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Polytope of Type {4,22,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,22,8}*1408
Also Known As : {{4,22|2},{22,8|2}}. if this polytope has another name.
Group : SmallGroup(1408,16180)
Rank : 4
Schlafli Type : {4,22,8}
Number of vertices, edges, etc : 4, 44, 88, 8
Order of s0s1s2s3 : 88
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,22,4}*704, {2,22,8}*704
   4-fold quotients : {2,22,4}*352, {4,22,2}*352
   8-fold quotients : {2,22,2}*176
   11-fold quotients : {4,2,8}*128
   16-fold quotients : {2,11,2}*88
   22-fold quotients : {4,2,4}*64, {2,2,8}*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 := (  1,177)(  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);;
s1 := (  1,133)(  2,143)(  3,142)(  4,141)(  5,140)(  6,139)(  7,138)(  8,137)
(  9,136)( 10,135)( 11,134)( 12,144)( 13,154)( 14,153)( 15,152)( 16,151)
( 17,150)( 18,149)( 19,148)( 20,147)( 21,146)( 22,145)( 23,155)( 24,165)
( 25,164)( 26,163)( 27,162)( 28,161)( 29,160)( 30,159)( 31,158)( 32,157)
( 33,156)( 34,166)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)( 40,171)
( 41,170)( 42,169)( 43,168)( 44,167)( 45,100)( 46,110)( 47,109)( 48,108)
( 49,107)( 50,106)( 51,105)( 52,104)( 53,103)( 54,102)( 55,101)( 56, 89)
( 57, 99)( 58, 98)( 59, 97)( 60, 96)( 61, 95)( 62, 94)( 63, 93)( 64, 92)
( 65, 91)( 66, 90)( 67,122)( 68,132)( 69,131)( 70,130)( 71,129)( 72,128)
( 73,127)( 74,126)( 75,125)( 76,124)( 77,123)( 78,111)( 79,121)( 80,120)
( 81,119)( 82,118)( 83,117)( 84,116)( 85,115)( 86,114)( 87,113)( 88,112)
(177,331)(178,341)(179,340)(180,339)(181,338)(182,337)(183,336)(184,335)
(185,334)(186,333)(187,332)(188,342)(189,352)(190,351)(191,350)(192,349)
(193,348)(194,347)(195,346)(196,345)(197,344)(198,343)(199,309)(200,319)
(201,318)(202,317)(203,316)(204,315)(205,314)(206,313)(207,312)(208,311)
(209,310)(210,320)(211,330)(212,329)(213,328)(214,327)(215,326)(216,325)
(217,324)(218,323)(219,322)(220,321)(221,298)(222,308)(223,307)(224,306)
(225,305)(226,304)(227,303)(228,302)(229,301)(230,300)(231,299)(232,287)
(233,297)(234,296)(235,295)(236,294)(237,293)(238,292)(239,291)(240,290)
(241,289)(242,288)(243,276)(244,286)(245,285)(246,284)(247,283)(248,282)
(249,281)(250,280)(251,279)(252,278)(253,277)(254,265)(255,275)(256,274)
(257,273)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)(264,266)
(353,441)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)
(361,444)(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)
(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,463)(376,473)
(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)
(385,464)(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)
(393,478)(394,477)(395,476)(396,475)(397,485)(398,495)(399,494)(400,493)
(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)
(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)
(417,498)(418,497)(419,507)(420,517)(421,516)(422,515)(423,514)(424,513)
(425,512)(426,511)(427,510)(428,509)(429,508)(430,518)(431,528)(432,527)
(433,526)(434,525)(435,524)(436,523)(437,522)(438,521)(439,520)(440,519)
(529,639)(530,649)(531,648)(532,647)(533,646)(534,645)(535,644)(536,643)
(537,642)(538,641)(539,640)(540,650)(541,660)(542,659)(543,658)(544,657)
(545,656)(546,655)(547,654)(548,653)(549,652)(550,651)(551,617)(552,627)
(553,626)(554,625)(555,624)(556,623)(557,622)(558,621)(559,620)(560,619)
(561,618)(562,628)(563,638)(564,637)(565,636)(566,635)(567,634)(568,633)
(569,632)(570,631)(571,630)(572,629)(573,683)(574,693)(575,692)(576,691)
(577,690)(578,689)(579,688)(580,687)(581,686)(582,685)(583,684)(584,694)
(585,704)(586,703)(587,702)(588,701)(589,700)(590,699)(591,698)(592,697)
(593,696)(594,695)(595,661)(596,671)(597,670)(598,669)(599,668)(600,667)
(601,666)(602,665)(603,664)(604,663)(605,662)(606,672)(607,682)(608,681)
(609,680)(610,679)(611,678)(612,677)(613,676)(614,675)(615,674)(616,673);;
s2 := (  1, 90)(  2, 89)(  3, 99)(  4, 98)(  5, 97)(  6, 96)(  7, 95)(  8, 94)
(  9, 93)( 10, 92)( 11, 91)( 12,101)( 13,100)( 14,110)( 15,109)( 16,108)
( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,112)( 24,111)
( 25,121)( 26,120)( 27,119)( 28,118)( 29,117)( 30,116)( 31,115)( 32,114)
( 33,113)( 34,123)( 35,122)( 36,132)( 37,131)( 38,130)( 39,129)( 40,128)
( 41,127)( 42,126)( 43,125)( 44,124)( 45,145)( 46,144)( 47,154)( 48,153)
( 49,152)( 50,151)( 51,150)( 52,149)( 53,148)( 54,147)( 55,146)( 56,134)
( 57,133)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)( 64,137)
( 65,136)( 66,135)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)( 72,173)
( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,156)( 79,155)( 80,165)
( 81,164)( 82,163)( 83,162)( 84,161)( 85,160)( 86,159)( 87,158)( 88,157)
(177,266)(178,265)(179,275)(180,274)(181,273)(182,272)(183,271)(184,270)
(185,269)(186,268)(187,267)(188,277)(189,276)(190,286)(191,285)(192,284)
(193,283)(194,282)(195,281)(196,280)(197,279)(198,278)(199,288)(200,287)
(201,297)(202,296)(203,295)(204,294)(205,293)(206,292)(207,291)(208,290)
(209,289)(210,299)(211,298)(212,308)(213,307)(214,306)(215,305)(216,304)
(217,303)(218,302)(219,301)(220,300)(221,321)(222,320)(223,330)(224,329)
(225,328)(226,327)(227,326)(228,325)(229,324)(230,323)(231,322)(232,310)
(233,309)(234,319)(235,318)(236,317)(237,316)(238,315)(239,314)(240,313)
(241,312)(242,311)(243,343)(244,342)(245,352)(246,351)(247,350)(248,349)
(249,348)(250,347)(251,346)(252,345)(253,344)(254,332)(255,331)(256,341)
(257,340)(258,339)(259,338)(260,337)(261,336)(262,335)(263,334)(264,333)
(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)(397,497)(398,496)(399,506)(400,505)
(401,504)(402,503)(403,502)(404,501)(405,500)(406,499)(407,498)(408,486)
(409,485)(410,495)(411,494)(412,493)(413,492)(414,491)(415,490)(416,489)
(417,488)(418,487)(419,519)(420,518)(421,528)(422,527)(423,526)(424,525)
(425,524)(426,523)(427,522)(428,521)(429,520)(430,508)(431,507)(432,517)
(433,516)(434,515)(435,514)(436,513)(437,512)(438,511)(439,510)(440,509)
(529,618)(530,617)(531,627)(532,626)(533,625)(534,624)(535,623)(536,622)
(537,621)(538,620)(539,619)(540,629)(541,628)(542,638)(543,637)(544,636)
(545,635)(546,634)(547,633)(548,632)(549,631)(550,630)(551,640)(552,639)
(553,649)(554,648)(555,647)(556,646)(557,645)(558,644)(559,643)(560,642)
(561,641)(562,651)(563,650)(564,660)(565,659)(566,658)(567,657)(568,656)
(569,655)(570,654)(571,653)(572,652)(573,673)(574,672)(575,682)(576,681)
(577,680)(578,679)(579,678)(580,677)(581,676)(582,675)(583,674)(584,662)
(585,661)(586,671)(587,670)(588,669)(589,668)(590,667)(591,666)(592,665)
(593,664)(594,663)(595,695)(596,694)(597,704)(598,703)(599,702)(600,701)
(601,700)(602,699)(603,698)(604,697)(605,696)(606,684)(607,683)(608,693)
(609,692)(610,691)(611,690)(612,689)(613,688)(614,687)(615,686)(616,685);;
s3 := (  1,353)(  2,354)(  3,355)(  4,356)(  5,357)(  6,358)(  7,359)(  8,360)
(  9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)( 16,368)
( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,375)( 24,376)
( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)( 32,384)
( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)( 40,392)
( 41,393)( 42,394)( 43,395)( 44,396)( 45,408)( 46,409)( 47,410)( 48,411)
( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)( 56,397)
( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)( 64,405)
( 65,406)( 66,407)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)( 72,435)
( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)( 80,421)
( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)( 88,429)
( 89,485)( 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);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(704)!(  1,133)(  2,143)(  3,142)(  4,141)(  5,140)(  6,139)(  7,138)
(  8,137)(  9,136)( 10,135)( 11,134)( 12,144)( 13,154)( 14,153)( 15,152)
( 16,151)( 17,150)( 18,149)( 19,148)( 20,147)( 21,146)( 22,145)( 23,155)
( 24,165)( 25,164)( 26,163)( 27,162)( 28,161)( 29,160)( 30,159)( 31,158)
( 32,157)( 33,156)( 34,166)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)
( 40,171)( 41,170)( 42,169)( 43,168)( 44,167)( 45,100)( 46,110)( 47,109)
( 48,108)( 49,107)( 50,106)( 51,105)( 52,104)( 53,103)( 54,102)( 55,101)
( 56, 89)( 57, 99)( 58, 98)( 59, 97)( 60, 96)( 61, 95)( 62, 94)( 63, 93)
( 64, 92)( 65, 91)( 66, 90)( 67,122)( 68,132)( 69,131)( 70,130)( 71,129)
( 72,128)( 73,127)( 74,126)( 75,125)( 76,124)( 77,123)( 78,111)( 79,121)
( 80,120)( 81,119)( 82,118)( 83,117)( 84,116)( 85,115)( 86,114)( 87,113)
( 88,112)(177,331)(178,341)(179,340)(180,339)(181,338)(182,337)(183,336)
(184,335)(185,334)(186,333)(187,332)(188,342)(189,352)(190,351)(191,350)
(192,349)(193,348)(194,347)(195,346)(196,345)(197,344)(198,343)(199,309)
(200,319)(201,318)(202,317)(203,316)(204,315)(205,314)(206,313)(207,312)
(208,311)(209,310)(210,320)(211,330)(212,329)(213,328)(214,327)(215,326)
(216,325)(217,324)(218,323)(219,322)(220,321)(221,298)(222,308)(223,307)
(224,306)(225,305)(226,304)(227,303)(228,302)(229,301)(230,300)(231,299)
(232,287)(233,297)(234,296)(235,295)(236,294)(237,293)(238,292)(239,291)
(240,290)(241,289)(242,288)(243,276)(244,286)(245,285)(246,284)(247,283)
(248,282)(249,281)(250,280)(251,279)(252,278)(253,277)(254,265)(255,275)
(256,274)(257,273)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)
(264,266)(353,441)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)
(360,445)(361,444)(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)
(368,459)(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,463)
(376,473)(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)
(384,465)(385,464)(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)
(392,479)(393,478)(394,477)(395,476)(396,475)(397,485)(398,495)(399,494)
(400,493)(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)
(408,496)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)
(416,499)(417,498)(418,497)(419,507)(420,517)(421,516)(422,515)(423,514)
(424,513)(425,512)(426,511)(427,510)(428,509)(429,508)(430,518)(431,528)
(432,527)(433,526)(434,525)(435,524)(436,523)(437,522)(438,521)(439,520)
(440,519)(529,639)(530,649)(531,648)(532,647)(533,646)(534,645)(535,644)
(536,643)(537,642)(538,641)(539,640)(540,650)(541,660)(542,659)(543,658)
(544,657)(545,656)(546,655)(547,654)(548,653)(549,652)(550,651)(551,617)
(552,627)(553,626)(554,625)(555,624)(556,623)(557,622)(558,621)(559,620)
(560,619)(561,618)(562,628)(563,638)(564,637)(565,636)(566,635)(567,634)
(568,633)(569,632)(570,631)(571,630)(572,629)(573,683)(574,693)(575,692)
(576,691)(577,690)(578,689)(579,688)(580,687)(581,686)(582,685)(583,684)
(584,694)(585,704)(586,703)(587,702)(588,701)(589,700)(590,699)(591,698)
(592,697)(593,696)(594,695)(595,661)(596,671)(597,670)(598,669)(599,668)
(600,667)(601,666)(602,665)(603,664)(604,663)(605,662)(606,672)(607,682)
(608,681)(609,680)(610,679)(611,678)(612,677)(613,676)(614,675)(615,674)
(616,673);
s2 := Sym(704)!(  1, 90)(  2, 89)(  3, 99)(  4, 98)(  5, 97)(  6, 96)(  7, 95)
(  8, 94)(  9, 93)( 10, 92)( 11, 91)( 12,101)( 13,100)( 14,110)( 15,109)
( 16,108)( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,112)
( 24,111)( 25,121)( 26,120)( 27,119)( 28,118)( 29,117)( 30,116)( 31,115)
( 32,114)( 33,113)( 34,123)( 35,122)( 36,132)( 37,131)( 38,130)( 39,129)
( 40,128)( 41,127)( 42,126)( 43,125)( 44,124)( 45,145)( 46,144)( 47,154)
( 48,153)( 49,152)( 50,151)( 51,150)( 52,149)( 53,148)( 54,147)( 55,146)
( 56,134)( 57,133)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)
( 64,137)( 65,136)( 66,135)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)
( 72,173)( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,156)( 79,155)
( 80,165)( 81,164)( 82,163)( 83,162)( 84,161)( 85,160)( 86,159)( 87,158)
( 88,157)(177,266)(178,265)(179,275)(180,274)(181,273)(182,272)(183,271)
(184,270)(185,269)(186,268)(187,267)(188,277)(189,276)(190,286)(191,285)
(192,284)(193,283)(194,282)(195,281)(196,280)(197,279)(198,278)(199,288)
(200,287)(201,297)(202,296)(203,295)(204,294)(205,293)(206,292)(207,291)
(208,290)(209,289)(210,299)(211,298)(212,308)(213,307)(214,306)(215,305)
(216,304)(217,303)(218,302)(219,301)(220,300)(221,321)(222,320)(223,330)
(224,329)(225,328)(226,327)(227,326)(228,325)(229,324)(230,323)(231,322)
(232,310)(233,309)(234,319)(235,318)(236,317)(237,316)(238,315)(239,314)
(240,313)(241,312)(242,311)(243,343)(244,342)(245,352)(246,351)(247,350)
(248,349)(249,348)(250,347)(251,346)(252,345)(253,344)(254,332)(255,331)
(256,341)(257,340)(258,339)(259,338)(260,337)(261,336)(262,335)(263,334)
(264,333)(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)(397,497)(398,496)(399,506)
(400,505)(401,504)(402,503)(403,502)(404,501)(405,500)(406,499)(407,498)
(408,486)(409,485)(410,495)(411,494)(412,493)(413,492)(414,491)(415,490)
(416,489)(417,488)(418,487)(419,519)(420,518)(421,528)(422,527)(423,526)
(424,525)(425,524)(426,523)(427,522)(428,521)(429,520)(430,508)(431,507)
(432,517)(433,516)(434,515)(435,514)(436,513)(437,512)(438,511)(439,510)
(440,509)(529,618)(530,617)(531,627)(532,626)(533,625)(534,624)(535,623)
(536,622)(537,621)(538,620)(539,619)(540,629)(541,628)(542,638)(543,637)
(544,636)(545,635)(546,634)(547,633)(548,632)(549,631)(550,630)(551,640)
(552,639)(553,649)(554,648)(555,647)(556,646)(557,645)(558,644)(559,643)
(560,642)(561,641)(562,651)(563,650)(564,660)(565,659)(566,658)(567,657)
(568,656)(569,655)(570,654)(571,653)(572,652)(573,673)(574,672)(575,682)
(576,681)(577,680)(578,679)(579,678)(580,677)(581,676)(582,675)(583,674)
(584,662)(585,661)(586,671)(587,670)(588,669)(589,668)(590,667)(591,666)
(592,665)(593,664)(594,663)(595,695)(596,694)(597,704)(598,703)(599,702)
(600,701)(601,700)(602,699)(603,698)(604,697)(605,696)(606,684)(607,683)
(608,693)(609,692)(610,691)(611,690)(612,689)(613,688)(614,687)(615,686)
(616,685);
s3 := Sym(704)!(  1,353)(  2,354)(  3,355)(  4,356)(  5,357)(  6,358)(  7,359)
(  8,360)(  9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)
( 16,368)( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,375)
( 24,376)( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)
( 32,384)( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)
( 40,392)( 41,393)( 42,394)( 43,395)( 44,396)( 45,408)( 46,409)( 47,410)
( 48,411)( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)
( 56,397)( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)
( 64,405)( 65,406)( 66,407)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)
( 72,435)( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)
( 80,421)( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)
( 88,429)( 89,485)( 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);
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*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 >; 
 
References : None.
to this polytope