Polytope of Type {4,4,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,38}*1216
Also Known As : {{4,4|2},{4,38|2}}. if this polytope has another name.
Group : SmallGroup(1216,1033)
Rank : 4
Schlafli Type : {4,4,38}
Number of vertices, edges, etc : 4, 8, 76, 38
Order of s0s1s2s3 : 76
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 : {2,4,38}*608, {4,2,38}*608
   4-fold quotients : {4,2,19}*304, {2,2,38}*304
   8-fold quotients : {2,2,19}*152
   19-fold quotients : {4,4,2}*64
   38-fold quotients : {2,4,2}*32, {4,2,2}*32
   76-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1,305)(  2,306)(  3,307)(  4,308)(  5,309)(  6,310)(  7,311)(  8,312)
(  9,313)( 10,314)( 11,315)( 12,316)( 13,317)( 14,318)( 15,319)( 16,320)
( 17,321)( 18,322)( 19,323)( 20,324)( 21,325)( 22,326)( 23,327)( 24,328)
( 25,329)( 26,330)( 27,331)( 28,332)( 29,333)( 30,334)( 31,335)( 32,336)
( 33,337)( 34,338)( 35,339)( 36,340)( 37,341)( 38,342)( 39,343)( 40,344)
( 41,345)( 42,346)( 43,347)( 44,348)( 45,349)( 46,350)( 47,351)( 48,352)
( 49,353)( 50,354)( 51,355)( 52,356)( 53,357)( 54,358)( 55,359)( 56,360)
( 57,361)( 58,362)( 59,363)( 60,364)( 61,365)( 62,366)( 63,367)( 64,368)
( 65,369)( 66,370)( 67,371)( 68,372)( 69,373)( 70,374)( 71,375)( 72,376)
( 73,377)( 74,378)( 75,379)( 76,380)( 77,381)( 78,382)( 79,383)( 80,384)
( 81,385)( 82,386)( 83,387)( 84,388)( 85,389)( 86,390)( 87,391)( 88,392)
( 89,393)( 90,394)( 91,395)( 92,396)( 93,397)( 94,398)( 95,399)( 96,400)
( 97,401)( 98,402)( 99,403)(100,404)(101,405)(102,406)(103,407)(104,408)
(105,409)(106,410)(107,411)(108,412)(109,413)(110,414)(111,415)(112,416)
(113,417)(114,418)(115,419)(116,420)(117,421)(118,422)(119,423)(120,424)
(121,425)(122,426)(123,427)(124,428)(125,429)(126,430)(127,431)(128,432)
(129,433)(130,434)(131,435)(132,436)(133,437)(134,438)(135,439)(136,440)
(137,441)(138,442)(139,443)(140,444)(141,445)(142,446)(143,447)(144,448)
(145,449)(146,450)(147,451)(148,452)(149,453)(150,454)(151,455)(152,456)
(153,457)(154,458)(155,459)(156,460)(157,461)(158,462)(159,463)(160,464)
(161,465)(162,466)(163,467)(164,468)(165,469)(166,470)(167,471)(168,472)
(169,473)(170,474)(171,475)(172,476)(173,477)(174,478)(175,479)(176,480)
(177,481)(178,482)(179,483)(180,484)(181,485)(182,486)(183,487)(184,488)
(185,489)(186,490)(187,491)(188,492)(189,493)(190,494)(191,495)(192,496)
(193,497)(194,498)(195,499)(196,500)(197,501)(198,502)(199,503)(200,504)
(201,505)(202,506)(203,507)(204,508)(205,509)(206,510)(207,511)(208,512)
(209,513)(210,514)(211,515)(212,516)(213,517)(214,518)(215,519)(216,520)
(217,521)(218,522)(219,523)(220,524)(221,525)(222,526)(223,527)(224,528)
(225,529)(226,530)(227,531)(228,532)(229,533)(230,534)(231,535)(232,536)
(233,537)(234,538)(235,539)(236,540)(237,541)(238,542)(239,543)(240,544)
(241,545)(242,546)(243,547)(244,548)(245,549)(246,550)(247,551)(248,552)
(249,553)(250,554)(251,555)(252,556)(253,557)(254,558)(255,559)(256,560)
(257,561)(258,562)(259,563)(260,564)(261,565)(262,566)(263,567)(264,568)
(265,569)(266,570)(267,571)(268,572)(269,573)(270,574)(271,575)(272,576)
(273,577)(274,578)(275,579)(276,580)(277,581)(278,582)(279,583)(280,584)
(281,585)(282,586)(283,587)(284,588)(285,589)(286,590)(287,591)(288,592)
(289,593)(290,594)(291,595)(292,596)(293,597)(294,598)(295,599)(296,600)
(297,601)(298,602)(299,603)(300,604)(301,605)(302,606)(303,607)(304,608);;
s1 := (153,172)(154,173)(155,174)(156,175)(157,176)(158,177)(159,178)(160,179)
(161,180)(162,181)(163,182)(164,183)(165,184)(166,185)(167,186)(168,187)
(169,188)(170,189)(171,190)(191,210)(192,211)(193,212)(194,213)(195,214)
(196,215)(197,216)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)
(204,223)(205,224)(206,225)(207,226)(208,227)(209,228)(229,248)(230,249)
(231,250)(232,251)(233,252)(234,253)(235,254)(236,255)(237,256)(238,257)
(239,258)(240,259)(241,260)(242,261)(243,262)(244,263)(245,264)(246,265)
(247,266)(267,286)(268,287)(269,288)(270,289)(271,290)(272,291)(273,292)
(274,293)(275,294)(276,295)(277,296)(278,297)(279,298)(280,299)(281,300)
(282,301)(283,302)(284,303)(285,304)(305,343)(306,344)(307,345)(308,346)
(309,347)(310,348)(311,349)(312,350)(313,351)(314,352)(315,353)(316,354)
(317,355)(318,356)(319,357)(320,358)(321,359)(322,360)(323,361)(324,362)
(325,363)(326,364)(327,365)(328,366)(329,367)(330,368)(331,369)(332,370)
(333,371)(334,372)(335,373)(336,374)(337,375)(338,376)(339,377)(340,378)
(341,379)(342,380)(381,419)(382,420)(383,421)(384,422)(385,423)(386,424)
(387,425)(388,426)(389,427)(390,428)(391,429)(392,430)(393,431)(394,432)
(395,433)(396,434)(397,435)(398,436)(399,437)(400,438)(401,439)(402,440)
(403,441)(404,442)(405,443)(406,444)(407,445)(408,446)(409,447)(410,448)
(411,449)(412,450)(413,451)(414,452)(415,453)(416,454)(417,455)(418,456)
(457,514)(458,515)(459,516)(460,517)(461,518)(462,519)(463,520)(464,521)
(465,522)(466,523)(467,524)(468,525)(469,526)(470,527)(471,528)(472,529)
(473,530)(474,531)(475,532)(476,495)(477,496)(478,497)(479,498)(480,499)
(481,500)(482,501)(483,502)(484,503)(485,504)(486,505)(487,506)(488,507)
(489,508)(490,509)(491,510)(492,511)(493,512)(494,513)(533,590)(534,591)
(535,592)(536,593)(537,594)(538,595)(539,596)(540,597)(541,598)(542,599)
(543,600)(544,601)(545,602)(546,603)(547,604)(548,605)(549,606)(550,607)
(551,608)(552,571)(553,572)(554,573)(555,574)(556,575)(557,576)(558,577)
(559,578)(560,579)(561,580)(562,581)(563,582)(564,583)(565,584)(566,585)
(567,586)(568,587)(569,588)(570,589);;
s2 := (  1,229)(  2,247)(  3,246)(  4,245)(  5,244)(  6,243)(  7,242)(  8,241)
(  9,240)( 10,239)( 11,238)( 12,237)( 13,236)( 14,235)( 15,234)( 16,233)
( 17,232)( 18,231)( 19,230)( 20,248)( 21,266)( 22,265)( 23,264)( 24,263)
( 25,262)( 26,261)( 27,260)( 28,259)( 29,258)( 30,257)( 31,256)( 32,255)
( 33,254)( 34,253)( 35,252)( 36,251)( 37,250)( 38,249)( 39,267)( 40,285)
( 41,284)( 42,283)( 43,282)( 44,281)( 45,280)( 46,279)( 47,278)( 48,277)
( 49,276)( 50,275)( 51,274)( 52,273)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,268)( 58,286)( 59,304)( 60,303)( 61,302)( 62,301)( 63,300)( 64,299)
( 65,298)( 66,297)( 67,296)( 68,295)( 69,294)( 70,293)( 71,292)( 72,291)
( 73,290)( 74,289)( 75,288)( 76,287)( 77,153)( 78,171)( 79,170)( 80,169)
( 81,168)( 82,167)( 83,166)( 84,165)( 85,164)( 86,163)( 87,162)( 88,161)
( 89,160)( 90,159)( 91,158)( 92,157)( 93,156)( 94,155)( 95,154)( 96,172)
( 97,190)( 98,189)( 99,188)(100,187)(101,186)(102,185)(103,184)(104,183)
(105,182)(106,181)(107,180)(108,179)(109,178)(110,177)(111,176)(112,175)
(113,174)(114,173)(115,191)(116,209)(117,208)(118,207)(119,206)(120,205)
(121,204)(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)
(129,196)(130,195)(131,194)(132,193)(133,192)(134,210)(135,228)(136,227)
(137,226)(138,225)(139,224)(140,223)(141,222)(142,221)(143,220)(144,219)
(145,218)(146,217)(147,216)(148,215)(149,214)(150,213)(151,212)(152,211)
(305,533)(306,551)(307,550)(308,549)(309,548)(310,547)(311,546)(312,545)
(313,544)(314,543)(315,542)(316,541)(317,540)(318,539)(319,538)(320,537)
(321,536)(322,535)(323,534)(324,552)(325,570)(326,569)(327,568)(328,567)
(329,566)(330,565)(331,564)(332,563)(333,562)(334,561)(335,560)(336,559)
(337,558)(338,557)(339,556)(340,555)(341,554)(342,553)(343,571)(344,589)
(345,588)(346,587)(347,586)(348,585)(349,584)(350,583)(351,582)(352,581)
(353,580)(354,579)(355,578)(356,577)(357,576)(358,575)(359,574)(360,573)
(361,572)(362,590)(363,608)(364,607)(365,606)(366,605)(367,604)(368,603)
(369,602)(370,601)(371,600)(372,599)(373,598)(374,597)(375,596)(376,595)
(377,594)(378,593)(379,592)(380,591)(381,457)(382,475)(383,474)(384,473)
(385,472)(386,471)(387,470)(388,469)(389,468)(390,467)(391,466)(392,465)
(393,464)(394,463)(395,462)(396,461)(397,460)(398,459)(399,458)(400,476)
(401,494)(402,493)(403,492)(404,491)(405,490)(406,489)(407,488)(408,487)
(409,486)(410,485)(411,484)(412,483)(413,482)(414,481)(415,480)(416,479)
(417,478)(418,477)(419,495)(420,513)(421,512)(422,511)(423,510)(424,509)
(425,508)(426,507)(427,506)(428,505)(429,504)(430,503)(431,502)(432,501)
(433,500)(434,499)(435,498)(436,497)(437,496)(438,514)(439,532)(440,531)
(441,530)(442,529)(443,528)(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);;
s3 := (  1, 78)(  2, 77)(  3, 95)(  4, 94)(  5, 93)(  6, 92)(  7, 91)(  8, 90)
(  9, 89)( 10, 88)( 11, 87)( 12, 86)( 13, 85)( 14, 84)( 15, 83)( 16, 82)
( 17, 81)( 18, 80)( 19, 79)( 20, 97)( 21, 96)( 22,114)( 23,113)( 24,112)
( 25,111)( 26,110)( 27,109)( 28,108)( 29,107)( 30,106)( 31,105)( 32,104)
( 33,103)( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 98)( 39,116)( 40,115)
( 41,133)( 42,132)( 43,131)( 44,130)( 45,129)( 46,128)( 47,127)( 48,126)
( 49,125)( 50,124)( 51,123)( 52,122)( 53,121)( 54,120)( 55,119)( 56,118)
( 57,117)( 58,135)( 59,134)( 60,152)( 61,151)( 62,150)( 63,149)( 64,148)
( 65,147)( 66,146)( 67,145)( 68,144)( 69,143)( 70,142)( 71,141)( 72,140)
( 73,139)( 74,138)( 75,137)( 76,136)(153,230)(154,229)(155,247)(156,246)
(157,245)(158,244)(159,243)(160,242)(161,241)(162,240)(163,239)(164,238)
(165,237)(166,236)(167,235)(168,234)(169,233)(170,232)(171,231)(172,249)
(173,248)(174,266)(175,265)(176,264)(177,263)(178,262)(179,261)(180,260)
(181,259)(182,258)(183,257)(184,256)(185,255)(186,254)(187,253)(188,252)
(189,251)(190,250)(191,268)(192,267)(193,285)(194,284)(195,283)(196,282)
(197,281)(198,280)(199,279)(200,278)(201,277)(202,276)(203,275)(204,274)
(205,273)(206,272)(207,271)(208,270)(209,269)(210,287)(211,286)(212,304)
(213,303)(214,302)(215,301)(216,300)(217,299)(218,298)(219,297)(220,296)
(221,295)(222,294)(223,293)(224,292)(225,291)(226,290)(227,289)(228,288)
(305,382)(306,381)(307,399)(308,398)(309,397)(310,396)(311,395)(312,394)
(313,393)(314,392)(315,391)(316,390)(317,389)(318,388)(319,387)(320,386)
(321,385)(322,384)(323,383)(324,401)(325,400)(326,418)(327,417)(328,416)
(329,415)(330,414)(331,413)(332,412)(333,411)(334,410)(335,409)(336,408)
(337,407)(338,406)(339,405)(340,404)(341,403)(342,402)(343,420)(344,419)
(345,437)(346,436)(347,435)(348,434)(349,433)(350,432)(351,431)(352,430)
(353,429)(354,428)(355,427)(356,426)(357,425)(358,424)(359,423)(360,422)
(361,421)(362,439)(363,438)(364,456)(365,455)(366,454)(367,453)(368,452)
(369,451)(370,450)(371,449)(372,448)(373,447)(374,446)(375,445)(376,444)
(377,443)(378,442)(379,441)(380,440)(457,534)(458,533)(459,551)(460,550)
(461,549)(462,548)(463,547)(464,546)(465,545)(466,544)(467,543)(468,542)
(469,541)(470,540)(471,539)(472,538)(473,537)(474,536)(475,535)(476,553)
(477,552)(478,570)(479,569)(480,568)(481,567)(482,566)(483,565)(484,564)
(485,563)(486,562)(487,561)(488,560)(489,559)(490,558)(491,557)(492,556)
(493,555)(494,554)(495,572)(496,571)(497,589)(498,588)(499,587)(500,586)
(501,585)(502,584)(503,583)(504,582)(505,581)(506,580)(507,579)(508,578)
(509,577)(510,576)(511,575)(512,574)(513,573)(514,591)(515,590)(516,608)
(517,607)(518,606)(519,605)(520,604)(521,603)(522,602)(523,601)(524,600)
(525,599)(526,598)(527,597)(528,596)(529,595)(530,594)(531,593)(532,592);;
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*s0*s1*s0*s1*s0*s1, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(608)!(  1,305)(  2,306)(  3,307)(  4,308)(  5,309)(  6,310)(  7,311)
(  8,312)(  9,313)( 10,314)( 11,315)( 12,316)( 13,317)( 14,318)( 15,319)
( 16,320)( 17,321)( 18,322)( 19,323)( 20,324)( 21,325)( 22,326)( 23,327)
( 24,328)( 25,329)( 26,330)( 27,331)( 28,332)( 29,333)( 30,334)( 31,335)
( 32,336)( 33,337)( 34,338)( 35,339)( 36,340)( 37,341)( 38,342)( 39,343)
( 40,344)( 41,345)( 42,346)( 43,347)( 44,348)( 45,349)( 46,350)( 47,351)
( 48,352)( 49,353)( 50,354)( 51,355)( 52,356)( 53,357)( 54,358)( 55,359)
( 56,360)( 57,361)( 58,362)( 59,363)( 60,364)( 61,365)( 62,366)( 63,367)
( 64,368)( 65,369)( 66,370)( 67,371)( 68,372)( 69,373)( 70,374)( 71,375)
( 72,376)( 73,377)( 74,378)( 75,379)( 76,380)( 77,381)( 78,382)( 79,383)
( 80,384)( 81,385)( 82,386)( 83,387)( 84,388)( 85,389)( 86,390)( 87,391)
( 88,392)( 89,393)( 90,394)( 91,395)( 92,396)( 93,397)( 94,398)( 95,399)
( 96,400)( 97,401)( 98,402)( 99,403)(100,404)(101,405)(102,406)(103,407)
(104,408)(105,409)(106,410)(107,411)(108,412)(109,413)(110,414)(111,415)
(112,416)(113,417)(114,418)(115,419)(116,420)(117,421)(118,422)(119,423)
(120,424)(121,425)(122,426)(123,427)(124,428)(125,429)(126,430)(127,431)
(128,432)(129,433)(130,434)(131,435)(132,436)(133,437)(134,438)(135,439)
(136,440)(137,441)(138,442)(139,443)(140,444)(141,445)(142,446)(143,447)
(144,448)(145,449)(146,450)(147,451)(148,452)(149,453)(150,454)(151,455)
(152,456)(153,457)(154,458)(155,459)(156,460)(157,461)(158,462)(159,463)
(160,464)(161,465)(162,466)(163,467)(164,468)(165,469)(166,470)(167,471)
(168,472)(169,473)(170,474)(171,475)(172,476)(173,477)(174,478)(175,479)
(176,480)(177,481)(178,482)(179,483)(180,484)(181,485)(182,486)(183,487)
(184,488)(185,489)(186,490)(187,491)(188,492)(189,493)(190,494)(191,495)
(192,496)(193,497)(194,498)(195,499)(196,500)(197,501)(198,502)(199,503)
(200,504)(201,505)(202,506)(203,507)(204,508)(205,509)(206,510)(207,511)
(208,512)(209,513)(210,514)(211,515)(212,516)(213,517)(214,518)(215,519)
(216,520)(217,521)(218,522)(219,523)(220,524)(221,525)(222,526)(223,527)
(224,528)(225,529)(226,530)(227,531)(228,532)(229,533)(230,534)(231,535)
(232,536)(233,537)(234,538)(235,539)(236,540)(237,541)(238,542)(239,543)
(240,544)(241,545)(242,546)(243,547)(244,548)(245,549)(246,550)(247,551)
(248,552)(249,553)(250,554)(251,555)(252,556)(253,557)(254,558)(255,559)
(256,560)(257,561)(258,562)(259,563)(260,564)(261,565)(262,566)(263,567)
(264,568)(265,569)(266,570)(267,571)(268,572)(269,573)(270,574)(271,575)
(272,576)(273,577)(274,578)(275,579)(276,580)(277,581)(278,582)(279,583)
(280,584)(281,585)(282,586)(283,587)(284,588)(285,589)(286,590)(287,591)
(288,592)(289,593)(290,594)(291,595)(292,596)(293,597)(294,598)(295,599)
(296,600)(297,601)(298,602)(299,603)(300,604)(301,605)(302,606)(303,607)
(304,608);
s1 := Sym(608)!(153,172)(154,173)(155,174)(156,175)(157,176)(158,177)(159,178)
(160,179)(161,180)(162,181)(163,182)(164,183)(165,184)(166,185)(167,186)
(168,187)(169,188)(170,189)(171,190)(191,210)(192,211)(193,212)(194,213)
(195,214)(196,215)(197,216)(198,217)(199,218)(200,219)(201,220)(202,221)
(203,222)(204,223)(205,224)(206,225)(207,226)(208,227)(209,228)(229,248)
(230,249)(231,250)(232,251)(233,252)(234,253)(235,254)(236,255)(237,256)
(238,257)(239,258)(240,259)(241,260)(242,261)(243,262)(244,263)(245,264)
(246,265)(247,266)(267,286)(268,287)(269,288)(270,289)(271,290)(272,291)
(273,292)(274,293)(275,294)(276,295)(277,296)(278,297)(279,298)(280,299)
(281,300)(282,301)(283,302)(284,303)(285,304)(305,343)(306,344)(307,345)
(308,346)(309,347)(310,348)(311,349)(312,350)(313,351)(314,352)(315,353)
(316,354)(317,355)(318,356)(319,357)(320,358)(321,359)(322,360)(323,361)
(324,362)(325,363)(326,364)(327,365)(328,366)(329,367)(330,368)(331,369)
(332,370)(333,371)(334,372)(335,373)(336,374)(337,375)(338,376)(339,377)
(340,378)(341,379)(342,380)(381,419)(382,420)(383,421)(384,422)(385,423)
(386,424)(387,425)(388,426)(389,427)(390,428)(391,429)(392,430)(393,431)
(394,432)(395,433)(396,434)(397,435)(398,436)(399,437)(400,438)(401,439)
(402,440)(403,441)(404,442)(405,443)(406,444)(407,445)(408,446)(409,447)
(410,448)(411,449)(412,450)(413,451)(414,452)(415,453)(416,454)(417,455)
(418,456)(457,514)(458,515)(459,516)(460,517)(461,518)(462,519)(463,520)
(464,521)(465,522)(466,523)(467,524)(468,525)(469,526)(470,527)(471,528)
(472,529)(473,530)(474,531)(475,532)(476,495)(477,496)(478,497)(479,498)
(480,499)(481,500)(482,501)(483,502)(484,503)(485,504)(486,505)(487,506)
(488,507)(489,508)(490,509)(491,510)(492,511)(493,512)(494,513)(533,590)
(534,591)(535,592)(536,593)(537,594)(538,595)(539,596)(540,597)(541,598)
(542,599)(543,600)(544,601)(545,602)(546,603)(547,604)(548,605)(549,606)
(550,607)(551,608)(552,571)(553,572)(554,573)(555,574)(556,575)(557,576)
(558,577)(559,578)(560,579)(561,580)(562,581)(563,582)(564,583)(565,584)
(566,585)(567,586)(568,587)(569,588)(570,589);
s2 := Sym(608)!(  1,229)(  2,247)(  3,246)(  4,245)(  5,244)(  6,243)(  7,242)
(  8,241)(  9,240)( 10,239)( 11,238)( 12,237)( 13,236)( 14,235)( 15,234)
( 16,233)( 17,232)( 18,231)( 19,230)( 20,248)( 21,266)( 22,265)( 23,264)
( 24,263)( 25,262)( 26,261)( 27,260)( 28,259)( 29,258)( 30,257)( 31,256)
( 32,255)( 33,254)( 34,253)( 35,252)( 36,251)( 37,250)( 38,249)( 39,267)
( 40,285)( 41,284)( 42,283)( 43,282)( 44,281)( 45,280)( 46,279)( 47,278)
( 48,277)( 49,276)( 50,275)( 51,274)( 52,273)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,268)( 58,286)( 59,304)( 60,303)( 61,302)( 62,301)( 63,300)
( 64,299)( 65,298)( 66,297)( 67,296)( 68,295)( 69,294)( 70,293)( 71,292)
( 72,291)( 73,290)( 74,289)( 75,288)( 76,287)( 77,153)( 78,171)( 79,170)
( 80,169)( 81,168)( 82,167)( 83,166)( 84,165)( 85,164)( 86,163)( 87,162)
( 88,161)( 89,160)( 90,159)( 91,158)( 92,157)( 93,156)( 94,155)( 95,154)
( 96,172)( 97,190)( 98,189)( 99,188)(100,187)(101,186)(102,185)(103,184)
(104,183)(105,182)(106,181)(107,180)(108,179)(109,178)(110,177)(111,176)
(112,175)(113,174)(114,173)(115,191)(116,209)(117,208)(118,207)(119,206)
(120,205)(121,204)(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)
(128,197)(129,196)(130,195)(131,194)(132,193)(133,192)(134,210)(135,228)
(136,227)(137,226)(138,225)(139,224)(140,223)(141,222)(142,221)(143,220)
(144,219)(145,218)(146,217)(147,216)(148,215)(149,214)(150,213)(151,212)
(152,211)(305,533)(306,551)(307,550)(308,549)(309,548)(310,547)(311,546)
(312,545)(313,544)(314,543)(315,542)(316,541)(317,540)(318,539)(319,538)
(320,537)(321,536)(322,535)(323,534)(324,552)(325,570)(326,569)(327,568)
(328,567)(329,566)(330,565)(331,564)(332,563)(333,562)(334,561)(335,560)
(336,559)(337,558)(338,557)(339,556)(340,555)(341,554)(342,553)(343,571)
(344,589)(345,588)(346,587)(347,586)(348,585)(349,584)(350,583)(351,582)
(352,581)(353,580)(354,579)(355,578)(356,577)(357,576)(358,575)(359,574)
(360,573)(361,572)(362,590)(363,608)(364,607)(365,606)(366,605)(367,604)
(368,603)(369,602)(370,601)(371,600)(372,599)(373,598)(374,597)(375,596)
(376,595)(377,594)(378,593)(379,592)(380,591)(381,457)(382,475)(383,474)
(384,473)(385,472)(386,471)(387,470)(388,469)(389,468)(390,467)(391,466)
(392,465)(393,464)(394,463)(395,462)(396,461)(397,460)(398,459)(399,458)
(400,476)(401,494)(402,493)(403,492)(404,491)(405,490)(406,489)(407,488)
(408,487)(409,486)(410,485)(411,484)(412,483)(413,482)(414,481)(415,480)
(416,479)(417,478)(418,477)(419,495)(420,513)(421,512)(422,511)(423,510)
(424,509)(425,508)(426,507)(427,506)(428,505)(429,504)(430,503)(431,502)
(432,501)(433,500)(434,499)(435,498)(436,497)(437,496)(438,514)(439,532)
(440,531)(441,530)(442,529)(443,528)(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);
s3 := Sym(608)!(  1, 78)(  2, 77)(  3, 95)(  4, 94)(  5, 93)(  6, 92)(  7, 91)
(  8, 90)(  9, 89)( 10, 88)( 11, 87)( 12, 86)( 13, 85)( 14, 84)( 15, 83)
( 16, 82)( 17, 81)( 18, 80)( 19, 79)( 20, 97)( 21, 96)( 22,114)( 23,113)
( 24,112)( 25,111)( 26,110)( 27,109)( 28,108)( 29,107)( 30,106)( 31,105)
( 32,104)( 33,103)( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 98)( 39,116)
( 40,115)( 41,133)( 42,132)( 43,131)( 44,130)( 45,129)( 46,128)( 47,127)
( 48,126)( 49,125)( 50,124)( 51,123)( 52,122)( 53,121)( 54,120)( 55,119)
( 56,118)( 57,117)( 58,135)( 59,134)( 60,152)( 61,151)( 62,150)( 63,149)
( 64,148)( 65,147)( 66,146)( 67,145)( 68,144)( 69,143)( 70,142)( 71,141)
( 72,140)( 73,139)( 74,138)( 75,137)( 76,136)(153,230)(154,229)(155,247)
(156,246)(157,245)(158,244)(159,243)(160,242)(161,241)(162,240)(163,239)
(164,238)(165,237)(166,236)(167,235)(168,234)(169,233)(170,232)(171,231)
(172,249)(173,248)(174,266)(175,265)(176,264)(177,263)(178,262)(179,261)
(180,260)(181,259)(182,258)(183,257)(184,256)(185,255)(186,254)(187,253)
(188,252)(189,251)(190,250)(191,268)(192,267)(193,285)(194,284)(195,283)
(196,282)(197,281)(198,280)(199,279)(200,278)(201,277)(202,276)(203,275)
(204,274)(205,273)(206,272)(207,271)(208,270)(209,269)(210,287)(211,286)
(212,304)(213,303)(214,302)(215,301)(216,300)(217,299)(218,298)(219,297)
(220,296)(221,295)(222,294)(223,293)(224,292)(225,291)(226,290)(227,289)
(228,288)(305,382)(306,381)(307,399)(308,398)(309,397)(310,396)(311,395)
(312,394)(313,393)(314,392)(315,391)(316,390)(317,389)(318,388)(319,387)
(320,386)(321,385)(322,384)(323,383)(324,401)(325,400)(326,418)(327,417)
(328,416)(329,415)(330,414)(331,413)(332,412)(333,411)(334,410)(335,409)
(336,408)(337,407)(338,406)(339,405)(340,404)(341,403)(342,402)(343,420)
(344,419)(345,437)(346,436)(347,435)(348,434)(349,433)(350,432)(351,431)
(352,430)(353,429)(354,428)(355,427)(356,426)(357,425)(358,424)(359,423)
(360,422)(361,421)(362,439)(363,438)(364,456)(365,455)(366,454)(367,453)
(368,452)(369,451)(370,450)(371,449)(372,448)(373,447)(374,446)(375,445)
(376,444)(377,443)(378,442)(379,441)(380,440)(457,534)(458,533)(459,551)
(460,550)(461,549)(462,548)(463,547)(464,546)(465,545)(466,544)(467,543)
(468,542)(469,541)(470,540)(471,539)(472,538)(473,537)(474,536)(475,535)
(476,553)(477,552)(478,570)(479,569)(480,568)(481,567)(482,566)(483,565)
(484,564)(485,563)(486,562)(487,561)(488,560)(489,559)(490,558)(491,557)
(492,556)(493,555)(494,554)(495,572)(496,571)(497,589)(498,588)(499,587)
(500,586)(501,585)(502,584)(503,583)(504,582)(505,581)(506,580)(507,579)
(508,578)(509,577)(510,576)(511,575)(512,574)(513,573)(514,591)(515,590)
(516,608)(517,607)(518,606)(519,605)(520,604)(521,603)(522,602)(523,601)
(524,600)(525,599)(526,598)(527,597)(528,596)(529,595)(530,594)(531,593)
(532,592);
poly := sub<Sym(608)|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*s0*s1*s0*s1*s0*s1, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope