Polytope of Type {22,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,8,4}*1408a
Also Known As : {{22,8|2},{8,4|2}}. if this polytope has another name.
Group : SmallGroup(1408,13683)
Rank : 4
Schlafli Type : {22,8,4}
Number of vertices, edges, etc : 22, 88, 16, 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 : {22,4,4}*704, {22,8,2}*704
4-fold quotients : {22,2,4}*352, {22,4,2}*352
8-fold quotients : {11,2,4}*176, {22,2,2}*176
11-fold quotients : {2,8,4}*128a
16-fold quotients : {11,2,2}*88
22-fold quotients : {2,4,4}*64, {2,8,2}*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 := ( 1,442)( 2,441)( 3,451)( 4,450)( 5,449)( 6,448)( 7,447)( 8,446)
( 9,445)( 10,444)( 11,443)( 12,453)( 13,452)( 14,462)( 15,461)( 16,460)
( 17,459)( 18,458)( 19,457)( 20,456)( 21,455)( 22,454)( 23,464)( 24,463)
( 25,473)( 26,472)( 27,471)( 28,470)( 29,469)( 30,468)( 31,467)( 32,466)
( 33,465)( 34,475)( 35,474)( 36,484)( 37,483)( 38,482)( 39,481)( 40,480)
( 41,479)( 42,478)( 43,477)( 44,476)( 45,497)( 46,496)( 47,506)( 48,505)
( 49,504)( 50,503)( 51,502)( 52,501)( 53,500)( 54,499)( 55,498)( 56,486)
( 57,485)( 58,495)( 59,494)( 60,493)( 61,492)( 62,491)( 63,490)( 64,489)
( 65,488)( 66,487)( 67,519)( 68,518)( 69,528)( 70,527)( 71,526)( 72,525)
( 73,524)( 74,523)( 75,522)( 76,521)( 77,520)( 78,508)( 79,507)( 80,517)
( 81,516)( 82,515)( 83,514)( 84,513)( 85,512)( 86,511)( 87,510)( 88,509)
( 89,354)( 90,353)( 91,363)( 92,362)( 93,361)( 94,360)( 95,359)( 96,358)
( 97,357)( 98,356)( 99,355)(100,365)(101,364)(102,374)(103,373)(104,372)
(105,371)(106,370)(107,369)(108,368)(109,367)(110,366)(111,376)(112,375)
(113,385)(114,384)(115,383)(116,382)(117,381)(118,380)(119,379)(120,378)
(121,377)(122,387)(123,386)(124,396)(125,395)(126,394)(127,393)(128,392)
(129,391)(130,390)(131,389)(132,388)(133,409)(134,408)(135,418)(136,417)
(137,416)(138,415)(139,414)(140,413)(141,412)(142,411)(143,410)(144,398)
(145,397)(146,407)(147,406)(148,405)(149,404)(150,403)(151,402)(152,401)
(153,400)(154,399)(155,431)(156,430)(157,440)(158,439)(159,438)(160,437)
(161,436)(162,435)(163,434)(164,433)(165,432)(166,420)(167,419)(168,429)
(169,428)(170,427)(171,426)(172,425)(173,424)(174,423)(175,422)(176,421)
(177,618)(178,617)(179,627)(180,626)(181,625)(182,624)(183,623)(184,622)
(185,621)(186,620)(187,619)(188,629)(189,628)(190,638)(191,637)(192,636)
(193,635)(194,634)(195,633)(196,632)(197,631)(198,630)(199,640)(200,639)
(201,649)(202,648)(203,647)(204,646)(205,645)(206,644)(207,643)(208,642)
(209,641)(210,651)(211,650)(212,660)(213,659)(214,658)(215,657)(216,656)
(217,655)(218,654)(219,653)(220,652)(221,673)(222,672)(223,682)(224,681)
(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,662)
(233,661)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)(240,665)
(241,664)(242,663)(243,695)(244,694)(245,704)(246,703)(247,702)(248,701)
(249,700)(250,699)(251,698)(252,697)(253,696)(254,684)(255,683)(256,693)
(257,692)(258,691)(259,690)(260,689)(261,688)(262,687)(263,686)(264,685)
(265,530)(266,529)(267,539)(268,538)(269,537)(270,536)(271,535)(272,534)
(273,533)(274,532)(275,531)(276,541)(277,540)(278,550)(279,549)(280,548)
(281,547)(282,546)(283,545)(284,544)(285,543)(286,542)(287,552)(288,551)
(289,561)(290,560)(291,559)(292,558)(293,557)(294,556)(295,555)(296,554)
(297,553)(298,563)(299,562)(300,572)(301,571)(302,570)(303,569)(304,568)
(305,567)(306,566)(307,565)(308,564)(309,585)(310,584)(311,594)(312,593)
(313,592)(314,591)(315,590)(316,589)(317,588)(318,587)(319,586)(320,574)
(321,573)(322,583)(323,582)(324,581)(325,580)(326,579)(327,578)(328,577)
(329,576)(330,575)(331,607)(332,606)(333,616)(334,615)(335,614)(336,613)
(337,612)(338,611)(339,610)(340,609)(341,608)(342,596)(343,595)(344,605)
(345,604)(346,603)(347,602)(348,601)(349,600)(350,599)(351,598)(352,597);;
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 := ( 1,177)( 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!( 1,442)( 2,441)( 3,451)( 4,450)( 5,449)( 6,448)( 7,447)
( 8,446)( 9,445)( 10,444)( 11,443)( 12,453)( 13,452)( 14,462)( 15,461)
( 16,460)( 17,459)( 18,458)( 19,457)( 20,456)( 21,455)( 22,454)( 23,464)
( 24,463)( 25,473)( 26,472)( 27,471)( 28,470)( 29,469)( 30,468)( 31,467)
( 32,466)( 33,465)( 34,475)( 35,474)( 36,484)( 37,483)( 38,482)( 39,481)
( 40,480)( 41,479)( 42,478)( 43,477)( 44,476)( 45,497)( 46,496)( 47,506)
( 48,505)( 49,504)( 50,503)( 51,502)( 52,501)( 53,500)( 54,499)( 55,498)
( 56,486)( 57,485)( 58,495)( 59,494)( 60,493)( 61,492)( 62,491)( 63,490)
( 64,489)( 65,488)( 66,487)( 67,519)( 68,518)( 69,528)( 70,527)( 71,526)
( 72,525)( 73,524)( 74,523)( 75,522)( 76,521)( 77,520)( 78,508)( 79,507)
( 80,517)( 81,516)( 82,515)( 83,514)( 84,513)( 85,512)( 86,511)( 87,510)
( 88,509)( 89,354)( 90,353)( 91,363)( 92,362)( 93,361)( 94,360)( 95,359)
( 96,358)( 97,357)( 98,356)( 99,355)(100,365)(101,364)(102,374)(103,373)
(104,372)(105,371)(106,370)(107,369)(108,368)(109,367)(110,366)(111,376)
(112,375)(113,385)(114,384)(115,383)(116,382)(117,381)(118,380)(119,379)
(120,378)(121,377)(122,387)(123,386)(124,396)(125,395)(126,394)(127,393)
(128,392)(129,391)(130,390)(131,389)(132,388)(133,409)(134,408)(135,418)
(136,417)(137,416)(138,415)(139,414)(140,413)(141,412)(142,411)(143,410)
(144,398)(145,397)(146,407)(147,406)(148,405)(149,404)(150,403)(151,402)
(152,401)(153,400)(154,399)(155,431)(156,430)(157,440)(158,439)(159,438)
(160,437)(161,436)(162,435)(163,434)(164,433)(165,432)(166,420)(167,419)
(168,429)(169,428)(170,427)(171,426)(172,425)(173,424)(174,423)(175,422)
(176,421)(177,618)(178,617)(179,627)(180,626)(181,625)(182,624)(183,623)
(184,622)(185,621)(186,620)(187,619)(188,629)(189,628)(190,638)(191,637)
(192,636)(193,635)(194,634)(195,633)(196,632)(197,631)(198,630)(199,640)
(200,639)(201,649)(202,648)(203,647)(204,646)(205,645)(206,644)(207,643)
(208,642)(209,641)(210,651)(211,650)(212,660)(213,659)(214,658)(215,657)
(216,656)(217,655)(218,654)(219,653)(220,652)(221,673)(222,672)(223,682)
(224,681)(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)
(232,662)(233,661)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)
(240,665)(241,664)(242,663)(243,695)(244,694)(245,704)(246,703)(247,702)
(248,701)(249,700)(250,699)(251,698)(252,697)(253,696)(254,684)(255,683)
(256,693)(257,692)(258,691)(259,690)(260,689)(261,688)(262,687)(263,686)
(264,685)(265,530)(266,529)(267,539)(268,538)(269,537)(270,536)(271,535)
(272,534)(273,533)(274,532)(275,531)(276,541)(277,540)(278,550)(279,549)
(280,548)(281,547)(282,546)(283,545)(284,544)(285,543)(286,542)(287,552)
(288,551)(289,561)(290,560)(291,559)(292,558)(293,557)(294,556)(295,555)
(296,554)(297,553)(298,563)(299,562)(300,572)(301,571)(302,570)(303,569)
(304,568)(305,567)(306,566)(307,565)(308,564)(309,585)(310,584)(311,594)
(312,593)(313,592)(314,591)(315,590)(316,589)(317,588)(318,587)(319,586)
(320,574)(321,573)(322,583)(323,582)(324,581)(325,580)(326,579)(327,578)
(328,577)(329,576)(330,575)(331,607)(332,606)(333,616)(334,615)(335,614)
(336,613)(337,612)(338,611)(339,610)(340,609)(341,608)(342,596)(343,595)
(344,605)(345,604)(346,603)(347,602)(348,601)(349,600)(350,599)(351,598)
(352,597);
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)!( 1,177)( 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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