Polytope of Type {4,75}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,75}*1200
if this polytope has a name.
Group : SmallGroup(1200,198)
Rank : 3
Schlafli Type : {4,75}
Number of vertices, edges, etc : 8, 300, 150
Order of s₀s₁s₂ : 150
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,75}*600
   4-fold quotients : {2,75}*300
   5-fold quotients : {4,15}*240
   10-fold quotients : {4,15}*120
   12-fold quotients : {2,25}*100
   20-fold quotients : {2,15}*60
   25-fold quotients : {4,3}*48
   50-fold quotients : {4,3}*24
   60-fold quotients : {2,5}*20
   100-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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