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Polytope of Type {135,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {135,4}*1080
if this polytope has a name.
Group : SmallGroup(1080,53)
Rank : 3
Schlafli Type : {135,4}
Number of vertices, edges, etc : 135, 270, 4
Order of s0s1s2 : 135
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) :
   3-fold quotients : {45,4}*360
   5-fold quotients : {27,4}*216
   9-fold quotients : {15,4}*120
   15-fold quotients : {9,4}*72
   45-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37,145)( 38,146)( 39,148)( 40,147)( 41,153)( 42,154)( 43,156)
( 44,155)( 45,149)( 46,150)( 47,152)( 48,151)( 49,177)( 50,178)( 51,180)
( 52,179)( 53,173)( 54,174)( 55,176)( 56,175)( 57,169)( 58,170)( 59,172)
( 60,171)( 61,165)( 62,166)( 63,168)( 64,167)( 65,161)( 66,162)( 67,164)
( 68,163)( 69,157)( 70,158)( 71,160)( 72,159)( 73,109)( 74,110)( 75,112)
( 76,111)( 77,117)( 78,118)( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)
( 84,115)( 85,141)( 86,142)( 87,144)( 88,143)( 89,137)( 90,138)( 91,140)
( 92,139)( 93,133)( 94,134)( 95,136)( 96,135)( 97,129)( 98,130)( 99,132)
(100,131)(101,125)(102,126)(103,128)(104,127)(105,121)(106,122)(107,124)
(108,123)(181,393)(182,394)(183,396)(184,395)(185,389)(186,390)(187,392)
(188,391)(189,385)(190,386)(191,388)(192,387)(193,381)(194,382)(195,384)
(196,383)(197,377)(198,378)(199,380)(200,379)(201,373)(202,374)(203,376)
(204,375)(205,369)(206,370)(207,372)(208,371)(209,365)(210,366)(211,368)
(212,367)(213,361)(214,362)(215,364)(216,363)(217,537)(218,538)(219,540)
(220,539)(221,533)(222,534)(223,536)(224,535)(225,529)(226,530)(227,532)
(228,531)(229,525)(230,526)(231,528)(232,527)(233,521)(234,522)(235,524)
(236,523)(237,517)(238,518)(239,520)(240,519)(241,513)(242,514)(243,516)
(244,515)(245,509)(246,510)(247,512)(248,511)(249,505)(250,506)(251,508)
(252,507)(253,501)(254,502)(255,504)(256,503)(257,497)(258,498)(259,500)
(260,499)(261,493)(262,494)(263,496)(264,495)(265,489)(266,490)(267,492)
(268,491)(269,485)(270,486)(271,488)(272,487)(273,481)(274,482)(275,484)
(276,483)(277,477)(278,478)(279,480)(280,479)(281,473)(282,474)(283,476)
(284,475)(285,469)(286,470)(287,472)(288,471)(289,465)(290,466)(291,468)
(292,467)(293,461)(294,462)(295,464)(296,463)(297,457)(298,458)(299,460)
(300,459)(301,453)(302,454)(303,456)(304,455)(305,449)(306,450)(307,452)
(308,451)(309,445)(310,446)(311,448)(312,447)(313,441)(314,442)(315,444)
(316,443)(317,437)(318,438)(319,440)(320,439)(321,433)(322,434)(323,436)
(324,435)(325,429)(326,430)(327,432)(328,431)(329,425)(330,426)(331,428)
(332,427)(333,421)(334,422)(335,424)(336,423)(337,417)(338,418)(339,420)
(340,419)(341,413)(342,414)(343,416)(344,415)(345,409)(346,410)(347,412)
(348,411)(349,405)(350,406)(351,408)(352,407)(353,401)(354,402)(355,404)
(356,403)(357,397)(358,398)(359,400)(360,399);;
s1 := (  1,217)(  2,220)(  3,219)(  4,218)(  5,225)(  6,228)(  7,227)(  8,226)
(  9,221)( 10,224)( 11,223)( 12,222)( 13,249)( 14,252)( 15,251)( 16,250)
( 17,245)( 18,248)( 19,247)( 20,246)( 21,241)( 22,244)( 23,243)( 24,242)
( 25,237)( 26,240)( 27,239)( 28,238)( 29,233)( 30,236)( 31,235)( 32,234)
( 33,229)( 34,232)( 35,231)( 36,230)( 37,181)( 38,184)( 39,183)( 40,182)
( 41,189)( 42,192)( 43,191)( 44,190)( 45,185)( 46,188)( 47,187)( 48,186)
( 49,213)( 50,216)( 51,215)( 52,214)( 53,209)( 54,212)( 55,211)( 56,210)
( 57,205)( 58,208)( 59,207)( 60,206)( 61,201)( 62,204)( 63,203)( 64,202)
( 65,197)( 66,200)( 67,199)( 68,198)( 69,193)( 70,196)( 71,195)( 72,194)
( 73,325)( 74,328)( 75,327)( 76,326)( 77,333)( 78,336)( 79,335)( 80,334)
( 81,329)( 82,332)( 83,331)( 84,330)( 85,357)( 86,360)( 87,359)( 88,358)
( 89,353)( 90,356)( 91,355)( 92,354)( 93,349)( 94,352)( 95,351)( 96,350)
( 97,345)( 98,348)( 99,347)(100,346)(101,341)(102,344)(103,343)(104,342)
(105,337)(106,340)(107,339)(108,338)(109,289)(110,292)(111,291)(112,290)
(113,297)(114,300)(115,299)(116,298)(117,293)(118,296)(119,295)(120,294)
(121,321)(122,324)(123,323)(124,322)(125,317)(126,320)(127,319)(128,318)
(129,313)(130,316)(131,315)(132,314)(133,309)(134,312)(135,311)(136,310)
(137,305)(138,308)(139,307)(140,306)(141,301)(142,304)(143,303)(144,302)
(145,253)(146,256)(147,255)(148,254)(149,261)(150,264)(151,263)(152,262)
(153,257)(154,260)(155,259)(156,258)(157,285)(158,288)(159,287)(160,286)
(161,281)(162,284)(163,283)(164,282)(165,277)(166,280)(167,279)(168,278)
(169,273)(170,276)(171,275)(172,274)(173,269)(174,272)(175,271)(176,270)
(177,265)(178,268)(179,267)(180,266)(361,429)(362,432)(363,431)(364,430)
(365,425)(366,428)(367,427)(368,426)(369,421)(370,424)(371,423)(372,422)
(373,417)(374,420)(375,419)(376,418)(377,413)(378,416)(379,415)(380,414)
(381,409)(382,412)(383,411)(384,410)(385,405)(386,408)(387,407)(388,406)
(389,401)(390,404)(391,403)(392,402)(393,397)(394,400)(395,399)(396,398)
(433,537)(434,540)(435,539)(436,538)(437,533)(438,536)(439,535)(440,534)
(441,529)(442,532)(443,531)(444,530)(445,525)(446,528)(447,527)(448,526)
(449,521)(450,524)(451,523)(452,522)(453,517)(454,520)(455,519)(456,518)
(457,513)(458,516)(459,515)(460,514)(461,509)(462,512)(463,511)(464,510)
(465,505)(466,508)(467,507)(468,506)(469,501)(470,504)(471,503)(472,502)
(473,497)(474,500)(475,499)(476,498)(477,493)(478,496)(479,495)(480,494)
(481,489)(482,492)(483,491)(484,490)(486,488);;
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);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(540)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37,145)( 38,146)( 39,148)( 40,147)( 41,153)( 42,154)
( 43,156)( 44,155)( 45,149)( 46,150)( 47,152)( 48,151)( 49,177)( 50,178)
( 51,180)( 52,179)( 53,173)( 54,174)( 55,176)( 56,175)( 57,169)( 58,170)
( 59,172)( 60,171)( 61,165)( 62,166)( 63,168)( 64,167)( 65,161)( 66,162)
( 67,164)( 68,163)( 69,157)( 70,158)( 71,160)( 72,159)( 73,109)( 74,110)
( 75,112)( 76,111)( 77,117)( 78,118)( 79,120)( 80,119)( 81,113)( 82,114)
( 83,116)( 84,115)( 85,141)( 86,142)( 87,144)( 88,143)( 89,137)( 90,138)
( 91,140)( 92,139)( 93,133)( 94,134)( 95,136)( 96,135)( 97,129)( 98,130)
( 99,132)(100,131)(101,125)(102,126)(103,128)(104,127)(105,121)(106,122)
(107,124)(108,123)(181,393)(182,394)(183,396)(184,395)(185,389)(186,390)
(187,392)(188,391)(189,385)(190,386)(191,388)(192,387)(193,381)(194,382)
(195,384)(196,383)(197,377)(198,378)(199,380)(200,379)(201,373)(202,374)
(203,376)(204,375)(205,369)(206,370)(207,372)(208,371)(209,365)(210,366)
(211,368)(212,367)(213,361)(214,362)(215,364)(216,363)(217,537)(218,538)
(219,540)(220,539)(221,533)(222,534)(223,536)(224,535)(225,529)(226,530)
(227,532)(228,531)(229,525)(230,526)(231,528)(232,527)(233,521)(234,522)
(235,524)(236,523)(237,517)(238,518)(239,520)(240,519)(241,513)(242,514)
(243,516)(244,515)(245,509)(246,510)(247,512)(248,511)(249,505)(250,506)
(251,508)(252,507)(253,501)(254,502)(255,504)(256,503)(257,497)(258,498)
(259,500)(260,499)(261,493)(262,494)(263,496)(264,495)(265,489)(266,490)
(267,492)(268,491)(269,485)(270,486)(271,488)(272,487)(273,481)(274,482)
(275,484)(276,483)(277,477)(278,478)(279,480)(280,479)(281,473)(282,474)
(283,476)(284,475)(285,469)(286,470)(287,472)(288,471)(289,465)(290,466)
(291,468)(292,467)(293,461)(294,462)(295,464)(296,463)(297,457)(298,458)
(299,460)(300,459)(301,453)(302,454)(303,456)(304,455)(305,449)(306,450)
(307,452)(308,451)(309,445)(310,446)(311,448)(312,447)(313,441)(314,442)
(315,444)(316,443)(317,437)(318,438)(319,440)(320,439)(321,433)(322,434)
(323,436)(324,435)(325,429)(326,430)(327,432)(328,431)(329,425)(330,426)
(331,428)(332,427)(333,421)(334,422)(335,424)(336,423)(337,417)(338,418)
(339,420)(340,419)(341,413)(342,414)(343,416)(344,415)(345,409)(346,410)
(347,412)(348,411)(349,405)(350,406)(351,408)(352,407)(353,401)(354,402)
(355,404)(356,403)(357,397)(358,398)(359,400)(360,399);
s1 := Sym(540)!(  1,217)(  2,220)(  3,219)(  4,218)(  5,225)(  6,228)(  7,227)
(  8,226)(  9,221)( 10,224)( 11,223)( 12,222)( 13,249)( 14,252)( 15,251)
( 16,250)( 17,245)( 18,248)( 19,247)( 20,246)( 21,241)( 22,244)( 23,243)
( 24,242)( 25,237)( 26,240)( 27,239)( 28,238)( 29,233)( 30,236)( 31,235)
( 32,234)( 33,229)( 34,232)( 35,231)( 36,230)( 37,181)( 38,184)( 39,183)
( 40,182)( 41,189)( 42,192)( 43,191)( 44,190)( 45,185)( 46,188)( 47,187)
( 48,186)( 49,213)( 50,216)( 51,215)( 52,214)( 53,209)( 54,212)( 55,211)
( 56,210)( 57,205)( 58,208)( 59,207)( 60,206)( 61,201)( 62,204)( 63,203)
( 64,202)( 65,197)( 66,200)( 67,199)( 68,198)( 69,193)( 70,196)( 71,195)
( 72,194)( 73,325)( 74,328)( 75,327)( 76,326)( 77,333)( 78,336)( 79,335)
( 80,334)( 81,329)( 82,332)( 83,331)( 84,330)( 85,357)( 86,360)( 87,359)
( 88,358)( 89,353)( 90,356)( 91,355)( 92,354)( 93,349)( 94,352)( 95,351)
( 96,350)( 97,345)( 98,348)( 99,347)(100,346)(101,341)(102,344)(103,343)
(104,342)(105,337)(106,340)(107,339)(108,338)(109,289)(110,292)(111,291)
(112,290)(113,297)(114,300)(115,299)(116,298)(117,293)(118,296)(119,295)
(120,294)(121,321)(122,324)(123,323)(124,322)(125,317)(126,320)(127,319)
(128,318)(129,313)(130,316)(131,315)(132,314)(133,309)(134,312)(135,311)
(136,310)(137,305)(138,308)(139,307)(140,306)(141,301)(142,304)(143,303)
(144,302)(145,253)(146,256)(147,255)(148,254)(149,261)(150,264)(151,263)
(152,262)(153,257)(154,260)(155,259)(156,258)(157,285)(158,288)(159,287)
(160,286)(161,281)(162,284)(163,283)(164,282)(165,277)(166,280)(167,279)
(168,278)(169,273)(170,276)(171,275)(172,274)(173,269)(174,272)(175,271)
(176,270)(177,265)(178,268)(179,267)(180,266)(361,429)(362,432)(363,431)
(364,430)(365,425)(366,428)(367,427)(368,426)(369,421)(370,424)(371,423)
(372,422)(373,417)(374,420)(375,419)(376,418)(377,413)(378,416)(379,415)
(380,414)(381,409)(382,412)(383,411)(384,410)(385,405)(386,408)(387,407)
(388,406)(389,401)(390,404)(391,403)(392,402)(393,397)(394,400)(395,399)
(396,398)(433,537)(434,540)(435,539)(436,538)(437,533)(438,536)(439,535)
(440,534)(441,529)(442,532)(443,531)(444,530)(445,525)(446,528)(447,527)
(448,526)(449,521)(450,524)(451,523)(452,522)(453,517)(454,520)(455,519)
(456,518)(457,513)(458,516)(459,515)(460,514)(461,509)(462,512)(463,511)
(464,510)(465,505)(466,508)(467,507)(468,506)(469,501)(470,504)(471,503)
(472,502)(473,497)(474,500)(475,499)(476,498)(477,493)(478,496)(479,495)
(480,494)(481,489)(482,492)(483,491)(484,490)(486,488);
s2 := Sym(540)!(  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);
poly := sub<Sym(540)|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 >; 
 
References : None.
to this polytope