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Polytope of Type {4,138}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,138}*1104b
if this polytope has a name.
Group : SmallGroup(1104,162)
Rank : 3
Schlafli Type : {4,138}
Number of vertices, edges, etc : 4, 276, 138
Order of s0s1s2 : 138
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,69}*552
   23-fold quotients : {4,6}*48c
   46-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)
(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)
(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)
(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480)
(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)(494,496)
(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)(510,512)
(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)(526,528)
(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)(542,544)
(545,547)(546,548)(549,551)(550,552);;
s1 := (  3,  4)(  5, 89)(  6, 90)(  7, 92)(  8, 91)(  9, 85)( 10, 86)( 11, 88)
( 12, 87)( 13, 81)( 14, 82)( 15, 84)( 16, 83)( 17, 77)( 18, 78)( 19, 80)
( 20, 79)( 21, 73)( 22, 74)( 23, 76)( 24, 75)( 25, 69)( 26, 70)( 27, 72)
( 28, 71)( 29, 65)( 30, 66)( 31, 68)( 32, 67)( 33, 61)( 34, 62)( 35, 64)
( 36, 63)( 37, 57)( 38, 58)( 39, 60)( 40, 59)( 41, 53)( 42, 54)( 43, 56)
( 44, 55)( 45, 49)( 46, 50)( 47, 52)( 48, 51)( 93,185)( 94,186)( 95,188)
( 96,187)( 97,273)( 98,274)( 99,276)(100,275)(101,269)(102,270)(103,272)
(104,271)(105,265)(106,266)(107,268)(108,267)(109,261)(110,262)(111,264)
(112,263)(113,257)(114,258)(115,260)(116,259)(117,253)(118,254)(119,256)
(120,255)(121,249)(122,250)(123,252)(124,251)(125,245)(126,246)(127,248)
(128,247)(129,241)(130,242)(131,244)(132,243)(133,237)(134,238)(135,240)
(136,239)(137,233)(138,234)(139,236)(140,235)(141,229)(142,230)(143,232)
(144,231)(145,225)(146,226)(147,228)(148,227)(149,221)(150,222)(151,224)
(152,223)(153,217)(154,218)(155,220)(156,219)(157,213)(158,214)(159,216)
(160,215)(161,209)(162,210)(163,212)(164,211)(165,205)(166,206)(167,208)
(168,207)(169,201)(170,202)(171,204)(172,203)(173,197)(174,198)(175,200)
(176,199)(177,193)(178,194)(179,196)(180,195)(181,189)(182,190)(183,192)
(184,191)(279,280)(281,365)(282,366)(283,368)(284,367)(285,361)(286,362)
(287,364)(288,363)(289,357)(290,358)(291,360)(292,359)(293,353)(294,354)
(295,356)(296,355)(297,349)(298,350)(299,352)(300,351)(301,345)(302,346)
(303,348)(304,347)(305,341)(306,342)(307,344)(308,343)(309,337)(310,338)
(311,340)(312,339)(313,333)(314,334)(315,336)(316,335)(317,329)(318,330)
(319,332)(320,331)(321,325)(322,326)(323,328)(324,327)(369,461)(370,462)
(371,464)(372,463)(373,549)(374,550)(375,552)(376,551)(377,545)(378,546)
(379,548)(380,547)(381,541)(382,542)(383,544)(384,543)(385,537)(386,538)
(387,540)(388,539)(389,533)(390,534)(391,536)(392,535)(393,529)(394,530)
(395,532)(396,531)(397,525)(398,526)(399,528)(400,527)(401,521)(402,522)
(403,524)(404,523)(405,517)(406,518)(407,520)(408,519)(409,513)(410,514)
(411,516)(412,515)(413,509)(414,510)(415,512)(416,511)(417,505)(418,506)
(419,508)(420,507)(421,501)(422,502)(423,504)(424,503)(425,497)(426,498)
(427,500)(428,499)(429,493)(430,494)(431,496)(432,495)(433,489)(434,490)
(435,492)(436,491)(437,485)(438,486)(439,488)(440,487)(441,481)(442,482)
(443,484)(444,483)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)
(451,476)(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)
(459,468)(460,467);;
s2 := (  1,373)(  2,376)(  3,375)(  4,374)(  5,369)(  6,372)(  7,371)(  8,370)
(  9,457)( 10,460)( 11,459)( 12,458)( 13,453)( 14,456)( 15,455)( 16,454)
( 17,449)( 18,452)( 19,451)( 20,450)( 21,445)( 22,448)( 23,447)( 24,446)
( 25,441)( 26,444)( 27,443)( 28,442)( 29,437)( 30,440)( 31,439)( 32,438)
( 33,433)( 34,436)( 35,435)( 36,434)( 37,429)( 38,432)( 39,431)( 40,430)
( 41,425)( 42,428)( 43,427)( 44,426)( 45,421)( 46,424)( 47,423)( 48,422)
( 49,417)( 50,420)( 51,419)( 52,418)( 53,413)( 54,416)( 55,415)( 56,414)
( 57,409)( 58,412)( 59,411)( 60,410)( 61,405)( 62,408)( 63,407)( 64,406)
( 65,401)( 66,404)( 67,403)( 68,402)( 69,397)( 70,400)( 71,399)( 72,398)
( 73,393)( 74,396)( 75,395)( 76,394)( 77,389)( 78,392)( 79,391)( 80,390)
( 81,385)( 82,388)( 83,387)( 84,386)( 85,381)( 86,384)( 87,383)( 88,382)
( 89,377)( 90,380)( 91,379)( 92,378)( 93,281)( 94,284)( 95,283)( 96,282)
( 97,277)( 98,280)( 99,279)(100,278)(101,365)(102,368)(103,367)(104,366)
(105,361)(106,364)(107,363)(108,362)(109,357)(110,360)(111,359)(112,358)
(113,353)(114,356)(115,355)(116,354)(117,349)(118,352)(119,351)(120,350)
(121,345)(122,348)(123,347)(124,346)(125,341)(126,344)(127,343)(128,342)
(129,337)(130,340)(131,339)(132,338)(133,333)(134,336)(135,335)(136,334)
(137,329)(138,332)(139,331)(140,330)(141,325)(142,328)(143,327)(144,326)
(145,321)(146,324)(147,323)(148,322)(149,317)(150,320)(151,319)(152,318)
(153,313)(154,316)(155,315)(156,314)(157,309)(158,312)(159,311)(160,310)
(161,305)(162,308)(163,307)(164,306)(165,301)(166,304)(167,303)(168,302)
(169,297)(170,300)(171,299)(172,298)(173,293)(174,296)(175,295)(176,294)
(177,289)(178,292)(179,291)(180,290)(181,285)(182,288)(183,287)(184,286)
(185,465)(186,468)(187,467)(188,466)(189,461)(190,464)(191,463)(192,462)
(193,549)(194,552)(195,551)(196,550)(197,545)(198,548)(199,547)(200,546)
(201,541)(202,544)(203,543)(204,542)(205,537)(206,540)(207,539)(208,538)
(209,533)(210,536)(211,535)(212,534)(213,529)(214,532)(215,531)(216,530)
(217,525)(218,528)(219,527)(220,526)(221,521)(222,524)(223,523)(224,522)
(225,517)(226,520)(227,519)(228,518)(229,513)(230,516)(231,515)(232,514)
(233,509)(234,512)(235,511)(236,510)(237,505)(238,508)(239,507)(240,506)
(241,501)(242,504)(243,503)(244,502)(245,497)(246,500)(247,499)(248,498)
(249,493)(250,496)(251,495)(252,494)(253,489)(254,492)(255,491)(256,490)
(257,485)(258,488)(259,487)(260,486)(261,481)(262,484)(263,483)(264,482)
(265,477)(266,480)(267,479)(268,478)(269,473)(270,476)(271,475)(272,474)
(273,469)(274,472)(275,471)(276,470);;
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*s0*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*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(552)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)
(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)
(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)
(478,480)(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)
(494,496)(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)
(510,512)(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)
(526,528)(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)
(542,544)(545,547)(546,548)(549,551)(550,552);
s1 := Sym(552)!(  3,  4)(  5, 89)(  6, 90)(  7, 92)(  8, 91)(  9, 85)( 10, 86)
( 11, 88)( 12, 87)( 13, 81)( 14, 82)( 15, 84)( 16, 83)( 17, 77)( 18, 78)
( 19, 80)( 20, 79)( 21, 73)( 22, 74)( 23, 76)( 24, 75)( 25, 69)( 26, 70)
( 27, 72)( 28, 71)( 29, 65)( 30, 66)( 31, 68)( 32, 67)( 33, 61)( 34, 62)
( 35, 64)( 36, 63)( 37, 57)( 38, 58)( 39, 60)( 40, 59)( 41, 53)( 42, 54)
( 43, 56)( 44, 55)( 45, 49)( 46, 50)( 47, 52)( 48, 51)( 93,185)( 94,186)
( 95,188)( 96,187)( 97,273)( 98,274)( 99,276)(100,275)(101,269)(102,270)
(103,272)(104,271)(105,265)(106,266)(107,268)(108,267)(109,261)(110,262)
(111,264)(112,263)(113,257)(114,258)(115,260)(116,259)(117,253)(118,254)
(119,256)(120,255)(121,249)(122,250)(123,252)(124,251)(125,245)(126,246)
(127,248)(128,247)(129,241)(130,242)(131,244)(132,243)(133,237)(134,238)
(135,240)(136,239)(137,233)(138,234)(139,236)(140,235)(141,229)(142,230)
(143,232)(144,231)(145,225)(146,226)(147,228)(148,227)(149,221)(150,222)
(151,224)(152,223)(153,217)(154,218)(155,220)(156,219)(157,213)(158,214)
(159,216)(160,215)(161,209)(162,210)(163,212)(164,211)(165,205)(166,206)
(167,208)(168,207)(169,201)(170,202)(171,204)(172,203)(173,197)(174,198)
(175,200)(176,199)(177,193)(178,194)(179,196)(180,195)(181,189)(182,190)
(183,192)(184,191)(279,280)(281,365)(282,366)(283,368)(284,367)(285,361)
(286,362)(287,364)(288,363)(289,357)(290,358)(291,360)(292,359)(293,353)
(294,354)(295,356)(296,355)(297,349)(298,350)(299,352)(300,351)(301,345)
(302,346)(303,348)(304,347)(305,341)(306,342)(307,344)(308,343)(309,337)
(310,338)(311,340)(312,339)(313,333)(314,334)(315,336)(316,335)(317,329)
(318,330)(319,332)(320,331)(321,325)(322,326)(323,328)(324,327)(369,461)
(370,462)(371,464)(372,463)(373,549)(374,550)(375,552)(376,551)(377,545)
(378,546)(379,548)(380,547)(381,541)(382,542)(383,544)(384,543)(385,537)
(386,538)(387,540)(388,539)(389,533)(390,534)(391,536)(392,535)(393,529)
(394,530)(395,532)(396,531)(397,525)(398,526)(399,528)(400,527)(401,521)
(402,522)(403,524)(404,523)(405,517)(406,518)(407,520)(408,519)(409,513)
(410,514)(411,516)(412,515)(413,509)(414,510)(415,512)(416,511)(417,505)
(418,506)(419,508)(420,507)(421,501)(422,502)(423,504)(424,503)(425,497)
(426,498)(427,500)(428,499)(429,493)(430,494)(431,496)(432,495)(433,489)
(434,490)(435,492)(436,491)(437,485)(438,486)(439,488)(440,487)(441,481)
(442,482)(443,484)(444,483)(445,477)(446,478)(447,480)(448,479)(449,473)
(450,474)(451,476)(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)
(458,466)(459,468)(460,467);
s2 := Sym(552)!(  1,373)(  2,376)(  3,375)(  4,374)(  5,369)(  6,372)(  7,371)
(  8,370)(  9,457)( 10,460)( 11,459)( 12,458)( 13,453)( 14,456)( 15,455)
( 16,454)( 17,449)( 18,452)( 19,451)( 20,450)( 21,445)( 22,448)( 23,447)
( 24,446)( 25,441)( 26,444)( 27,443)( 28,442)( 29,437)( 30,440)( 31,439)
( 32,438)( 33,433)( 34,436)( 35,435)( 36,434)( 37,429)( 38,432)( 39,431)
( 40,430)( 41,425)( 42,428)( 43,427)( 44,426)( 45,421)( 46,424)( 47,423)
( 48,422)( 49,417)( 50,420)( 51,419)( 52,418)( 53,413)( 54,416)( 55,415)
( 56,414)( 57,409)( 58,412)( 59,411)( 60,410)( 61,405)( 62,408)( 63,407)
( 64,406)( 65,401)( 66,404)( 67,403)( 68,402)( 69,397)( 70,400)( 71,399)
( 72,398)( 73,393)( 74,396)( 75,395)( 76,394)( 77,389)( 78,392)( 79,391)
( 80,390)( 81,385)( 82,388)( 83,387)( 84,386)( 85,381)( 86,384)( 87,383)
( 88,382)( 89,377)( 90,380)( 91,379)( 92,378)( 93,281)( 94,284)( 95,283)
( 96,282)( 97,277)( 98,280)( 99,279)(100,278)(101,365)(102,368)(103,367)
(104,366)(105,361)(106,364)(107,363)(108,362)(109,357)(110,360)(111,359)
(112,358)(113,353)(114,356)(115,355)(116,354)(117,349)(118,352)(119,351)
(120,350)(121,345)(122,348)(123,347)(124,346)(125,341)(126,344)(127,343)
(128,342)(129,337)(130,340)(131,339)(132,338)(133,333)(134,336)(135,335)
(136,334)(137,329)(138,332)(139,331)(140,330)(141,325)(142,328)(143,327)
(144,326)(145,321)(146,324)(147,323)(148,322)(149,317)(150,320)(151,319)
(152,318)(153,313)(154,316)(155,315)(156,314)(157,309)(158,312)(159,311)
(160,310)(161,305)(162,308)(163,307)(164,306)(165,301)(166,304)(167,303)
(168,302)(169,297)(170,300)(171,299)(172,298)(173,293)(174,296)(175,295)
(176,294)(177,289)(178,292)(179,291)(180,290)(181,285)(182,288)(183,287)
(184,286)(185,465)(186,468)(187,467)(188,466)(189,461)(190,464)(191,463)
(192,462)(193,549)(194,552)(195,551)(196,550)(197,545)(198,548)(199,547)
(200,546)(201,541)(202,544)(203,543)(204,542)(205,537)(206,540)(207,539)
(208,538)(209,533)(210,536)(211,535)(212,534)(213,529)(214,532)(215,531)
(216,530)(217,525)(218,528)(219,527)(220,526)(221,521)(222,524)(223,523)
(224,522)(225,517)(226,520)(227,519)(228,518)(229,513)(230,516)(231,515)
(232,514)(233,509)(234,512)(235,511)(236,510)(237,505)(238,508)(239,507)
(240,506)(241,501)(242,504)(243,503)(244,502)(245,497)(246,500)(247,499)
(248,498)(249,493)(250,496)(251,495)(252,494)(253,489)(254,492)(255,491)
(256,490)(257,485)(258,488)(259,487)(260,486)(261,481)(262,484)(263,483)
(264,482)(265,477)(266,480)(267,479)(268,478)(269,473)(270,476)(271,475)
(272,474)(273,469)(274,472)(275,471)(276,470);
poly := sub<Sym(552)|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*s0*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*s1*s2*s1*s2 >; 
 
References : None.
to this polytope