Polytope of Type {24,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98791)
Rank : 4
Schlafli Type : {24,4,6}
Number of vertices, edges, etc : 24, 48, 12, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {12,4,6}*576
3-fold quotients : {24,4,2}*384b, {8,4,6}*384b
4-fold quotients : {12,2,6}*288, {6,4,6}*288
6-fold quotients : {12,4,2}*192a, {4,4,6}*192
8-fold quotients : {12,2,3}*144, {6,2,6}*144
9-fold quotients : {8,4,2}*128b
12-fold quotients : {12,2,2}*96, {2,4,6}*96a, {4,2,6}*96, {6,4,2}*96a
16-fold quotients : {3,2,6}*72, {6,2,3}*72
18-fold quotients : {4,4,2}*64
24-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
32-fold quotients : {3,2,3}*36
36-fold quotients : {2,4,2}*32, {4,2,2}*32
48-fold quotients : {2,2,3}*24, {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,361)( 2,368)( 3,366)( 4,367)( 5,365)( 6,363)( 7,364)( 8,362)
( 9,369)( 10,370)( 11,377)( 12,375)( 13,376)( 14,374)( 15,372)( 16,373)
( 17,371)( 18,378)( 19,388)( 20,395)( 21,393)( 22,394)( 23,392)( 24,390)
( 25,391)( 26,389)( 27,396)( 28,379)( 29,386)( 30,384)( 31,385)( 32,383)
( 33,381)( 34,382)( 35,380)( 36,387)( 37,406)( 38,413)( 39,411)( 40,412)
( 41,410)( 42,408)( 43,409)( 44,407)( 45,414)( 46,397)( 47,404)( 48,402)
( 49,403)( 50,401)( 51,399)( 52,400)( 53,398)( 54,405)( 55,415)( 56,422)
( 57,420)( 58,421)( 59,419)( 60,417)( 61,418)( 62,416)( 63,423)( 64,424)
( 65,431)( 66,429)( 67,430)( 68,428)( 69,426)( 70,427)( 71,425)( 72,432)
( 73,289)( 74,296)( 75,294)( 76,295)( 77,293)( 78,291)( 79,292)( 80,290)
( 81,297)( 82,298)( 83,305)( 84,303)( 85,304)( 86,302)( 87,300)( 88,301)
( 89,299)( 90,306)( 91,316)( 92,323)( 93,321)( 94,322)( 95,320)( 96,318)
( 97,319)( 98,317)( 99,324)(100,307)(101,314)(102,312)(103,313)(104,311)
(105,309)(106,310)(107,308)(108,315)(109,334)(110,341)(111,339)(112,340)
(113,338)(114,336)(115,337)(116,335)(117,342)(118,325)(119,332)(120,330)
(121,331)(122,329)(123,327)(124,328)(125,326)(126,333)(127,343)(128,350)
(129,348)(130,349)(131,347)(132,345)(133,346)(134,344)(135,351)(136,352)
(137,359)(138,357)(139,358)(140,356)(141,354)(142,355)(143,353)(144,360)
(145,505)(146,512)(147,510)(148,511)(149,509)(150,507)(151,508)(152,506)
(153,513)(154,514)(155,521)(156,519)(157,520)(158,518)(159,516)(160,517)
(161,515)(162,522)(163,532)(164,539)(165,537)(166,538)(167,536)(168,534)
(169,535)(170,533)(171,540)(172,523)(173,530)(174,528)(175,529)(176,527)
(177,525)(178,526)(179,524)(180,531)(181,550)(182,557)(183,555)(184,556)
(185,554)(186,552)(187,553)(188,551)(189,558)(190,541)(191,548)(192,546)
(193,547)(194,545)(195,543)(196,544)(197,542)(198,549)(199,559)(200,566)
(201,564)(202,565)(203,563)(204,561)(205,562)(206,560)(207,567)(208,568)
(209,575)(210,573)(211,574)(212,572)(213,570)(214,571)(215,569)(216,576)
(217,433)(218,440)(219,438)(220,439)(221,437)(222,435)(223,436)(224,434)
(225,441)(226,442)(227,449)(228,447)(229,448)(230,446)(231,444)(232,445)
(233,443)(234,450)(235,460)(236,467)(237,465)(238,466)(239,464)(240,462)
(241,463)(242,461)(243,468)(244,451)(245,458)(246,456)(247,457)(248,455)
(249,453)(250,454)(251,452)(252,459)(253,478)(254,485)(255,483)(256,484)
(257,482)(258,480)(259,481)(260,479)(261,486)(262,469)(263,476)(264,474)
(265,475)(266,473)(267,471)(268,472)(269,470)(270,477)(271,487)(272,494)
(273,492)(274,493)(275,491)(276,489)(277,490)(278,488)(279,495)(280,496)
(281,503)(282,501)(283,502)(284,500)(285,498)(286,499)(287,497)(288,504);;
s1 := ( 1, 76)( 2, 74)( 3, 81)( 4, 73)( 5, 80)( 6, 78)( 7, 79)( 8, 77)
( 9, 75)( 10, 85)( 11, 83)( 12, 90)( 13, 82)( 14, 89)( 15, 87)( 16, 88)
( 17, 86)( 18, 84)( 19, 94)( 20, 92)( 21, 99)( 22, 91)( 23, 98)( 24, 96)
( 25, 97)( 26, 95)( 27, 93)( 28,103)( 29,101)( 30,108)( 31,100)( 32,107)
( 33,105)( 34,106)( 35,104)( 36,102)( 37,121)( 38,119)( 39,126)( 40,118)
( 41,125)( 42,123)( 43,124)( 44,122)( 45,120)( 46,112)( 47,110)( 48,117)
( 49,109)( 50,116)( 51,114)( 52,115)( 53,113)( 54,111)( 55,139)( 56,137)
( 57,144)( 58,136)( 59,143)( 60,141)( 61,142)( 62,140)( 63,138)( 64,130)
( 65,128)( 66,135)( 67,127)( 68,134)( 69,132)( 70,133)( 71,131)( 72,129)
(145,238)(146,236)(147,243)(148,235)(149,242)(150,240)(151,241)(152,239)
(153,237)(154,247)(155,245)(156,252)(157,244)(158,251)(159,249)(160,250)
(161,248)(162,246)(163,220)(164,218)(165,225)(166,217)(167,224)(168,222)
(169,223)(170,221)(171,219)(172,229)(173,227)(174,234)(175,226)(176,233)
(177,231)(178,232)(179,230)(180,228)(181,283)(182,281)(183,288)(184,280)
(185,287)(186,285)(187,286)(188,284)(189,282)(190,274)(191,272)(192,279)
(193,271)(194,278)(195,276)(196,277)(197,275)(198,273)(199,265)(200,263)
(201,270)(202,262)(203,269)(204,267)(205,268)(206,266)(207,264)(208,256)
(209,254)(210,261)(211,253)(212,260)(213,258)(214,259)(215,257)(216,255)
(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)
(433,571)(434,569)(435,576)(436,568)(437,575)(438,573)(439,574)(440,572)
(441,570)(442,562)(443,560)(444,567)(445,559)(446,566)(447,564)(448,565)
(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)(455,557)(456,555)
(457,556)(458,554)(459,552)(460,544)(461,542)(462,549)(463,541)(464,548)
(465,546)(466,547)(467,545)(468,543)(469,535)(470,533)(471,540)(472,532)
(473,539)(474,537)(475,538)(476,536)(477,534)(478,526)(479,524)(480,531)
(481,523)(482,530)(483,528)(484,529)(485,527)(486,525)(487,517)(488,515)
(489,522)(490,514)(491,521)(492,519)(493,520)(494,518)(495,516)(496,508)
(497,506)(498,513)(499,505)(500,512)(501,510)(502,511)(503,509)(504,507);;
s2 := ( 1,217)( 2,222)( 3,224)( 4,220)( 5,225)( 6,218)( 7,223)( 8,219)
( 9,221)( 10,226)( 11,231)( 12,233)( 13,229)( 14,234)( 15,227)( 16,232)
( 17,228)( 18,230)( 19,235)( 20,240)( 21,242)( 22,238)( 23,243)( 24,236)
( 25,241)( 26,237)( 27,239)( 28,244)( 29,249)( 30,251)( 31,247)( 32,252)
( 33,245)( 34,250)( 35,246)( 36,248)( 37,262)( 38,267)( 39,269)( 40,265)
( 41,270)( 42,263)( 43,268)( 44,264)( 45,266)( 46,253)( 47,258)( 48,260)
( 49,256)( 50,261)( 51,254)( 52,259)( 53,255)( 54,257)( 55,280)( 56,285)
( 57,287)( 58,283)( 59,288)( 60,281)( 61,286)( 62,282)( 63,284)( 64,271)
( 65,276)( 66,278)( 67,274)( 68,279)( 69,272)( 70,277)( 71,273)( 72,275)
( 73,145)( 74,150)( 75,152)( 76,148)( 77,153)( 78,146)( 79,151)( 80,147)
( 81,149)( 82,154)( 83,159)( 84,161)( 85,157)( 86,162)( 87,155)( 88,160)
( 89,156)( 90,158)( 91,163)( 92,168)( 93,170)( 94,166)( 95,171)( 96,164)
( 97,169)( 98,165)( 99,167)(100,172)(101,177)(102,179)(103,175)(104,180)
(105,173)(106,178)(107,174)(108,176)(109,190)(110,195)(111,197)(112,193)
(113,198)(114,191)(115,196)(116,192)(117,194)(118,181)(119,186)(120,188)
(121,184)(122,189)(123,182)(124,187)(125,183)(126,185)(127,208)(128,213)
(129,215)(130,211)(131,216)(132,209)(133,214)(134,210)(135,212)(136,199)
(137,204)(138,206)(139,202)(140,207)(141,200)(142,205)(143,201)(144,203)
(289,505)(290,510)(291,512)(292,508)(293,513)(294,506)(295,511)(296,507)
(297,509)(298,514)(299,519)(300,521)(301,517)(302,522)(303,515)(304,520)
(305,516)(306,518)(307,523)(308,528)(309,530)(310,526)(311,531)(312,524)
(313,529)(314,525)(315,527)(316,532)(317,537)(318,539)(319,535)(320,540)
(321,533)(322,538)(323,534)(324,536)(325,550)(326,555)(327,557)(328,553)
(329,558)(330,551)(331,556)(332,552)(333,554)(334,541)(335,546)(336,548)
(337,544)(338,549)(339,542)(340,547)(341,543)(342,545)(343,568)(344,573)
(345,575)(346,571)(347,576)(348,569)(349,574)(350,570)(351,572)(352,559)
(353,564)(354,566)(355,562)(356,567)(357,560)(358,565)(359,561)(360,563)
(361,433)(362,438)(363,440)(364,436)(365,441)(366,434)(367,439)(368,435)
(369,437)(370,442)(371,447)(372,449)(373,445)(374,450)(375,443)(376,448)
(377,444)(378,446)(379,451)(380,456)(381,458)(382,454)(383,459)(384,452)
(385,457)(386,453)(387,455)(388,460)(389,465)(390,467)(391,463)(392,468)
(393,461)(394,466)(395,462)(396,464)(397,478)(398,483)(399,485)(400,481)
(401,486)(402,479)(403,484)(404,480)(405,482)(406,469)(407,474)(408,476)
(409,472)(410,477)(411,470)(412,475)(413,471)(414,473)(415,496)(416,501)
(417,503)(418,499)(419,504)(420,497)(421,502)(422,498)(423,500)(424,487)
(425,492)(426,494)(427,490)(428,495)(429,488)(430,493)(431,489)(432,491);;
s3 := ( 1, 77)( 2, 79)( 3, 75)( 4, 80)( 5, 73)( 6, 78)( 7, 74)( 8, 76)
( 9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)( 16, 83)
( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)( 24, 96)
( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)( 32,100)
( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)( 40,116)
( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)( 48,120)
( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)( 56,133)
( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)( 64,140)
( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)( 72,144)
(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)(152,220)
(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)(160,227)
(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)(168,240)
(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)(176,244)
(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)(184,260)
(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)(192,264)
(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)(200,277)
(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)(208,284)
(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)(216,288)
(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)(296,364)
(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)(304,371)
(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)(312,384)
(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)(320,388)
(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)(328,404)
(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)(336,408)
(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)(344,421)
(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)(352,428)
(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)(360,432)
(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)(440,508)
(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)(448,515)
(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)(456,528)
(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)(464,532)
(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)(472,548)
(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)(480,552)
(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)(488,565)
(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)(496,572)
(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)(504,576);;
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*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,361)( 2,368)( 3,366)( 4,367)( 5,365)( 6,363)( 7,364)
( 8,362)( 9,369)( 10,370)( 11,377)( 12,375)( 13,376)( 14,374)( 15,372)
( 16,373)( 17,371)( 18,378)( 19,388)( 20,395)( 21,393)( 22,394)( 23,392)
( 24,390)( 25,391)( 26,389)( 27,396)( 28,379)( 29,386)( 30,384)( 31,385)
( 32,383)( 33,381)( 34,382)( 35,380)( 36,387)( 37,406)( 38,413)( 39,411)
( 40,412)( 41,410)( 42,408)( 43,409)( 44,407)( 45,414)( 46,397)( 47,404)
( 48,402)( 49,403)( 50,401)( 51,399)( 52,400)( 53,398)( 54,405)( 55,415)
( 56,422)( 57,420)( 58,421)( 59,419)( 60,417)( 61,418)( 62,416)( 63,423)
( 64,424)( 65,431)( 66,429)( 67,430)( 68,428)( 69,426)( 70,427)( 71,425)
( 72,432)( 73,289)( 74,296)( 75,294)( 76,295)( 77,293)( 78,291)( 79,292)
( 80,290)( 81,297)( 82,298)( 83,305)( 84,303)( 85,304)( 86,302)( 87,300)
( 88,301)( 89,299)( 90,306)( 91,316)( 92,323)( 93,321)( 94,322)( 95,320)
( 96,318)( 97,319)( 98,317)( 99,324)(100,307)(101,314)(102,312)(103,313)
(104,311)(105,309)(106,310)(107,308)(108,315)(109,334)(110,341)(111,339)
(112,340)(113,338)(114,336)(115,337)(116,335)(117,342)(118,325)(119,332)
(120,330)(121,331)(122,329)(123,327)(124,328)(125,326)(126,333)(127,343)
(128,350)(129,348)(130,349)(131,347)(132,345)(133,346)(134,344)(135,351)
(136,352)(137,359)(138,357)(139,358)(140,356)(141,354)(142,355)(143,353)
(144,360)(145,505)(146,512)(147,510)(148,511)(149,509)(150,507)(151,508)
(152,506)(153,513)(154,514)(155,521)(156,519)(157,520)(158,518)(159,516)
(160,517)(161,515)(162,522)(163,532)(164,539)(165,537)(166,538)(167,536)
(168,534)(169,535)(170,533)(171,540)(172,523)(173,530)(174,528)(175,529)
(176,527)(177,525)(178,526)(179,524)(180,531)(181,550)(182,557)(183,555)
(184,556)(185,554)(186,552)(187,553)(188,551)(189,558)(190,541)(191,548)
(192,546)(193,547)(194,545)(195,543)(196,544)(197,542)(198,549)(199,559)
(200,566)(201,564)(202,565)(203,563)(204,561)(205,562)(206,560)(207,567)
(208,568)(209,575)(210,573)(211,574)(212,572)(213,570)(214,571)(215,569)
(216,576)(217,433)(218,440)(219,438)(220,439)(221,437)(222,435)(223,436)
(224,434)(225,441)(226,442)(227,449)(228,447)(229,448)(230,446)(231,444)
(232,445)(233,443)(234,450)(235,460)(236,467)(237,465)(238,466)(239,464)
(240,462)(241,463)(242,461)(243,468)(244,451)(245,458)(246,456)(247,457)
(248,455)(249,453)(250,454)(251,452)(252,459)(253,478)(254,485)(255,483)
(256,484)(257,482)(258,480)(259,481)(260,479)(261,486)(262,469)(263,476)
(264,474)(265,475)(266,473)(267,471)(268,472)(269,470)(270,477)(271,487)
(272,494)(273,492)(274,493)(275,491)(276,489)(277,490)(278,488)(279,495)
(280,496)(281,503)(282,501)(283,502)(284,500)(285,498)(286,499)(287,497)
(288,504);
s1 := Sym(576)!( 1, 76)( 2, 74)( 3, 81)( 4, 73)( 5, 80)( 6, 78)( 7, 79)
( 8, 77)( 9, 75)( 10, 85)( 11, 83)( 12, 90)( 13, 82)( 14, 89)( 15, 87)
( 16, 88)( 17, 86)( 18, 84)( 19, 94)( 20, 92)( 21, 99)( 22, 91)( 23, 98)
( 24, 96)( 25, 97)( 26, 95)( 27, 93)( 28,103)( 29,101)( 30,108)( 31,100)
( 32,107)( 33,105)( 34,106)( 35,104)( 36,102)( 37,121)( 38,119)( 39,126)
( 40,118)( 41,125)( 42,123)( 43,124)( 44,122)( 45,120)( 46,112)( 47,110)
( 48,117)( 49,109)( 50,116)( 51,114)( 52,115)( 53,113)( 54,111)( 55,139)
( 56,137)( 57,144)( 58,136)( 59,143)( 60,141)( 61,142)( 62,140)( 63,138)
( 64,130)( 65,128)( 66,135)( 67,127)( 68,134)( 69,132)( 70,133)( 71,131)
( 72,129)(145,238)(146,236)(147,243)(148,235)(149,242)(150,240)(151,241)
(152,239)(153,237)(154,247)(155,245)(156,252)(157,244)(158,251)(159,249)
(160,250)(161,248)(162,246)(163,220)(164,218)(165,225)(166,217)(167,224)
(168,222)(169,223)(170,221)(171,219)(172,229)(173,227)(174,234)(175,226)
(176,233)(177,231)(178,232)(179,230)(180,228)(181,283)(182,281)(183,288)
(184,280)(185,287)(186,285)(187,286)(188,284)(189,282)(190,274)(191,272)
(192,279)(193,271)(194,278)(195,276)(196,277)(197,275)(198,273)(199,265)
(200,263)(201,270)(202,262)(203,269)(204,267)(205,268)(206,266)(207,264)
(208,256)(209,254)(210,261)(211,253)(212,260)(213,258)(214,259)(215,257)
(216,255)(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)(433,571)(434,569)(435,576)(436,568)(437,575)(438,573)(439,574)
(440,572)(441,570)(442,562)(443,560)(444,567)(445,559)(446,566)(447,564)
(448,565)(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)(455,557)
(456,555)(457,556)(458,554)(459,552)(460,544)(461,542)(462,549)(463,541)
(464,548)(465,546)(466,547)(467,545)(468,543)(469,535)(470,533)(471,540)
(472,532)(473,539)(474,537)(475,538)(476,536)(477,534)(478,526)(479,524)
(480,531)(481,523)(482,530)(483,528)(484,529)(485,527)(486,525)(487,517)
(488,515)(489,522)(490,514)(491,521)(492,519)(493,520)(494,518)(495,516)
(496,508)(497,506)(498,513)(499,505)(500,512)(501,510)(502,511)(503,509)
(504,507);
s2 := Sym(576)!( 1,217)( 2,222)( 3,224)( 4,220)( 5,225)( 6,218)( 7,223)
( 8,219)( 9,221)( 10,226)( 11,231)( 12,233)( 13,229)( 14,234)( 15,227)
( 16,232)( 17,228)( 18,230)( 19,235)( 20,240)( 21,242)( 22,238)( 23,243)
( 24,236)( 25,241)( 26,237)( 27,239)( 28,244)( 29,249)( 30,251)( 31,247)
( 32,252)( 33,245)( 34,250)( 35,246)( 36,248)( 37,262)( 38,267)( 39,269)
( 40,265)( 41,270)( 42,263)( 43,268)( 44,264)( 45,266)( 46,253)( 47,258)
( 48,260)( 49,256)( 50,261)( 51,254)( 52,259)( 53,255)( 54,257)( 55,280)
( 56,285)( 57,287)( 58,283)( 59,288)( 60,281)( 61,286)( 62,282)( 63,284)
( 64,271)( 65,276)( 66,278)( 67,274)( 68,279)( 69,272)( 70,277)( 71,273)
( 72,275)( 73,145)( 74,150)( 75,152)( 76,148)( 77,153)( 78,146)( 79,151)
( 80,147)( 81,149)( 82,154)( 83,159)( 84,161)( 85,157)( 86,162)( 87,155)
( 88,160)( 89,156)( 90,158)( 91,163)( 92,168)( 93,170)( 94,166)( 95,171)
( 96,164)( 97,169)( 98,165)( 99,167)(100,172)(101,177)(102,179)(103,175)
(104,180)(105,173)(106,178)(107,174)(108,176)(109,190)(110,195)(111,197)
(112,193)(113,198)(114,191)(115,196)(116,192)(117,194)(118,181)(119,186)
(120,188)(121,184)(122,189)(123,182)(124,187)(125,183)(126,185)(127,208)
(128,213)(129,215)(130,211)(131,216)(132,209)(133,214)(134,210)(135,212)
(136,199)(137,204)(138,206)(139,202)(140,207)(141,200)(142,205)(143,201)
(144,203)(289,505)(290,510)(291,512)(292,508)(293,513)(294,506)(295,511)
(296,507)(297,509)(298,514)(299,519)(300,521)(301,517)(302,522)(303,515)
(304,520)(305,516)(306,518)(307,523)(308,528)(309,530)(310,526)(311,531)
(312,524)(313,529)(314,525)(315,527)(316,532)(317,537)(318,539)(319,535)
(320,540)(321,533)(322,538)(323,534)(324,536)(325,550)(326,555)(327,557)
(328,553)(329,558)(330,551)(331,556)(332,552)(333,554)(334,541)(335,546)
(336,548)(337,544)(338,549)(339,542)(340,547)(341,543)(342,545)(343,568)
(344,573)(345,575)(346,571)(347,576)(348,569)(349,574)(350,570)(351,572)
(352,559)(353,564)(354,566)(355,562)(356,567)(357,560)(358,565)(359,561)
(360,563)(361,433)(362,438)(363,440)(364,436)(365,441)(366,434)(367,439)
(368,435)(369,437)(370,442)(371,447)(372,449)(373,445)(374,450)(375,443)
(376,448)(377,444)(378,446)(379,451)(380,456)(381,458)(382,454)(383,459)
(384,452)(385,457)(386,453)(387,455)(388,460)(389,465)(390,467)(391,463)
(392,468)(393,461)(394,466)(395,462)(396,464)(397,478)(398,483)(399,485)
(400,481)(401,486)(402,479)(403,484)(404,480)(405,482)(406,469)(407,474)
(408,476)(409,472)(410,477)(411,470)(412,475)(413,471)(414,473)(415,496)
(416,501)(417,503)(418,499)(419,504)(420,497)(421,502)(422,498)(423,500)
(424,487)(425,492)(426,494)(427,490)(428,495)(429,488)(430,493)(431,489)
(432,491);
s3 := Sym(576)!( 1, 77)( 2, 79)( 3, 75)( 4, 80)( 5, 73)( 6, 78)( 7, 74)
( 8, 76)( 9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)
( 16, 83)( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)
( 24, 96)( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)
( 32,100)( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)
( 40,116)( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)
( 48,120)( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)
( 56,133)( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)
( 64,140)( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)
( 72,144)(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)
(152,220)(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)
(160,227)(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)
(168,240)(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)
(176,244)(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)
(184,260)(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)
(192,264)(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)
(200,277)(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)
(208,284)(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)
(216,288)(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)
(296,364)(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)
(304,371)(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)
(312,384)(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)
(320,388)(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)
(328,404)(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)
(336,408)(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)
(344,421)(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)
(352,428)(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)
(360,432)(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)
(440,508)(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)
(448,515)(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)
(456,528)(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)
(464,532)(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)
(472,548)(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)
(480,552)(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)
(488,565)(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)
(496,572)(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)
(504,576);
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*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope