565,637)(566,636)(567,635)
(568,634)(569,633)(570,632)(571,631)(572,630)(573,684)(574,683)(575,693)
(576,692)(577,691)(578,690)(579,689)(580,688)(581,687)(582,686)(583,685)
(584,695)(585,694)(586,704)(587,703)(588,702)(589,701)(590,700)(591,699)
(592,698)(593,697)(594,696)(595,662)(596,661)(597,671)(598,670)(599,669)
(600,668)(601,667)(602,666)(603,665)(604,664)(605,663)(606,673)(607,672)
(608,682)(609,681)(610,680)(611,679)(612,678)(613,677)(614,676)(615,675)
(616,674);
s3 := Sym(704)!(  1,177)(  2,178)(  3,179)(  4,180)(  5,181)(  6,182)(  7,183)
(  8,184)(  9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)
( 16,192)( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)
( 24,200)( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)
( 32,208)( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)
( 40,216)( 41,217)( 42,218)( 43,219)( 44,220)( 45,221)( 46,222)( 47,223)
( 48,224)( 49,225)( 50,226)( 51,227)( 52,228)( 53,229)( 54,230)( 55,231)
( 56,232)( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)
( 64,240)( 65,241)( 66,242)( 67,243)( 68,244)( 69,245)( 70,246)( 71,247)
( 72,248)( 73,249)( 74,250)( 75,251)( 76,252)( 77,253)( 78,254)( 79,255)
( 80,256)( 81,257)( 82,258)( 83,259)( 84,260)( 85,261)( 86,262)( 87,263)
( 88,264)( 89,265)( 90,266)( 91,267)( 92,268)( 93,269)( 94,270)( 95,271)
( 96,272)( 97,273)( 98,274)( 99,275)(100,276)(101,277)(102,278)(103,279)
(104,280)(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)
(112,288)(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)
(120,296)(121,297)(122,298)(123,299)(124,300)(125,301)(126,302)(127,303)
(128,304)(129,305)(130,306)(131,307)(132,308)(133,309)(134,310)(135,311)
(136,312)(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)
(144,320)(145,321)(146,322)(147,323)(148,324)(149,325)(150,326)(151,327)
(152,328)(153,329)(154,330)(155,331)(156,332)(157,333)(158,334)(159,335)
(160,336)(161,337)(162,338)(163,339)(164,340)(165,341)(166,342)(167,343)
(168,344)(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)
(176,352)(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)
(360,536)(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)
(368,544)(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)
(376,552)(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)
(384,560)(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)
(392,568)(393,569)(394,570)(395,571)(396,572)(397,573)(398,574)(399,575)
(400,576)(401,577)(402,578)(403,579)(404,580)(405,581)(406,582)(407,583)
(408,584)(409,585)(410,586)(411,587)(412,588)(413,589)(414,590)(415,591)
(416,592)(417,593)(418,594)(419,595)(420,596)(421,597)(422,598)(423,599)
(424,600)(425,601)(426,602)(427,603)(428,604)(429,605)(430,606)(431,607)
(432,608)(433,609)(434,610)(435,611)(436,612)(437,613)(438,614)(439,615)
(440,616)(441,617)(442,618)(443,619)(444,620)(445,621)(446,622)(447,623)
(448,624)(449,625)(450,626)(451,627)(452,628)(453,629)(454,630)(455,631)
(456,632)(457,633)(458,634)(459,635)(460,636)(461,637)(462,638)(463,639)
(464,640)(465,641)(466,642)(467,643)(468,644)(469,645)(470,646)(471,647)
(472,648)(473,649)(474,650)(475,651)(476,652)(477,653)(478,654)(479,655)
(480,656)(481,657)(482,658)(483,659)(484,660)(485,661)(486,662)(487,663)
(488,664)(489,665)(490,666)(491,667)(492,668)(493,669)(494,670)(495,671)
(496,672)(497,673)(498,674)(499,675)(500,676)(501,677)(502,678)(503,679)
(504,680)(505,681)(506,682)(507,683)(508,684)(509,685)(510,686)(511,687)
(512,688)(513,689)(514,690)(515,691)(516,692)(517,693)(518,694)(519,695)
(520,696)(521,697)(522,698)(523,699)(524,700)(525,701)(526,702)(527,703)
(528,704);
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*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, 
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