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Polytope of Type {4,34,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,34,4}*1088
Also Known As : {{4,34|2},{34,4|2}}. if this polytope has another name.
Group : SmallGroup(1088,1181)
Rank : 4
Schlafli Type : {4,34,4}
Number of vertices, edges, etc : 4, 68, 68, 4
Order of s0s1s2s3 : 68
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,34,4}*544, {4,34,2}*544
   4-fold quotients : {2,34,2}*272
   8-fold quotients : {2,17,2}*136
   17-fold quotients : {4,2,4}*64
   34-fold quotients : {2,2,4}*32, {4,2,2}*32
   68-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,273)(  2,274)(  3,275)(  4,276)(  5,277)(  6,278)(  7,279)(  8,280)
(  9,281)( 10,282)( 11,283)( 12,284)( 13,285)( 14,286)( 15,287)( 16,288)
( 17,289)( 18,290)( 19,291)( 20,292)( 21,293)( 22,294)( 23,295)( 24,296)
( 25,297)( 26,298)( 27,299)( 28,300)( 29,301)( 30,302)( 31,303)( 32,304)
( 33,305)( 34,306)( 35,307)( 36,308)( 37,309)( 38,310)( 39,311)( 40,312)
( 41,313)( 42,314)( 43,315)( 44,316)( 45,317)( 46,318)( 47,319)( 48,320)
( 49,321)( 50,322)( 51,323)( 52,324)( 53,325)( 54,326)( 55,327)( 56,328)
( 57,329)( 58,330)( 59,331)( 60,332)( 61,333)( 62,334)( 63,335)( 64,336)
( 65,337)( 66,338)( 67,339)( 68,340)( 69,375)( 70,376)( 71,377)( 72,378)
( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)( 80,386)
( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)( 88,394)
( 89,395)( 90,396)( 91,397)( 92,398)( 93,399)( 94,400)( 95,401)( 96,402)
( 97,403)( 98,404)( 99,405)(100,406)(101,407)(102,408)(103,341)(104,342)
(105,343)(106,344)(107,345)(108,346)(109,347)(110,348)(111,349)(112,350)
(113,351)(114,352)(115,353)(116,354)(117,355)(118,356)(119,357)(120,358)
(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,365)(128,366)
(129,367)(130,368)(131,369)(132,370)(133,371)(134,372)(135,373)(136,374)
(137,409)(138,410)(139,411)(140,412)(141,413)(142,414)(143,415)(144,416)
(145,417)(146,418)(147,419)(148,420)(149,421)(150,422)(151,423)(152,424)
(153,425)(154,426)(155,427)(156,428)(157,429)(158,430)(159,431)(160,432)
(161,433)(162,434)(163,435)(164,436)(165,437)(166,438)(167,439)(168,440)
(169,441)(170,442)(171,443)(172,444)(173,445)(174,446)(175,447)(176,448)
(177,449)(178,450)(179,451)(180,452)(181,453)(182,454)(183,455)(184,456)
(185,457)(186,458)(187,459)(188,460)(189,461)(190,462)(191,463)(192,464)
(193,465)(194,466)(195,467)(196,468)(197,469)(198,470)(199,471)(200,472)
(201,473)(202,474)(203,475)(204,476)(205,511)(206,512)(207,513)(208,514)
(209,515)(210,516)(211,517)(212,518)(213,519)(214,520)(215,521)(216,522)
(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)(224,530)
(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)(232,538)
(233,539)(234,540)(235,541)(236,542)(237,543)(238,544)(239,477)(240,478)
(241,479)(242,480)(243,481)(244,482)(245,483)(246,484)(247,485)(248,486)
(249,487)(250,488)(251,489)(252,490)(253,491)(254,492)(255,493)(256,494)
(257,495)(258,496)(259,497)(260,498)(261,499)(262,500)(263,501)(264,502)
(265,503)(266,504)(267,505)(268,506)(269,507)(270,508)(271,509)(272,510);;
s1 := (  1, 69)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 81)(  7, 80)(  8, 79)
(  9, 78)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 71)
( 17, 70)( 18, 86)( 19,102)( 20,101)( 21,100)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)
( 33, 88)( 34, 87)( 35,103)( 36,119)( 37,118)( 38,117)( 39,116)( 40,115)
( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)( 48,107)
( 49,106)( 50,105)( 51,104)( 52,120)( 53,136)( 54,135)( 55,134)( 56,133)
( 57,132)( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)( 64,125)
( 65,124)( 66,123)( 67,122)( 68,121)(137,205)(138,221)(139,220)(140,219)
(141,218)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,211)
(149,210)(150,209)(151,208)(152,207)(153,206)(154,222)(155,238)(156,237)
(157,236)(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)
(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,239)(172,255)
(173,254)(174,253)(175,252)(176,251)(177,250)(178,249)(179,248)(180,247)
(181,246)(182,245)(183,244)(184,243)(185,242)(186,241)(187,240)(188,256)
(189,272)(190,271)(191,270)(192,269)(193,268)(194,267)(195,266)(196,265)
(197,264)(198,263)(199,262)(200,261)(201,260)(202,259)(203,258)(204,257)
(273,341)(274,357)(275,356)(276,355)(277,354)(278,353)(279,352)(280,351)
(281,350)(282,349)(283,348)(284,347)(285,346)(286,345)(287,344)(288,343)
(289,342)(290,358)(291,374)(292,373)(293,372)(294,371)(295,370)(296,369)
(297,368)(298,367)(299,366)(300,365)(301,364)(302,363)(303,362)(304,361)
(305,360)(306,359)(307,375)(308,391)(309,390)(310,389)(311,388)(312,387)
(313,386)(314,385)(315,384)(316,383)(317,382)(318,381)(319,380)(320,379)
(321,378)(322,377)(323,376)(324,392)(325,408)(326,407)(327,406)(328,405)
(329,404)(330,403)(331,402)(332,401)(333,400)(334,399)(335,398)(336,397)
(337,396)(338,395)(339,394)(340,393)(409,477)(410,493)(411,492)(412,491)
(413,490)(414,489)(415,488)(416,487)(417,486)(418,485)(419,484)(420,483)
(421,482)(422,481)(423,480)(424,479)(425,478)(426,494)(427,510)(428,509)
(429,508)(430,507)(431,506)(432,505)(433,504)(434,503)(435,502)(436,501)
(437,500)(438,499)(439,498)(440,497)(441,496)(442,495)(443,511)(444,527)
(445,526)(446,525)(447,524)(448,523)(449,522)(450,521)(451,520)(452,519)
(453,518)(454,517)(455,516)(456,515)(457,514)(458,513)(459,512)(460,528)
(461,544)(462,543)(463,542)(464,541)(465,540)(466,539)(467,538)(468,537)
(469,536)(470,535)(471,534)(472,533)(473,532)(474,531)(475,530)(476,529);;
s2 := (  1, 70)(  2, 69)(  3, 85)(  4, 84)(  5, 83)(  6, 82)(  7, 81)(  8, 80)
(  9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)( 16, 72)
( 17, 71)( 18, 87)( 19, 86)( 20,102)( 21,101)( 22,100)( 23, 99)( 24, 98)
( 25, 97)( 26, 96)( 27, 95)( 28, 94)( 29, 93)( 30, 92)( 31, 91)( 32, 90)
( 33, 89)( 34, 88)( 35,104)( 36,103)( 37,119)( 38,118)( 39,117)( 40,116)
( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)( 46,110)( 47,109)( 48,108)
( 49,107)( 50,106)( 51,105)( 52,121)( 53,120)( 54,136)( 55,135)( 56,134)
( 57,133)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)
( 65,125)( 66,124)( 67,123)( 68,122)(137,223)(138,222)(139,238)(140,237)
(141,236)(142,235)(143,234)(144,233)(145,232)(146,231)(147,230)(148,229)
(149,228)(150,227)(151,226)(152,225)(153,224)(154,206)(155,205)(156,221)
(157,220)(158,219)(159,218)(160,217)(161,216)(162,215)(163,214)(164,213)
(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,257)(172,256)
(173,272)(174,271)(175,270)(176,269)(177,268)(178,267)(179,266)(180,265)
(181,264)(182,263)(183,262)(184,261)(185,260)(186,259)(187,258)(188,240)
(189,239)(190,255)(191,254)(192,253)(193,252)(194,251)(195,250)(196,249)
(197,248)(198,247)(199,246)(200,245)(201,244)(202,243)(203,242)(204,241)
(273,376)(274,375)(275,391)(276,390)(277,389)(278,388)(279,387)(280,386)
(281,385)(282,384)(283,383)(284,382)(285,381)(286,380)(287,379)(288,378)
(289,377)(290,393)(291,392)(292,408)(293,407)(294,406)(295,405)(296,404)
(297,403)(298,402)(299,401)(300,400)(301,399)(302,398)(303,397)(304,396)
(305,395)(306,394)(307,342)(308,341)(309,357)(310,356)(311,355)(312,354)
(313,353)(314,352)(315,351)(316,350)(317,349)(318,348)(319,347)(320,346)
(321,345)(322,344)(323,343)(324,359)(325,358)(326,374)(327,373)(328,372)
(329,371)(330,370)(331,369)(332,368)(333,367)(334,366)(335,365)(336,364)
(337,363)(338,362)(339,361)(340,360)(409,529)(410,528)(411,544)(412,543)
(413,542)(414,541)(415,540)(416,539)(417,538)(418,537)(419,536)(420,535)
(421,534)(422,533)(423,532)(424,531)(425,530)(426,512)(427,511)(428,527)
(429,526)(430,525)(431,524)(432,523)(433,522)(434,521)(435,520)(436,519)
(437,518)(438,517)(439,516)(440,515)(441,514)(442,513)(443,495)(444,494)
(445,510)(446,509)(447,508)(448,507)(449,506)(450,505)(451,504)(452,503)
(453,502)(454,501)(455,500)(456,499)(457,498)(458,497)(459,496)(460,478)
(461,477)(462,493)(463,492)(464,491)(465,490)(466,489)(467,488)(468,487)
(469,486)(470,485)(471,484)(472,483)(473,482)(474,481)(475,480)(476,479);;
s3 := (  1,137)(  2,138)(  3,139)(  4,140)(  5,141)(  6,142)(  7,143)(  8,144)
(  9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)
( 17,153)( 18,154)( 19,155)( 20,156)( 21,157)( 22,158)( 23,159)( 24,160)
( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)
( 33,169)( 34,170)( 35,171)( 36,172)( 37,173)( 38,174)( 39,175)( 40,176)
( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,185)( 50,186)( 51,187)( 52,188)( 53,189)( 54,190)( 55,191)( 56,192)
( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)
( 65,201)( 66,202)( 67,203)( 68,204)( 69,205)( 70,206)( 71,207)( 72,208)
( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)( 80,216)
( 81,217)( 82,218)( 83,219)( 84,220)( 85,221)( 86,222)( 87,223)( 88,224)
( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,233)( 98,234)( 99,235)(100,236)(101,237)(102,238)(103,239)(104,240)
(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)(112,248)
(113,249)(114,250)(115,251)(116,252)(117,253)(118,254)(119,255)(120,256)
(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)(128,264)
(129,265)(130,266)(131,267)(132,268)(133,269)(134,270)(135,271)(136,272)
(273,409)(274,410)(275,411)(276,412)(277,413)(278,414)(279,415)(280,416)
(281,417)(282,418)(283,419)(284,420)(285,421)(286,422)(287,423)(288,424)
(289,425)(290,426)(291,427)(292,428)(293,429)(294,430)(295,431)(296,432)
(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)(304,440)
(305,441)(306,442)(307,443)(308,444)(309,445)(310,446)(311,447)(312,448)
(313,449)(314,450)(315,451)(316,452)(317,453)(318,454)(319,455)(320,456)
(321,457)(322,458)(323,459)(324,460)(325,461)(326,462)(327,463)(328,464)
(329,465)(330,466)(331,467)(332,468)(333,469)(334,470)(335,471)(336,472)
(337,473)(338,474)(339,475)(340,476)(341,477)(342,478)(343,479)(344,480)
(345,481)(346,482)(347,483)(348,484)(349,485)(350,486)(351,487)(352,488)
(353,489)(354,490)(355,491)(356,492)(357,493)(358,494)(359,495)(360,496)
(361,497)(362,498)(363,499)(364,500)(365,501)(366,502)(367,503)(368,504)
(369,505)(370,506)(371,507)(372,508)(373,509)(374,510)(375,511)(376,512)
(377,513)(378,514)(379,515)(380,516)(381,517)(382,518)(383,519)(384,520)
(385,521)(386,522)(387,523)(388,524)(389,525)(390,526)(391,527)(392,528)
(393,529)(394,530)(395,531)(396,532)(397,533)(398,534)(399,535)(400,536)
(401,537)(402,538)(403,539)(404,540)(405,541)(406,542)(407,543)(408,544);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(544)!(  1,273)(  2,274)(  3,275)(  4,276)(  5,277)(  6,278)(  7,279)
(  8,280)(  9,281)( 10,282)( 11,283)( 12,284)( 13,285)( 14,286)( 15,287)
( 16,288)( 17,289)( 18,290)( 19,291)( 20,292)( 21,293)( 22,294)( 23,295)
( 24,296)( 25,297)( 26,298)( 27,299)( 28,300)( 29,301)( 30,302)( 31,303)
( 32,304)( 33,305)( 34,306)( 35,307)( 36,308)( 37,309)( 38,310)( 39,311)
( 40,312)( 41,313)( 42,314)( 43,315)( 44,316)( 45,317)( 46,318)( 47,319)
( 48,320)( 49,321)( 50,322)( 51,323)( 52,324)( 53,325)( 54,326)( 55,327)
( 56,328)( 57,329)( 58,330)( 59,331)( 60,332)( 61,333)( 62,334)( 63,335)
( 64,336)( 65,337)( 66,338)( 67,339)( 68,340)( 69,375)( 70,376)( 71,377)
( 72,378)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)
( 80,386)( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)
( 88,394)( 89,395)( 90,396)( 91,397)( 92,398)( 93,399)( 94,400)( 95,401)
( 96,402)( 97,403)( 98,404)( 99,405)(100,406)(101,407)(102,408)(103,341)
(104,342)(105,343)(106,344)(107,345)(108,346)(109,347)(110,348)(111,349)
(112,350)(113,351)(114,352)(115,353)(116,354)(117,355)(118,356)(119,357)
(120,358)(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,365)
(128,366)(129,367)(130,368)(131,369)(132,370)(133,371)(134,372)(135,373)
(136,374)(137,409)(138,410)(139,411)(140,412)(141,413)(142,414)(143,415)
(144,416)(145,417)(146,418)(147,419)(148,420)(149,421)(150,422)(151,423)
(152,424)(153,425)(154,426)(155,427)(156,428)(157,429)(158,430)(159,431)
(160,432)(161,433)(162,434)(163,435)(164,436)(165,437)(166,438)(167,439)
(168,440)(169,441)(170,442)(171,443)(172,444)(173,445)(174,446)(175,447)
(176,448)(177,449)(178,450)(179,451)(180,452)(181,453)(182,454)(183,455)
(184,456)(185,457)(186,458)(187,459)(188,460)(189,461)(190,462)(191,463)
(192,464)(193,465)(194,466)(195,467)(196,468)(197,469)(198,470)(199,471)
(200,472)(201,473)(202,474)(203,475)(204,476)(205,511)(206,512)(207,513)
(208,514)(209,515)(210,516)(211,517)(212,518)(213,519)(214,520)(215,521)
(216,522)(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)
(224,530)(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)
(232,538)(233,539)(234,540)(235,541)(236,542)(237,543)(238,544)(239,477)
(240,478)(241,479)(242,480)(243,481)(244,482)(245,483)(246,484)(247,485)
(248,486)(249,487)(250,488)(251,489)(252,490)(253,491)(254,492)(255,493)
(256,494)(257,495)(258,496)(259,497)(260,498)(261,499)(262,500)(263,501)
(264,502)(265,503)(266,504)(267,505)(268,506)(269,507)(270,508)(271,509)
(272,510);
s1 := Sym(544)!(  1, 69)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 81)(  7, 80)
(  8, 79)(  9, 78)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 71)( 17, 70)( 18, 86)( 19,102)( 20,101)( 21,100)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)
( 32, 89)( 33, 88)( 34, 87)( 35,103)( 36,119)( 37,118)( 38,117)( 39,116)
( 40,115)( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)
( 48,107)( 49,106)( 50,105)( 51,104)( 52,120)( 53,136)( 54,135)( 55,134)
( 56,133)( 57,132)( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)
( 64,125)( 65,124)( 66,123)( 67,122)( 68,121)(137,205)(138,221)(139,220)
(140,219)(141,218)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)
(148,211)(149,210)(150,209)(151,208)(152,207)(153,206)(154,222)(155,238)
(156,237)(157,236)(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)
(164,229)(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,239)
(172,255)(173,254)(174,253)(175,252)(176,251)(177,250)(178,249)(179,248)
(180,247)(181,246)(182,245)(183,244)(184,243)(185,242)(186,241)(187,240)
(188,256)(189,272)(190,271)(191,270)(192,269)(193,268)(194,267)(195,266)
(196,265)(197,264)(198,263)(199,262)(200,261)(201,260)(202,259)(203,258)
(204,257)(273,341)(274,357)(275,356)(276,355)(277,354)(278,353)(279,352)
(280,351)(281,350)(282,349)(283,348)(284,347)(285,346)(286,345)(287,344)
(288,343)(289,342)(290,358)(291,374)(292,373)(293,372)(294,371)(295,370)
(296,369)(297,368)(298,367)(299,366)(300,365)(301,364)(302,363)(303,362)
(304,361)(305,360)(306,359)(307,375)(308,391)(309,390)(310,389)(311,388)
(312,387)(313,386)(314,385)(315,384)(316,383)(317,382)(318,381)(319,380)
(320,379)(321,378)(322,377)(323,376)(324,392)(325,408)(326,407)(327,406)
(328,405)(329,404)(330,403)(331,402)(332,401)(333,400)(334,399)(335,398)
(336,397)(337,396)(338,395)(339,394)(340,393)(409,477)(410,493)(411,492)
(412,491)(413,490)(414,489)(415,488)(416,487)(417,486)(418,485)(419,484)
(420,483)(421,482)(422,481)(423,480)(424,479)(425,478)(426,494)(427,510)
(428,509)(429,508)(430,507)(431,506)(432,505)(433,504)(434,503)(435,502)
(436,501)(437,500)(438,499)(439,498)(440,497)(441,496)(442,495)(443,511)
(444,527)(445,526)(446,525)(447,524)(448,523)(449,522)(450,521)(451,520)
(452,519)(453,518)(454,517)(455,516)(456,515)(457,514)(458,513)(459,512)
(460,528)(461,544)(462,543)(463,542)(464,541)(465,540)(466,539)(467,538)
(468,537)(469,536)(470,535)(471,534)(472,533)(473,532)(474,531)(475,530)
(476,529);
s2 := Sym(544)!(  1, 70)(  2, 69)(  3, 85)(  4, 84)(  5, 83)(  6, 82)(  7, 81)
(  8, 80)(  9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)
( 16, 72)( 17, 71)( 18, 87)( 19, 86)( 20,102)( 21,101)( 22,100)( 23, 99)
( 24, 98)( 25, 97)( 26, 96)( 27, 95)( 28, 94)( 29, 93)( 30, 92)( 31, 91)
( 32, 90)( 33, 89)( 34, 88)( 35,104)( 36,103)( 37,119)( 38,118)( 39,117)
( 40,116)( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)( 46,110)( 47,109)
( 48,108)( 49,107)( 50,106)( 51,105)( 52,121)( 53,120)( 54,136)( 55,135)
( 56,134)( 57,133)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)
( 64,126)( 65,125)( 66,124)( 67,123)( 68,122)(137,223)(138,222)(139,238)
(140,237)(141,236)(142,235)(143,234)(144,233)(145,232)(146,231)(147,230)
(148,229)(149,228)(150,227)(151,226)(152,225)(153,224)(154,206)(155,205)
(156,221)(157,220)(158,219)(159,218)(160,217)(161,216)(162,215)(163,214)
(164,213)(165,212)(166,211)(167,210)(168,209)(169,208)(170,207)(171,257)
(172,256)(173,272)(174,271)(175,270)(176,269)(177,268)(178,267)(179,266)
(180,265)(181,264)(182,263)(183,262)(184,261)(185,260)(186,259)(187,258)
(188,240)(189,239)(190,255)(191,254)(192,253)(193,252)(194,251)(195,250)
(196,249)(197,248)(198,247)(199,246)(200,245)(201,244)(202,243)(203,242)
(204,241)(273,376)(274,375)(275,391)(276,390)(277,389)(278,388)(279,387)
(280,386)(281,385)(282,384)(283,383)(284,382)(285,381)(286,380)(287,379)
(288,378)(289,377)(290,393)(291,392)(292,408)(293,407)(294,406)(295,405)
(296,404)(297,403)(298,402)(299,401)(300,400)(301,399)(302,398)(303,397)
(304,396)(305,395)(306,394)(307,342)(308,341)(309,357)(310,356)(311,355)
(312,354)(313,353)(314,352)(315,351)(316,350)(317,349)(318,348)(319,347)
(320,346)(321,345)(322,344)(323,343)(324,359)(325,358)(326,374)(327,373)
(328,372)(329,371)(330,370)(331,369)(332,368)(333,367)(334,366)(335,365)
(336,364)(337,363)(338,362)(339,361)(340,360)(409,529)(410,528)(411,544)
(412,543)(413,542)(414,541)(415,540)(416,539)(417,538)(418,537)(419,536)
(420,535)(421,534)(422,533)(423,532)(424,531)(425,530)(426,512)(427,511)
(428,527)(429,526)(430,525)(431,524)(432,523)(433,522)(434,521)(435,520)
(436,519)(437,518)(438,517)(439,516)(440,515)(441,514)(442,513)(443,495)
(444,494)(445,510)(446,509)(447,508)(448,507)(449,506)(450,505)(451,504)
(452,503)(453,502)(454,501)(455,500)(456,499)(457,498)(458,497)(459,496)
(460,478)(461,477)(462,493)(463,492)(464,491)(465,490)(466,489)(467,488)
(468,487)(469,486)(470,485)(471,484)(472,483)(473,482)(474,481)(475,480)
(476,479);
s3 := Sym(544)!(  1,137)(  2,138)(  3,139)(  4,140)(  5,141)(  6,142)(  7,143)
(  8,144)(  9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)
( 16,152)( 17,153)( 18,154)( 19,155)( 20,156)( 21,157)( 22,158)( 23,159)
( 24,160)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)
( 32,168)( 33,169)( 34,170)( 35,171)( 36,172)( 37,173)( 38,174)( 39,175)
( 40,176)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,185)( 50,186)( 51,187)( 52,188)( 53,189)( 54,190)( 55,191)
( 56,192)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)
( 64,200)( 65,201)( 66,202)( 67,203)( 68,204)( 69,205)( 70,206)( 71,207)
( 72,208)( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)
( 80,216)( 81,217)( 82,218)( 83,219)( 84,220)( 85,221)( 86,222)( 87,223)
( 88,224)( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,233)( 98,234)( 99,235)(100,236)(101,237)(102,238)(103,239)
(104,240)(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)
(112,248)(113,249)(114,250)(115,251)(116,252)(117,253)(118,254)(119,255)
(120,256)(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)
(128,264)(129,265)(130,266)(131,267)(132,268)(133,269)(134,270)(135,271)
(136,272)(273,409)(274,410)(275,411)(276,412)(277,413)(278,414)(279,415)
(280,416)(281,417)(282,418)(283,419)(284,420)(285,421)(286,422)(287,423)
(288,424)(289,425)(290,426)(291,427)(292,428)(293,429)(294,430)(295,431)
(296,432)(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)
(304,440)(305,441)(306,442)(307,443)(308,444)(309,445)(310,446)(311,447)
(312,448)(313,449)(314,450)(315,451)(316,452)(317,453)(318,454)(319,455)
(320,456)(321,457)(322,458)(323,459)(324,460)(325,461)(326,462)(327,463)
(328,464)(329,465)(330,466)(331,467)(332,468)(333,469)(334,470)(335,471)
(336,472)(337,473)(338,474)(339,475)(340,476)(341,477)(342,478)(343,479)
(344,480)(345,481)(346,482)(347,483)(348,484)(349,485)(350,486)(351,487)
(352,488)(353,489)(354,490)(355,491)(356,492)(357,493)(358,494)(359,495)
(360,496)(361,497)(362,498)(363,499)(364,500)(365,501)(366,502)(367,503)
(368,504)(369,505)(370,506)(371,507)(372,508)(373,509)(374,510)(375,511)
(376,512)(377,513)(378,514)(379,515)(380,516)(381,517)(382,518)(383,519)
(384,520)(385,521)(386,522)(387,523)(388,524)(389,525)(390,526)(391,527)
(392,528)(393,529)(394,530)(395,531)(396,532)(397,533)(398,534)(399,535)
(400,536)(401,537)(402,538)(403,539)(404,540)(405,541)(406,542)(407,543)
(408,544);
poly := sub<Sym(544)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope