Polytope of Type {24,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,24}*1152d
if this polytope has a name.
Group : SmallGroup(1152,12917)
Rank : 3
Schlafli Type : {24,24}
Number of vertices, edges, etc : 24, 288, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {12,24}*576b, {24,12}*576f
3-fold quotients : {24,8}*384d
4-fold quotients : {12,12}*288c, {6,24}*288c
6-fold quotients : {24,4}*192b, {12,8}*192a
8-fold quotients : {12,6}*144b, {6,12}*144c
9-fold quotients : {8,8}*128a
12-fold quotients : {12,4}*96a, {6,8}*96
16-fold quotients : {6,6}*72c
18-fold quotients : {4,8}*64a, {8,4}*64b
24-fold quotients : {12,2}*48, {6,4}*48a
32-fold quotients : {3,6}*36
36-fold quotients : {4,4}*32, {2,8}*32
48-fold quotients : {6,2}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {3,2}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,145)( 2,147)( 3,146)( 4,151)( 5,153)( 6,152)( 7,148)( 8,150)
( 9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)( 16,157)
( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)( 24,170)
( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)( 32,180)
( 33,179)( 34,175)( 35,177)( 36,176)( 37,190)( 38,192)( 39,191)( 40,196)
( 41,198)( 42,197)( 43,193)( 44,195)( 45,194)( 46,181)( 47,183)( 48,182)
( 49,187)( 50,189)( 51,188)( 52,184)( 53,186)( 54,185)( 55,208)( 56,210)
( 57,209)( 58,214)( 59,216)( 60,215)( 61,211)( 62,213)( 63,212)( 64,199)
( 65,201)( 66,200)( 67,205)( 68,207)( 69,206)( 70,202)( 71,204)( 72,203)
( 73,226)( 74,228)( 75,227)( 76,232)( 77,234)( 78,233)( 79,229)( 80,231)
( 81,230)( 82,217)( 83,219)( 84,218)( 85,223)( 86,225)( 87,224)( 88,220)
( 89,222)( 90,221)( 91,244)( 92,246)( 93,245)( 94,250)( 95,252)( 96,251)
( 97,247)( 98,249)( 99,248)(100,235)(101,237)(102,236)(103,241)(104,243)
(105,242)(106,238)(107,240)(108,239)(109,253)(110,255)(111,254)(112,259)
(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)(120,263)
(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)(128,273)
(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)(136,280)
(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)(144,284)
(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)(296,438)
(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)(304,445)
(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)(312,458)
(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)(320,468)
(321,467)(322,463)(323,465)(324,464)(325,478)(326,480)(327,479)(328,484)
(329,486)(330,485)(331,481)(332,483)(333,482)(334,469)(335,471)(336,470)
(337,475)(338,477)(339,476)(340,472)(341,474)(342,473)(343,496)(344,498)
(345,497)(346,502)(347,504)(348,503)(349,499)(350,501)(351,500)(352,487)
(353,489)(354,488)(355,493)(356,495)(357,494)(358,490)(359,492)(360,491)
(361,514)(362,516)(363,515)(364,520)(365,522)(366,521)(367,517)(368,519)
(369,518)(370,505)(371,507)(372,506)(373,511)(374,513)(375,512)(376,508)
(377,510)(378,509)(379,532)(380,534)(381,533)(382,538)(383,540)(384,539)
(385,535)(386,537)(387,536)(388,523)(389,525)(390,524)(391,529)(392,531)
(393,530)(394,526)(395,528)(396,527)(397,541)(398,543)(399,542)(400,547)
(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)(408,551)
(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)(416,561)
(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)(424,568)
(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)(432,572);;
s1 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)
( 19, 20)( 22, 26)( 23, 25)( 24, 27)( 28, 29)( 31, 35)( 32, 34)( 33, 36)
( 37, 47)( 38, 46)( 39, 48)( 40, 53)( 41, 52)( 42, 54)( 43, 50)( 44, 49)
( 45, 51)( 55, 65)( 56, 64)( 57, 66)( 58, 71)( 59, 70)( 60, 72)( 61, 68)
( 62, 67)( 63, 69)( 73, 92)( 74, 91)( 75, 93)( 76, 98)( 77, 97)( 78, 99)
( 79, 95)( 80, 94)( 81, 96)( 82,101)( 83,100)( 84,102)( 85,107)( 86,106)
( 87,108)( 88,104)( 89,103)( 90,105)(109,137)(110,136)(111,138)(112,143)
(113,142)(114,144)(115,140)(116,139)(117,141)(118,128)(119,127)(120,129)
(121,134)(122,133)(123,135)(124,131)(125,130)(126,132)(145,182)(146,181)
(147,183)(148,188)(149,187)(150,189)(151,185)(152,184)(153,186)(154,191)
(155,190)(156,192)(157,197)(158,196)(159,198)(160,194)(161,193)(162,195)
(163,200)(164,199)(165,201)(166,206)(167,205)(168,207)(169,203)(170,202)
(171,204)(172,209)(173,208)(174,210)(175,215)(176,214)(177,216)(178,212)
(179,211)(180,213)(217,272)(218,271)(219,273)(220,278)(221,277)(222,279)
(223,275)(224,274)(225,276)(226,281)(227,280)(228,282)(229,287)(230,286)
(231,288)(232,284)(233,283)(234,285)(235,254)(236,253)(237,255)(238,260)
(239,259)(240,261)(241,257)(242,256)(243,258)(244,263)(245,262)(246,264)
(247,269)(248,268)(249,270)(250,266)(251,265)(252,267)(289,362)(290,361)
(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)(298,371)
(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)(306,375)
(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)(313,383)(314,382)
(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)(321,396)(322,392)
(323,391)(324,393)(325,407)(326,406)(327,408)(328,413)(329,412)(330,414)
(331,410)(332,409)(333,411)(334,398)(335,397)(336,399)(337,404)(338,403)
(339,405)(340,401)(341,400)(342,402)(343,425)(344,424)(345,426)(346,431)
(347,430)(348,432)(349,428)(350,427)(351,429)(352,416)(353,415)(354,417)
(355,422)(356,421)(357,423)(358,419)(359,418)(360,420)(433,551)(434,550)
(435,552)(436,557)(437,556)(438,558)(439,554)(440,553)(441,555)(442,542)
(443,541)(444,543)(445,548)(446,547)(447,549)(448,545)(449,544)(450,546)
(451,569)(452,568)(453,570)(454,575)(455,574)(456,576)(457,572)(458,571)
(459,573)(460,560)(461,559)(462,561)(463,566)(464,565)(465,567)(466,563)
(467,562)(468,564)(469,515)(470,514)(471,516)(472,521)(473,520)(474,522)
(475,518)(476,517)(477,519)(478,506)(479,505)(480,507)(481,512)(482,511)
(483,513)(484,509)(485,508)(486,510)(487,533)(488,532)(489,534)(490,539)
(491,538)(492,540)(493,536)(494,535)(495,537)(496,524)(497,523)(498,525)
(499,530)(500,529)(501,531)(502,527)(503,526)(504,528);;
s2 := ( 1,289)( 2,294)( 3,296)( 4,292)( 5,297)( 6,290)( 7,295)( 8,291)
( 9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)( 16,304)
( 17,300)( 18,302)( 19,307)( 20,312)( 21,314)( 22,310)( 23,315)( 24,308)
( 25,313)( 26,309)( 27,311)( 28,316)( 29,321)( 30,323)( 31,319)( 32,324)
( 33,317)( 34,322)( 35,318)( 36,320)( 37,334)( 38,339)( 39,341)( 40,337)
( 41,342)( 42,335)( 43,340)( 44,336)( 45,338)( 46,325)( 47,330)( 48,332)
( 49,328)( 50,333)( 51,326)( 52,331)( 53,327)( 54,329)( 55,352)( 56,357)
( 57,359)( 58,355)( 59,360)( 60,353)( 61,358)( 62,354)( 63,356)( 64,343)
( 65,348)( 66,350)( 67,346)( 68,351)( 69,344)( 70,349)( 71,345)( 72,347)
( 73,379)( 74,384)( 75,386)( 76,382)( 77,387)( 78,380)( 79,385)( 80,381)
( 81,383)( 82,388)( 83,393)( 84,395)( 85,391)( 86,396)( 87,389)( 88,394)
( 89,390)( 90,392)( 91,361)( 92,366)( 93,368)( 94,364)( 95,369)( 96,362)
( 97,367)( 98,363)( 99,365)(100,370)(101,375)(102,377)(103,373)(104,378)
(105,371)(106,376)(107,372)(108,374)(109,424)(110,429)(111,431)(112,427)
(113,432)(114,425)(115,430)(116,426)(117,428)(118,415)(119,420)(120,422)
(121,418)(122,423)(123,416)(124,421)(125,417)(126,419)(127,406)(128,411)
(129,413)(130,409)(131,414)(132,407)(133,412)(134,408)(135,410)(136,397)
(137,402)(138,404)(139,400)(140,405)(141,398)(142,403)(143,399)(144,401)
(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)(152,435)
(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)(160,448)
(161,444)(162,446)(163,451)(164,456)(165,458)(166,454)(167,459)(168,452)
(169,457)(170,453)(171,455)(172,460)(173,465)(174,467)(175,463)(176,468)
(177,461)(178,466)(179,462)(180,464)(181,478)(182,483)(183,485)(184,481)
(185,486)(186,479)(187,484)(188,480)(189,482)(190,469)(191,474)(192,476)
(193,472)(194,477)(195,470)(196,475)(197,471)(198,473)(199,496)(200,501)
(201,503)(202,499)(203,504)(204,497)(205,502)(206,498)(207,500)(208,487)
(209,492)(210,494)(211,490)(212,495)(213,488)(214,493)(215,489)(216,491)
(217,523)(218,528)(219,530)(220,526)(221,531)(222,524)(223,529)(224,525)
(225,527)(226,532)(227,537)(228,539)(229,535)(230,540)(231,533)(232,538)
(233,534)(234,536)(235,505)(236,510)(237,512)(238,508)(239,513)(240,506)
(241,511)(242,507)(243,509)(244,514)(245,519)(246,521)(247,517)(248,522)
(249,515)(250,520)(251,516)(252,518)(253,568)(254,573)(255,575)(256,571)
(257,576)(258,569)(259,574)(260,570)(261,572)(262,559)(263,564)(264,566)
(265,562)(266,567)(267,560)(268,565)(269,561)(270,563)(271,550)(272,555)
(273,557)(274,553)(275,558)(276,551)(277,556)(278,552)(279,554)(280,541)
(281,546)(282,548)(283,544)(284,549)(285,542)(286,547)(287,543)(288,545);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,145)( 2,147)( 3,146)( 4,151)( 5,153)( 6,152)( 7,148)
( 8,150)( 9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)
( 16,157)( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)
( 24,170)( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)
( 32,180)( 33,179)( 34,175)( 35,177)( 36,176)( 37,190)( 38,192)( 39,191)
( 40,196)( 41,198)( 42,197)( 43,193)( 44,195)( 45,194)( 46,181)( 47,183)
( 48,182)( 49,187)( 50,189)( 51,188)( 52,184)( 53,186)( 54,185)( 55,208)
( 56,210)( 57,209)( 58,214)( 59,216)( 60,215)( 61,211)( 62,213)( 63,212)
( 64,199)( 65,201)( 66,200)( 67,205)( 68,207)( 69,206)( 70,202)( 71,204)
( 72,203)( 73,226)( 74,228)( 75,227)( 76,232)( 77,234)( 78,233)( 79,229)
( 80,231)( 81,230)( 82,217)( 83,219)( 84,218)( 85,223)( 86,225)( 87,224)
( 88,220)( 89,222)( 90,221)( 91,244)( 92,246)( 93,245)( 94,250)( 95,252)
( 96,251)( 97,247)( 98,249)( 99,248)(100,235)(101,237)(102,236)(103,241)
(104,243)(105,242)(106,238)(107,240)(108,239)(109,253)(110,255)(111,254)
(112,259)(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)
(120,263)(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)
(128,273)(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)
(136,280)(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)
(144,284)(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)
(296,438)(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)
(304,445)(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)
(312,458)(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)
(320,468)(321,467)(322,463)(323,465)(324,464)(325,478)(326,480)(327,479)
(328,484)(329,486)(330,485)(331,481)(332,483)(333,482)(334,469)(335,471)
(336,470)(337,475)(338,477)(339,476)(340,472)(341,474)(342,473)(343,496)
(344,498)(345,497)(346,502)(347,504)(348,503)(349,499)(350,501)(351,500)
(352,487)(353,489)(354,488)(355,493)(356,495)(357,494)(358,490)(359,492)
(360,491)(361,514)(362,516)(363,515)(364,520)(365,522)(366,521)(367,517)
(368,519)(369,518)(370,505)(371,507)(372,506)(373,511)(374,513)(375,512)
(376,508)(377,510)(378,509)(379,532)(380,534)(381,533)(382,538)(383,540)
(384,539)(385,535)(386,537)(387,536)(388,523)(389,525)(390,524)(391,529)
(392,531)(393,530)(394,526)(395,528)(396,527)(397,541)(398,543)(399,542)
(400,547)(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)
(408,551)(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)
(416,561)(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)
(424,568)(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)
(432,572);
s1 := Sym(576)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)
( 15, 18)( 19, 20)( 22, 26)( 23, 25)( 24, 27)( 28, 29)( 31, 35)( 32, 34)
( 33, 36)( 37, 47)( 38, 46)( 39, 48)( 40, 53)( 41, 52)( 42, 54)( 43, 50)
( 44, 49)( 45, 51)( 55, 65)( 56, 64)( 57, 66)( 58, 71)( 59, 70)( 60, 72)
( 61, 68)( 62, 67)( 63, 69)( 73, 92)( 74, 91)( 75, 93)( 76, 98)( 77, 97)
( 78, 99)( 79, 95)( 80, 94)( 81, 96)( 82,101)( 83,100)( 84,102)( 85,107)
( 86,106)( 87,108)( 88,104)( 89,103)( 90,105)(109,137)(110,136)(111,138)
(112,143)(113,142)(114,144)(115,140)(116,139)(117,141)(118,128)(119,127)
(120,129)(121,134)(122,133)(123,135)(124,131)(125,130)(126,132)(145,182)
(146,181)(147,183)(148,188)(149,187)(150,189)(151,185)(152,184)(153,186)
(154,191)(155,190)(156,192)(157,197)(158,196)(159,198)(160,194)(161,193)
(162,195)(163,200)(164,199)(165,201)(166,206)(167,205)(168,207)(169,203)
(170,202)(171,204)(172,209)(173,208)(174,210)(175,215)(176,214)(177,216)
(178,212)(179,211)(180,213)(217,272)(218,271)(219,273)(220,278)(221,277)
(222,279)(223,275)(224,274)(225,276)(226,281)(227,280)(228,282)(229,287)
(230,286)(231,288)(232,284)(233,283)(234,285)(235,254)(236,253)(237,255)
(238,260)(239,259)(240,261)(241,257)(242,256)(243,258)(244,263)(245,262)
(246,264)(247,269)(248,268)(249,270)(250,266)(251,265)(252,267)(289,362)
(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)
(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)
(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)(313,383)
(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)(321,396)
(322,392)(323,391)(324,393)(325,407)(326,406)(327,408)(328,413)(329,412)
(330,414)(331,410)(332,409)(333,411)(334,398)(335,397)(336,399)(337,404)
(338,403)(339,405)(340,401)(341,400)(342,402)(343,425)(344,424)(345,426)
(346,431)(347,430)(348,432)(349,428)(350,427)(351,429)(352,416)(353,415)
(354,417)(355,422)(356,421)(357,423)(358,419)(359,418)(360,420)(433,551)
(434,550)(435,552)(436,557)(437,556)(438,558)(439,554)(440,553)(441,555)
(442,542)(443,541)(444,543)(445,548)(446,547)(447,549)(448,545)(449,544)
(450,546)(451,569)(452,568)(453,570)(454,575)(455,574)(456,576)(457,572)
(458,571)(459,573)(460,560)(461,559)(462,561)(463,566)(464,565)(465,567)
(466,563)(467,562)(468,564)(469,515)(470,514)(471,516)(472,521)(473,520)
(474,522)(475,518)(476,517)(477,519)(478,506)(479,505)(480,507)(481,512)
(482,511)(483,513)(484,509)(485,508)(486,510)(487,533)(488,532)(489,534)
(490,539)(491,538)(492,540)(493,536)(494,535)(495,537)(496,524)(497,523)
(498,525)(499,530)(500,529)(501,531)(502,527)(503,526)(504,528);
s2 := Sym(576)!( 1,289)( 2,294)( 3,296)( 4,292)( 5,297)( 6,290)( 7,295)
( 8,291)( 9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)
( 16,304)( 17,300)( 18,302)( 19,307)( 20,312)( 21,314)( 22,310)( 23,315)
( 24,308)( 25,313)( 26,309)( 27,311)( 28,316)( 29,321)( 30,323)( 31,319)
( 32,324)( 33,317)( 34,322)( 35,318)( 36,320)( 37,334)( 38,339)( 39,341)
( 40,337)( 41,342)( 42,335)( 43,340)( 44,336)( 45,338)( 46,325)( 47,330)
( 48,332)( 49,328)( 50,333)( 51,326)( 52,331)( 53,327)( 54,329)( 55,352)
( 56,357)( 57,359)( 58,355)( 59,360)( 60,353)( 61,358)( 62,354)( 63,356)
( 64,343)( 65,348)( 66,350)( 67,346)( 68,351)( 69,344)( 70,349)( 71,345)
( 72,347)( 73,379)( 74,384)( 75,386)( 76,382)( 77,387)( 78,380)( 79,385)
( 80,381)( 81,383)( 82,388)( 83,393)( 84,395)( 85,391)( 86,396)( 87,389)
( 88,394)( 89,390)( 90,392)( 91,361)( 92,366)( 93,368)( 94,364)( 95,369)
( 96,362)( 97,367)( 98,363)( 99,365)(100,370)(101,375)(102,377)(103,373)
(104,378)(105,371)(106,376)(107,372)(108,374)(109,424)(110,429)(111,431)
(112,427)(113,432)(114,425)(115,430)(116,426)(117,428)(118,415)(119,420)
(120,422)(121,418)(122,423)(123,416)(124,421)(125,417)(126,419)(127,406)
(128,411)(129,413)(130,409)(131,414)(132,407)(133,412)(134,408)(135,410)
(136,397)(137,402)(138,404)(139,400)(140,405)(141,398)(142,403)(143,399)
(144,401)(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)
(152,435)(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)
(160,448)(161,444)(162,446)(163,451)(164,456)(165,458)(166,454)(167,459)
(168,452)(169,457)(170,453)(171,455)(172,460)(173,465)(174,467)(175,463)
(176,468)(177,461)(178,466)(179,462)(180,464)(181,478)(182,483)(183,485)
(184,481)(185,486)(186,479)(187,484)(188,480)(189,482)(190,469)(191,474)
(192,476)(193,472)(194,477)(195,470)(196,475)(197,471)(198,473)(199,496)
(200,501)(201,503)(202,499)(203,504)(204,497)(205,502)(206,498)(207,500)
(208,487)(209,492)(210,494)(211,490)(212,495)(213,488)(214,493)(215,489)
(216,491)(217,523)(218,528)(219,530)(220,526)(221,531)(222,524)(223,529)
(224,525)(225,527)(226,532)(227,537)(228,539)(229,535)(230,540)(231,533)
(232,538)(233,534)(234,536)(235,505)(236,510)(237,512)(238,508)(239,513)
(240,506)(241,511)(242,507)(243,509)(244,514)(245,519)(246,521)(247,517)
(248,522)(249,515)(250,520)(251,516)(252,518)(253,568)(254,573)(255,575)
(256,571)(257,576)(258,569)(259,574)(260,570)(261,572)(262,559)(263,564)
(264,566)(265,562)(266,567)(267,560)(268,565)(269,561)(270,563)(271,550)
(272,555)(273,557)(274,553)(275,558)(276,551)(277,556)(278,552)(279,554)
(280,541)(281,546)(282,548)(283,544)(284,549)(285,542)(286,547)(287,543)
(288,545);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope