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Polytope of Type {22,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,4,8}*1408a
Also Known As : {{22,4|2},{4,8|2}}. if this polytope has another name.
Group : SmallGroup(1408,13683)
Rank : 4
Schlafli Type : {22,4,8}
Number of vertices, edges, etc : 22, 44, 16, 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 : {22,4,4}*704, {22,2,8}*704
   4-fold quotients : {11,2,8}*352, {22,2,4}*352, {22,4,2}*352
   8-fold quotients : {11,2,4}*176, {22,2,2}*176
   11-fold quotients : {2,4,8}*128a
   16-fold quotients : {11,2,2}*88
   22-fold quotients : {2,4,4}*64, {2,2,8}*64
   44-fold quotients : {2,2,4}*32, {2,4,2}*32
   88-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 89)(  2, 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)( 45,133)( 46,143)( 47,142)( 48,141)
( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)( 56,144)
( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)
( 65,146)( 66,145)( 67,155)( 68,165)( 69,164)( 70,163)( 71,162)( 72,161)
( 73,160)( 74,159)( 75,158)( 76,157)( 77,156)( 78,166)( 79,176)( 80,175)
( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167)
(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)(221,309)(222,319)(223,318)(224,317)
(225,316)(226,315)(227,314)(228,313)(229,312)(230,311)(231,310)(232,320)
(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)(240,323)
(241,322)(242,321)(243,331)(244,341)(245,340)(246,339)(247,338)(248,337)
(249,336)(250,335)(251,334)(252,333)(253,332)(254,342)(255,352)(256,351)
(257,350)(258,349)(259,348)(260,347)(261,346)(262,345)(263,344)(264,343)
(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)
(529,617)(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)(573,661)(574,671)(575,670)(576,669)
(577,668)(578,667)(579,666)(580,665)(581,664)(582,663)(583,662)(584,672)
(585,682)(586,681)(587,680)(588,679)(589,678)(590,677)(591,676)(592,675)
(593,674)(594,673)(595,683)(596,693)(597,692)(598,691)(599,690)(600,689)
(601,688)(602,687)(603,686)(604,685)(605,684)(606,694)(607,704)(608,703)
(609,702)(610,701)(611,700)(612,699)(613,698)(614,697)(615,696)(616,695);;
s1 := (  1,266)(  2,265)(  3,275)(  4,274)(  5,273)(  6,272)(  7,271)(  8,270)
(  9,269)( 10,268)( 11,267)( 12,277)( 13,276)( 14,286)( 15,285)( 16,284)
( 17,283)( 18,282)( 19,281)( 20,280)( 21,279)( 22,278)( 23,288)( 24,287)
( 25,297)( 26,296)( 27,295)( 28,294)( 29,293)( 30,292)( 31,291)( 32,290)
( 33,289)( 34,299)( 35,298)( 36,308)( 37,307)( 38,306)( 39,305)( 40,304)
( 41,303)( 42,302)( 43,301)( 44,300)( 45,310)( 46,309)( 47,319)( 48,318)
( 49,317)( 50,316)( 51,315)( 52,314)( 53,313)( 54,312)( 55,311)( 56,321)
( 57,320)( 58,330)( 59,329)( 60,328)( 61,327)( 62,326)( 63,325)( 64,324)
( 65,323)( 66,322)( 67,332)( 68,331)( 69,341)( 70,340)( 71,339)( 72,338)
( 73,337)( 74,336)( 75,335)( 76,334)( 77,333)( 78,343)( 79,342)( 80,352)
( 81,351)( 82,350)( 83,349)( 84,348)( 85,347)( 86,346)( 87,345)( 88,344)
( 89,178)( 90,177)( 91,187)( 92,186)( 93,185)( 94,184)( 95,183)( 96,182)
( 97,181)( 98,180)( 99,179)(100,189)(101,188)(102,198)(103,197)(104,196)
(105,195)(106,194)(107,193)(108,192)(109,191)(110,190)(111,200)(112,199)
(113,209)(114,208)(115,207)(116,206)(117,205)(118,204)(119,203)(120,202)
(121,201)(122,211)(123,210)(124,220)(125,219)(126,218)(127,217)(128,216)
(129,215)(130,214)(131,213)(132,212)(133,222)(134,221)(135,231)(136,230)
(137,229)(138,228)(139,227)(140,226)(141,225)(142,224)(143,223)(144,233)
(145,232)(146,242)(147,241)(148,240)(149,239)(150,238)(151,237)(152,236)
(153,235)(154,234)(155,244)(156,243)(157,253)(158,252)(159,251)(160,250)
(161,249)(162,248)(163,247)(164,246)(165,245)(166,255)(167,254)(168,264)
(169,263)(170,262)(171,261)(172,260)(173,259)(174,258)(175,257)(176,256)
(353,618)(354,617)(355,627)(356,626)(357,625)(358,624)(359,623)(360,622)
(361,621)(362,620)(363,619)(364,629)(365,628)(366,638)(367,637)(368,636)
(369,635)(370,634)(371,633)(372,632)(373,631)(374,630)(375,640)(376,639)
(377,649)(378,648)(379,647)(380,646)(381,645)(382,644)(383,643)(384,642)
(385,641)(386,651)(387,650)(388,660)(389,659)(390,658)(391,657)(392,656)
(393,655)(394,654)(395,653)(396,652)(397,662)(398,661)(399,671)(400,670)
(401,669)(402,668)(403,667)(404,666)(405,665)(406,664)(407,663)(408,673)
(409,672)(410,682)(411,681)(412,680)(413,679)(414,678)(415,677)(416,676)
(417,675)(418,674)(419,684)(420,683)(421,693)(422,692)(423,691)(424,690)
(425,689)(426,688)(427,687)(428,686)(429,685)(430,695)(431,694)(432,704)
(433,703)(434,702)(435,701)(436,700)(437,699)(438,698)(439,697)(440,696)
(441,530)(442,529)(443,539)(444,538)(445,537)(446,536)(447,535)(448,534)
(449,533)(450,532)(451,531)(452,541)(453,540)(454,550)(455,549)(456,548)
(457,547)(458,546)(459,545)(460,544)(461,543)(462,542)(463,552)(464,551)
(465,561)(466,560)(467,559)(468,558)(469,557)(470,556)(471,555)(472,554)
(473,553)(474,563)(475,562)(476,572)(477,571)(478,570)(479,569)(480,568)
(481,567)(482,566)(483,565)(484,564)(485,574)(486,573)(487,583)(488,582)
(489,581)(490,580)(491,579)(492,578)(493,577)(494,576)(495,575)(496,585)
(497,584)(498,594)(499,593)(500,592)(501,591)(502,590)(503,589)(504,588)
(505,587)(506,586)(507,596)(508,595)(509,605)(510,604)(511,603)(512,602)
(513,601)(514,600)(515,599)(516,598)(517,597)(518,607)(519,606)(520,616)
(521,615)(522,614)(523,613)(524,612)(525,611)(526,610)(527,609)(528,608);;
s2 := ( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)
( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)
( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(133,144)(134,145)
(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)
(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)
(162,173)(163,174)(164,175)(165,176)(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)(221,254)(222,255)(223,256)(224,257)(225,258)(226,259)
(227,260)(228,261)(229,262)(230,263)(231,264)(232,243)(233,244)(234,245)
(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)
(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)
(273,295)(274,296)(275,297)(276,298)(277,299)(278,300)(279,301)(280,302)
(281,303)(282,304)(283,305)(284,306)(285,307)(286,308)(309,342)(310,343)
(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)(318,351)
(319,352)(320,331)(321,332)(322,333)(323,334)(324,335)(325,336)(326,337)
(327,338)(328,339)(329,340)(330,341)(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)
(441,485)(442,486)(443,487)(444,488)(445,489)(446,490)(447,491)(448,492)
(449,493)(450,494)(451,495)(452,496)(453,497)(454,498)(455,499)(456,500)
(457,501)(458,502)(459,503)(460,504)(461,505)(462,506)(463,507)(464,508)
(465,509)(466,510)(467,511)(468,512)(469,513)(470,514)(471,515)(472,516)
(473,517)(474,518)(475,519)(476,520)(477,521)(478,522)(479,523)(480,524)
(481,525)(482,526)(483,527)(484,528)(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)
(617,683)(618,684)(619,685)(620,686)(621,687)(622,688)(623,689)(624,690)
(625,691)(626,692)(627,693)(628,694)(629,695)(630,696)(631,697)(632,698)
(633,699)(634,700)(635,701)(636,702)(637,703)(638,704)(639,661)(640,662)
(641,663)(642,664)(643,665)(644,666)(645,667)(646,668)(647,669)(648,670)
(649,671)(650,672)(651,673)(652,674)(653,675)(654,676)(655,677)(656,678)
(657,679)(658,680)(659,681)(660,682);;
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)
( 89,441)( 90,442)( 91,443)( 92,444)( 93,445)( 94,446)( 95,447)( 96,448)
( 97,449)( 98,450)( 99,451)(100,452)(101,453)(102,454)(103,455)(104,456)
(105,457)(106,458)(107,459)(108,460)(109,461)(110,462)(111,463)(112,464)
(113,465)(114,466)(115,467)(116,468)(117,469)(118,470)(119,471)(120,472)
(121,473)(122,474)(123,475)(124,476)(125,477)(126,478)(127,479)(128,480)
(129,481)(130,482)(131,483)(132,484)(133,496)(134,497)(135,498)(136,499)
(137,500)(138,501)(139,502)(140,503)(141,504)(142,505)(143,506)(144,485)
(145,486)(146,487)(147,488)(148,489)(149,490)(150,491)(151,492)(152,493)
(153,494)(154,495)(155,518)(156,519)(157,520)(158,521)(159,522)(160,523)
(161,524)(162,525)(163,526)(164,527)(165,528)(166,507)(167,508)(168,509)
(169,510)(170,511)(171,512)(172,513)(173,514)(174,515)(175,516)(176,517)
(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)
(265,617)(266,618)(267,619)(268,620)(269,621)(270,622)(271,623)(272,624)
(273,625)(274,626)(275,627)(276,628)(277,629)(278,630)(279,631)(280,632)
(281,633)(282,634)(283,635)(284,636)(285,637)(286,638)(287,639)(288,640)
(289,641)(290,642)(291,643)(292,644)(293,645)(294,646)(295,647)(296,648)
(297,649)(298,650)(299,651)(300,652)(301,653)(302,654)(303,655)(304,656)
(305,657)(306,658)(307,659)(308,660)(309,672)(310,673)(311,674)(312,675)
(313,676)(314,677)(315,678)(316,679)(317,680)(318,681)(319,682)(320,661)
(321,662)(322,663)(323,664)(324,665)(325,666)(326,667)(327,668)(328,669)
(329,670)(330,671)(331,694)(332,695)(333,696)(334,697)(335,698)(336,699)
(337,700)(338,701)(339,702)(340,703)(341,704)(342,683)(343,684)(344,685)
(345,686)(346,687)(347,688)(348,689)(349,690)(350,691)(351,692)(352,693);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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)( 45,133)( 46,143)( 47,142)
( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,134)
( 56,144)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)
( 64,147)( 65,146)( 66,145)( 67,155)( 68,165)( 69,164)( 70,163)( 71,162)
( 72,161)( 73,160)( 74,159)( 75,158)( 76,157)( 77,156)( 78,166)( 79,176)
( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)
( 88,167)(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)(221,309)(222,319)(223,318)
(224,317)(225,316)(226,315)(227,314)(228,313)(229,312)(230,311)(231,310)
(232,320)(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)
(240,323)(241,322)(242,321)(243,331)(244,341)(245,340)(246,339)(247,338)
(248,337)(249,336)(250,335)(251,334)(252,333)(253,332)(254,342)(255,352)
(256,351)(257,350)(258,349)(259,348)(260,347)(261,346)(262,345)(263,344)
(264,343)(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)(529,617)(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)(573,661)(574,671)(575,670)
(576,669)(577,668)(578,667)(579,666)(580,665)(581,664)(582,663)(583,662)
(584,672)(585,682)(586,681)(587,680)(588,679)(589,678)(590,677)(591,676)
(592,675)(593,674)(594,673)(595,683)(596,693)(597,692)(598,691)(599,690)
(600,689)(601,688)(602,687)(603,686)(604,685)(605,684)(606,694)(607,704)
(608,703)(609,702)(610,701)(611,700)(612,699)(613,698)(614,697)(615,696)
(616,695);
s1 := Sym(704)!(  1,266)(  2,265)(  3,275)(  4,274)(  5,273)(  6,272)(  7,271)
(  8,270)(  9,269)( 10,268)( 11,267)( 12,277)( 13,276)( 14,286)( 15,285)
( 16,284)( 17,283)( 18,282)( 19,281)( 20,280)( 21,279)( 22,278)( 23,288)
( 24,287)( 25,297)( 26,296)( 27,295)( 28,294)( 29,293)( 30,292)( 31,291)
( 32,290)( 33,289)( 34,299)( 35,298)( 36,308)( 37,307)( 38,306)( 39,305)
( 40,304)( 41,303)( 42,302)( 43,301)( 44,300)( 45,310)( 46,309)( 47,319)
( 48,318)( 49,317)( 50,316)( 51,315)( 52,314)( 53,313)( 54,312)( 55,311)
( 56,321)( 57,320)( 58,330)( 59,329)( 60,328)( 61,327)( 62,326)( 63,325)
( 64,324)( 65,323)( 66,322)( 67,332)( 68,331)( 69,341)( 70,340)( 71,339)
( 72,338)( 73,337)( 74,336)( 75,335)( 76,334)( 77,333)( 78,343)( 79,342)
( 80,352)( 81,351)( 82,350)( 83,349)( 84,348)( 85,347)( 86,346)( 87,345)
( 88,344)( 89,178)( 90,177)( 91,187)( 92,186)( 93,185)( 94,184)( 95,183)
( 96,182)( 97,181)( 98,180)( 99,179)(100,189)(101,188)(102,198)(103,197)
(104,196)(105,195)(106,194)(107,193)(108,192)(109,191)(110,190)(111,200)
(112,199)(113,209)(114,208)(115,207)(116,206)(117,205)(118,204)(119,203)
(120,202)(121,201)(122,211)(123,210)(124,220)(125,219)(126,218)(127,217)
(128,216)(129,215)(130,214)(131,213)(132,212)(133,222)(134,221)(135,231)
(136,230)(137,229)(138,228)(139,227)(140,226)(141,225)(142,224)(143,223)
(144,233)(145,232)(146,242)(147,241)(148,240)(149,239)(150,238)(151,237)
(152,236)(153,235)(154,234)(155,244)(156,243)(157,253)(158,252)(159,251)
(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)(166,255)(167,254)
(168,264)(169,263)(170,262)(171,261)(172,260)(173,259)(174,258)(175,257)
(176,256)(353,618)(354,617)(355,627)(356,626)(357,625)(358,624)(359,623)
(360,622)(361,621)(362,620)(363,619)(364,629)(365,628)(366,638)(367,637)
(368,636)(369,635)(370,634)(371,633)(372,632)(373,631)(374,630)(375,640)
(376,639)(377,649)(378,648)(379,647)(380,646)(381,645)(382,644)(383,643)
(384,642)(385,641)(386,651)(387,650)(388,660)(389,659)(390,658)(391,657)
(392,656)(393,655)(394,654)(395,653)(396,652)(397,662)(398,661)(399,671)
(400,670)(401,669)(402,668)(403,667)(404,666)(405,665)(406,664)(407,663)
(408,673)(409,672)(410,682)(411,681)(412,680)(413,679)(414,678)(415,677)
(416,676)(417,675)(418,674)(419,684)(420,683)(421,693)(422,692)(423,691)
(424,690)(425,689)(426,688)(427,687)(428,686)(429,685)(430,695)(431,694)
(432,704)(433,703)(434,702)(435,701)(436,700)(437,699)(438,698)(439,697)
(440,696)(441,530)(442,529)(443,539)(444,538)(445,537)(446,536)(447,535)
(448,534)(449,533)(450,532)(451,531)(452,541)(453,540)(454,550)(455,549)
(456,548)(457,547)(458,546)(459,545)(460,544)(461,543)(462,542)(463,552)
(464,551)(465,561)(466,560)(467,559)(468,558)(469,557)(470,556)(471,555)
(472,554)(473,553)(474,563)(475,562)(476,572)(477,571)(478,570)(479,569)
(480,568)(481,567)(482,566)(483,565)(484,564)(485,574)(486,573)(487,583)
(488,582)(489,581)(490,580)(491,579)(492,578)(493,577)(494,576)(495,575)
(496,585)(497,584)(498,594)(499,593)(500,592)(501,591)(502,590)(503,589)
(504,588)(505,587)(506,586)(507,596)(508,595)(509,605)(510,604)(511,603)
(512,602)(513,601)(514,600)(515,599)(516,598)(517,597)(518,607)(519,606)
(520,616)(521,615)(522,614)(523,613)(524,612)(525,611)(526,610)(527,609)
(528,608);
s2 := Sym(704)!( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)
( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)
( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(133,144)
(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)
(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)
(161,172)(162,173)(163,174)(164,175)(165,176)(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)(221,254)(222,255)(223,256)(224,257)(225,258)
(226,259)(227,260)(228,261)(229,262)(230,263)(231,264)(232,243)(233,244)
(234,245)(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)
(242,253)(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)
(272,294)(273,295)(274,296)(275,297)(276,298)(277,299)(278,300)(279,301)
(280,302)(281,303)(282,304)(283,305)(284,306)(285,307)(286,308)(309,342)
(310,343)(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)
(318,351)(319,352)(320,331)(321,332)(322,333)(323,334)(324,335)(325,336)
(326,337)(327,338)(328,339)(329,340)(330,341)(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)(441,485)(442,486)(443,487)(444,488)(445,489)(446,490)(447,491)
(448,492)(449,493)(450,494)(451,495)(452,496)(453,497)(454,498)(455,499)
(456,500)(457,501)(458,502)(459,503)(460,504)(461,505)(462,506)(463,507)
(464,508)(465,509)(466,510)(467,511)(468,512)(469,513)(470,514)(471,515)
(472,516)(473,517)(474,518)(475,519)(476,520)(477,521)(478,522)(479,523)
(480,524)(481,525)(482,526)(483,527)(484,528)(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)(617,683)(618,684)(619,685)(620,686)(621,687)(622,688)(623,689)
(624,690)(625,691)(626,692)(627,693)(628,694)(629,695)(630,696)(631,697)
(632,698)(633,699)(634,700)(635,701)(636,702)(637,703)(638,704)(639,661)
(640,662)(641,663)(642,664)(643,665)(644,666)(645,667)(646,668)(647,669)
(648,670)(649,671)(650,672)(651,673)(652,674)(653,675)(654,676)(655,677)
(656,678)(657,679)(658,680)(659,681)(660,682);
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)( 89,441)( 90,442)( 91,443)( 92,444)( 93,445)( 94,446)( 95,447)
( 96,448)( 97,449)( 98,450)( 99,451)(100,452)(101,453)(102,454)(103,455)
(104,456)(105,457)(106,458)(107,459)(108,460)(109,461)(110,462)(111,463)
(112,464)(113,465)(114,466)(115,467)(116,468)(117,469)(118,470)(119,471)
(120,472)(121,473)(122,474)(123,475)(124,476)(125,477)(126,478)(127,479)
(128,480)(129,481)(130,482)(131,483)(132,484)(133,496)(134,497)(135,498)
(136,499)(137,500)(138,501)(139,502)(140,503)(141,504)(142,505)(143,506)
(144,485)(145,486)(146,487)(147,488)(148,489)(149,490)(150,491)(151,492)
(152,493)(153,494)(154,495)(155,518)(156,519)(157,520)(158,521)(159,522)
(160,523)(161,524)(162,525)(163,526)(164,527)(165,528)(166,507)(167,508)
(168,509)(169,510)(170,511)(171,512)(172,513)(173,514)(174,515)(175,516)
(176,517)(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)(265,617)(266,618)(267,619)(268,620)(269,621)(270,622)(271,623)
(272,624)(273,625)(274,626)(275,627)(276,628)(277,629)(278,630)(279,631)
(280,632)(281,633)(282,634)(283,635)(284,636)(285,637)(286,638)(287,639)
(288,640)(289,641)(290,642)(291,643)(292,644)(293,645)(294,646)(295,647)
(296,648)(297,649)(298,650)(299,651)(300,652)(301,653)(302,654)(303,655)
(304,656)(305,657)(306,658)(307,659)(308,660)(309,672)(310,673)(311,674)
(312,675)(313,676)(314,677)(315,678)(316,679)(317,680)(318,681)(319,682)
(320,661)(321,662)(322,663)(323,664)(324,665)(325,666)(326,667)(327,668)
(328,669)(329,670)(330,671)(331,694)(332,695)(333,696)(334,697)(335,698)
(336,699)(337,700)(338,701)(339,702)(340,703)(341,704)(342,683)(343,684)
(344,685)(345,686)(346,687)(347,688)(348,689)(349,690)(350,691)(351,692)
(352,693);
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*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 >; 
 
References : None.
to this polytope