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