Polytope of Type {16,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,38}*1216
Also Known As : {16,38|2}. if this polytope has another name.
Group : SmallGroup(1216,968)
Rank : 3
Schlafli Type : {16,38}
Number of vertices, edges, etc : 16, 304, 38
Order of s₀s₁s₂ : 304
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {8,38}*608
   4-fold quotients : {4,38}*304
   8-fold quotients : {2,38}*152
   16-fold quotients : {2,19}*76
   19-fold quotients : {16,2}*64
   38-fold quotients : {8,2}*32
   76-fold quotients : {4,2}*16
   152-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 39, 58)( 40, 59)( 41, 60)( 42, 61)( 43, 62)( 44, 63)( 45, 64)( 46, 65)
( 47, 66)( 48, 67)( 49, 68)( 50, 69)( 51, 70)( 52, 71)( 53, 72)( 54, 73)
( 55, 74)( 56, 75)( 57, 76)( 77,115)( 78,116)( 79,117)( 80,118)( 81,119)
( 82,120)( 83,121)( 84,122)( 85,123)( 86,124)( 87,125)( 88,126)( 89,127)
( 90,128)( 91,129)( 92,130)( 93,131)( 94,132)( 95,133)( 96,134)( 97,135)
( 98,136)( 99,137)(100,138)(101,139)(102,140)(103,141)(104,142)(105,143)
(106,144)(107,145)(108,146)(109,147)(110,148)(111,149)(112,150)(113,151)
(114,152)(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)(229,267)(230,268)(231,269)(232,270)
(233,271)(234,272)(235,273)(236,274)(237,275)(238,276)(239,277)(240,278)
(241,279)(242,280)(243,281)(244,282)(245,283)(246,284)(247,285)(248,286)
(249,287)(250,288)(251,289)(252,290)(253,291)(254,292)(255,293)(256,294)
(257,295)(258,296)(259,297)(260,298)(261,299)(262,300)(263,301)(264,302)
(265,303)(266,304)(305,381)(306,382)(307,383)(308,384)(309,385)(310,386)
(311,387)(312,388)(313,389)(314,390)(315,391)(316,392)(317,393)(318,394)
(319,395)(320,396)(321,397)(322,398)(323,399)(324,400)(325,401)(326,402)
(327,403)(328,404)(329,405)(330,406)(331,407)(332,408)(333,409)(334,410)
(335,411)(336,412)(337,413)(338,414)(339,415)(340,416)(341,417)(342,418)
(343,438)(344,439)(345,440)(346,441)(347,442)(348,443)(349,444)(350,445)
(351,446)(352,447)(353,448)(354,449)(355,450)(356,451)(357,452)(358,453)
(359,454)(360,455)(361,456)(362,419)(363,420)(364,421)(365,422)(366,423)
(367,424)(368,425)(369,426)(370,427)(371,428)(372,429)(373,430)(374,431)
(375,432)(376,433)(377,434)(378,435)(379,436)(380,437)(457,533)(458,534)
(459,535)(460,536)(461,537)(462,538)(463,539)(464,540)(465,541)(466,542)
(467,543)(468,544)(469,545)(470,546)(471,547)(472,548)(473,549)(474,550)
(475,551)(476,552)(477,553)(478,554)(479,555)(480,556)(481,557)(482,558)
(483,559)(484,560)(485,561)(486,562)(487,563)(488,564)(489,565)(490,566)
(491,567)(492,568)(493,569)(494,570)(495,590)(496,591)(497,592)(498,593)
(499,594)(500,595)(501,596)(502,597)(503,598)(504,599)(505,600)(506,601)
(507,602)(508,603)(509,604)(510,605)(511,606)(512,607)(513,608)(514,571)
(515,572)(516,573)(517,574)(518,575)(519,576)(520,577)(521,578)(522,579)
(523,580)(524,581)(525,582)(526,583)(527,584)(528,585)(529,586)(530,587)
(531,588)(532,589);;
s1 := (  1,457)(  2,475)(  3,474)(  4,473)(  5,472)(  6,471)(  7,470)(  8,469)
(  9,468)( 10,467)( 11,466)( 12,465)( 13,464)( 14,463)( 15,462)( 16,461)
( 17,460)( 18,459)( 19,458)( 20,476)( 21,494)( 22,493)( 23,492)( 24,491)
( 25,490)( 26,489)( 27,488)( 28,487)( 29,486)( 30,485)( 31,484)( 32,483)
( 33,482)( 34,481)( 35,480)( 36,479)( 37,478)( 38,477)( 39,514)( 40,532)
( 41,531)( 42,530)( 43,529)( 44,528)( 45,527)( 46,526)( 47,525)( 48,524)
( 49,523)( 50,522)( 51,521)( 52,520)( 53,519)( 54,518)( 55,517)( 56,516)
( 57,515)( 58,495)( 59,513)( 60,512)( 61,511)( 62,510)( 63,509)( 64,508)
( 65,507)( 66,506)( 67,505)( 68,504)( 69,503)( 70,502)( 71,501)( 72,500)
( 73,499)( 74,498)( 75,497)( 76,496)( 77,571)( 78,589)( 79,588)( 80,587)
( 81,586)( 82,585)( 83,584)( 84,583)( 85,582)( 86,581)( 87,580)( 88,579)
( 89,578)( 90,577)( 91,576)( 92,575)( 93,574)( 94,573)( 95,572)( 96,590)
( 97,608)( 98,607)( 99,606)(100,605)(101,604)(102,603)(103,602)(104,601)
(105,600)(106,599)(107,598)(108,597)(109,596)(110,595)(111,594)(112,593)
(113,592)(114,591)(115,533)(116,551)(117,550)(118,549)(119,548)(120,547)
(121,546)(122,545)(123,544)(124,543)(125,542)(126,541)(127,540)(128,539)
(129,538)(130,537)(131,536)(132,535)(133,534)(134,552)(135,570)(136,569)
(137,568)(138,567)(139,566)(140,565)(141,564)(142,563)(143,562)(144,561)
(145,560)(146,559)(147,558)(148,557)(149,556)(150,555)(151,554)(152,553)
(153,305)(154,323)(155,322)(156,321)(157,320)(158,319)(159,318)(160,317)
(161,316)(162,315)(163,314)(164,313)(165,312)(166,311)(167,310)(168,309)
(169,308)(170,307)(171,306)(172,324)(173,342)(174,341)(175,340)(176,339)
(177,338)(178,337)(179,336)(180,335)(181,334)(182,333)(183,332)(184,331)
(185,330)(186,329)(187,328)(188,327)(189,326)(190,325)(191,362)(192,380)
(193,379)(194,378)(195,377)(196,376)(197,375)(198,374)(199,373)(200,372)
(201,371)(202,370)(203,369)(204,368)(205,367)(206,366)(207,365)(208,364)
(209,363)(210,343)(211,361)(212,360)(213,359)(214,358)(215,357)(216,356)
(217,355)(218,354)(219,353)(220,352)(221,351)(222,350)(223,349)(224,348)
(225,347)(226,346)(227,345)(228,344)(229,419)(230,437)(231,436)(232,435)
(233,434)(234,433)(235,432)(236,431)(237,430)(238,429)(239,428)(240,427)
(241,426)(242,425)(243,424)(244,423)(245,422)(246,421)(247,420)(248,438)
(249,456)(250,455)(251,454)(252,453)(253,452)(254,451)(255,450)(256,449)
(257,448)(258,447)(259,446)(260,445)(261,444)(262,443)(263,442)(264,441)
(265,440)(266,439)(267,381)(268,399)(269,398)(270,397)(271,396)(272,395)
(273,394)(274,393)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)
(281,386)(282,385)(283,384)(284,383)(285,382)(286,400)(287,418)(288,417)
(289,416)(290,415)(291,414)(292,413)(293,412)(294,411)(295,410)(296,409)
(297,408)(298,407)(299,406)(300,405)(301,404)(302,403)(303,402)(304,401);;
s2 := (  1,154)(  2,153)(  3,171)(  4,170)(  5,169)(  6,168)(  7,167)(  8,166)
(  9,165)( 10,164)( 11,163)( 12,162)( 13,161)( 14,160)( 15,159)( 16,158)
( 17,157)( 18,156)( 19,155)( 20,173)( 21,172)( 22,190)( 23,189)( 24,188)
( 25,187)( 26,186)( 27,185)( 28,184)( 29,183)( 30,182)( 31,181)( 32,180)
( 33,179)( 34,178)( 35,177)( 36,176)( 37,175)( 38,174)( 39,192)( 40,191)
( 41,209)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)( 48,202)
( 49,201)( 50,200)( 51,199)( 52,198)( 53,197)( 54,196)( 55,195)( 56,194)
( 57,193)( 58,211)( 59,210)( 60,228)( 61,227)( 62,226)( 63,225)( 64,224)
( 65,223)( 66,222)( 67,221)( 68,220)( 69,219)( 70,218)( 71,217)( 72,216)
( 73,215)( 74,214)( 75,213)( 76,212)( 77,230)( 78,229)( 79,247)( 80,246)
( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)( 88,238)
( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)( 96,249)
( 97,248)( 98,266)( 99,265)(100,264)(101,263)(102,262)(103,261)(104,260)
(105,259)(106,258)(107,257)(108,256)(109,255)(110,254)(111,253)(112,252)
(113,251)(114,250)(115,268)(116,267)(117,285)(118,284)(119,283)(120,282)
(121,281)(122,280)(123,279)(124,278)(125,277)(126,276)(127,275)(128,274)
(129,273)(130,272)(131,271)(132,270)(133,269)(134,287)(135,286)(136,304)
(137,303)(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)(144,296)
(145,295)(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)(152,288)
(305,458)(306,457)(307,475)(308,474)(309,473)(310,472)(311,471)(312,470)
(313,469)(314,468)(315,467)(316,466)(317,465)(318,464)(319,463)(320,462)
(321,461)(322,460)(323,459)(324,477)(325,476)(326,494)(327,493)(328,492)
(329,491)(330,490)(331,489)(332,488)(333,487)(334,486)(335,485)(336,484)
(337,483)(338,482)(339,481)(340,480)(341,479)(342,478)(343,496)(344,495)
(345,513)(346,512)(347,511)(348,510)(349,509)(350,508)(351,507)(352,506)
(353,505)(354,504)(355,503)(356,502)(357,501)(358,500)(359,499)(360,498)
(361,497)(362,515)(363,514)(364,532)(365,531)(366,530)(367,529)(368,528)
(369,527)(370,526)(371,525)(372,524)(373,523)(374,522)(375,521)(376,520)
(377,519)(378,518)(379,517)(380,516)(381,534)(382,533)(383,551)(384,550)
(385,549)(386,548)(387,547)(388,546)(389,545)(390,544)(391,543)(392,542)
(393,541)(394,540)(395,539)(396,538)(397,537)(398,536)(399,535)(400,553)
(401,552)(402,570)(403,569)(404,568)(405,567)(406,566)(407,565)(408,564)
(409,563)(410,562)(411,561)(412,560)(413,559)(414,558)(415,557)(416,556)
(417,555)(418,554)(419,572)(420,571)(421,589)(422,588)(423,587)(424,586)
(425,585)(426,584)(427,583)(428,582)(429,581)(430,580)(431,579)(432,578)
(433,577)(434,576)(435,575)(436,574)(437,573)(438,591)(439,590)(440,608)
(441,607)(442,606)(443,605)(444,604)(445,603)(446,602)(447,601)(448,600)
(449,599)(450,598)(451,597)(452,596)(453,595)(454,594)(455,593)(456,592);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(608)!( 39, 58)( 40, 59)( 41, 60)( 42, 61)( 43, 62)( 44, 63)( 45, 64)
( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)( 51, 70)( 52, 71)( 53, 72)
( 54, 73)( 55, 74)( 56, 75)( 57, 76)( 77,115)( 78,116)( 79,117)( 80,118)
( 81,119)( 82,120)( 83,121)( 84,122)( 85,123)( 86,124)( 87,125)( 88,126)
( 89,127)( 90,128)( 91,129)( 92,130)( 93,131)( 94,132)( 95,133)( 96,134)
( 97,135)( 98,136)( 99,137)(100,138)(101,139)(102,140)(103,141)(104,142)
(105,143)(106,144)(107,145)(108,146)(109,147)(110,148)(111,149)(112,150)
(113,151)(114,152)(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)(229,267)(230,268)(231,269)
(232,270)(233,271)(234,272)(235,273)(236,274)(237,275)(238,276)(239,277)
(240,278)(241,279)(242,280)(243,281)(244,282)(245,283)(246,284)(247,285)
(248,286)(249,287)(250,288)(251,289)(252,290)(253,291)(254,292)(255,293)
(256,294)(257,295)(258,296)(259,297)(260,298)(261,299)(262,300)(263,301)
(264,302)(265,303)(266,304)(305,381)(306,382)(307,383)(308,384)(309,385)
(310,386)(311,387)(312,388)(313,389)(314,390)(315,391)(316,392)(317,393)
(318,394)(319,395)(320,396)(321,397)(322,398)(323,399)(324,400)(325,401)
(326,402)(327,403)(328,404)(329,405)(330,406)(331,407)(332,408)(333,409)
(334,410)(335,411)(336,412)(337,413)(338,414)(339,415)(340,416)(341,417)
(342,418)(343,438)(344,439)(345,440)(346,441)(347,442)(348,443)(349,444)
(350,445)(351,446)(352,447)(353,448)(354,449)(355,450)(356,451)(357,452)
(358,453)(359,454)(360,455)(361,456)(362,419)(363,420)(364,421)(365,422)
(366,423)(367,424)(368,425)(369,426)(370,427)(371,428)(372,429)(373,430)
(374,431)(375,432)(376,433)(377,434)(378,435)(379,436)(380,437)(457,533)
(458,534)(459,535)(460,536)(461,537)(462,538)(463,539)(464,540)(465,541)
(466,542)(467,543)(468,544)(469,545)(470,546)(471,547)(472,548)(473,549)
(474,550)(475,551)(476,552)(477,553)(478,554)(479,555)(480,556)(481,557)
(482,558)(483,559)(484,560)(485,561)(486,562)(487,563)(488,564)(489,565)
(490,566)(491,567)(492,568)(493,569)(494,570)(495,590)(496,591)(497,592)
(498,593)(499,594)(500,595)(501,596)(502,597)(503,598)(504,599)(505,600)
(506,601)(507,602)(508,603)(509,604)(510,605)(511,606)(512,607)(513,608)
(514,571)(515,572)(516,573)(517,574)(518,575)(519,576)(520,577)(521,578)
(522,579)(523,580)(524,581)(525,582)(526,583)(527,584)(528,585)(529,586)
(530,587)(531,588)(532,589);
s1 := Sym(608)!(  1,457)(  2,475)(  3,474)(  4,473)(  5,472)(  6,471)(  7,470)
(  8,469)(  9,468)( 10,467)( 11,466)( 12,465)( 13,464)( 14,463)( 15,462)
( 16,461)( 17,460)( 18,459)( 19,458)( 20,476)( 21,494)( 22,493)( 23,492)
( 24,491)( 25,490)( 26,489)( 27,488)( 28,487)( 29,486)( 30,485)( 31,484)
( 32,483)( 33,482)( 34,481)( 35,480)( 36,479)( 37,478)( 38,477)( 39,514)
( 40,532)( 41,531)( 42,530)( 43,529)( 44,528)( 45,527)( 46,526)( 47,525)
( 48,524)( 49,523)( 50,522)( 51,521)( 52,520)( 53,519)( 54,518)( 55,517)
( 56,516)( 57,515)( 58,495)( 59,513)( 60,512)( 61,511)( 62,510)( 63,509)
( 64,508)( 65,507)( 66,506)( 67,505)( 68,504)( 69,503)( 70,502)( 71,501)
( 72,500)( 73,499)( 74,498)( 75,497)( 76,496)( 77,571)( 78,589)( 79,588)
( 80,587)( 81,586)( 82,585)( 83,584)( 84,583)( 85,582)( 86,581)( 87,580)
( 88,579)( 89,578)( 90,577)( 91,576)( 92,575)( 93,574)( 94,573)( 95,572)
( 96,590)( 97,608)( 98,607)( 99,606)(100,605)(101,604)(102,603)(103,602)
(104,601)(105,600)(106,599)(107,598)(108,597)(109,596)(110,595)(111,594)
(112,593)(113,592)(114,591)(115,533)(116,551)(117,550)(118,549)(119,548)
(120,547)(121,546)(122,545)(123,544)(124,543)(125,542)(126,541)(127,540)
(128,539)(129,538)(130,537)(131,536)(132,535)(133,534)(134,552)(135,570)
(136,569)(137,568)(138,567)(139,566)(140,565)(141,564)(142,563)(143,562)
(144,561)(145,560)(146,559)(147,558)(148,557)(149,556)(150,555)(151,554)
(152,553)(153,305)(154,323)(155,322)(156,321)(157,320)(158,319)(159,318)
(160,317)(161,316)(162,315)(163,314)(164,313)(165,312)(166,311)(167,310)
(168,309)(169,308)(170,307)(171,306)(172,324)(173,342)(174,341)(175,340)
(176,339)(177,338)(178,337)(179,336)(180,335)(181,334)(182,333)(183,332)
(184,331)(185,330)(186,329)(187,328)(188,327)(189,326)(190,325)(191,362)
(192,380)(193,379)(194,378)(195,377)(196,376)(197,375)(198,374)(199,373)
(200,372)(201,371)(202,370)(203,369)(204,368)(205,367)(206,366)(207,365)
(208,364)(209,363)(210,343)(211,361)(212,360)(213,359)(214,358)(215,357)
(216,356)(217,355)(218,354)(219,353)(220,352)(221,351)(222,350)(223,349)
(224,348)(225,347)(226,346)(227,345)(228,344)(229,419)(230,437)(231,436)
(232,435)(233,434)(234,433)(235,432)(236,431)(237,430)(238,429)(239,428)
(240,427)(241,426)(242,425)(243,424)(244,423)(245,422)(246,421)(247,420)
(248,438)(249,456)(250,455)(251,454)(252,453)(253,452)(254,451)(255,450)
(256,449)(257,448)(258,447)(259,446)(260,445)(261,444)(262,443)(263,442)
(264,441)(265,440)(266,439)(267,381)(268,399)(269,398)(270,397)(271,396)
(272,395)(273,394)(274,393)(275,392)(276,391)(277,390)(278,389)(279,388)
(280,387)(281,386)(282,385)(283,384)(284,383)(285,382)(286,400)(287,418)
(288,417)(289,416)(290,415)(291,414)(292,413)(293,412)(294,411)(295,410)
(296,409)(297,408)(298,407)(299,406)(300,405)(301,404)(302,403)(303,402)
(304,401);
s2 := Sym(608)!(  1,154)(  2,153)(  3,171)(  4,170)(  5,169)(  6,168)(  7,167)
(  8,166)(  9,165)( 10,164)( 11,163)( 12,162)( 13,161)( 14,160)( 15,159)
( 16,158)( 17,157)( 18,156)( 19,155)( 20,173)( 21,172)( 22,190)( 23,189)
( 24,188)( 25,187)( 26,186)( 27,185)( 28,184)( 29,183)( 30,182)( 31,181)
( 32,180)( 33,179)( 34,178)( 35,177)( 36,176)( 37,175)( 38,174)( 39,192)
( 40,191)( 41,209)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)
( 48,202)( 49,201)( 50,200)( 51,199)( 52,198)( 53,197)( 54,196)( 55,195)
( 56,194)( 57,193)( 58,211)( 59,210)( 60,228)( 61,227)( 62,226)( 63,225)
( 64,224)( 65,223)( 66,222)( 67,221)( 68,220)( 69,219)( 70,218)( 71,217)
( 72,216)( 73,215)( 74,214)( 75,213)( 76,212)( 77,230)( 78,229)( 79,247)
( 80,246)( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)
( 88,238)( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)
( 96,249)( 97,248)( 98,266)( 99,265)(100,264)(101,263)(102,262)(103,261)
(104,260)(105,259)(106,258)(107,257)(108,256)(109,255)(110,254)(111,253)
(112,252)(113,251)(114,250)(115,268)(116,267)(117,285)(118,284)(119,283)
(120,282)(121,281)(122,280)(123,279)(124,278)(125,277)(126,276)(127,275)
(128,274)(129,273)(130,272)(131,271)(132,270)(133,269)(134,287)(135,286)
(136,304)(137,303)(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)
(144,296)(145,295)(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)
(152,288)(305,458)(306,457)(307,475)(308,474)(309,473)(310,472)(311,471)
(312,470)(313,469)(314,468)(315,467)(316,466)(317,465)(318,464)(319,463)
(320,462)(321,461)(322,460)(323,459)(324,477)(325,476)(326,494)(327,493)
(328,492)(329,491)(330,490)(331,489)(332,488)(333,487)(334,486)(335,485)
(336,484)(337,483)(338,482)(339,481)(340,480)(341,479)(342,478)(343,496)
(344,495)(345,513)(346,512)(347,511)(348,510)(349,509)(350,508)(351,507)
(352,506)(353,505)(354,504)(355,503)(356,502)(357,501)(358,500)(359,499)
(360,498)(361,497)(362,515)(363,514)(364,532)(365,531)(366,530)(367,529)
(368,528)(369,527)(370,526)(371,525)(372,524)(373,523)(374,522)(375,521)
(376,520)(377,519)(378,518)(379,517)(380,516)(381,534)(382,533)(383,551)
(384,550)(385,549)(386,548)(387,547)(388,546)(389,545)(390,544)(391,543)
(392,542)(393,541)(394,540)(395,539)(396,538)(397,537)(398,536)(399,535)
(400,553)(401,552)(402,570)(403,569)(404,568)(405,567)(406,566)(407,565)
(408,564)(409,563)(410,562)(411,561)(412,560)(413,559)(414,558)(415,557)
(416,556)(417,555)(418,554)(419,572)(420,571)(421,589)(422,588)(423,587)
(424,586)(425,585)(426,584)(427,583)(428,582)(429,581)(430,580)(431,579)
(432,578)(433,577)(434,576)(435,575)(436,574)(437,573)(438,591)(439,590)
(440,608)(441,607)(442,606)(443,605)(444,604)(445,603)(446,602)(447,601)
(448,600)(449,599)(450,598)(451,597)(452,596)(453,595)(454,594)(455,593)
(456,592);
poly := sub<Sym(608)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope