Polytope of Type {4,3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157458)
Rank : 4
Schlafli Type : {4,3,12}
Number of vertices, edges, etc : 4, 24, 72, 48
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,3,6}*576
8-fold quotients : {4,3,6}*144
24-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 17)( 2, 18)( 3, 19)( 4, 20)( 5, 21)( 6, 22)( 7, 23)( 8, 24)
( 9, 25)( 10, 26)( 11, 27)( 12, 28)( 13, 29)( 14, 30)( 15, 31)( 16, 32)
( 33, 49)( 34, 50)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)
( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)
( 65, 81)( 66, 82)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)
( 73, 89)( 74, 90)( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)( 80, 96)
( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)
(105,121)(106,122)(107,123)(108,124)(109,125)(110,126)(111,127)(112,128)
(129,145)(130,146)(131,147)(132,148)(133,149)(134,150)(135,151)(136,152)
(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)
(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)
(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)(176,192)
(193,209)(194,210)(195,211)(196,212)(197,213)(198,214)(199,215)(200,216)
(201,217)(202,218)(203,219)(204,220)(205,221)(206,222)(207,223)(208,224)
(225,241)(226,242)(227,243)(228,244)(229,245)(230,246)(231,247)(232,248)
(233,249)(234,250)(235,251)(236,252)(237,253)(238,254)(239,255)(240,256)
(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)(264,280)
(265,281)(266,282)(267,283)(268,284)(269,285)(270,286)(271,287)(272,288)
(289,305)(290,306)(291,307)(292,308)(293,309)(294,310)(295,311)(296,312)
(297,313)(298,314)(299,315)(300,316)(301,317)(302,318)(303,319)(304,320)
(321,337)(322,338)(323,339)(324,340)(325,341)(326,342)(327,343)(328,344)
(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)(336,352)
(353,369)(354,370)(355,371)(356,372)(357,373)(358,374)(359,375)(360,376)
(361,377)(362,378)(363,379)(364,380)(365,381)(366,382)(367,383)(368,384)
(385,401)(386,402)(387,403)(388,404)(389,405)(390,406)(391,407)(392,408)
(393,409)(394,410)(395,411)(396,412)(397,413)(398,414)(399,415)(400,416)
(417,433)(418,434)(419,435)(420,436)(421,437)(422,438)(423,439)(424,440)
(425,441)(426,442)(427,443)(428,444)(429,445)(430,446)(431,447)(432,448)
(449,465)(450,466)(451,467)(452,468)(453,469)(454,470)(455,471)(456,472)
(457,473)(458,474)(459,475)(460,476)(461,477)(462,478)(463,479)(464,480)
(481,497)(482,498)(483,499)(484,500)(485,501)(486,502)(487,503)(488,504)
(489,505)(490,506)(491,507)(492,508)(493,509)(494,510)(495,511)(496,512)
(513,529)(514,530)(515,531)(516,532)(517,533)(518,534)(519,535)(520,536)
(521,537)(522,538)(523,539)(524,540)(525,541)(526,542)(527,543)(528,544)
(545,561)(546,562)(547,563)(548,564)(549,565)(550,566)(551,567)(552,568)
(553,569)(554,570)(555,571)(556,572)(557,573)(558,574)(559,575)(560,576);;
s1 := ( 1,289)( 2,290)( 3,292)( 4,291)( 5,295)( 6,296)( 7,293)( 8,294)
( 9,297)( 10,298)( 11,300)( 12,299)( 13,303)( 14,304)( 15,301)( 16,302)
( 17,313)( 18,314)( 19,316)( 20,315)( 21,319)( 22,320)( 23,317)( 24,318)
( 25,305)( 26,306)( 27,308)( 28,307)( 29,311)( 30,312)( 31,309)( 32,310)
( 33,353)( 34,354)( 35,356)( 36,355)( 37,359)( 38,360)( 39,357)( 40,358)
( 41,361)( 42,362)( 43,364)( 44,363)( 45,367)( 46,368)( 47,365)( 48,366)
( 49,377)( 50,378)( 51,380)( 52,379)( 53,383)( 54,384)( 55,381)( 56,382)
( 57,369)( 58,370)( 59,372)( 60,371)( 61,375)( 62,376)( 63,373)( 64,374)
( 65,321)( 66,322)( 67,324)( 68,323)( 69,327)( 70,328)( 71,325)( 72,326)
( 73,329)( 74,330)( 75,332)( 76,331)( 77,335)( 78,336)( 79,333)( 80,334)
( 81,345)( 82,346)( 83,348)( 84,347)( 85,351)( 86,352)( 87,349)( 88,350)
( 89,337)( 90,338)( 91,340)( 92,339)( 93,343)( 94,344)( 95,341)( 96,342)
( 97,481)( 98,482)( 99,484)(100,483)(101,487)(102,488)(103,485)(104,486)
(105,489)(106,490)(107,492)(108,491)(109,495)(110,496)(111,493)(112,494)
(113,505)(114,506)(115,508)(116,507)(117,511)(118,512)(119,509)(120,510)
(121,497)(122,498)(123,500)(124,499)(125,503)(126,504)(127,501)(128,502)
(129,545)(130,546)(131,548)(132,547)(133,551)(134,552)(135,549)(136,550)
(137,553)(138,554)(139,556)(140,555)(141,559)(142,560)(143,557)(144,558)
(145,569)(146,570)(147,572)(148,571)(149,575)(150,576)(151,573)(152,574)
(153,561)(154,562)(155,564)(156,563)(157,567)(158,568)(159,565)(160,566)
(161,513)(162,514)(163,516)(164,515)(165,519)(166,520)(167,517)(168,518)
(169,521)(170,522)(171,524)(172,523)(173,527)(174,528)(175,525)(176,526)
(177,537)(178,538)(179,540)(180,539)(181,543)(182,544)(183,541)(184,542)
(185,529)(186,530)(187,532)(188,531)(189,535)(190,536)(191,533)(192,534)
(193,385)(194,386)(195,388)(196,387)(197,391)(198,392)(199,389)(200,390)
(201,393)(202,394)(203,396)(204,395)(205,399)(206,400)(207,397)(208,398)
(209,409)(210,410)(211,412)(212,411)(213,415)(214,416)(215,413)(216,414)
(217,401)(218,402)(219,404)(220,403)(221,407)(222,408)(223,405)(224,406)
(225,449)(226,450)(227,452)(228,451)(229,455)(230,456)(231,453)(232,454)
(233,457)(234,458)(235,460)(236,459)(237,463)(238,464)(239,461)(240,462)
(241,473)(242,474)(243,476)(244,475)(245,479)(246,480)(247,477)(248,478)
(249,465)(250,466)(251,468)(252,467)(253,471)(254,472)(255,469)(256,470)
(257,417)(258,418)(259,420)(260,419)(261,423)(262,424)(263,421)(264,422)
(265,425)(266,426)(267,428)(268,427)(269,431)(270,432)(271,429)(272,430)
(273,441)(274,442)(275,444)(276,443)(277,447)(278,448)(279,445)(280,446)
(281,433)(282,434)(283,436)(284,435)(285,439)(286,440)(287,437)(288,438);;
s2 := ( 1,417)( 2,418)( 3,423)( 4,424)( 5,422)( 6,421)( 7,419)( 8,420)
( 9,441)( 10,442)( 11,447)( 12,448)( 13,446)( 14,445)( 15,443)( 16,444)
( 17,433)( 18,434)( 19,439)( 20,440)( 21,438)( 22,437)( 23,435)( 24,436)
( 25,425)( 26,426)( 27,431)( 28,432)( 29,430)( 30,429)( 31,427)( 32,428)
( 33,385)( 34,386)( 35,391)( 36,392)( 37,390)( 38,389)( 39,387)( 40,388)
( 41,409)( 42,410)( 43,415)( 44,416)( 45,414)( 46,413)( 47,411)( 48,412)
( 49,401)( 50,402)( 51,407)( 52,408)( 53,406)( 54,405)( 55,403)( 56,404)
( 57,393)( 58,394)( 59,399)( 60,400)( 61,398)( 62,397)( 63,395)( 64,396)
( 65,449)( 66,450)( 67,455)( 68,456)( 69,454)( 70,453)( 71,451)( 72,452)
( 73,473)( 74,474)( 75,479)( 76,480)( 77,478)( 78,477)( 79,475)( 80,476)
( 81,465)( 82,466)( 83,471)( 84,472)( 85,470)( 86,469)( 87,467)( 88,468)
( 89,457)( 90,458)( 91,463)( 92,464)( 93,462)( 94,461)( 95,459)( 96,460)
( 97,321)( 98,322)( 99,327)(100,328)(101,326)(102,325)(103,323)(104,324)
(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)(112,348)
(113,337)(114,338)(115,343)(116,344)(117,342)(118,341)(119,339)(120,340)
(121,329)(122,330)(123,335)(124,336)(125,334)(126,333)(127,331)(128,332)
(129,289)(130,290)(131,295)(132,296)(133,294)(134,293)(135,291)(136,292)
(137,313)(138,314)(139,319)(140,320)(141,318)(142,317)(143,315)(144,316)
(145,305)(146,306)(147,311)(148,312)(149,310)(150,309)(151,307)(152,308)
(153,297)(154,298)(155,303)(156,304)(157,302)(158,301)(159,299)(160,300)
(161,353)(162,354)(163,359)(164,360)(165,358)(166,357)(167,355)(168,356)
(169,377)(170,378)(171,383)(172,384)(173,382)(174,381)(175,379)(176,380)
(177,369)(178,370)(179,375)(180,376)(181,374)(182,373)(183,371)(184,372)
(185,361)(186,362)(187,367)(188,368)(189,366)(190,365)(191,363)(192,364)
(193,513)(194,514)(195,519)(196,520)(197,518)(198,517)(199,515)(200,516)
(201,537)(202,538)(203,543)(204,544)(205,542)(206,541)(207,539)(208,540)
(209,529)(210,530)(211,535)(212,536)(213,534)(214,533)(215,531)(216,532)
(217,521)(218,522)(219,527)(220,528)(221,526)(222,525)(223,523)(224,524)
(225,481)(226,482)(227,487)(228,488)(229,486)(230,485)(231,483)(232,484)
(233,505)(234,506)(235,511)(236,512)(237,510)(238,509)(239,507)(240,508)
(241,497)(242,498)(243,503)(244,504)(245,502)(246,501)(247,499)(248,500)
(249,489)(250,490)(251,495)(252,496)(253,494)(254,493)(255,491)(256,492)
(257,545)(258,546)(259,551)(260,552)(261,550)(262,549)(263,547)(264,548)
(265,569)(266,570)(267,575)(268,576)(269,574)(270,573)(271,571)(272,572)
(273,561)(274,562)(275,567)(276,568)(277,566)(278,565)(279,563)(280,564)
(281,553)(282,554)(283,559)(284,560)(285,558)(286,557)(287,555)(288,556);;
s3 := ( 1, 3)( 2, 4)( 5, 6)( 9, 11)( 10, 12)( 13, 14)( 17, 19)( 18, 20)
( 21, 22)( 25, 27)( 26, 28)( 29, 30)( 33, 35)( 34, 36)( 37, 38)( 41, 43)
( 42, 44)( 45, 46)( 49, 51)( 50, 52)( 53, 54)( 57, 59)( 58, 60)( 61, 62)
( 65, 67)( 66, 68)( 69, 70)( 73, 75)( 74, 76)( 77, 78)( 81, 83)( 82, 84)
( 85, 86)( 89, 91)( 90, 92)( 93, 94)( 97,195)( 98,196)( 99,193)(100,194)
(101,198)(102,197)(103,199)(104,200)(105,203)(106,204)(107,201)(108,202)
(109,206)(110,205)(111,207)(112,208)(113,211)(114,212)(115,209)(116,210)
(117,214)(118,213)(119,215)(120,216)(121,219)(122,220)(123,217)(124,218)
(125,222)(126,221)(127,223)(128,224)(129,227)(130,228)(131,225)(132,226)
(133,230)(134,229)(135,231)(136,232)(137,235)(138,236)(139,233)(140,234)
(141,238)(142,237)(143,239)(144,240)(145,243)(146,244)(147,241)(148,242)
(149,246)(150,245)(151,247)(152,248)(153,251)(154,252)(155,249)(156,250)
(157,254)(158,253)(159,255)(160,256)(161,259)(162,260)(163,257)(164,258)
(165,262)(166,261)(167,263)(168,264)(169,267)(170,268)(171,265)(172,266)
(173,270)(174,269)(175,271)(176,272)(177,275)(178,276)(179,273)(180,274)
(181,278)(182,277)(183,279)(184,280)(185,283)(186,284)(187,281)(188,282)
(189,286)(190,285)(191,287)(192,288)(289,292)(290,291)(295,296)(297,300)
(298,299)(303,304)(305,308)(306,307)(311,312)(313,316)(314,315)(319,320)
(321,324)(322,323)(327,328)(329,332)(330,331)(335,336)(337,340)(338,339)
(343,344)(345,348)(346,347)(351,352)(353,356)(354,355)(359,360)(361,364)
(362,363)(367,368)(369,372)(370,371)(375,376)(377,380)(378,379)(383,384)
(385,484)(386,483)(387,482)(388,481)(389,485)(390,486)(391,488)(392,487)
(393,492)(394,491)(395,490)(396,489)(397,493)(398,494)(399,496)(400,495)
(401,500)(402,499)(403,498)(404,497)(405,501)(406,502)(407,504)(408,503)
(409,508)(410,507)(411,506)(412,505)(413,509)(414,510)(415,512)(416,511)
(417,516)(418,515)(419,514)(420,513)(421,517)(422,518)(423,520)(424,519)
(425,524)(426,523)(427,522)(428,521)(429,525)(430,526)(431,528)(432,527)
(433,532)(434,531)(435,530)(436,529)(437,533)(438,534)(439,536)(440,535)
(441,540)(442,539)(443,538)(444,537)(445,541)(446,542)(447,544)(448,543)
(449,548)(450,547)(451,546)(452,545)(453,549)(454,550)(455,552)(456,551)
(457,556)(458,555)(459,554)(460,553)(461,557)(462,558)(463,560)(464,559)
(465,564)(466,563)(467,562)(468,561)(469,565)(470,566)(471,568)(472,567)
(473,572)(474,571)(475,570)(476,569)(477,573)(478,574)(479,576)(480,575);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1, 17)( 2, 18)( 3, 19)( 4, 20)( 5, 21)( 6, 22)( 7, 23)
( 8, 24)( 9, 25)( 10, 26)( 11, 27)( 12, 28)( 13, 29)( 14, 30)( 15, 31)
( 16, 32)( 33, 49)( 34, 50)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)
( 40, 56)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)
( 48, 64)( 65, 81)( 66, 82)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)
( 72, 88)( 73, 89)( 74, 90)( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)
( 80, 96)( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)
(104,120)(105,121)(106,122)(107,123)(108,124)(109,125)(110,126)(111,127)
(112,128)(129,145)(130,146)(131,147)(132,148)(133,149)(134,150)(135,151)
(136,152)(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)
(144,160)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)
(168,184)(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)
(176,192)(193,209)(194,210)(195,211)(196,212)(197,213)(198,214)(199,215)
(200,216)(201,217)(202,218)(203,219)(204,220)(205,221)(206,222)(207,223)
(208,224)(225,241)(226,242)(227,243)(228,244)(229,245)(230,246)(231,247)
(232,248)(233,249)(234,250)(235,251)(236,252)(237,253)(238,254)(239,255)
(240,256)(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)
(264,280)(265,281)(266,282)(267,283)(268,284)(269,285)(270,286)(271,287)
(272,288)(289,305)(290,306)(291,307)(292,308)(293,309)(294,310)(295,311)
(296,312)(297,313)(298,314)(299,315)(300,316)(301,317)(302,318)(303,319)
(304,320)(321,337)(322,338)(323,339)(324,340)(325,341)(326,342)(327,343)
(328,344)(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)
(336,352)(353,369)(354,370)(355,371)(356,372)(357,373)(358,374)(359,375)
(360,376)(361,377)(362,378)(363,379)(364,380)(365,381)(366,382)(367,383)
(368,384)(385,401)(386,402)(387,403)(388,404)(389,405)(390,406)(391,407)
(392,408)(393,409)(394,410)(395,411)(396,412)(397,413)(398,414)(399,415)
(400,416)(417,433)(418,434)(419,435)(420,436)(421,437)(422,438)(423,439)
(424,440)(425,441)(426,442)(427,443)(428,444)(429,445)(430,446)(431,447)
(432,448)(449,465)(450,466)(451,467)(452,468)(453,469)(454,470)(455,471)
(456,472)(457,473)(458,474)(459,475)(460,476)(461,477)(462,478)(463,479)
(464,480)(481,497)(482,498)(483,499)(484,500)(485,501)(486,502)(487,503)
(488,504)(489,505)(490,506)(491,507)(492,508)(493,509)(494,510)(495,511)
(496,512)(513,529)(514,530)(515,531)(516,532)(517,533)(518,534)(519,535)
(520,536)(521,537)(522,538)(523,539)(524,540)(525,541)(526,542)(527,543)
(528,544)(545,561)(546,562)(547,563)(548,564)(549,565)(550,566)(551,567)
(552,568)(553,569)(554,570)(555,571)(556,572)(557,573)(558,574)(559,575)
(560,576);
s1 := Sym(576)!( 1,289)( 2,290)( 3,292)( 4,291)( 5,295)( 6,296)( 7,293)
( 8,294)( 9,297)( 10,298)( 11,300)( 12,299)( 13,303)( 14,304)( 15,301)
( 16,302)( 17,313)( 18,314)( 19,316)( 20,315)( 21,319)( 22,320)( 23,317)
( 24,318)( 25,305)( 26,306)( 27,308)( 28,307)( 29,311)( 30,312)( 31,309)
( 32,310)( 33,353)( 34,354)( 35,356)( 36,355)( 37,359)( 38,360)( 39,357)
( 40,358)( 41,361)( 42,362)( 43,364)( 44,363)( 45,367)( 46,368)( 47,365)
( 48,366)( 49,377)( 50,378)( 51,380)( 52,379)( 53,383)( 54,384)( 55,381)
( 56,382)( 57,369)( 58,370)( 59,372)( 60,371)( 61,375)( 62,376)( 63,373)
( 64,374)( 65,321)( 66,322)( 67,324)( 68,323)( 69,327)( 70,328)( 71,325)
( 72,326)( 73,329)( 74,330)( 75,332)( 76,331)( 77,335)( 78,336)( 79,333)
( 80,334)( 81,345)( 82,346)( 83,348)( 84,347)( 85,351)( 86,352)( 87,349)
( 88,350)( 89,337)( 90,338)( 91,340)( 92,339)( 93,343)( 94,344)( 95,341)
( 96,342)( 97,481)( 98,482)( 99,484)(100,483)(101,487)(102,488)(103,485)
(104,486)(105,489)(106,490)(107,492)(108,491)(109,495)(110,496)(111,493)
(112,494)(113,505)(114,506)(115,508)(116,507)(117,511)(118,512)(119,509)
(120,510)(121,497)(122,498)(123,500)(124,499)(125,503)(126,504)(127,501)
(128,502)(129,545)(130,546)(131,548)(132,547)(133,551)(134,552)(135,549)
(136,550)(137,553)(138,554)(139,556)(140,555)(141,559)(142,560)(143,557)
(144,558)(145,569)(146,570)(147,572)(148,571)(149,575)(150,576)(151,573)
(152,574)(153,561)(154,562)(155,564)(156,563)(157,567)(158,568)(159,565)
(160,566)(161,513)(162,514)(163,516)(164,515)(165,519)(166,520)(167,517)
(168,518)(169,521)(170,522)(171,524)(172,523)(173,527)(174,528)(175,525)
(176,526)(177,537)(178,538)(179,540)(180,539)(181,543)(182,544)(183,541)
(184,542)(185,529)(186,530)(187,532)(188,531)(189,535)(190,536)(191,533)
(192,534)(193,385)(194,386)(195,388)(196,387)(197,391)(198,392)(199,389)
(200,390)(201,393)(202,394)(203,396)(204,395)(205,399)(206,400)(207,397)
(208,398)(209,409)(210,410)(211,412)(212,411)(213,415)(214,416)(215,413)
(216,414)(217,401)(218,402)(219,404)(220,403)(221,407)(222,408)(223,405)
(224,406)(225,449)(226,450)(227,452)(228,451)(229,455)(230,456)(231,453)
(232,454)(233,457)(234,458)(235,460)(236,459)(237,463)(238,464)(239,461)
(240,462)(241,473)(242,474)(243,476)(244,475)(245,479)(246,480)(247,477)
(248,478)(249,465)(250,466)(251,468)(252,467)(253,471)(254,472)(255,469)
(256,470)(257,417)(258,418)(259,420)(260,419)(261,423)(262,424)(263,421)
(264,422)(265,425)(266,426)(267,428)(268,427)(269,431)(270,432)(271,429)
(272,430)(273,441)(274,442)(275,444)(276,443)(277,447)(278,448)(279,445)
(280,446)(281,433)(282,434)(283,436)(284,435)(285,439)(286,440)(287,437)
(288,438);
s2 := Sym(576)!( 1,417)( 2,418)( 3,423)( 4,424)( 5,422)( 6,421)( 7,419)
( 8,420)( 9,441)( 10,442)( 11,447)( 12,448)( 13,446)( 14,445)( 15,443)
( 16,444)( 17,433)( 18,434)( 19,439)( 20,440)( 21,438)( 22,437)( 23,435)
( 24,436)( 25,425)( 26,426)( 27,431)( 28,432)( 29,430)( 30,429)( 31,427)
( 32,428)( 33,385)( 34,386)( 35,391)( 36,392)( 37,390)( 38,389)( 39,387)
( 40,388)( 41,409)( 42,410)( 43,415)( 44,416)( 45,414)( 46,413)( 47,411)
( 48,412)( 49,401)( 50,402)( 51,407)( 52,408)( 53,406)( 54,405)( 55,403)
( 56,404)( 57,393)( 58,394)( 59,399)( 60,400)( 61,398)( 62,397)( 63,395)
( 64,396)( 65,449)( 66,450)( 67,455)( 68,456)( 69,454)( 70,453)( 71,451)
( 72,452)( 73,473)( 74,474)( 75,479)( 76,480)( 77,478)( 78,477)( 79,475)
( 80,476)( 81,465)( 82,466)( 83,471)( 84,472)( 85,470)( 86,469)( 87,467)
( 88,468)( 89,457)( 90,458)( 91,463)( 92,464)( 93,462)( 94,461)( 95,459)
( 96,460)( 97,321)( 98,322)( 99,327)(100,328)(101,326)(102,325)(103,323)
(104,324)(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)
(112,348)(113,337)(114,338)(115,343)(116,344)(117,342)(118,341)(119,339)
(120,340)(121,329)(122,330)(123,335)(124,336)(125,334)(126,333)(127,331)
(128,332)(129,289)(130,290)(131,295)(132,296)(133,294)(134,293)(135,291)
(136,292)(137,313)(138,314)(139,319)(140,320)(141,318)(142,317)(143,315)
(144,316)(145,305)(146,306)(147,311)(148,312)(149,310)(150,309)(151,307)
(152,308)(153,297)(154,298)(155,303)(156,304)(157,302)(158,301)(159,299)
(160,300)(161,353)(162,354)(163,359)(164,360)(165,358)(166,357)(167,355)
(168,356)(169,377)(170,378)(171,383)(172,384)(173,382)(174,381)(175,379)
(176,380)(177,369)(178,370)(179,375)(180,376)(181,374)(182,373)(183,371)
(184,372)(185,361)(186,362)(187,367)(188,368)(189,366)(190,365)(191,363)
(192,364)(193,513)(194,514)(195,519)(196,520)(197,518)(198,517)(199,515)
(200,516)(201,537)(202,538)(203,543)(204,544)(205,542)(206,541)(207,539)
(208,540)(209,529)(210,530)(211,535)(212,536)(213,534)(214,533)(215,531)
(216,532)(217,521)(218,522)(219,527)(220,528)(221,526)(222,525)(223,523)
(224,524)(225,481)(226,482)(227,487)(228,488)(229,486)(230,485)(231,483)
(232,484)(233,505)(234,506)(235,511)(236,512)(237,510)(238,509)(239,507)
(240,508)(241,497)(242,498)(243,503)(244,504)(245,502)(246,501)(247,499)
(248,500)(249,489)(250,490)(251,495)(252,496)(253,494)(254,493)(255,491)
(256,492)(257,545)(258,546)(259,551)(260,552)(261,550)(262,549)(263,547)
(264,548)(265,569)(266,570)(267,575)(268,576)(269,574)(270,573)(271,571)
(272,572)(273,561)(274,562)(275,567)(276,568)(277,566)(278,565)(279,563)
(280,564)(281,553)(282,554)(283,559)(284,560)(285,558)(286,557)(287,555)
(288,556);
s3 := Sym(576)!( 1, 3)( 2, 4)( 5, 6)( 9, 11)( 10, 12)( 13, 14)( 17, 19)
( 18, 20)( 21, 22)( 25, 27)( 26, 28)( 29, 30)( 33, 35)( 34, 36)( 37, 38)
( 41, 43)( 42, 44)( 45, 46)( 49, 51)( 50, 52)( 53, 54)( 57, 59)( 58, 60)
( 61, 62)( 65, 67)( 66, 68)( 69, 70)( 73, 75)( 74, 76)( 77, 78)( 81, 83)
( 82, 84)( 85, 86)( 89, 91)( 90, 92)( 93, 94)( 97,195)( 98,196)( 99,193)
(100,194)(101,198)(102,197)(103,199)(104,200)(105,203)(106,204)(107,201)
(108,202)(109,206)(110,205)(111,207)(112,208)(113,211)(114,212)(115,209)
(116,210)(117,214)(118,213)(119,215)(120,216)(121,219)(122,220)(123,217)
(124,218)(125,222)(126,221)(127,223)(128,224)(129,227)(130,228)(131,225)
(132,226)(133,230)(134,229)(135,231)(136,232)(137,235)(138,236)(139,233)
(140,234)(141,238)(142,237)(143,239)(144,240)(145,243)(146,244)(147,241)
(148,242)(149,246)(150,245)(151,247)(152,248)(153,251)(154,252)(155,249)
(156,250)(157,254)(158,253)(159,255)(160,256)(161,259)(162,260)(163,257)
(164,258)(165,262)(166,261)(167,263)(168,264)(169,267)(170,268)(171,265)
(172,266)(173,270)(174,269)(175,271)(176,272)(177,275)(178,276)(179,273)
(180,274)(181,278)(182,277)(183,279)(184,280)(185,283)(186,284)(187,281)
(188,282)(189,286)(190,285)(191,287)(192,288)(289,292)(290,291)(295,296)
(297,300)(298,299)(303,304)(305,308)(306,307)(311,312)(313,316)(314,315)
(319,320)(321,324)(322,323)(327,328)(329,332)(330,331)(335,336)(337,340)
(338,339)(343,344)(345,348)(346,347)(351,352)(353,356)(354,355)(359,360)
(361,364)(362,363)(367,368)(369,372)(370,371)(375,376)(377,380)(378,379)
(383,384)(385,484)(386,483)(387,482)(388,481)(389,485)(390,486)(391,488)
(392,487)(393,492)(394,491)(395,490)(396,489)(397,493)(398,494)(399,496)
(400,495)(401,500)(402,499)(403,498)(404,497)(405,501)(406,502)(407,504)
(408,503)(409,508)(410,507)(411,506)(412,505)(413,509)(414,510)(415,512)
(416,511)(417,516)(418,515)(419,514)(420,513)(421,517)(422,518)(423,520)
(424,519)(425,524)(426,523)(427,522)(428,521)(429,525)(430,526)(431,528)
(432,527)(433,532)(434,531)(435,530)(436,529)(437,533)(438,534)(439,536)
(440,535)(441,540)(442,539)(443,538)(444,537)(445,541)(446,542)(447,544)
(448,543)(449,548)(450,547)(451,546)(452,545)(453,549)(454,550)(455,552)
(456,551)(457,556)(458,555)(459,554)(460,553)(461,557)(462,558)(463,560)
(464,559)(465,564)(466,563)(467,562)(468,561)(469,565)(470,566)(471,568)
(472,567)(473,572)(474,571)(475,570)(476,569)(477,573)(478,574)(479,576)
(480,575);
poly := sub<Sym(576)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 >;
References : None.
to this polytope