Polytope of Type {24,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,12919)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 72, 288, 24
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,4}*576a, {12,8}*576b
   4-fold quotients : {12,4}*288
   8-fold quotients : {6,4}*144
   9-fold quotients : {8,8}*128c
   16-fold quotients : {6,4}*72
   18-fold quotients : {8,4}*64a, {4,8}*64b
   36-fold quotients : {4,4}*32, {8,2}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1,325)(  2,327)(  3,326)(  4,331)(  5,333)(  6,332)(  7,328)(  8,330)
(  9,329)( 10,334)( 11,336)( 12,335)( 13,340)( 14,342)( 15,341)( 16,337)
( 17,339)( 18,338)( 19,343)( 20,345)( 21,344)( 22,349)( 23,351)( 24,350)
( 25,346)( 26,348)( 27,347)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)
( 33,359)( 34,355)( 35,357)( 36,356)( 37,289)( 38,291)( 39,290)( 40,295)
( 41,297)( 42,296)( 43,292)( 44,294)( 45,293)( 46,298)( 47,300)( 48,299)
( 49,304)( 50,306)( 51,305)( 52,301)( 53,303)( 54,302)( 55,307)( 56,309)
( 57,308)( 58,313)( 59,315)( 60,314)( 61,310)( 62,312)( 63,311)( 64,316)
( 65,318)( 66,317)( 67,322)( 68,324)( 69,323)( 70,319)( 71,321)( 72,320)
( 73,415)( 74,417)( 75,416)( 76,421)( 77,423)( 78,422)( 79,418)( 80,420)
( 81,419)( 82,424)( 83,426)( 84,425)( 85,430)( 86,432)( 87,431)( 88,427)
( 89,429)( 90,428)( 91,397)( 92,399)( 93,398)( 94,403)( 95,405)( 96,404)
( 97,400)( 98,402)( 99,401)(100,406)(101,408)(102,407)(103,412)(104,414)
(105,413)(106,409)(107,411)(108,410)(109,379)(110,381)(111,380)(112,385)
(113,387)(114,386)(115,382)(116,384)(117,383)(118,388)(119,390)(120,389)
(121,394)(122,396)(123,395)(124,391)(125,393)(126,392)(127,361)(128,363)
(129,362)(130,367)(131,369)(132,368)(133,364)(134,366)(135,365)(136,370)
(137,372)(138,371)(139,376)(140,378)(141,377)(142,373)(143,375)(144,374)
(145,469)(146,471)(147,470)(148,475)(149,477)(150,476)(151,472)(152,474)
(153,473)(154,478)(155,480)(156,479)(157,484)(158,486)(159,485)(160,481)
(161,483)(162,482)(163,487)(164,489)(165,488)(166,493)(167,495)(168,494)
(169,490)(170,492)(171,491)(172,496)(173,498)(174,497)(175,502)(176,504)
(177,503)(178,499)(179,501)(180,500)(181,433)(182,435)(183,434)(184,439)
(185,441)(186,440)(187,436)(188,438)(189,437)(190,442)(191,444)(192,443)
(193,448)(194,450)(195,449)(196,445)(197,447)(198,446)(199,451)(200,453)
(201,452)(202,457)(203,459)(204,458)(205,454)(206,456)(207,455)(208,460)
(209,462)(210,461)(211,466)(212,468)(213,467)(214,463)(215,465)(216,464)
(217,559)(218,561)(219,560)(220,565)(221,567)(222,566)(223,562)(224,564)
(225,563)(226,568)(227,570)(228,569)(229,574)(230,576)(231,575)(232,571)
(233,573)(234,572)(235,541)(236,543)(237,542)(238,547)(239,549)(240,548)
(241,544)(242,546)(243,545)(244,550)(245,552)(246,551)(247,556)(248,558)
(249,557)(250,553)(251,555)(252,554)(253,523)(254,525)(255,524)(256,529)
(257,531)(258,530)(259,526)(260,528)(261,527)(262,532)(263,534)(264,533)
(265,538)(266,540)(267,539)(268,535)(269,537)(270,536)(271,505)(272,507)
(273,506)(274,511)(275,513)(276,512)(277,508)(278,510)(279,509)(280,514)
(281,516)(282,515)(283,520)(284,522)(285,521)(286,517)(287,519)(288,518);;
s1 := (  1, 40)(  2, 38)(  3, 45)(  4, 37)(  5, 44)(  6, 42)(  7, 43)(  8, 41)
(  9, 39)( 10, 49)( 11, 47)( 12, 54)( 13, 46)( 14, 53)( 15, 51)( 16, 52)
( 17, 50)( 18, 48)( 19, 58)( 20, 56)( 21, 63)( 22, 55)( 23, 62)( 24, 60)
( 25, 61)( 26, 59)( 27, 57)( 28, 67)( 29, 65)( 30, 72)( 31, 64)( 32, 71)
( 33, 69)( 34, 70)( 35, 68)( 36, 66)( 73,130)( 74,128)( 75,135)( 76,127)
( 77,134)( 78,132)( 79,133)( 80,131)( 81,129)( 82,139)( 83,137)( 84,144)
( 85,136)( 86,143)( 87,141)( 88,142)( 89,140)( 90,138)( 91,112)( 92,110)
( 93,117)( 94,109)( 95,116)( 96,114)( 97,115)( 98,113)( 99,111)(100,121)
(101,119)(102,126)(103,118)(104,125)(105,123)(106,124)(107,122)(108,120)
(145,157)(146,155)(147,162)(148,154)(149,161)(150,159)(151,160)(152,158)
(153,156)(163,175)(164,173)(165,180)(166,172)(167,179)(168,177)(169,178)
(170,176)(171,174)(181,184)(183,189)(185,188)(190,193)(192,198)(194,197)
(199,202)(201,207)(203,206)(208,211)(210,216)(212,215)(217,247)(218,245)
(219,252)(220,244)(221,251)(222,249)(223,250)(224,248)(225,246)(226,238)
(227,236)(228,243)(229,235)(230,242)(231,240)(232,241)(233,239)(234,237)
(253,274)(254,272)(255,279)(256,271)(257,278)(258,276)(259,277)(260,275)
(261,273)(262,283)(263,281)(264,288)(265,280)(266,287)(267,285)(268,286)
(269,284)(270,282)(289,400)(290,398)(291,405)(292,397)(293,404)(294,402)
(295,403)(296,401)(297,399)(298,409)(299,407)(300,414)(301,406)(302,413)
(303,411)(304,412)(305,410)(306,408)(307,418)(308,416)(309,423)(310,415)
(311,422)(312,420)(313,421)(314,419)(315,417)(316,427)(317,425)(318,432)
(319,424)(320,431)(321,429)(322,430)(323,428)(324,426)(325,364)(326,362)
(327,369)(328,361)(329,368)(330,366)(331,367)(332,365)(333,363)(334,373)
(335,371)(336,378)(337,370)(338,377)(339,375)(340,376)(341,374)(342,372)
(343,382)(344,380)(345,387)(346,379)(347,386)(348,384)(349,385)(350,383)
(351,381)(352,391)(353,389)(354,396)(355,388)(356,395)(357,393)(358,394)
(359,392)(360,390)(433,508)(434,506)(435,513)(436,505)(437,512)(438,510)
(439,511)(440,509)(441,507)(442,517)(443,515)(444,522)(445,514)(446,521)
(447,519)(448,520)(449,518)(450,516)(451,526)(452,524)(453,531)(454,523)
(455,530)(456,528)(457,529)(458,527)(459,525)(460,535)(461,533)(462,540)
(463,532)(464,539)(465,537)(466,538)(467,536)(468,534)(469,553)(470,551)
(471,558)(472,550)(473,557)(474,555)(475,556)(476,554)(477,552)(478,544)
(479,542)(480,549)(481,541)(482,548)(483,546)(484,547)(485,545)(486,543)
(487,571)(488,569)(489,576)(490,568)(491,575)(492,573)(493,574)(494,572)
(495,570)(496,562)(497,560)(498,567)(499,559)(500,566)(501,564)(502,565)
(503,563)(504,561);;
s2 := (  1,433)(  2,435)(  3,434)(  4,437)(  5,436)(  6,438)(  7,441)(  8,440)
(  9,439)( 10,442)( 11,444)( 12,443)( 13,446)( 14,445)( 15,447)( 16,450)
( 17,449)( 18,448)( 19,451)( 20,453)( 21,452)( 22,455)( 23,454)( 24,456)
( 25,459)( 26,458)( 27,457)( 28,460)( 29,462)( 30,461)( 31,464)( 32,463)
( 33,465)( 34,468)( 35,467)( 36,466)( 37,469)( 38,471)( 39,470)( 40,473)
( 41,472)( 42,474)( 43,477)( 44,476)( 45,475)( 46,478)( 47,480)( 48,479)
( 49,482)( 50,481)( 51,483)( 52,486)( 53,485)( 54,484)( 55,487)( 56,489)
( 57,488)( 58,491)( 59,490)( 60,492)( 61,495)( 62,494)( 63,493)( 64,496)
( 65,498)( 66,497)( 67,500)( 68,499)( 69,501)( 70,504)( 71,503)( 72,502)
( 73,532)( 74,534)( 75,533)( 76,536)( 77,535)( 78,537)( 79,540)( 80,539)
( 81,538)( 82,523)( 83,525)( 84,524)( 85,527)( 86,526)( 87,528)( 88,531)
( 89,530)( 90,529)( 91,514)( 92,516)( 93,515)( 94,518)( 95,517)( 96,519)
( 97,522)( 98,521)( 99,520)(100,505)(101,507)(102,506)(103,509)(104,508)
(105,510)(106,513)(107,512)(108,511)(109,568)(110,570)(111,569)(112,572)
(113,571)(114,573)(115,576)(116,575)(117,574)(118,559)(119,561)(120,560)
(121,563)(122,562)(123,564)(124,567)(125,566)(126,565)(127,550)(128,552)
(129,551)(130,554)(131,553)(132,555)(133,558)(134,557)(135,556)(136,541)
(137,543)(138,542)(139,545)(140,544)(141,546)(142,549)(143,548)(144,547)
(145,289)(146,291)(147,290)(148,293)(149,292)(150,294)(151,297)(152,296)
(153,295)(154,298)(155,300)(156,299)(157,302)(158,301)(159,303)(160,306)
(161,305)(162,304)(163,307)(164,309)(165,308)(166,311)(167,310)(168,312)
(169,315)(170,314)(171,313)(172,316)(173,318)(174,317)(175,320)(176,319)
(177,321)(178,324)(179,323)(180,322)(181,325)(182,327)(183,326)(184,329)
(185,328)(186,330)(187,333)(188,332)(189,331)(190,334)(191,336)(192,335)
(193,338)(194,337)(195,339)(196,342)(197,341)(198,340)(199,343)(200,345)
(201,344)(202,347)(203,346)(204,348)(205,351)(206,350)(207,349)(208,352)
(209,354)(210,353)(211,356)(212,355)(213,357)(214,360)(215,359)(216,358)
(217,388)(218,390)(219,389)(220,392)(221,391)(222,393)(223,396)(224,395)
(225,394)(226,379)(227,381)(228,380)(229,383)(230,382)(231,384)(232,387)
(233,386)(234,385)(235,370)(236,372)(237,371)(238,374)(239,373)(240,375)
(241,378)(242,377)(243,376)(244,361)(245,363)(246,362)(247,365)(248,364)
(249,366)(250,369)(251,368)(252,367)(253,424)(254,426)(255,425)(256,428)
(257,427)(258,429)(259,432)(260,431)(261,430)(262,415)(263,417)(264,416)
(265,419)(266,418)(267,420)(268,423)(269,422)(270,421)(271,406)(272,408)
(273,407)(274,410)(275,409)(276,411)(277,414)(278,413)(279,412)(280,397)
(281,399)(282,398)(283,401)(284,400)(285,402)(286,405)(287,404)(288,403);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(576)!(  1,325)(  2,327)(  3,326)(  4,331)(  5,333)(  6,332)(  7,328)
(  8,330)(  9,329)( 10,334)( 11,336)( 12,335)( 13,340)( 14,342)( 15,341)
( 16,337)( 17,339)( 18,338)( 19,343)( 20,345)( 21,344)( 22,349)( 23,351)
( 24,350)( 25,346)( 26,348)( 27,347)( 28,352)( 29,354)( 30,353)( 31,358)
( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,289)( 38,291)( 39,290)
( 40,295)( 41,297)( 42,296)( 43,292)( 44,294)( 45,293)( 46,298)( 47,300)
( 48,299)( 49,304)( 50,306)( 51,305)( 52,301)( 53,303)( 54,302)( 55,307)
( 56,309)( 57,308)( 58,313)( 59,315)( 60,314)( 61,310)( 62,312)( 63,311)
( 64,316)( 65,318)( 66,317)( 67,322)( 68,324)( 69,323)( 70,319)( 71,321)
( 72,320)( 73,415)( 74,417)( 75,416)( 76,421)( 77,423)( 78,422)( 79,418)
( 80,420)( 81,419)( 82,424)( 83,426)( 84,425)( 85,430)( 86,432)( 87,431)
( 88,427)( 89,429)( 90,428)( 91,397)( 92,399)( 93,398)( 94,403)( 95,405)
( 96,404)( 97,400)( 98,402)( 99,401)(100,406)(101,408)(102,407)(103,412)
(104,414)(105,413)(106,409)(107,411)(108,410)(109,379)(110,381)(111,380)
(112,385)(113,387)(114,386)(115,382)(116,384)(117,383)(118,388)(119,390)
(120,389)(121,394)(122,396)(123,395)(124,391)(125,393)(126,392)(127,361)
(128,363)(129,362)(130,367)(131,369)(132,368)(133,364)(134,366)(135,365)
(136,370)(137,372)(138,371)(139,376)(140,378)(141,377)(142,373)(143,375)
(144,374)(145,469)(146,471)(147,470)(148,475)(149,477)(150,476)(151,472)
(152,474)(153,473)(154,478)(155,480)(156,479)(157,484)(158,486)(159,485)
(160,481)(161,483)(162,482)(163,487)(164,489)(165,488)(166,493)(167,495)
(168,494)(169,490)(170,492)(171,491)(172,496)(173,498)(174,497)(175,502)
(176,504)(177,503)(178,499)(179,501)(180,500)(181,433)(182,435)(183,434)
(184,439)(185,441)(186,440)(187,436)(188,438)(189,437)(190,442)(191,444)
(192,443)(193,448)(194,450)(195,449)(196,445)(197,447)(198,446)(199,451)
(200,453)(201,452)(202,457)(203,459)(204,458)(205,454)(206,456)(207,455)
(208,460)(209,462)(210,461)(211,466)(212,468)(213,467)(214,463)(215,465)
(216,464)(217,559)(218,561)(219,560)(220,565)(221,567)(222,566)(223,562)
(224,564)(225,563)(226,568)(227,570)(228,569)(229,574)(230,576)(231,575)
(232,571)(233,573)(234,572)(235,541)(236,543)(237,542)(238,547)(239,549)
(240,548)(241,544)(242,546)(243,545)(244,550)(245,552)(246,551)(247,556)
(248,558)(249,557)(250,553)(251,555)(252,554)(253,523)(254,525)(255,524)
(256,529)(257,531)(258,530)(259,526)(260,528)(261,527)(262,532)(263,534)
(264,533)(265,538)(266,540)(267,539)(268,535)(269,537)(270,536)(271,505)
(272,507)(273,506)(274,511)(275,513)(276,512)(277,508)(278,510)(279,509)
(280,514)(281,516)(282,515)(283,520)(284,522)(285,521)(286,517)(287,519)
(288,518);
s1 := Sym(576)!(  1, 40)(  2, 38)(  3, 45)(  4, 37)(  5, 44)(  6, 42)(  7, 43)
(  8, 41)(  9, 39)( 10, 49)( 11, 47)( 12, 54)( 13, 46)( 14, 53)( 15, 51)
( 16, 52)( 17, 50)( 18, 48)( 19, 58)( 20, 56)( 21, 63)( 22, 55)( 23, 62)
( 24, 60)( 25, 61)( 26, 59)( 27, 57)( 28, 67)( 29, 65)( 30, 72)( 31, 64)
( 32, 71)( 33, 69)( 34, 70)( 35, 68)( 36, 66)( 73,130)( 74,128)( 75,135)
( 76,127)( 77,134)( 78,132)( 79,133)( 80,131)( 81,129)( 82,139)( 83,137)
( 84,144)( 85,136)( 86,143)( 87,141)( 88,142)( 89,140)( 90,138)( 91,112)
( 92,110)( 93,117)( 94,109)( 95,116)( 96,114)( 97,115)( 98,113)( 99,111)
(100,121)(101,119)(102,126)(103,118)(104,125)(105,123)(106,124)(107,122)
(108,120)(145,157)(146,155)(147,162)(148,154)(149,161)(150,159)(151,160)
(152,158)(153,156)(163,175)(164,173)(165,180)(166,172)(167,179)(168,177)
(169,178)(170,176)(171,174)(181,184)(183,189)(185,188)(190,193)(192,198)
(194,197)(199,202)(201,207)(203,206)(208,211)(210,216)(212,215)(217,247)
(218,245)(219,252)(220,244)(221,251)(222,249)(223,250)(224,248)(225,246)
(226,238)(227,236)(228,243)(229,235)(230,242)(231,240)(232,241)(233,239)
(234,237)(253,274)(254,272)(255,279)(256,271)(257,278)(258,276)(259,277)
(260,275)(261,273)(262,283)(263,281)(264,288)(265,280)(266,287)(267,285)
(268,286)(269,284)(270,282)(289,400)(290,398)(291,405)(292,397)(293,404)
(294,402)(295,403)(296,401)(297,399)(298,409)(299,407)(300,414)(301,406)
(302,413)(303,411)(304,412)(305,410)(306,408)(307,418)(308,416)(309,423)
(310,415)(311,422)(312,420)(313,421)(314,419)(315,417)(316,427)(317,425)
(318,432)(319,424)(320,431)(321,429)(322,430)(323,428)(324,426)(325,364)
(326,362)(327,369)(328,361)(329,368)(330,366)(331,367)(332,365)(333,363)
(334,373)(335,371)(336,378)(337,370)(338,377)(339,375)(340,376)(341,374)
(342,372)(343,382)(344,380)(345,387)(346,379)(347,386)(348,384)(349,385)
(350,383)(351,381)(352,391)(353,389)(354,396)(355,388)(356,395)(357,393)
(358,394)(359,392)(360,390)(433,508)(434,506)(435,513)(436,505)(437,512)
(438,510)(439,511)(440,509)(441,507)(442,517)(443,515)(444,522)(445,514)
(446,521)(447,519)(448,520)(449,518)(450,516)(451,526)(452,524)(453,531)
(454,523)(455,530)(456,528)(457,529)(458,527)(459,525)(460,535)(461,533)
(462,540)(463,532)(464,539)(465,537)(466,538)(467,536)(468,534)(469,553)
(470,551)(471,558)(472,550)(473,557)(474,555)(475,556)(476,554)(477,552)
(478,544)(479,542)(480,549)(481,541)(482,548)(483,546)(484,547)(485,545)
(486,543)(487,571)(488,569)(489,576)(490,568)(491,575)(492,573)(493,574)
(494,572)(495,570)(496,562)(497,560)(498,567)(499,559)(500,566)(501,564)
(502,565)(503,563)(504,561);
s2 := Sym(576)!(  1,433)(  2,435)(  3,434)(  4,437)(  5,436)(  6,438)(  7,441)
(  8,440)(  9,439)( 10,442)( 11,444)( 12,443)( 13,446)( 14,445)( 15,447)
( 16,450)( 17,449)( 18,448)( 19,451)( 20,453)( 21,452)( 22,455)( 23,454)
( 24,456)( 25,459)( 26,458)( 27,457)( 28,460)( 29,462)( 30,461)( 31,464)
( 32,463)( 33,465)( 34,468)( 35,467)( 36,466)( 37,469)( 38,471)( 39,470)
( 40,473)( 41,472)( 42,474)( 43,477)( 44,476)( 45,475)( 46,478)( 47,480)
( 48,479)( 49,482)( 50,481)( 51,483)( 52,486)( 53,485)( 54,484)( 55,487)
( 56,489)( 57,488)( 58,491)( 59,490)( 60,492)( 61,495)( 62,494)( 63,493)
( 64,496)( 65,498)( 66,497)( 67,500)( 68,499)( 69,501)( 70,504)( 71,503)
( 72,502)( 73,532)( 74,534)( 75,533)( 76,536)( 77,535)( 78,537)( 79,540)
( 80,539)( 81,538)( 82,523)( 83,525)( 84,524)( 85,527)( 86,526)( 87,528)
( 88,531)( 89,530)( 90,529)( 91,514)( 92,516)( 93,515)( 94,518)( 95,517)
( 96,519)( 97,522)( 98,521)( 99,520)(100,505)(101,507)(102,506)(103,509)
(104,508)(105,510)(106,513)(107,512)(108,511)(109,568)(110,570)(111,569)
(112,572)(113,571)(114,573)(115,576)(116,575)(117,574)(118,559)(119,561)
(120,560)(121,563)(122,562)(123,564)(124,567)(125,566)(126,565)(127,550)
(128,552)(129,551)(130,554)(131,553)(132,555)(133,558)(134,557)(135,556)
(136,541)(137,543)(138,542)(139,545)(140,544)(141,546)(142,549)(143,548)
(144,547)(145,289)(146,291)(147,290)(148,293)(149,292)(150,294)(151,297)
(152,296)(153,295)(154,298)(155,300)(156,299)(157,302)(158,301)(159,303)
(160,306)(161,305)(162,304)(163,307)(164,309)(165,308)(166,311)(167,310)
(168,312)(169,315)(170,314)(171,313)(172,316)(173,318)(174,317)(175,320)
(176,319)(177,321)(178,324)(179,323)(180,322)(181,325)(182,327)(183,326)
(184,329)(185,328)(186,330)(187,333)(188,332)(189,331)(190,334)(191,336)
(192,335)(193,338)(194,337)(195,339)(196,342)(197,341)(198,340)(199,343)
(200,345)(201,344)(202,347)(203,346)(204,348)(205,351)(206,350)(207,349)
(208,352)(209,354)(210,353)(211,356)(212,355)(213,357)(214,360)(215,359)
(216,358)(217,388)(218,390)(219,389)(220,392)(221,391)(222,393)(223,396)
(224,395)(225,394)(226,379)(227,381)(228,380)(229,383)(230,382)(231,384)
(232,387)(233,386)(234,385)(235,370)(236,372)(237,371)(238,374)(239,373)
(240,375)(241,378)(242,377)(243,376)(244,361)(245,363)(246,362)(247,365)
(248,364)(249,366)(250,369)(251,368)(252,367)(253,424)(254,426)(255,425)
(256,428)(257,427)(258,429)(259,432)(260,431)(261,430)(262,415)(263,417)
(264,416)(265,419)(266,418)(267,420)(268,423)(269,422)(270,421)(271,406)
(272,408)(273,407)(274,410)(275,409)(276,411)(277,414)(278,413)(279,412)
(280,397)(281,399)(282,398)(283,401)(284,400)(285,402)(286,405)(287,404)
(288,403);
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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope