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