Polytope of Type {22,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,4,8}*1408b
if this polytope has a name.
Group : SmallGroup(1408,13831)
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
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 : {2,4,8}*128b
16-fold quotients : {11,2,2}*88
22-fold quotients : {2,4,4}*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)( 45,321)( 46,320)( 47,330)( 48,329)
( 49,328)( 50,327)( 51,326)( 52,325)( 53,324)( 54,323)( 55,322)( 56,310)
( 57,309)( 58,319)( 59,318)( 60,317)( 61,316)( 62,315)( 63,314)( 64,313)
( 65,312)( 66,311)( 67,343)( 68,342)( 69,352)( 70,351)( 71,350)( 72,349)
( 73,348)( 74,347)( 75,346)( 76,345)( 77,344)( 78,332)( 79,331)( 80,341)
( 81,340)( 82,339)( 83,338)( 84,337)( 85,336)( 86,335)( 87,334)( 88,333)
( 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)(133,233)(134,232)(135,242)(136,241)
(137,240)(138,239)(139,238)(140,237)(141,236)(142,235)(143,234)(144,222)
(145,221)(146,231)(147,230)(148,229)(149,228)(150,227)(151,226)(152,225)
(153,224)(154,223)(155,255)(156,254)(157,264)(158,263)(159,262)(160,261)
(161,260)(162,259)(163,258)(164,257)(165,256)(166,244)(167,243)(168,253)
(169,252)(170,251)(171,250)(172,249)(173,248)(174,247)(175,246)(176,245)
(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)(397,673)(398,672)(399,682)(400,681)
(401,680)(402,679)(403,678)(404,677)(405,676)(406,675)(407,674)(408,662)
(409,661)(410,671)(411,670)(412,669)(413,668)(414,667)(415,666)(416,665)
(417,664)(418,663)(419,695)(420,694)(421,704)(422,703)(423,702)(424,701)
(425,700)(426,699)(427,698)(428,697)(429,696)(430,684)(431,683)(432,693)
(433,692)(434,691)(435,690)(436,689)(437,688)(438,687)(439,686)(440,685)
(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)(485,585)(486,584)(487,594)(488,593)
(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)(495,586)(496,574)
(497,573)(498,583)(499,582)(500,581)(501,580)(502,579)(503,578)(504,577)
(505,576)(506,575)(507,607)(508,606)(509,616)(510,615)(511,614)(512,613)
(513,612)(514,611)(515,610)(516,609)(517,608)(518,596)(519,595)(520,605)
(521,604)(522,603)(523,602)(524,601)(525,600)(526,599)(527,598)(528,597);;
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)(529,606)(530,607)(531,608)(532,609)
(533,610)(534,611)(535,612)(536,613)(537,614)(538,615)(539,616)(540,595)
(541,596)(542,597)(543,598)(544,599)(545,600)(546,601)(547,602)(548,603)
(549,604)(550,605)(551,584)(552,585)(553,586)(554,587)(555,588)(556,589)
(557,590)(558,591)(559,592)(560,593)(561,594)(562,573)(563,574)(564,575)
(565,576)(566,577)(567,578)(568,579)(569,580)(570,581)(571,582)(572,583)
(617,694)(618,695)(619,696)(620,697)(621,698)(622,699)(623,700)(624,701)
(625,702)(626,703)(627,704)(628,683)(629,684)(630,685)(631,686)(632,687)
(633,688)(634,689)(635,690)(636,691)(637,692)(638,693)(639,672)(640,673)
(641,674)(642,675)(643,676)(644,677)(645,678)(646,679)(647,680)(648,681)
(649,682)(650,661)(651,662)(652,663)(653,664)(654,665)(655,666)(656,667)
(657,668)(658,669)(659,670)(660,671);;
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)( 23,386)( 24,387)
( 25,388)( 26,389)( 27,390)( 28,391)( 29,392)( 30,393)( 31,394)( 32,395)
( 33,396)( 34,375)( 35,376)( 36,377)( 37,378)( 38,379)( 39,380)( 40,381)
( 41,382)( 42,383)( 43,384)( 44,385)( 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)( 67,419)( 68,420)( 69,421)( 70,422)( 71,423)( 72,424)
( 73,425)( 74,426)( 75,427)( 76,428)( 77,429)( 78,430)( 79,431)( 80,432)
( 81,433)( 82,434)( 83,435)( 84,436)( 85,437)( 86,438)( 87,439)( 88,440)
( 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)(111,474)(112,475)
(113,476)(114,477)(115,478)(116,479)(117,480)(118,481)(119,482)(120,483)
(121,484)(122,463)(123,464)(124,465)(125,466)(126,467)(127,468)(128,469)
(129,470)(130,471)(131,472)(132,473)(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)(155,507)(156,508)(157,509)(158,510)(159,511)(160,512)
(161,513)(162,514)(163,515)(164,516)(165,517)(166,518)(167,519)(168,520)
(169,521)(170,522)(171,523)(172,524)(173,525)(174,526)(175,527)(176,528)
(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)(199,562)(200,563)
(201,564)(202,565)(203,566)(204,567)(205,568)(206,569)(207,570)(208,571)
(209,572)(210,551)(211,552)(212,553)(213,554)(214,555)(215,556)(216,557)
(217,558)(218,559)(219,560)(220,561)(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)(243,595)(244,596)(245,597)(246,598)(247,599)(248,600)
(249,601)(250,602)(251,603)(252,604)(253,605)(254,606)(255,607)(256,608)
(257,609)(258,610)(259,611)(260,612)(261,613)(262,614)(263,615)(264,616)
(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)(287,650)(288,651)
(289,652)(290,653)(291,654)(292,655)(293,656)(294,657)(295,658)(296,659)
(297,660)(298,639)(299,640)(300,641)(301,642)(302,643)(303,644)(304,645)
(305,646)(306,647)(307,648)(308,649)(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)(331,683)(332,684)(333,685)(334,686)(335,687)(336,688)
(337,689)(338,690)(339,691)(340,692)(341,693)(342,694)(343,695)(344,696)
(345,697)(346,698)(347,699)(348,700)(349,701)(350,702)(351,703)(352,704);;
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*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*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)!( 1,266)( 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)( 45,321)( 46,320)( 47,330)
( 48,329)( 49,328)( 50,327)( 51,326)( 52,325)( 53,324)( 54,323)( 55,322)
( 56,310)( 57,309)( 58,319)( 59,318)( 60,317)( 61,316)( 62,315)( 63,314)
( 64,313)( 65,312)( 66,311)( 67,343)( 68,342)( 69,352)( 70,351)( 71,350)
( 72,349)( 73,348)( 74,347)( 75,346)( 76,345)( 77,344)( 78,332)( 79,331)
( 80,341)( 81,340)( 82,339)( 83,338)( 84,337)( 85,336)( 86,335)( 87,334)
( 88,333)( 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)(133,233)(134,232)(135,242)
(136,241)(137,240)(138,239)(139,238)(140,237)(141,236)(142,235)(143,234)
(144,222)(145,221)(146,231)(147,230)(148,229)(149,228)(150,227)(151,226)
(152,225)(153,224)(154,223)(155,255)(156,254)(157,264)(158,263)(159,262)
(160,261)(161,260)(162,259)(163,258)(164,257)(165,256)(166,244)(167,243)
(168,253)(169,252)(170,251)(171,250)(172,249)(173,248)(174,247)(175,246)
(176,245)(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)(397,673)(398,672)(399,682)
(400,681)(401,680)(402,679)(403,678)(404,677)(405,676)(406,675)(407,674)
(408,662)(409,661)(410,671)(411,670)(412,669)(413,668)(414,667)(415,666)
(416,665)(417,664)(418,663)(419,695)(420,694)(421,704)(422,703)(423,702)
(424,701)(425,700)(426,699)(427,698)(428,697)(429,696)(430,684)(431,683)
(432,693)(433,692)(434,691)(435,690)(436,689)(437,688)(438,687)(439,686)
(440,685)(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)(485,585)(486,584)(487,594)
(488,593)(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)(495,586)
(496,574)(497,573)(498,583)(499,582)(500,581)(501,580)(502,579)(503,578)
(504,577)(505,576)(506,575)(507,607)(508,606)(509,616)(510,615)(511,614)
(512,613)(513,612)(514,611)(515,610)(516,609)(517,608)(518,596)(519,595)
(520,605)(521,604)(522,603)(523,602)(524,601)(525,600)(526,599)(527,598)
(528,597);
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)(529,606)(530,607)(531,608)
(532,609)(533,610)(534,611)(535,612)(536,613)(537,614)(538,615)(539,616)
(540,595)(541,596)(542,597)(543,598)(544,599)(545,600)(546,601)(547,602)
(548,603)(549,604)(550,605)(551,584)(552,585)(553,586)(554,587)(555,588)
(556,589)(557,590)(558,591)(559,592)(560,593)(561,594)(562,573)(563,574)
(564,575)(565,576)(566,577)(567,578)(568,579)(569,580)(570,581)(571,582)
(572,583)(617,694)(618,695)(619,696)(620,697)(621,698)(622,699)(623,700)
(624,701)(625,702)(626,703)(627,704)(628,683)(629,684)(630,685)(631,686)
(632,687)(633,688)(634,689)(635,690)(636,691)(637,692)(638,693)(639,672)
(640,673)(641,674)(642,675)(643,676)(644,677)(645,678)(646,679)(647,680)
(648,681)(649,682)(650,661)(651,662)(652,663)(653,664)(654,665)(655,666)
(656,667)(657,668)(658,669)(659,670)(660,671);
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)( 23,386)
( 24,387)( 25,388)( 26,389)( 27,390)( 28,391)( 29,392)( 30,393)( 31,394)
( 32,395)( 33,396)( 34,375)( 35,376)( 36,377)( 37,378)( 38,379)( 39,380)
( 40,381)( 41,382)( 42,383)( 43,384)( 44,385)( 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)( 67,419)( 68,420)( 69,421)( 70,422)( 71,423)
( 72,424)( 73,425)( 74,426)( 75,427)( 76,428)( 77,429)( 78,430)( 79,431)
( 80,432)( 81,433)( 82,434)( 83,435)( 84,436)( 85,437)( 86,438)( 87,439)
( 88,440)( 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)(111,474)
(112,475)(113,476)(114,477)(115,478)(116,479)(117,480)(118,481)(119,482)
(120,483)(121,484)(122,463)(123,464)(124,465)(125,466)(126,467)(127,468)
(128,469)(129,470)(130,471)(131,472)(132,473)(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)(155,507)(156,508)(157,509)(158,510)(159,511)
(160,512)(161,513)(162,514)(163,515)(164,516)(165,517)(166,518)(167,519)
(168,520)(169,521)(170,522)(171,523)(172,524)(173,525)(174,526)(175,527)
(176,528)(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)(199,562)
(200,563)(201,564)(202,565)(203,566)(204,567)(205,568)(206,569)(207,570)
(208,571)(209,572)(210,551)(211,552)(212,553)(213,554)(214,555)(215,556)
(216,557)(217,558)(218,559)(219,560)(220,561)(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)(243,595)(244,596)(245,597)(246,598)(247,599)
(248,600)(249,601)(250,602)(251,603)(252,604)(253,605)(254,606)(255,607)
(256,608)(257,609)(258,610)(259,611)(260,612)(261,613)(262,614)(263,615)
(264,616)(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)(287,650)
(288,651)(289,652)(290,653)(291,654)(292,655)(293,656)(294,657)(295,658)
(296,659)(297,660)(298,639)(299,640)(300,641)(301,642)(302,643)(303,644)
(304,645)(305,646)(306,647)(307,648)(308,649)(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)(331,683)(332,684)(333,685)(334,686)(335,687)
(336,688)(337,689)(338,690)(339,691)(340,692)(341,693)(342,694)(343,695)
(344,696)(345,697)(346,698)(347,699)(348,700)(349,701)(350,702)(351,703)
(352,704);
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*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*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