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Polytope of Type {8,4,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,22}*1408a
Also Known As : {{8,4|2},{4,22|2}}. if this polytope has another name.
Group : SmallGroup(1408,13683)
Rank : 4
Schlafli Type : {8,4,22}
Number of vertices, edges, etc : 8, 16, 44, 22
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 : {4,4,22}*704, {8,2,22}*704
   4-fold quotients : {8,2,11}*352, {2,4,22}*352, {4,2,22}*352
   8-fold quotients : {4,2,11}*176, {2,2,22}*176
   11-fold quotients : {8,4,2}*128a
   16-fold quotients : {2,2,11}*88
   22-fold quotients : {4,4,2}*64, {8,2,2}*64
   44-fold quotients : {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 := (  1,353)(  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);;
s1 := ( 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);;
s2 := (  1,265)(  2,275)(  3,274)(  4,273)(  5,272)(  6,271)(  7,270)(  8,269)
(  9,268)( 10,267)( 11,266)( 12,276)( 13,286)( 14,285)( 15,284)( 16,283)
( 17,282)( 18,281)( 19,280)( 20,279)( 21,278)( 22,277)( 23,287)( 24,297)
( 25,296)( 26,295)( 27,294)( 28,293)( 29,292)( 30,291)( 31,290)( 32,289)
( 33,288)( 34,298)( 35,308)( 36,307)( 37,306)( 38,305)( 39,304)( 40,303)
( 41,302)( 42,301)( 43,300)( 44,299)( 45,309)( 46,319)( 47,318)( 48,317)
( 49,316)( 50,315)( 51,314)( 52,313)( 53,312)( 54,311)( 55,310)( 56,320)
( 57,330)( 58,329)( 59,328)( 60,327)( 61,326)( 62,325)( 63,324)( 64,323)
( 65,322)( 66,321)( 67,331)( 68,341)( 69,340)( 70,339)( 71,338)( 72,337)
( 73,336)( 74,335)( 75,334)( 76,333)( 77,332)( 78,342)( 79,352)( 80,351)
( 81,350)( 82,349)( 83,348)( 84,347)( 85,346)( 86,345)( 87,344)( 88,343)
( 89,177)( 90,187)( 91,186)( 92,185)( 93,184)( 94,183)( 95,182)( 96,181)
( 97,180)( 98,179)( 99,178)(100,188)(101,198)(102,197)(103,196)(104,195)
(105,194)(106,193)(107,192)(108,191)(109,190)(110,189)(111,199)(112,209)
(113,208)(114,207)(115,206)(116,205)(117,204)(118,203)(119,202)(120,201)
(121,200)(122,210)(123,220)(124,219)(125,218)(126,217)(127,216)(128,215)
(129,214)(130,213)(131,212)(132,211)(133,221)(134,231)(135,230)(136,229)
(137,228)(138,227)(139,226)(140,225)(141,224)(142,223)(143,222)(144,232)
(145,242)(146,241)(147,240)(148,239)(149,238)(150,237)(151,236)(152,235)
(153,234)(154,233)(155,243)(156,253)(157,252)(158,251)(159,250)(160,249)
(161,248)(162,247)(163,246)(164,245)(165,244)(166,254)(167,264)(168,263)
(169,262)(170,261)(171,260)(172,259)(173,258)(174,257)(175,256)(176,255)
(353,617)(354,627)(355,626)(356,625)(357,624)(358,623)(359,622)(360,621)
(361,620)(362,619)(363,618)(364,628)(365,638)(366,637)(367,636)(368,635)
(369,634)(370,633)(371,632)(372,631)(373,630)(374,629)(375,639)(376,649)
(377,648)(378,647)(379,646)(380,645)(381,644)(382,643)(383,642)(384,641)
(385,640)(386,650)(387,660)(388,659)(389,658)(390,657)(391,656)(392,655)
(393,654)(394,653)(395,652)(396,651)(397,661)(398,671)(399,670)(400,669)
(401,668)(402,667)(403,666)(404,665)(405,664)(406,663)(407,662)(408,672)
(409,682)(410,681)(411,680)(412,679)(413,678)(414,677)(415,676)(416,675)
(417,674)(418,673)(419,683)(420,693)(421,692)(422,691)(423,690)(424,689)
(425,688)(426,687)(427,686)(428,685)(429,684)(430,694)(431,704)(432,703)
(433,702)(434,701)(435,700)(436,699)(437,698)(438,697)(439,696)(440,695)
(441,529)(442,539)(443,538)(444,537)(445,536)(446,535)(447,534)(448,533)
(449,532)(450,531)(451,530)(452,540)(453,550)(454,549)(455,548)(456,547)
(457,546)(458,545)(459,544)(460,543)(461,542)(462,541)(463,551)(464,561)
(465,560)(466,559)(467,558)(468,557)(469,556)(470,555)(471,554)(472,553)
(473,552)(474,562)(475,572)(476,571)(477,570)(478,569)(479,568)(480,567)
(481,566)(482,565)(483,564)(484,563)(485,573)(486,583)(487,582)(488,581)
(489,580)(490,579)(491,578)(492,577)(493,576)(494,575)(495,574)(496,584)
(497,594)(498,593)(499,592)(500,591)(501,590)(502,589)(503,588)(504,587)
(505,586)(506,585)(507,595)(508,605)(509,604)(510,603)(511,602)(512,601)
(513,600)(514,599)(515,598)(516,597)(517,596)(518,606)(519,616)(520,615)
(521,614)(522,613)(523,612)(524,611)(525,610)(526,609)(527,608)(528,607);;
s3 := (  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)( 45,134)( 46,133)( 47,143)( 48,142)
( 49,141)( 50,140)( 51,139)( 52,138)( 53,137)( 54,136)( 55,135)( 56,145)
( 57,144)( 58,154)( 59,153)( 60,152)( 61,151)( 62,150)( 63,149)( 64,148)
( 65,147)( 66,146)( 67,156)( 68,155)( 69,165)( 70,164)( 71,163)( 72,162)
( 73,161)( 74,160)( 75,159)( 76,158)( 77,157)( 78,167)( 79,166)( 80,176)
( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)( 88,168)
(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)(221,310)(222,309)(223,319)(224,318)
(225,317)(226,316)(227,315)(228,314)(229,313)(230,312)(231,311)(232,321)
(233,320)(234,330)(235,329)(236,328)(237,327)(238,326)(239,325)(240,324)
(241,323)(242,322)(243,332)(244,331)(245,341)(246,340)(247,339)(248,338)
(249,337)(250,336)(251,335)(252,334)(253,333)(254,343)(255,342)(256,352)
(257,351)(258,350)(259,349)(260,348)(261,347)(262,346)(263,345)(264,344)
(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)
(529,618)(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)(573,662)(574,661)(575,671)(576,670)
(577,669)(578,668)(579,667)(580,666)(581,665)(582,664)(583,663)(584,673)
(585,672)(586,682)(587,681)(588,680)(589,679)(590,678)(591,677)(592,676)
(593,675)(594,674)(595,684)(596,683)(597,693)(598,692)(599,691)(600,690)
(601,689)(602,688)(603,687)(604,686)(605,685)(606,695)(607,694)(608,704)
(609,703)(610,702)(611,701)(612,700)(613,699)(614,698)(615,697)(616,696);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 89,441)( 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);
s1 := 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);
s2 := Sym(704)!(  1,265)(  2,275)(  3,274)(  4,273)(  5,272)(  6,271)(  7,270)
(  8,269)(  9,268)( 10,267)( 11,266)( 12,276)( 13,286)( 14,285)( 15,284)
( 16,283)( 17,282)( 18,281)( 19,280)( 20,279)( 21,278)( 22,277)( 23,287)
( 24,297)( 25,296)( 26,295)( 27,294)( 28,293)( 29,292)( 30,291)( 31,290)
( 32,289)( 33,288)( 34,298)( 35,308)( 36,307)( 37,306)( 38,305)( 39,304)
( 40,303)( 41,302)( 42,301)( 43,300)( 44,299)( 45,309)( 46,319)( 47,318)
( 48,317)( 49,316)( 50,315)( 51,314)( 52,313)( 53,312)( 54,311)( 55,310)
( 56,320)( 57,330)( 58,329)( 59,328)( 60,327)( 61,326)( 62,325)( 63,324)
( 64,323)( 65,322)( 66,321)( 67,331)( 68,341)( 69,340)( 70,339)( 71,338)
( 72,337)( 73,336)( 74,335)( 75,334)( 76,333)( 77,332)( 78,342)( 79,352)
( 80,351)( 81,350)( 82,349)( 83,348)( 84,347)( 85,346)( 86,345)( 87,344)
( 88,343)( 89,177)( 90,187)( 91,186)( 92,185)( 93,184)( 94,183)( 95,182)
( 96,181)( 97,180)( 98,179)( 99,178)(100,188)(101,198)(102,197)(103,196)
(104,195)(105,194)(106,193)(107,192)(108,191)(109,190)(110,189)(111,199)
(112,209)(113,208)(114,207)(115,206)(116,205)(117,204)(118,203)(119,202)
(120,201)(121,200)(122,210)(123,220)(124,219)(125,218)(126,217)(127,216)
(128,215)(129,214)(130,213)(131,212)(132,211)(133,221)(134,231)(135,230)
(136,229)(137,228)(138,227)(139,226)(140,225)(141,224)(142,223)(143,222)
(144,232)(145,242)(146,241)(147,240)(148,239)(149,238)(150,237)(151,236)
(152,235)(153,234)(154,233)(155,243)(156,253)(157,252)(158,251)(159,250)
(160,249)(161,248)(162,247)(163,246)(164,245)(165,244)(166,254)(167,264)
(168,263)(169,262)(170,261)(171,260)(172,259)(173,258)(174,257)(175,256)
(176,255)(353,617)(354,627)(355,626)(356,625)(357,624)(358,623)(359,622)
(360,621)(361,620)(362,619)(363,618)(364,628)(365,638)(366,637)(367,636)
(368,635)(369,634)(370,633)(371,632)(372,631)(373,630)(374,629)(375,639)
(376,649)(377,648)(378,647)(379,646)(380,645)(381,644)(382,643)(383,642)
(384,641)(385,640)(386,650)(387,660)(388,659)(389,658)(390,657)(391,656)
(392,655)(393,654)(394,653)(395,652)(396,651)(397,661)(398,671)(399,670)
(400,669)(401,668)(402,667)(403,666)(404,665)(405,664)(406,663)(407,662)
(408,672)(409,682)(410,681)(411,680)(412,679)(413,678)(414,677)(415,676)
(416,675)(417,674)(418,673)(419,683)(420,693)(421,692)(422,691)(423,690)
(424,689)(425,688)(426,687)(427,686)(428,685)(429,684)(430,694)(431,704)
(432,703)(433,702)(434,701)(435,700)(436,699)(437,698)(438,697)(439,696)
(440,695)(441,529)(442,539)(443,538)(444,537)(445,536)(446,535)(447,534)
(448,533)(449,532)(450,531)(451,530)(452,540)(453,550)(454,549)(455,548)
(456,547)(457,546)(458,545)(459,544)(460,543)(461,542)(462,541)(463,551)
(464,561)(465,560)(466,559)(467,558)(468,557)(469,556)(470,555)(471,554)
(472,553)(473,552)(474,562)(475,572)(476,571)(477,570)(478,569)(479,568)
(480,567)(481,566)(482,565)(483,564)(484,563)(485,573)(486,583)(487,582)
(488,581)(489,580)(490,579)(491,578)(492,577)(493,576)(494,575)(495,574)
(496,584)(497,594)(498,593)(499,592)(500,591)(501,590)(502,589)(503,588)
(504,587)(505,586)(506,585)(507,595)(508,605)(509,604)(510,603)(511,602)
(512,601)(513,600)(514,599)(515,598)(516,597)(517,596)(518,606)(519,616)
(520,615)(521,614)(522,613)(523,612)(524,611)(525,610)(526,609)(527,608)
(528,607);
s3 := 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)( 45,134)( 46,133)( 47,143)
( 48,142)( 49,141)( 50,140)( 51,139)( 52,138)( 53,137)( 54,136)( 55,135)
( 56,145)( 57,144)( 58,154)( 59,153)( 60,152)( 61,151)( 62,150)( 63,149)
( 64,148)( 65,147)( 66,146)( 67,156)( 68,155)( 69,165)( 70,164)( 71,163)
( 72,162)( 73,161)( 74,160)( 75,159)( 76,158)( 77,157)( 78,167)( 79,166)
( 80,176)( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)
( 88,168)(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)(221,310)(222,309)(223,319)
(224,318)(225,317)(226,316)(227,315)(228,314)(229,313)(230,312)(231,311)
(232,321)(233,320)(234,330)(235,329)(236,328)(237,327)(238,326)(239,325)
(240,324)(241,323)(242,322)(243,332)(244,331)(245,341)(246,340)(247,339)
(248,338)(249,337)(250,336)(251,335)(252,334)(253,333)(254,343)(255,342)
(256,352)(257,351)(258,350)(259,349)(260,348)(261,347)(262,346)(263,345)
(264,344)(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)(529,618)(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)(573,662)(574,661)(575,671)
(576,670)(577,669)(578,668)(579,667)(580,666)(581,665)(582,664)(583,663)
(584,673)(585,672)(586,682)(587,681)(588,680)(589,679)(590,678)(591,677)
(592,676)(593,675)(594,674)(595,684)(596,683)(597,693)(598,692)(599,691)
(600,690)(601,689)(602,688)(603,687)(604,686)(605,685)(606,695)(607,694)
(608,704)(609,703)(610,702)(611,701)(612,700)(613,699)(614,698)(615,697)
(616,696);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope