Polytope of Type {12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1152y
if this polytope has a name.
Group : SmallGroup(1152,157458)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 24, 288, 48
Order of s0s1s2 : 3
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {12,12}*576l
   8-fold quotients : {6,12}*144d, {12,6}*144d
   24-fold quotients : {4,6}*48b, {6,4}*48b
   48-fold quotients : {3,4}*24, {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1, 17)(  2, 18)(  3, 20)(  4, 19)(  5, 23)(  6, 24)(  7, 21)(  8, 22)
(  9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 31)( 14, 32)( 15, 29)( 16, 30)
( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 55)( 38, 56)( 39, 53)( 40, 54)
( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 63)( 46, 64)( 47, 61)( 48, 62)
( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 87)( 70, 88)( 71, 85)( 72, 86)
( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 95)( 78, 96)( 79, 93)( 80, 94)
( 97,209)( 98,210)( 99,212)(100,211)(101,215)(102,216)(103,213)(104,214)
(105,217)(106,218)(107,220)(108,219)(109,223)(110,224)(111,221)(112,222)
(113,193)(114,194)(115,196)(116,195)(117,199)(118,200)(119,197)(120,198)
(121,201)(122,202)(123,204)(124,203)(125,207)(126,208)(127,205)(128,206)
(129,241)(130,242)(131,244)(132,243)(133,247)(134,248)(135,245)(136,246)
(137,249)(138,250)(139,252)(140,251)(141,255)(142,256)(143,253)(144,254)
(145,225)(146,226)(147,228)(148,227)(149,231)(150,232)(151,229)(152,230)
(153,233)(154,234)(155,236)(156,235)(157,239)(158,240)(159,237)(160,238)
(161,273)(162,274)(163,276)(164,275)(165,279)(166,280)(167,277)(168,278)
(169,281)(170,282)(171,284)(172,283)(173,287)(174,288)(175,285)(176,286)
(177,257)(178,258)(179,260)(180,259)(181,263)(182,264)(183,261)(184,262)
(185,265)(186,266)(187,268)(188,267)(189,271)(190,272)(191,269)(192,270)
(289,306)(290,305)(291,307)(292,308)(293,312)(294,311)(295,310)(296,309)
(297,314)(298,313)(299,315)(300,316)(301,320)(302,319)(303,318)(304,317)
(321,338)(322,337)(323,339)(324,340)(325,344)(326,343)(327,342)(328,341)
(329,346)(330,345)(331,347)(332,348)(333,352)(334,351)(335,350)(336,349)
(353,370)(354,369)(355,371)(356,372)(357,376)(358,375)(359,374)(360,373)
(361,378)(362,377)(363,379)(364,380)(365,384)(366,383)(367,382)(368,381)
(385,498)(386,497)(387,499)(388,500)(389,504)(390,503)(391,502)(392,501)
(393,506)(394,505)(395,507)(396,508)(397,512)(398,511)(399,510)(400,509)
(401,482)(402,481)(403,483)(404,484)(405,488)(406,487)(407,486)(408,485)
(409,490)(410,489)(411,491)(412,492)(413,496)(414,495)(415,494)(416,493)
(417,530)(418,529)(419,531)(420,532)(421,536)(422,535)(423,534)(424,533)
(425,538)(426,537)(427,539)(428,540)(429,544)(430,543)(431,542)(432,541)
(433,514)(434,513)(435,515)(436,516)(437,520)(438,519)(439,518)(440,517)
(441,522)(442,521)(443,523)(444,524)(445,528)(446,527)(447,526)(448,525)
(449,562)(450,561)(451,563)(452,564)(453,568)(454,567)(455,566)(456,565)
(457,570)(458,569)(459,571)(460,572)(461,576)(462,575)(463,574)(464,573)
(465,546)(466,545)(467,547)(468,548)(469,552)(470,551)(471,550)(472,549)
(473,554)(474,553)(475,555)(476,556)(477,560)(478,559)(479,558)(480,557);;
s1 := (  1,385)(  2,386)(  3,391)(  4,392)(  5,390)(  6,389)(  7,387)(  8,388)
(  9,393)( 10,394)( 11,399)( 12,400)( 13,398)( 14,397)( 15,395)( 16,396)
( 17,409)( 18,410)( 19,415)( 20,416)( 21,414)( 22,413)( 23,411)( 24,412)
( 25,401)( 26,402)( 27,407)( 28,408)( 29,406)( 30,405)( 31,403)( 32,404)
( 33,449)( 34,450)( 35,455)( 36,456)( 37,454)( 38,453)( 39,451)( 40,452)
( 41,457)( 42,458)( 43,463)( 44,464)( 45,462)( 46,461)( 47,459)( 48,460)
( 49,473)( 50,474)( 51,479)( 52,480)( 53,478)( 54,477)( 55,475)( 56,476)
( 57,465)( 58,466)( 59,471)( 60,472)( 61,470)( 62,469)( 63,467)( 64,468)
( 65,417)( 66,418)( 67,423)( 68,424)( 69,422)( 70,421)( 71,419)( 72,420)
( 73,425)( 74,426)( 75,431)( 76,432)( 77,430)( 78,429)( 79,427)( 80,428)
( 81,441)( 82,442)( 83,447)( 84,448)( 85,446)( 86,445)( 87,443)( 88,444)
( 89,433)( 90,434)( 91,439)( 92,440)( 93,438)( 94,437)( 95,435)( 96,436)
( 97,289)( 98,290)( 99,295)(100,296)(101,294)(102,293)(103,291)(104,292)
(105,297)(106,298)(107,303)(108,304)(109,302)(110,301)(111,299)(112,300)
(113,313)(114,314)(115,319)(116,320)(117,318)(118,317)(119,315)(120,316)
(121,305)(122,306)(123,311)(124,312)(125,310)(126,309)(127,307)(128,308)
(129,353)(130,354)(131,359)(132,360)(133,358)(134,357)(135,355)(136,356)
(137,361)(138,362)(139,367)(140,368)(141,366)(142,365)(143,363)(144,364)
(145,377)(146,378)(147,383)(148,384)(149,382)(150,381)(151,379)(152,380)
(153,369)(154,370)(155,375)(156,376)(157,374)(158,373)(159,371)(160,372)
(161,321)(162,322)(163,327)(164,328)(165,326)(166,325)(167,323)(168,324)
(169,329)(170,330)(171,335)(172,336)(173,334)(174,333)(175,331)(176,332)
(177,345)(178,346)(179,351)(180,352)(181,350)(182,349)(183,347)(184,348)
(185,337)(186,338)(187,343)(188,344)(189,342)(190,341)(191,339)(192,340)
(193,481)(194,482)(195,487)(196,488)(197,486)(198,485)(199,483)(200,484)
(201,489)(202,490)(203,495)(204,496)(205,494)(206,493)(207,491)(208,492)
(209,505)(210,506)(211,511)(212,512)(213,510)(214,509)(215,507)(216,508)
(217,497)(218,498)(219,503)(220,504)(221,502)(222,501)(223,499)(224,500)
(225,545)(226,546)(227,551)(228,552)(229,550)(230,549)(231,547)(232,548)
(233,553)(234,554)(235,559)(236,560)(237,558)(238,557)(239,555)(240,556)
(241,569)(242,570)(243,575)(244,576)(245,574)(246,573)(247,571)(248,572)
(249,561)(250,562)(251,567)(252,568)(253,566)(254,565)(255,563)(256,564)
(257,513)(258,514)(259,519)(260,520)(261,518)(262,517)(263,515)(264,516)
(265,521)(266,522)(267,527)(268,528)(269,526)(270,525)(271,523)(272,524)
(273,537)(274,538)(275,543)(276,544)(277,542)(278,541)(279,539)(280,540)
(281,529)(282,530)(283,535)(284,536)(285,534)(286,533)(287,531)(288,532);;
s2 := (  1,323)(  2,324)(  3,322)(  4,321)(  5,327)(  6,328)(  7,326)(  8,325)
(  9,347)( 10,348)( 11,346)( 12,345)( 13,351)( 14,352)( 15,350)( 16,349)
( 17,339)( 18,340)( 19,338)( 20,337)( 21,343)( 22,344)( 23,342)( 24,341)
( 25,331)( 26,332)( 27,330)( 28,329)( 29,335)( 30,336)( 31,334)( 32,333)
( 33,291)( 34,292)( 35,290)( 36,289)( 37,295)( 38,296)( 39,294)( 40,293)
( 41,315)( 42,316)( 43,314)( 44,313)( 45,319)( 46,320)( 47,318)( 48,317)
( 49,307)( 50,308)( 51,306)( 52,305)( 53,311)( 54,312)( 55,310)( 56,309)
( 57,299)( 58,300)( 59,298)( 60,297)( 61,303)( 62,304)( 63,302)( 64,301)
( 65,355)( 66,356)( 67,354)( 68,353)( 69,359)( 70,360)( 71,358)( 72,357)
( 73,379)( 74,380)( 75,378)( 76,377)( 77,383)( 78,384)( 79,382)( 80,381)
( 81,371)( 82,372)( 83,370)( 84,369)( 85,375)( 86,376)( 87,374)( 88,373)
( 89,363)( 90,364)( 91,362)( 92,361)( 93,367)( 94,368)( 95,366)( 96,365)
( 97,419)( 98,420)( 99,418)(100,417)(101,423)(102,424)(103,422)(104,421)
(105,443)(106,444)(107,442)(108,441)(109,447)(110,448)(111,446)(112,445)
(113,435)(114,436)(115,434)(116,433)(117,439)(118,440)(119,438)(120,437)
(121,427)(122,428)(123,426)(124,425)(125,431)(126,432)(127,430)(128,429)
(129,387)(130,388)(131,386)(132,385)(133,391)(134,392)(135,390)(136,389)
(137,411)(138,412)(139,410)(140,409)(141,415)(142,416)(143,414)(144,413)
(145,403)(146,404)(147,402)(148,401)(149,407)(150,408)(151,406)(152,405)
(153,395)(154,396)(155,394)(156,393)(157,399)(158,400)(159,398)(160,397)
(161,451)(162,452)(163,450)(164,449)(165,455)(166,456)(167,454)(168,453)
(169,475)(170,476)(171,474)(172,473)(173,479)(174,480)(175,478)(176,477)
(177,467)(178,468)(179,466)(180,465)(181,471)(182,472)(183,470)(184,469)
(185,459)(186,460)(187,458)(188,457)(189,463)(190,464)(191,462)(192,461)
(193,515)(194,516)(195,514)(196,513)(197,519)(198,520)(199,518)(200,517)
(201,539)(202,540)(203,538)(204,537)(205,543)(206,544)(207,542)(208,541)
(209,531)(210,532)(211,530)(212,529)(213,535)(214,536)(215,534)(216,533)
(217,523)(218,524)(219,522)(220,521)(221,527)(222,528)(223,526)(224,525)
(225,483)(226,484)(227,482)(228,481)(229,487)(230,488)(231,486)(232,485)
(233,507)(234,508)(235,506)(236,505)(237,511)(238,512)(239,510)(240,509)
(241,499)(242,500)(243,498)(244,497)(245,503)(246,504)(247,502)(248,501)
(249,491)(250,492)(251,490)(252,489)(253,495)(254,496)(255,494)(256,493)
(257,547)(258,548)(259,546)(260,545)(261,551)(262,552)(263,550)(264,549)
(265,571)(266,572)(267,570)(268,569)(269,575)(270,576)(271,574)(272,573)
(273,563)(274,564)(275,562)(276,561)(277,567)(278,568)(279,566)(280,565)
(281,555)(282,556)(283,554)(284,553)(285,559)(286,560)(287,558)(288,557);;
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*s0*s1*s2*s0*s1*s2, 
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*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(576)!(  1, 17)(  2, 18)(  3, 20)(  4, 19)(  5, 23)(  6, 24)(  7, 21)
(  8, 22)(  9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 31)( 14, 32)( 15, 29)
( 16, 30)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 55)( 38, 56)( 39, 53)
( 40, 54)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 63)( 46, 64)( 47, 61)
( 48, 62)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 87)( 70, 88)( 71, 85)
( 72, 86)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 95)( 78, 96)( 79, 93)
( 80, 94)( 97,209)( 98,210)( 99,212)(100,211)(101,215)(102,216)(103,213)
(104,214)(105,217)(106,218)(107,220)(108,219)(109,223)(110,224)(111,221)
(112,222)(113,193)(114,194)(115,196)(116,195)(117,199)(118,200)(119,197)
(120,198)(121,201)(122,202)(123,204)(124,203)(125,207)(126,208)(127,205)
(128,206)(129,241)(130,242)(131,244)(132,243)(133,247)(134,248)(135,245)
(136,246)(137,249)(138,250)(139,252)(140,251)(141,255)(142,256)(143,253)
(144,254)(145,225)(146,226)(147,228)(148,227)(149,231)(150,232)(151,229)
(152,230)(153,233)(154,234)(155,236)(156,235)(157,239)(158,240)(159,237)
(160,238)(161,273)(162,274)(163,276)(164,275)(165,279)(166,280)(167,277)
(168,278)(169,281)(170,282)(171,284)(172,283)(173,287)(174,288)(175,285)
(176,286)(177,257)(178,258)(179,260)(180,259)(181,263)(182,264)(183,261)
(184,262)(185,265)(186,266)(187,268)(188,267)(189,271)(190,272)(191,269)
(192,270)(289,306)(290,305)(291,307)(292,308)(293,312)(294,311)(295,310)
(296,309)(297,314)(298,313)(299,315)(300,316)(301,320)(302,319)(303,318)
(304,317)(321,338)(322,337)(323,339)(324,340)(325,344)(326,343)(327,342)
(328,341)(329,346)(330,345)(331,347)(332,348)(333,352)(334,351)(335,350)
(336,349)(353,370)(354,369)(355,371)(356,372)(357,376)(358,375)(359,374)
(360,373)(361,378)(362,377)(363,379)(364,380)(365,384)(366,383)(367,382)
(368,381)(385,498)(386,497)(387,499)(388,500)(389,504)(390,503)(391,502)
(392,501)(393,506)(394,505)(395,507)(396,508)(397,512)(398,511)(399,510)
(400,509)(401,482)(402,481)(403,483)(404,484)(405,488)(406,487)(407,486)
(408,485)(409,490)(410,489)(411,491)(412,492)(413,496)(414,495)(415,494)
(416,493)(417,530)(418,529)(419,531)(420,532)(421,536)(422,535)(423,534)
(424,533)(425,538)(426,537)(427,539)(428,540)(429,544)(430,543)(431,542)
(432,541)(433,514)(434,513)(435,515)(436,516)(437,520)(438,519)(439,518)
(440,517)(441,522)(442,521)(443,523)(444,524)(445,528)(446,527)(447,526)
(448,525)(449,562)(450,561)(451,563)(452,564)(453,568)(454,567)(455,566)
(456,565)(457,570)(458,569)(459,571)(460,572)(461,576)(462,575)(463,574)
(464,573)(465,546)(466,545)(467,547)(468,548)(469,552)(470,551)(471,550)
(472,549)(473,554)(474,553)(475,555)(476,556)(477,560)(478,559)(479,558)
(480,557);
s1 := Sym(576)!(  1,385)(  2,386)(  3,391)(  4,392)(  5,390)(  6,389)(  7,387)
(  8,388)(  9,393)( 10,394)( 11,399)( 12,400)( 13,398)( 14,397)( 15,395)
( 16,396)( 17,409)( 18,410)( 19,415)( 20,416)( 21,414)( 22,413)( 23,411)
( 24,412)( 25,401)( 26,402)( 27,407)( 28,408)( 29,406)( 30,405)( 31,403)
( 32,404)( 33,449)( 34,450)( 35,455)( 36,456)( 37,454)( 38,453)( 39,451)
( 40,452)( 41,457)( 42,458)( 43,463)( 44,464)( 45,462)( 46,461)( 47,459)
( 48,460)( 49,473)( 50,474)( 51,479)( 52,480)( 53,478)( 54,477)( 55,475)
( 56,476)( 57,465)( 58,466)( 59,471)( 60,472)( 61,470)( 62,469)( 63,467)
( 64,468)( 65,417)( 66,418)( 67,423)( 68,424)( 69,422)( 70,421)( 71,419)
( 72,420)( 73,425)( 74,426)( 75,431)( 76,432)( 77,430)( 78,429)( 79,427)
( 80,428)( 81,441)( 82,442)( 83,447)( 84,448)( 85,446)( 86,445)( 87,443)
( 88,444)( 89,433)( 90,434)( 91,439)( 92,440)( 93,438)( 94,437)( 95,435)
( 96,436)( 97,289)( 98,290)( 99,295)(100,296)(101,294)(102,293)(103,291)
(104,292)(105,297)(106,298)(107,303)(108,304)(109,302)(110,301)(111,299)
(112,300)(113,313)(114,314)(115,319)(116,320)(117,318)(118,317)(119,315)
(120,316)(121,305)(122,306)(123,311)(124,312)(125,310)(126,309)(127,307)
(128,308)(129,353)(130,354)(131,359)(132,360)(133,358)(134,357)(135,355)
(136,356)(137,361)(138,362)(139,367)(140,368)(141,366)(142,365)(143,363)
(144,364)(145,377)(146,378)(147,383)(148,384)(149,382)(150,381)(151,379)
(152,380)(153,369)(154,370)(155,375)(156,376)(157,374)(158,373)(159,371)
(160,372)(161,321)(162,322)(163,327)(164,328)(165,326)(166,325)(167,323)
(168,324)(169,329)(170,330)(171,335)(172,336)(173,334)(174,333)(175,331)
(176,332)(177,345)(178,346)(179,351)(180,352)(181,350)(182,349)(183,347)
(184,348)(185,337)(186,338)(187,343)(188,344)(189,342)(190,341)(191,339)
(192,340)(193,481)(194,482)(195,487)(196,488)(197,486)(198,485)(199,483)
(200,484)(201,489)(202,490)(203,495)(204,496)(205,494)(206,493)(207,491)
(208,492)(209,505)(210,506)(211,511)(212,512)(213,510)(214,509)(215,507)
(216,508)(217,497)(218,498)(219,503)(220,504)(221,502)(222,501)(223,499)
(224,500)(225,545)(226,546)(227,551)(228,552)(229,550)(230,549)(231,547)
(232,548)(233,553)(234,554)(235,559)(236,560)(237,558)(238,557)(239,555)
(240,556)(241,569)(242,570)(243,575)(244,576)(245,574)(246,573)(247,571)
(248,572)(249,561)(250,562)(251,567)(252,568)(253,566)(254,565)(255,563)
(256,564)(257,513)(258,514)(259,519)(260,520)(261,518)(262,517)(263,515)
(264,516)(265,521)(266,522)(267,527)(268,528)(269,526)(270,525)(271,523)
(272,524)(273,537)(274,538)(275,543)(276,544)(277,542)(278,541)(279,539)
(280,540)(281,529)(282,530)(283,535)(284,536)(285,534)(286,533)(287,531)
(288,532);
s2 := Sym(576)!(  1,323)(  2,324)(  3,322)(  4,321)(  5,327)(  6,328)(  7,326)
(  8,325)(  9,347)( 10,348)( 11,346)( 12,345)( 13,351)( 14,352)( 15,350)
( 16,349)( 17,339)( 18,340)( 19,338)( 20,337)( 21,343)( 22,344)( 23,342)
( 24,341)( 25,331)( 26,332)( 27,330)( 28,329)( 29,335)( 30,336)( 31,334)
( 32,333)( 33,291)( 34,292)( 35,290)( 36,289)( 37,295)( 38,296)( 39,294)
( 40,293)( 41,315)( 42,316)( 43,314)( 44,313)( 45,319)( 46,320)( 47,318)
( 48,317)( 49,307)( 50,308)( 51,306)( 52,305)( 53,311)( 54,312)( 55,310)
( 56,309)( 57,299)( 58,300)( 59,298)( 60,297)( 61,303)( 62,304)( 63,302)
( 64,301)( 65,355)( 66,356)( 67,354)( 68,353)( 69,359)( 70,360)( 71,358)
( 72,357)( 73,379)( 74,380)( 75,378)( 76,377)( 77,383)( 78,384)( 79,382)
( 80,381)( 81,371)( 82,372)( 83,370)( 84,369)( 85,375)( 86,376)( 87,374)
( 88,373)( 89,363)( 90,364)( 91,362)( 92,361)( 93,367)( 94,368)( 95,366)
( 96,365)( 97,419)( 98,420)( 99,418)(100,417)(101,423)(102,424)(103,422)
(104,421)(105,443)(106,444)(107,442)(108,441)(109,447)(110,448)(111,446)
(112,445)(113,435)(114,436)(115,434)(116,433)(117,439)(118,440)(119,438)
(120,437)(121,427)(122,428)(123,426)(124,425)(125,431)(126,432)(127,430)
(128,429)(129,387)(130,388)(131,386)(132,385)(133,391)(134,392)(135,390)
(136,389)(137,411)(138,412)(139,410)(140,409)(141,415)(142,416)(143,414)
(144,413)(145,403)(146,404)(147,402)(148,401)(149,407)(150,408)(151,406)
(152,405)(153,395)(154,396)(155,394)(156,393)(157,399)(158,400)(159,398)
(160,397)(161,451)(162,452)(163,450)(164,449)(165,455)(166,456)(167,454)
(168,453)(169,475)(170,476)(171,474)(172,473)(173,479)(174,480)(175,478)
(176,477)(177,467)(178,468)(179,466)(180,465)(181,471)(182,472)(183,470)
(184,469)(185,459)(186,460)(187,458)(188,457)(189,463)(190,464)(191,462)
(192,461)(193,515)(194,516)(195,514)(196,513)(197,519)(198,520)(199,518)
(200,517)(201,539)(202,540)(203,538)(204,537)(205,543)(206,544)(207,542)
(208,541)(209,531)(210,532)(211,530)(212,529)(213,535)(214,536)(215,534)
(216,533)(217,523)(218,524)(219,522)(220,521)(221,527)(222,528)(223,526)
(224,525)(225,483)(226,484)(227,482)(228,481)(229,487)(230,488)(231,486)
(232,485)(233,507)(234,508)(235,506)(236,505)(237,511)(238,512)(239,510)
(240,509)(241,499)(242,500)(243,498)(244,497)(245,503)(246,504)(247,502)
(248,501)(249,491)(250,492)(251,490)(252,489)(253,495)(254,496)(255,494)
(256,493)(257,547)(258,548)(259,546)(260,545)(261,551)(262,552)(263,550)
(264,549)(265,571)(266,572)(267,570)(268,569)(269,575)(270,576)(271,574)
(272,573)(273,563)(274,564)(275,562)(276,561)(277,567)(278,568)(279,566)
(280,565)(281,555)(282,556)(283,554)(284,553)(285,559)(286,560)(287,558)
(288,557);
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*s0*s1*s2*s0*s1*s2, 
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*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 >;
References : None.
to this polytope