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Polytope of Type {4,136}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,136}*1088a
Also Known As : {4,136|2}. if this polytope has another name.
Group : SmallGroup(1088,685)
Rank : 3
Schlafli Type : {4,136}
Number of vertices, edges, etc : 4, 272, 136
Order of s0s1s2 : 136
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,68}*544, {2,136}*544
   4-fold quotients : {2,68}*272, {4,34}*272
   8-fold quotients : {2,34}*136
   16-fold quotients : {2,17}*68
   17-fold quotients : {4,8}*64a
   34-fold quotients : {4,4}*32, {2,8}*32
   68-fold quotients : {2,4}*16, {4,2}*16
   136-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  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);;
s1 := (  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)
( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)
( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 43, 44)
( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)
( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76, 96)
( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)( 83, 89)( 84, 88)
( 85, 87)(103,120)(104,136)(105,135)(106,134)(107,133)(108,132)(109,131)
(110,130)(111,129)(112,128)(113,127)(114,126)(115,125)(116,124)(117,123)
(118,122)(119,121)(137,171)(138,187)(139,186)(140,185)(141,184)(142,183)
(143,182)(144,181)(145,180)(146,179)(147,178)(148,177)(149,176)(150,175)
(151,174)(152,173)(153,172)(154,188)(155,204)(156,203)(157,202)(158,201)
(159,200)(160,199)(161,198)(162,197)(163,196)(164,195)(165,194)(166,193)
(167,192)(168,191)(169,190)(170,189)(205,256)(206,272)(207,271)(208,270)
(209,269)(210,268)(211,267)(212,266)(213,265)(214,264)(215,263)(216,262)
(217,261)(218,260)(219,259)(220,258)(221,257)(222,239)(223,255)(224,254)
(225,253)(226,252)(227,251)(228,250)(229,249)(230,248)(231,247)(232,246)
(233,245)(234,244)(235,243)(236,242)(237,241)(238,240)(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)(409,511)(410,527)(411,526)(412,525)(413,524)(414,523)
(415,522)(416,521)(417,520)(418,519)(419,518)(420,517)(421,516)(422,515)
(423,514)(424,513)(425,512)(426,528)(427,544)(428,543)(429,542)(430,541)
(431,540)(432,539)(433,538)(434,537)(435,536)(436,535)(437,534)(438,533)
(439,532)(440,531)(441,530)(442,529)(443,477)(444,493)(445,492)(446,491)
(447,490)(448,489)(449,488)(450,487)(451,486)(452,485)(453,484)(454,483)
(455,482)(456,481)(457,480)(458,479)(459,478)(460,494)(461,510)(462,509)
(463,508)(464,507)(465,506)(466,505)(467,504)(468,503)(469,502)(470,501)
(471,500)(472,499)(473,498)(474,497)(475,496)(476,495);;
s2 := (  1,274)(  2,273)(  3,289)(  4,288)(  5,287)(  6,286)(  7,285)(  8,284)
(  9,283)( 10,282)( 11,281)( 12,280)( 13,279)( 14,278)( 15,277)( 16,276)
( 17,275)( 18,291)( 19,290)( 20,306)( 21,305)( 22,304)( 23,303)( 24,302)
( 25,301)( 26,300)( 27,299)( 28,298)( 29,297)( 30,296)( 31,295)( 32,294)
( 33,293)( 34,292)( 35,308)( 36,307)( 37,323)( 38,322)( 39,321)( 40,320)
( 41,319)( 42,318)( 43,317)( 44,316)( 45,315)( 46,314)( 47,313)( 48,312)
( 49,311)( 50,310)( 51,309)( 52,325)( 53,324)( 54,340)( 55,339)( 56,338)
( 57,337)( 58,336)( 59,335)( 60,334)( 61,333)( 62,332)( 63,331)( 64,330)
( 65,329)( 66,328)( 67,327)( 68,326)( 69,359)( 70,358)( 71,374)( 72,373)
( 73,372)( 74,371)( 75,370)( 76,369)( 77,368)( 78,367)( 79,366)( 80,365)
( 81,364)( 82,363)( 83,362)( 84,361)( 85,360)( 86,342)( 87,341)( 88,357)
( 89,356)( 90,355)( 91,354)( 92,353)( 93,352)( 94,351)( 95,350)( 96,349)
( 97,348)( 98,347)( 99,346)(100,345)(101,344)(102,343)(103,393)(104,392)
(105,408)(106,407)(107,406)(108,405)(109,404)(110,403)(111,402)(112,401)
(113,400)(114,399)(115,398)(116,397)(117,396)(118,395)(119,394)(120,376)
(121,375)(122,391)(123,390)(124,389)(125,388)(126,387)(127,386)(128,385)
(129,384)(130,383)(131,382)(132,381)(133,380)(134,379)(135,378)(136,377)
(137,410)(138,409)(139,425)(140,424)(141,423)(142,422)(143,421)(144,420)
(145,419)(146,418)(147,417)(148,416)(149,415)(150,414)(151,413)(152,412)
(153,411)(154,427)(155,426)(156,442)(157,441)(158,440)(159,439)(160,438)
(161,437)(162,436)(163,435)(164,434)(165,433)(166,432)(167,431)(168,430)
(169,429)(170,428)(171,444)(172,443)(173,459)(174,458)(175,457)(176,456)
(177,455)(178,454)(179,453)(180,452)(181,451)(182,450)(183,449)(184,448)
(185,447)(186,446)(187,445)(188,461)(189,460)(190,476)(191,475)(192,474)
(193,473)(194,472)(195,471)(196,470)(197,469)(198,468)(199,467)(200,466)
(201,465)(202,464)(203,463)(204,462)(205,495)(206,494)(207,510)(208,509)
(209,508)(210,507)(211,506)(212,505)(213,504)(214,503)(215,502)(216,501)
(217,500)(218,499)(219,498)(220,497)(221,496)(222,478)(223,477)(224,493)
(225,492)(226,491)(227,490)(228,489)(229,488)(230,487)(231,486)(232,485)
(233,484)(234,483)(235,482)(236,481)(237,480)(238,479)(239,529)(240,528)
(241,544)(242,543)(243,542)(244,541)(245,540)(246,539)(247,538)(248,537)
(249,536)(250,535)(251,534)(252,533)(253,532)(254,531)(255,530)(256,512)
(257,511)(258,527)(259,526)(260,525)(261,524)(262,523)(263,522)(264,521)
(265,520)(266,519)(267,518)(268,517)(269,516)(270,515)(271,514)(272,513);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*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*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*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)!(  1,137)(  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);
s1 := Sym(544)!(  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)
(  9, 10)( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)
( 26, 27)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)
( 43, 44)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)
( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)(103,120)(104,136)(105,135)(106,134)(107,133)(108,132)
(109,131)(110,130)(111,129)(112,128)(113,127)(114,126)(115,125)(116,124)
(117,123)(118,122)(119,121)(137,171)(138,187)(139,186)(140,185)(141,184)
(142,183)(143,182)(144,181)(145,180)(146,179)(147,178)(148,177)(149,176)
(150,175)(151,174)(152,173)(153,172)(154,188)(155,204)(156,203)(157,202)
(158,201)(159,200)(160,199)(161,198)(162,197)(163,196)(164,195)(165,194)
(166,193)(167,192)(168,191)(169,190)(170,189)(205,256)(206,272)(207,271)
(208,270)(209,269)(210,268)(211,267)(212,266)(213,265)(214,264)(215,263)
(216,262)(217,261)(218,260)(219,259)(220,258)(221,257)(222,239)(223,255)
(224,254)(225,253)(226,252)(227,251)(228,250)(229,249)(230,248)(231,247)
(232,246)(233,245)(234,244)(235,243)(236,242)(237,241)(238,240)(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)(409,511)(410,527)(411,526)(412,525)(413,524)
(414,523)(415,522)(416,521)(417,520)(418,519)(419,518)(420,517)(421,516)
(422,515)(423,514)(424,513)(425,512)(426,528)(427,544)(428,543)(429,542)
(430,541)(431,540)(432,539)(433,538)(434,537)(435,536)(436,535)(437,534)
(438,533)(439,532)(440,531)(441,530)(442,529)(443,477)(444,493)(445,492)
(446,491)(447,490)(448,489)(449,488)(450,487)(451,486)(452,485)(453,484)
(454,483)(455,482)(456,481)(457,480)(458,479)(459,478)(460,494)(461,510)
(462,509)(463,508)(464,507)(465,506)(466,505)(467,504)(468,503)(469,502)
(470,501)(471,500)(472,499)(473,498)(474,497)(475,496)(476,495);
s2 := Sym(544)!(  1,274)(  2,273)(  3,289)(  4,288)(  5,287)(  6,286)(  7,285)
(  8,284)(  9,283)( 10,282)( 11,281)( 12,280)( 13,279)( 14,278)( 15,277)
( 16,276)( 17,275)( 18,291)( 19,290)( 20,306)( 21,305)( 22,304)( 23,303)
( 24,302)( 25,301)( 26,300)( 27,299)( 28,298)( 29,297)( 30,296)( 31,295)
( 32,294)( 33,293)( 34,292)( 35,308)( 36,307)( 37,323)( 38,322)( 39,321)
( 40,320)( 41,319)( 42,318)( 43,317)( 44,316)( 45,315)( 46,314)( 47,313)
( 48,312)( 49,311)( 50,310)( 51,309)( 52,325)( 53,324)( 54,340)( 55,339)
( 56,338)( 57,337)( 58,336)( 59,335)( 60,334)( 61,333)( 62,332)( 63,331)
( 64,330)( 65,329)( 66,328)( 67,327)( 68,326)( 69,359)( 70,358)( 71,374)
( 72,373)( 73,372)( 74,371)( 75,370)( 76,369)( 77,368)( 78,367)( 79,366)
( 80,365)( 81,364)( 82,363)( 83,362)( 84,361)( 85,360)( 86,342)( 87,341)
( 88,357)( 89,356)( 90,355)( 91,354)( 92,353)( 93,352)( 94,351)( 95,350)
( 96,349)( 97,348)( 98,347)( 99,346)(100,345)(101,344)(102,343)(103,393)
(104,392)(105,408)(106,407)(107,406)(108,405)(109,404)(110,403)(111,402)
(112,401)(113,400)(114,399)(115,398)(116,397)(117,396)(118,395)(119,394)
(120,376)(121,375)(122,391)(123,390)(124,389)(125,388)(126,387)(127,386)
(128,385)(129,384)(130,383)(131,382)(132,381)(133,380)(134,379)(135,378)
(136,377)(137,410)(138,409)(139,425)(140,424)(141,423)(142,422)(143,421)
(144,420)(145,419)(146,418)(147,417)(148,416)(149,415)(150,414)(151,413)
(152,412)(153,411)(154,427)(155,426)(156,442)(157,441)(158,440)(159,439)
(160,438)(161,437)(162,436)(163,435)(164,434)(165,433)(166,432)(167,431)
(168,430)(169,429)(170,428)(171,444)(172,443)(173,459)(174,458)(175,457)
(176,456)(177,455)(178,454)(179,453)(180,452)(181,451)(182,450)(183,449)
(184,448)(185,447)(186,446)(187,445)(188,461)(189,460)(190,476)(191,475)
(192,474)(193,473)(194,472)(195,471)(196,470)(197,469)(198,468)(199,467)
(200,466)(201,465)(202,464)(203,463)(204,462)(205,495)(206,494)(207,510)
(208,509)(209,508)(210,507)(211,506)(212,505)(213,504)(214,503)(215,502)
(216,501)(217,500)(218,499)(219,498)(220,497)(221,496)(222,478)(223,477)
(224,493)(225,492)(226,491)(227,490)(228,489)(229,488)(230,487)(231,486)
(232,485)(233,484)(234,483)(235,482)(236,481)(237,480)(238,479)(239,529)
(240,528)(241,544)(242,543)(243,542)(244,541)(245,540)(246,539)(247,538)
(248,537)(249,536)(250,535)(251,534)(252,533)(253,532)(254,531)(255,530)
(256,512)(257,511)(258,527)(259,526)(260,525)(261,524)(262,523)(263,522)
(264,521)(265,520)(266,519)(267,518)(268,517)(269,516)(270,515)(271,514)
(272,513);
poly := sub<Sym(544)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*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*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*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