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Polytope of Type {38,4,4}

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