Polytope of Type {34,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,4,4}*1088
Also Known As : {{34,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1088,1033)
Rank : 4
Schlafli Type : {34,4,4}
Number of vertices, edges, etc : 34, 68, 8, 4
Order of s0s1s2s3 : 68
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {34,2,4}*544, {34,4,2}*544
4-fold quotients : {17,2,4}*272, {34,2,2}*272
8-fold quotients : {17,2,2}*136
17-fold quotients : {2,4,4}*64
34-fold quotients : {2,2,4}*32, {2,4,2}*32
68-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 69)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 81)( 7, 80)( 8, 79)
( 9, 78)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 71)
( 17, 70)( 18, 86)( 19,102)( 20,101)( 21,100)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)
( 33, 88)( 34, 87)( 35,103)( 36,119)( 37,118)( 38,117)( 39,116)( 40,115)
( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)( 48,107)
( 49,106)( 50,105)( 51,104)( 52,120)( 53,136)( 54,135)( 55,134)( 56,133)
( 57,132)( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)( 64,125)
( 65,124)( 66,123)( 67,122)( 68,121)(137,205)(138,221)(139,220)(140,219)
(141,218)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,211)
(149,210)(150,209)(151,208)(152,207)(153,206)(154,222)(155,238)(156,237)
(157,236)(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)
(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,239)(172,255)
(173,254)(174,253)(175,252)(176,251)(177,250)(178,249)(179,248)(180,247)
(181,246)(182,245)(183,244)(184,243)(185,242)(186,241)(187,240)(188,256)
(189,272)(190,271)(191,270)(192,269)(193,268)(194,267)(195,266)(196,265)
(197,264)(198,263)(199,262)(200,261)(201,260)(202,259)(203,258)(204,257)
(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)(409,477)(410,493)(411,492)(412,491)
(413,490)(414,489)(415,488)(416,487)(417,486)(418,485)(419,484)(420,483)
(421,482)(422,481)(423,480)(424,479)(425,478)(426,494)(427,510)(428,509)
(429,508)(430,507)(431,506)(432,505)(433,504)(434,503)(435,502)(436,501)
(437,500)(438,499)(439,498)(440,497)(441,496)(442,495)(443,511)(444,527)
(445,526)(446,525)(447,524)(448,523)(449,522)(450,521)(451,520)(452,519)
(453,518)(454,517)(455,516)(456,515)(457,514)(458,513)(459,512)(460,528)
(461,544)(462,543)(463,542)(464,541)(465,540)(466,539)(467,538)(468,537)
(469,536)(470,535)(471,534)(472,533)(473,532)(474,531)(475,530)(476,529);;
s1 := ( 1,342)( 2,341)( 3,357)( 4,356)( 5,355)( 6,354)( 7,353)( 8,352)
( 9,351)( 10,350)( 11,349)( 12,348)( 13,347)( 14,346)( 15,345)( 16,344)
( 17,343)( 18,359)( 19,358)( 20,374)( 21,373)( 22,372)( 23,371)( 24,370)
( 25,369)( 26,368)( 27,367)( 28,366)( 29,365)( 30,364)( 31,363)( 32,362)
( 33,361)( 34,360)( 35,376)( 36,375)( 37,391)( 38,390)( 39,389)( 40,388)
( 41,387)( 42,386)( 43,385)( 44,384)( 45,383)( 46,382)( 47,381)( 48,380)
( 49,379)( 50,378)( 51,377)( 52,393)( 53,392)( 54,408)( 55,407)( 56,406)
( 57,405)( 58,404)( 59,403)( 60,402)( 61,401)( 62,400)( 63,399)( 64,398)
( 65,397)( 66,396)( 67,395)( 68,394)( 69,274)( 70,273)( 71,289)( 72,288)
( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,282)( 79,281)( 80,280)
( 81,279)( 82,278)( 83,277)( 84,276)( 85,275)( 86,291)( 87,290)( 88,306)
( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)( 96,298)
( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,308)(104,307)
(105,323)(106,322)(107,321)(108,320)(109,319)(110,318)(111,317)(112,316)
(113,315)(114,314)(115,313)(116,312)(117,311)(118,310)(119,309)(120,325)
(121,324)(122,340)(123,339)(124,338)(125,337)(126,336)(127,335)(128,334)
(129,333)(130,332)(131,331)(132,330)(133,329)(134,328)(135,327)(136,326)
(137,478)(138,477)(139,493)(140,492)(141,491)(142,490)(143,489)(144,488)
(145,487)(146,486)(147,485)(148,484)(149,483)(150,482)(151,481)(152,480)
(153,479)(154,495)(155,494)(156,510)(157,509)(158,508)(159,507)(160,506)
(161,505)(162,504)(163,503)(164,502)(165,501)(166,500)(167,499)(168,498)
(169,497)(170,496)(171,512)(172,511)(173,527)(174,526)(175,525)(176,524)
(177,523)(178,522)(179,521)(180,520)(181,519)(182,518)(183,517)(184,516)
(185,515)(186,514)(187,513)(188,529)(189,528)(190,544)(191,543)(192,542)
(193,541)(194,540)(195,539)(196,538)(197,537)(198,536)(199,535)(200,534)
(201,533)(202,532)(203,531)(204,530)(205,410)(206,409)(207,425)(208,424)
(209,423)(210,422)(211,421)(212,420)(213,419)(214,418)(215,417)(216,416)
(217,415)(218,414)(219,413)(220,412)(221,411)(222,427)(223,426)(224,442)
(225,441)(226,440)(227,439)(228,438)(229,437)(230,436)(231,435)(232,434)
(233,433)(234,432)(235,431)(236,430)(237,429)(238,428)(239,444)(240,443)
(241,459)(242,458)(243,457)(244,456)(245,455)(246,454)(247,453)(248,452)
(249,451)(250,450)(251,449)(252,448)(253,447)(254,446)(255,445)(256,461)
(257,460)(258,476)(259,475)(260,474)(261,473)(262,472)(263,471)(264,470)
(265,469)(266,468)(267,467)(268,466)(269,465)(270,464)(271,463)(272,462);;
s2 := (137,154)(138,155)(139,156)(140,157)(141,158)(142,159)(143,160)(144,161)
(145,162)(146,163)(147,164)(148,165)(149,166)(150,167)(151,168)(152,169)
(153,170)(171,188)(172,189)(173,190)(174,191)(175,192)(176,193)(177,194)
(178,195)(179,196)(180,197)(181,198)(182,199)(183,200)(184,201)(185,202)
(186,203)(187,204)(205,222)(206,223)(207,224)(208,225)(209,226)(210,227)
(211,228)(212,229)(213,230)(214,231)(215,232)(216,233)(217,234)(218,235)
(219,236)(220,237)(221,238)(239,256)(240,257)(241,258)(242,259)(243,260)
(244,261)(245,262)(246,263)(247,264)(248,265)(249,266)(250,267)(251,268)
(252,269)(253,270)(254,271)(255,272)(273,307)(274,308)(275,309)(276,310)
(277,311)(278,312)(279,313)(280,314)(281,315)(282,316)(283,317)(284,318)
(285,319)(286,320)(287,321)(288,322)(289,323)(290,324)(291,325)(292,326)
(293,327)(294,328)(295,329)(296,330)(297,331)(298,332)(299,333)(300,334)
(301,335)(302,336)(303,337)(304,338)(305,339)(306,340)(341,375)(342,376)
(343,377)(344,378)(345,379)(346,380)(347,381)(348,382)(349,383)(350,384)
(351,385)(352,386)(353,387)(354,388)(355,389)(356,390)(357,391)(358,392)
(359,393)(360,394)(361,395)(362,396)(363,397)(364,398)(365,399)(366,400)
(367,401)(368,402)(369,403)(370,404)(371,405)(372,406)(373,407)(374,408)
(409,460)(410,461)(411,462)(412,463)(413,464)(414,465)(415,466)(416,467)
(417,468)(418,469)(419,470)(420,471)(421,472)(422,473)(423,474)(424,475)
(425,476)(426,443)(427,444)(428,445)(429,446)(430,447)(431,448)(432,449)
(433,450)(434,451)(435,452)(436,453)(437,454)(438,455)(439,456)(440,457)
(441,458)(442,459)(477,528)(478,529)(479,530)(480,531)(481,532)(482,533)
(483,534)(484,535)(485,536)(486,537)(487,538)(488,539)(489,540)(490,541)
(491,542)(492,543)(493,544)(494,511)(495,512)(496,513)(497,514)(498,515)
(499,516)(500,517)(501,518)(502,519)(503,520)(504,521)(505,522)(506,523)
(507,524)(508,525)(509,526)(510,527);;
s3 := ( 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,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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, 69)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 81)( 7, 80)
( 8, 79)( 9, 78)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 71)( 17, 70)( 18, 86)( 19,102)( 20,101)( 21,100)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)
( 32, 89)( 33, 88)( 34, 87)( 35,103)( 36,119)( 37,118)( 38,117)( 39,116)
( 40,115)( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)
( 48,107)( 49,106)( 50,105)( 51,104)( 52,120)( 53,136)( 54,135)( 55,134)
( 56,133)( 57,132)( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)
( 64,125)( 65,124)( 66,123)( 67,122)( 68,121)(137,205)(138,221)(139,220)
(140,219)(141,218)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)
(148,211)(149,210)(150,209)(151,208)(152,207)(153,206)(154,222)(155,238)
(156,237)(157,236)(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)
(164,229)(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,239)
(172,255)(173,254)(174,253)(175,252)(176,251)(177,250)(178,249)(179,248)
(180,247)(181,246)(182,245)(183,244)(184,243)(185,242)(186,241)(187,240)
(188,256)(189,272)(190,271)(191,270)(192,269)(193,268)(194,267)(195,266)
(196,265)(197,264)(198,263)(199,262)(200,261)(201,260)(202,259)(203,258)
(204,257)(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)(409,477)(410,493)(411,492)
(412,491)(413,490)(414,489)(415,488)(416,487)(417,486)(418,485)(419,484)
(420,483)(421,482)(422,481)(423,480)(424,479)(425,478)(426,494)(427,510)
(428,509)(429,508)(430,507)(431,506)(432,505)(433,504)(434,503)(435,502)
(436,501)(437,500)(438,499)(439,498)(440,497)(441,496)(442,495)(443,511)
(444,527)(445,526)(446,525)(447,524)(448,523)(449,522)(450,521)(451,520)
(452,519)(453,518)(454,517)(455,516)(456,515)(457,514)(458,513)(459,512)
(460,528)(461,544)(462,543)(463,542)(464,541)(465,540)(466,539)(467,538)
(468,537)(469,536)(470,535)(471,534)(472,533)(473,532)(474,531)(475,530)
(476,529);
s1 := Sym(544)!( 1,342)( 2,341)( 3,357)( 4,356)( 5,355)( 6,354)( 7,353)
( 8,352)( 9,351)( 10,350)( 11,349)( 12,348)( 13,347)( 14,346)( 15,345)
( 16,344)( 17,343)( 18,359)( 19,358)( 20,374)( 21,373)( 22,372)( 23,371)
( 24,370)( 25,369)( 26,368)( 27,367)( 28,366)( 29,365)( 30,364)( 31,363)
( 32,362)( 33,361)( 34,360)( 35,376)( 36,375)( 37,391)( 38,390)( 39,389)
( 40,388)( 41,387)( 42,386)( 43,385)( 44,384)( 45,383)( 46,382)( 47,381)
( 48,380)( 49,379)( 50,378)( 51,377)( 52,393)( 53,392)( 54,408)( 55,407)
( 56,406)( 57,405)( 58,404)( 59,403)( 60,402)( 61,401)( 62,400)( 63,399)
( 64,398)( 65,397)( 66,396)( 67,395)( 68,394)( 69,274)( 70,273)( 71,289)
( 72,288)( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,282)( 79,281)
( 80,280)( 81,279)( 82,278)( 83,277)( 84,276)( 85,275)( 86,291)( 87,290)
( 88,306)( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)
( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,308)
(104,307)(105,323)(106,322)(107,321)(108,320)(109,319)(110,318)(111,317)
(112,316)(113,315)(114,314)(115,313)(116,312)(117,311)(118,310)(119,309)
(120,325)(121,324)(122,340)(123,339)(124,338)(125,337)(126,336)(127,335)
(128,334)(129,333)(130,332)(131,331)(132,330)(133,329)(134,328)(135,327)
(136,326)(137,478)(138,477)(139,493)(140,492)(141,491)(142,490)(143,489)
(144,488)(145,487)(146,486)(147,485)(148,484)(149,483)(150,482)(151,481)
(152,480)(153,479)(154,495)(155,494)(156,510)(157,509)(158,508)(159,507)
(160,506)(161,505)(162,504)(163,503)(164,502)(165,501)(166,500)(167,499)
(168,498)(169,497)(170,496)(171,512)(172,511)(173,527)(174,526)(175,525)
(176,524)(177,523)(178,522)(179,521)(180,520)(181,519)(182,518)(183,517)
(184,516)(185,515)(186,514)(187,513)(188,529)(189,528)(190,544)(191,543)
(192,542)(193,541)(194,540)(195,539)(196,538)(197,537)(198,536)(199,535)
(200,534)(201,533)(202,532)(203,531)(204,530)(205,410)(206,409)(207,425)
(208,424)(209,423)(210,422)(211,421)(212,420)(213,419)(214,418)(215,417)
(216,416)(217,415)(218,414)(219,413)(220,412)(221,411)(222,427)(223,426)
(224,442)(225,441)(226,440)(227,439)(228,438)(229,437)(230,436)(231,435)
(232,434)(233,433)(234,432)(235,431)(236,430)(237,429)(238,428)(239,444)
(240,443)(241,459)(242,458)(243,457)(244,456)(245,455)(246,454)(247,453)
(248,452)(249,451)(250,450)(251,449)(252,448)(253,447)(254,446)(255,445)
(256,461)(257,460)(258,476)(259,475)(260,474)(261,473)(262,472)(263,471)
(264,470)(265,469)(266,468)(267,467)(268,466)(269,465)(270,464)(271,463)
(272,462);
s2 := Sym(544)!(137,154)(138,155)(139,156)(140,157)(141,158)(142,159)(143,160)
(144,161)(145,162)(146,163)(147,164)(148,165)(149,166)(150,167)(151,168)
(152,169)(153,170)(171,188)(172,189)(173,190)(174,191)(175,192)(176,193)
(177,194)(178,195)(179,196)(180,197)(181,198)(182,199)(183,200)(184,201)
(185,202)(186,203)(187,204)(205,222)(206,223)(207,224)(208,225)(209,226)
(210,227)(211,228)(212,229)(213,230)(214,231)(215,232)(216,233)(217,234)
(218,235)(219,236)(220,237)(221,238)(239,256)(240,257)(241,258)(242,259)
(243,260)(244,261)(245,262)(246,263)(247,264)(248,265)(249,266)(250,267)
(251,268)(252,269)(253,270)(254,271)(255,272)(273,307)(274,308)(275,309)
(276,310)(277,311)(278,312)(279,313)(280,314)(281,315)(282,316)(283,317)
(284,318)(285,319)(286,320)(287,321)(288,322)(289,323)(290,324)(291,325)
(292,326)(293,327)(294,328)(295,329)(296,330)(297,331)(298,332)(299,333)
(300,334)(301,335)(302,336)(303,337)(304,338)(305,339)(306,340)(341,375)
(342,376)(343,377)(344,378)(345,379)(346,380)(347,381)(348,382)(349,383)
(350,384)(351,385)(352,386)(353,387)(354,388)(355,389)(356,390)(357,391)
(358,392)(359,393)(360,394)(361,395)(362,396)(363,397)(364,398)(365,399)
(366,400)(367,401)(368,402)(369,403)(370,404)(371,405)(372,406)(373,407)
(374,408)(409,460)(410,461)(411,462)(412,463)(413,464)(414,465)(415,466)
(416,467)(417,468)(418,469)(419,470)(420,471)(421,472)(422,473)(423,474)
(424,475)(425,476)(426,443)(427,444)(428,445)(429,446)(430,447)(431,448)
(432,449)(433,450)(434,451)(435,452)(436,453)(437,454)(438,455)(439,456)
(440,457)(441,458)(442,459)(477,528)(478,529)(479,530)(480,531)(481,532)
(482,533)(483,534)(484,535)(485,536)(486,537)(487,538)(488,539)(489,540)
(490,541)(491,542)(492,543)(493,544)(494,511)(495,512)(496,513)(497,514)
(498,515)(499,516)(500,517)(501,518)(502,519)(503,520)(504,521)(505,522)
(506,523)(507,524)(508,525)(509,526)(510,527);
s3 := 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,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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