Polytope of Type {4,72}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,72}*1152e
if this polytope has a name.
Group : SmallGroup(1152,154378)
Rank : 3
Schlafli Type : {4,72}
Number of vertices, edges, etc : 8, 288, 144
Order of s₀s₁s₂ : 36
Order of s₀s₁s₂s₁ : 8
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 : {4,36}*576c
   3-fold quotients : {4,24}*384e
   4-fold quotients : {4,18}*288
   6-fold quotients : {4,12}*192c
   8-fold quotients : {4,9}*144, {4,18}*144b, {4,18}*144c
   12-fold quotients : {4,6}*96
   16-fold quotients : {4,9}*72, {2,18}*72
   24-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {2,9}*36
   48-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,3}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope