Polytope of Type {24,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*1152d
if this polytope has a name.
Group : SmallGroup(1152,14487)
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}*576b, {12,8}*576b
4-fold quotients : {12,4}*288
8-fold quotients : {6,4}*144
9-fold quotients : {8,8}*128d
16-fold quotients : {6,4}*72
18-fold quotients : {4,8}*64b, {8,4}*64b
36-fold quotients : {4,4}*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 := ( 1,289)( 2,291)( 3,290)( 4,295)( 5,297)( 6,296)( 7,292)( 8,294)
( 9,293)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)
( 17,303)( 18,302)( 19,307)( 20,309)( 21,308)( 22,313)( 23,315)( 24,314)
( 25,310)( 26,312)( 27,311)( 28,316)( 29,318)( 30,317)( 31,322)( 32,324)
( 33,323)( 34,319)( 35,321)( 36,320)( 37,334)( 38,336)( 39,335)( 40,340)
( 41,342)( 42,341)( 43,337)( 44,339)( 45,338)( 46,325)( 47,327)( 48,326)
( 49,331)( 50,333)( 51,332)( 52,328)( 53,330)( 54,329)( 55,352)( 56,354)
( 57,353)( 58,358)( 59,360)( 60,359)( 61,355)( 62,357)( 63,356)( 64,343)
( 65,345)( 66,344)( 67,349)( 68,351)( 69,350)( 70,346)( 71,348)( 72,347)
( 73,379)( 74,381)( 75,380)( 76,385)( 77,387)( 78,386)( 79,382)( 80,384)
( 81,383)( 82,388)( 83,390)( 84,389)( 85,394)( 86,396)( 87,395)( 88,391)
( 89,393)( 90,392)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)
( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)
(105,377)(106,373)(107,375)(108,374)(109,424)(110,426)(111,425)(112,430)
(113,432)(114,431)(115,427)(116,429)(117,428)(118,415)(119,417)(120,416)
(121,421)(122,423)(123,422)(124,418)(125,420)(126,419)(127,406)(128,408)
(129,407)(130,412)(131,414)(132,413)(133,409)(134,411)(135,410)(136,397)
(137,399)(138,398)(139,403)(140,405)(141,404)(142,400)(143,402)(144,401)
(145,433)(146,435)(147,434)(148,439)(149,441)(150,440)(151,436)(152,438)
(153,437)(154,442)(155,444)(156,443)(157,448)(158,450)(159,449)(160,445)
(161,447)(162,446)(163,451)(164,453)(165,452)(166,457)(167,459)(168,458)
(169,454)(170,456)(171,455)(172,460)(173,462)(174,461)(175,466)(176,468)
(177,467)(178,463)(179,465)(180,464)(181,478)(182,480)(183,479)(184,484)
(185,486)(186,485)(187,481)(188,483)(189,482)(190,469)(191,471)(192,470)
(193,475)(194,477)(195,476)(196,472)(197,474)(198,473)(199,496)(200,498)
(201,497)(202,502)(203,504)(204,503)(205,499)(206,501)(207,500)(208,487)
(209,489)(210,488)(211,493)(212,495)(213,494)(214,490)(215,492)(216,491)
(217,523)(218,525)(219,524)(220,529)(221,531)(222,530)(223,526)(224,528)
(225,527)(226,532)(227,534)(228,533)(229,538)(230,540)(231,539)(232,535)
(233,537)(234,536)(235,505)(236,507)(237,506)(238,511)(239,513)(240,512)
(241,508)(242,510)(243,509)(244,514)(245,516)(246,515)(247,520)(248,522)
(249,521)(250,517)(251,519)(252,518)(253,568)(254,570)(255,569)(256,574)
(257,576)(258,575)(259,571)(260,573)(261,572)(262,559)(263,561)(264,560)
(265,565)(266,567)(267,566)(268,562)(269,564)(270,563)(271,550)(272,552)
(273,551)(274,556)(275,558)(276,557)(277,553)(278,555)(279,554)(280,541)
(281,543)(282,542)(283,547)(284,549)(285,548)(286,544)(287,546)(288,545);;
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)
(145,175)(146,173)(147,180)(148,172)(149,179)(150,177)(151,178)(152,176)
(153,174)(154,166)(155,164)(156,171)(157,163)(158,170)(159,168)(160,169)
(161,167)(162,165)(181,184)(183,189)(185,188)(190,193)(192,198)(194,197)
(199,202)(201,207)(203,206)(208,211)(210,216)(212,215)(217,229)(218,227)
(219,234)(220,226)(221,233)(222,231)(223,232)(224,230)(225,228)(235,247)
(236,245)(237,252)(238,244)(239,251)(240,249)(241,250)(242,248)(243,246)
(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)(433,526)(434,524)(435,531)(436,523)(437,530)(438,528)
(439,529)(440,527)(441,525)(442,535)(443,533)(444,540)(445,532)(446,539)
(447,537)(448,538)(449,536)(450,534)(451,508)(452,506)(453,513)(454,505)
(455,512)(456,510)(457,511)(458,509)(459,507)(460,517)(461,515)(462,522)
(463,514)(464,521)(465,519)(466,520)(467,518)(468,516)(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 := ( 1,145)( 2,147)( 3,146)( 4,149)( 5,148)( 6,150)( 7,153)( 8,152)
( 9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)( 16,162)
( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)( 24,168)
( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,208)( 38,210)( 39,209)( 40,212)
( 41,211)( 42,213)( 43,216)( 44,215)( 45,214)( 46,199)( 47,201)( 48,200)
( 49,203)( 50,202)( 51,204)( 52,207)( 53,206)( 54,205)( 55,190)( 56,192)
( 57,191)( 58,194)( 59,193)( 60,195)( 61,198)( 62,197)( 63,196)( 64,181)
( 65,183)( 66,182)( 67,185)( 68,184)( 69,186)( 70,189)( 71,188)( 72,187)
( 73,226)( 74,228)( 75,227)( 76,230)( 77,229)( 78,231)( 79,234)( 80,233)
( 81,232)( 82,217)( 83,219)( 84,218)( 85,221)( 86,220)( 87,222)( 88,225)
( 89,224)( 90,223)( 91,244)( 92,246)( 93,245)( 94,248)( 95,247)( 96,249)
( 97,252)( 98,251)( 99,250)(100,235)(101,237)(102,236)(103,239)(104,238)
(105,240)(106,243)(107,242)(108,241)(109,271)(110,273)(111,272)(112,275)
(113,274)(114,276)(115,279)(116,278)(117,277)(118,280)(119,282)(120,281)
(121,284)(122,283)(123,285)(124,288)(125,287)(126,286)(127,253)(128,255)
(129,254)(130,257)(131,256)(132,258)(133,261)(134,260)(135,259)(136,262)
(137,264)(138,263)(139,266)(140,265)(141,267)(142,270)(143,269)(144,268)
(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)(296,440)
(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)(304,450)
(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)(312,456)
(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)(320,463)
(321,465)(322,468)(323,467)(324,466)(325,496)(326,498)(327,497)(328,500)
(329,499)(330,501)(331,504)(332,503)(333,502)(334,487)(335,489)(336,488)
(337,491)(338,490)(339,492)(340,495)(341,494)(342,493)(343,478)(344,480)
(345,479)(346,482)(347,481)(348,483)(349,486)(350,485)(351,484)(352,469)
(353,471)(354,470)(355,473)(356,472)(357,474)(358,477)(359,476)(360,475)
(361,514)(362,516)(363,515)(364,518)(365,517)(366,519)(367,522)(368,521)
(369,520)(370,505)(371,507)(372,506)(373,509)(374,508)(375,510)(376,513)
(377,512)(378,511)(379,532)(380,534)(381,533)(382,536)(383,535)(384,537)
(385,540)(386,539)(387,538)(388,523)(389,525)(390,524)(391,527)(392,526)
(393,528)(394,531)(395,530)(396,529)(397,559)(398,561)(399,560)(400,563)
(401,562)(402,564)(403,567)(404,566)(405,565)(406,568)(407,570)(408,569)
(409,572)(410,571)(411,573)(412,576)(413,575)(414,574)(415,541)(416,543)
(417,542)(418,545)(419,544)(420,546)(421,549)(422,548)(423,547)(424,550)
(425,552)(426,551)(427,554)(428,553)(429,555)(430,558)(431,557)(432,556);;
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,
s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,289)( 2,291)( 3,290)( 4,295)( 5,297)( 6,296)( 7,292)
( 8,294)( 9,293)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)
( 16,301)( 17,303)( 18,302)( 19,307)( 20,309)( 21,308)( 22,313)( 23,315)
( 24,314)( 25,310)( 26,312)( 27,311)( 28,316)( 29,318)( 30,317)( 31,322)
( 32,324)( 33,323)( 34,319)( 35,321)( 36,320)( 37,334)( 38,336)( 39,335)
( 40,340)( 41,342)( 42,341)( 43,337)( 44,339)( 45,338)( 46,325)( 47,327)
( 48,326)( 49,331)( 50,333)( 51,332)( 52,328)( 53,330)( 54,329)( 55,352)
( 56,354)( 57,353)( 58,358)( 59,360)( 60,359)( 61,355)( 62,357)( 63,356)
( 64,343)( 65,345)( 66,344)( 67,349)( 68,351)( 69,350)( 70,346)( 71,348)
( 72,347)( 73,379)( 74,381)( 75,380)( 76,385)( 77,387)( 78,386)( 79,382)
( 80,384)( 81,383)( 82,388)( 83,390)( 84,389)( 85,394)( 86,396)( 87,395)
( 88,391)( 89,393)( 90,392)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)
( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)
(104,378)(105,377)(106,373)(107,375)(108,374)(109,424)(110,426)(111,425)
(112,430)(113,432)(114,431)(115,427)(116,429)(117,428)(118,415)(119,417)
(120,416)(121,421)(122,423)(123,422)(124,418)(125,420)(126,419)(127,406)
(128,408)(129,407)(130,412)(131,414)(132,413)(133,409)(134,411)(135,410)
(136,397)(137,399)(138,398)(139,403)(140,405)(141,404)(142,400)(143,402)
(144,401)(145,433)(146,435)(147,434)(148,439)(149,441)(150,440)(151,436)
(152,438)(153,437)(154,442)(155,444)(156,443)(157,448)(158,450)(159,449)
(160,445)(161,447)(162,446)(163,451)(164,453)(165,452)(166,457)(167,459)
(168,458)(169,454)(170,456)(171,455)(172,460)(173,462)(174,461)(175,466)
(176,468)(177,467)(178,463)(179,465)(180,464)(181,478)(182,480)(183,479)
(184,484)(185,486)(186,485)(187,481)(188,483)(189,482)(190,469)(191,471)
(192,470)(193,475)(194,477)(195,476)(196,472)(197,474)(198,473)(199,496)
(200,498)(201,497)(202,502)(203,504)(204,503)(205,499)(206,501)(207,500)
(208,487)(209,489)(210,488)(211,493)(212,495)(213,494)(214,490)(215,492)
(216,491)(217,523)(218,525)(219,524)(220,529)(221,531)(222,530)(223,526)
(224,528)(225,527)(226,532)(227,534)(228,533)(229,538)(230,540)(231,539)
(232,535)(233,537)(234,536)(235,505)(236,507)(237,506)(238,511)(239,513)
(240,512)(241,508)(242,510)(243,509)(244,514)(245,516)(246,515)(247,520)
(248,522)(249,521)(250,517)(251,519)(252,518)(253,568)(254,570)(255,569)
(256,574)(257,576)(258,575)(259,571)(260,573)(261,572)(262,559)(263,561)
(264,560)(265,565)(266,567)(267,566)(268,562)(269,564)(270,563)(271,550)
(272,552)(273,551)(274,556)(275,558)(276,557)(277,553)(278,555)(279,554)
(280,541)(281,543)(282,542)(283,547)(284,549)(285,548)(286,544)(287,546)
(288,545);
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)(145,175)(146,173)(147,180)(148,172)(149,179)(150,177)(151,178)
(152,176)(153,174)(154,166)(155,164)(156,171)(157,163)(158,170)(159,168)
(160,169)(161,167)(162,165)(181,184)(183,189)(185,188)(190,193)(192,198)
(194,197)(199,202)(201,207)(203,206)(208,211)(210,216)(212,215)(217,229)
(218,227)(219,234)(220,226)(221,233)(222,231)(223,232)(224,230)(225,228)
(235,247)(236,245)(237,252)(238,244)(239,251)(240,249)(241,250)(242,248)
(243,246)(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)(433,526)(434,524)(435,531)(436,523)(437,530)
(438,528)(439,529)(440,527)(441,525)(442,535)(443,533)(444,540)(445,532)
(446,539)(447,537)(448,538)(449,536)(450,534)(451,508)(452,506)(453,513)
(454,505)(455,512)(456,510)(457,511)(458,509)(459,507)(460,517)(461,515)
(462,522)(463,514)(464,521)(465,519)(466,520)(467,518)(468,516)(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)!( 1,145)( 2,147)( 3,146)( 4,149)( 5,148)( 6,150)( 7,153)
( 8,152)( 9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)
( 16,162)( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)
( 24,168)( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,177)( 34,180)( 35,179)( 36,178)( 37,208)( 38,210)( 39,209)
( 40,212)( 41,211)( 42,213)( 43,216)( 44,215)( 45,214)( 46,199)( 47,201)
( 48,200)( 49,203)( 50,202)( 51,204)( 52,207)( 53,206)( 54,205)( 55,190)
( 56,192)( 57,191)( 58,194)( 59,193)( 60,195)( 61,198)( 62,197)( 63,196)
( 64,181)( 65,183)( 66,182)( 67,185)( 68,184)( 69,186)( 70,189)( 71,188)
( 72,187)( 73,226)( 74,228)( 75,227)( 76,230)( 77,229)( 78,231)( 79,234)
( 80,233)( 81,232)( 82,217)( 83,219)( 84,218)( 85,221)( 86,220)( 87,222)
( 88,225)( 89,224)( 90,223)( 91,244)( 92,246)( 93,245)( 94,248)( 95,247)
( 96,249)( 97,252)( 98,251)( 99,250)(100,235)(101,237)(102,236)(103,239)
(104,238)(105,240)(106,243)(107,242)(108,241)(109,271)(110,273)(111,272)
(112,275)(113,274)(114,276)(115,279)(116,278)(117,277)(118,280)(119,282)
(120,281)(121,284)(122,283)(123,285)(124,288)(125,287)(126,286)(127,253)
(128,255)(129,254)(130,257)(131,256)(132,258)(133,261)(134,260)(135,259)
(136,262)(137,264)(138,263)(139,266)(140,265)(141,267)(142,270)(143,269)
(144,268)(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)
(296,440)(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)
(304,450)(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)
(312,456)(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)
(320,463)(321,465)(322,468)(323,467)(324,466)(325,496)(326,498)(327,497)
(328,500)(329,499)(330,501)(331,504)(332,503)(333,502)(334,487)(335,489)
(336,488)(337,491)(338,490)(339,492)(340,495)(341,494)(342,493)(343,478)
(344,480)(345,479)(346,482)(347,481)(348,483)(349,486)(350,485)(351,484)
(352,469)(353,471)(354,470)(355,473)(356,472)(357,474)(358,477)(359,476)
(360,475)(361,514)(362,516)(363,515)(364,518)(365,517)(366,519)(367,522)
(368,521)(369,520)(370,505)(371,507)(372,506)(373,509)(374,508)(375,510)
(376,513)(377,512)(378,511)(379,532)(380,534)(381,533)(382,536)(383,535)
(384,537)(385,540)(386,539)(387,538)(388,523)(389,525)(390,524)(391,527)
(392,526)(393,528)(394,531)(395,530)(396,529)(397,559)(398,561)(399,560)
(400,563)(401,562)(402,564)(403,567)(404,566)(405,565)(406,568)(407,570)
(408,569)(409,572)(410,571)(411,573)(412,576)(413,575)(414,574)(415,541)
(416,543)(417,542)(418,545)(419,544)(420,546)(421,549)(422,548)(423,547)
(424,550)(425,552)(426,551)(427,554)(428,553)(429,555)(430,558)(431,557)
(432,556);
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,
s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2 >;
References : None.
to this polytope