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Polytope of Type {18,4}

Atlas Canonical Name : {18,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,154282)
Rank : 3
Schlafli Type : {18,4}
Number of vertices, edges, etc : 144, 288, 32
Order of s0s1s2 : 18
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {18,4}*576a
3-fold quotients : {6,4}*384a
4-fold quotients : {18,4}*288
6-fold quotients : {6,4}*192a
8-fold quotients : {9,4}*144, {18,4}*144b, {18,4}*144c
12-fold quotients : {6,4}*96
16-fold quotients : {9,4}*72, {18,2}*72
24-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
32-fold quotients : {9,2}*36
48-fold quotients : {3,4}*24, {6,2}*24
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 := (  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,129)( 50,130)
( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)( 58,142)
( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)( 66,114)
( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)
( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)( 82, 98)
( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)(147,148)(151,152)
(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)
(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)
(173,185)(174,186)(175,188)(176,187)(193,273)(194,274)(195,276)(196,275)
(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)(203,288)(204,287)
(205,281)(206,282)(207,284)(208,283)(209,257)(210,258)(211,260)(212,259)
(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)(220,271)
(221,265)(222,266)(223,268)(224,267)(225,241)(226,242)(227,244)(228,243)
(229,245)(230,246)(231,248)(232,247)(233,253)(234,254)(235,256)(236,255)
(237,249)(238,250)(239,252)(240,251)(291,292)(295,296)(297,301)(298,302)
(299,304)(300,303)(305,321)(306,322)(307,324)(308,323)(309,325)(310,326)
(311,328)(312,327)(313,333)(314,334)(315,336)(316,335)(317,329)(318,330)
(319,332)(320,331)(337,417)(338,418)(339,420)(340,419)(341,421)(342,422)
(343,424)(344,423)(345,429)(346,430)(347,432)(348,431)(349,425)(350,426)
(351,428)(352,427)(353,401)(354,402)(355,404)(356,403)(357,405)(358,406)
(359,408)(360,407)(361,413)(362,414)(363,416)(364,415)(365,409)(366,410)
(367,412)(368,411)(369,385)(370,386)(371,388)(372,387)(373,389)(374,390)
(375,392)(376,391)(377,397)(378,398)(379,400)(380,399)(381,393)(382,394)
(383,396)(384,395)(435,436)(439,440)(441,445)(442,446)(443,448)(444,447)
(449,465)(450,466)(451,468)(452,467)(453,469)(454,470)(455,472)(456,471)
(457,477)(458,478)(459,480)(460,479)(461,473)(462,474)(463,476)(464,475)
(481,561)(482,562)(483,564)(484,563)(485,565)(486,566)(487,568)(488,567)
(489,573)(490,574)(491,576)(492,575)(493,569)(494,570)(495,572)(496,571)
(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)(503,552)(504,551)
(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)(511,556)(512,555)
(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)(519,536)(520,535)
(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)(527,540)(528,539);;
s1 := (  1,193)(  2,196)(  3,195)(  4,194)(  5,208)(  6,205)(  7,206)(  8,207)
(  9,203)( 10,202)( 11,201)( 12,204)( 13,198)( 14,199)( 15,200)( 16,197)
( 17,225)( 18,228)( 19,227)( 20,226)( 21,240)( 22,237)( 23,238)( 24,239)
( 25,235)( 26,234)( 27,233)( 28,236)( 29,230)( 30,231)( 31,232)( 32,229)
( 33,209)( 34,212)( 35,211)( 36,210)( 37,224)( 38,221)( 39,222)( 40,223)
( 41,219)( 42,218)( 43,217)( 44,220)( 45,214)( 46,215)( 47,216)( 48,213)
( 49,145)( 50,148)( 51,147)( 52,146)( 53,160)( 54,157)( 55,158)( 56,159)
( 57,155)( 58,154)( 59,153)( 60,156)( 61,150)( 62,151)( 63,152)( 64,149)
( 65,177)( 66,180)( 67,179)( 68,178)( 69,192)( 70,189)( 71,190)( 72,191)
( 73,187)( 74,186)( 75,185)( 76,188)( 77,182)( 78,183)( 79,184)( 80,181)
( 81,161)( 82,164)( 83,163)( 84,162)( 85,176)( 86,173)( 87,174)( 88,175)
( 89,171)( 90,170)( 91,169)( 92,172)( 93,166)( 94,167)( 95,168)( 96,165)
( 97,273)( 98,276)( 99,275)(100,274)(101,288)(102,285)(103,286)(104,287)
(105,283)(106,282)(107,281)(108,284)(109,278)(110,279)(111,280)(112,277)
(113,257)(114,260)(115,259)(116,258)(117,272)(118,269)(119,270)(120,271)
(121,267)(122,266)(123,265)(124,268)(125,262)(126,263)(127,264)(128,261)
(129,241)(130,244)(131,243)(132,242)(133,256)(134,253)(135,254)(136,255)
(137,251)(138,250)(139,249)(140,252)(141,246)(142,247)(143,248)(144,245)
(289,481)(290,484)(291,483)(292,482)(293,496)(294,493)(295,494)(296,495)
(297,491)(298,490)(299,489)(300,492)(301,486)(302,487)(303,488)(304,485)
(305,513)(306,516)(307,515)(308,514)(309,528)(310,525)(311,526)(312,527)
(313,523)(314,522)(315,521)(316,524)(317,518)(318,519)(319,520)(320,517)
(321,497)(322,500)(323,499)(324,498)(325,512)(326,509)(327,510)(328,511)
(329,507)(330,506)(331,505)(332,508)(333,502)(334,503)(335,504)(336,501)
(337,433)(338,436)(339,435)(340,434)(341,448)(342,445)(343,446)(344,447)
(345,443)(346,442)(347,441)(348,444)(349,438)(350,439)(351,440)(352,437)
(353,465)(354,468)(355,467)(356,466)(357,480)(358,477)(359,478)(360,479)
(361,475)(362,474)(363,473)(364,476)(365,470)(366,471)(367,472)(368,469)
(369,449)(370,452)(371,451)(372,450)(373,464)(374,461)(375,462)(376,463)
(377,459)(378,458)(379,457)(380,460)(381,454)(382,455)(383,456)(384,453)
(385,561)(386,564)(387,563)(388,562)(389,576)(390,573)(391,574)(392,575)
(393,571)(394,570)(395,569)(396,572)(397,566)(398,567)(399,568)(400,565)
(401,545)(402,548)(403,547)(404,546)(405,560)(406,557)(407,558)(408,559)
(409,555)(410,554)(411,553)(412,556)(413,550)(414,551)(415,552)(416,549)
(417,529)(418,532)(419,531)(420,530)(421,544)(422,541)(423,542)(424,543)
(425,539)(426,538)(427,537)(428,540)(429,534)(430,535)(431,536)(432,533);;
s2 := (  1,293)(  2,294)(  3,295)(  4,296)(  5,289)(  6,290)(  7,291)(  8,292)
(  9,301)( 10,302)( 11,303)( 12,304)( 13,297)( 14,298)( 15,299)( 16,300)
( 17,309)( 18,310)( 19,311)( 20,312)( 21,305)( 22,306)( 23,307)( 24,308)
( 25,317)( 26,318)( 27,319)( 28,320)( 29,313)( 30,314)( 31,315)( 32,316)
( 33,325)( 34,326)( 35,327)( 36,328)( 37,321)( 38,322)( 39,323)( 40,324)
( 41,333)( 42,334)( 43,335)( 44,336)( 45,329)( 46,330)( 47,331)( 48,332)
( 49,341)( 50,342)( 51,343)( 52,344)( 53,337)( 54,338)( 55,339)( 56,340)
( 57,349)( 58,350)( 59,351)( 60,352)( 61,345)( 62,346)( 63,347)( 64,348)
( 65,357)( 66,358)( 67,359)( 68,360)( 69,353)( 70,354)( 71,355)( 72,356)
( 73,365)( 74,366)( 75,367)( 76,368)( 77,361)( 78,362)( 79,363)( 80,364)
( 81,373)( 82,374)( 83,375)( 84,376)( 85,369)( 86,370)( 87,371)( 88,372)
( 89,381)( 90,382)( 91,383)( 92,384)( 93,377)( 94,378)( 95,379)( 96,380)
( 97,389)( 98,390)( 99,391)(100,392)(101,385)(102,386)(103,387)(104,388)
(105,397)(106,398)(107,399)(108,400)(109,393)(110,394)(111,395)(112,396)
(113,405)(114,406)(115,407)(116,408)(117,401)(118,402)(119,403)(120,404)
(121,413)(122,414)(123,415)(124,416)(125,409)(126,410)(127,411)(128,412)
(129,421)(130,422)(131,423)(132,424)(133,417)(134,418)(135,419)(136,420)
(137,429)(138,430)(139,431)(140,432)(141,425)(142,426)(143,427)(144,428)
(145,437)(146,438)(147,439)(148,440)(149,433)(150,434)(151,435)(152,436)
(153,445)(154,446)(155,447)(156,448)(157,441)(158,442)(159,443)(160,444)
(161,453)(162,454)(163,455)(164,456)(165,449)(166,450)(167,451)(168,452)
(169,461)(170,462)(171,463)(172,464)(173,457)(174,458)(175,459)(176,460)
(177,469)(178,470)(179,471)(180,472)(181,465)(182,466)(183,467)(184,468)
(185,477)(186,478)(187,479)(188,480)(189,473)(190,474)(191,475)(192,476)
(193,485)(194,486)(195,487)(196,488)(197,481)(198,482)(199,483)(200,484)
(201,493)(202,494)(203,495)(204,496)(205,489)(206,490)(207,491)(208,492)
(209,501)(210,502)(211,503)(212,504)(213,497)(214,498)(215,499)(216,500)
(217,509)(218,510)(219,511)(220,512)(221,505)(222,506)(223,507)(224,508)
(225,517)(226,518)(227,519)(228,520)(229,513)(230,514)(231,515)(232,516)
(233,525)(234,526)(235,527)(236,528)(237,521)(238,522)(239,523)(240,524)
(241,533)(242,534)(243,535)(244,536)(245,529)(246,530)(247,531)(248,532)
(249,541)(250,542)(251,543)(252,544)(253,537)(254,538)(255,539)(256,540)
(257,549)(258,550)(259,551)(260,552)(261,545)(262,546)(263,547)(264,548)
(265,557)(266,558)(267,559)(268,560)(269,553)(270,554)(271,555)(272,556)
(273,565)(274,566)(275,567)(276,568)(277,561)(278,562)(279,563)(280,564)
(281,573)(282,574)(283,575)(284,576)(285,569)(286,570)(287,571)(288,572);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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)!(  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,129)
( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)
( 58,142)( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)
( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)
( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)
( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)(147,148)
(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)
(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)
(172,191)(173,185)(174,186)(175,188)(176,187)(193,273)(194,274)(195,276)
(196,275)(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)(203,288)
(204,287)(205,281)(206,282)(207,284)(208,283)(209,257)(210,258)(211,260)
(212,259)(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)
(220,271)(221,265)(222,266)(223,268)(224,267)(225,241)(226,242)(227,244)
(228,243)(229,245)(230,246)(231,248)(232,247)(233,253)(234,254)(235,256)
(236,255)(237,249)(238,250)(239,252)(240,251)(291,292)(295,296)(297,301)
(298,302)(299,304)(300,303)(305,321)(306,322)(307,324)(308,323)(309,325)
(310,326)(311,328)(312,327)(313,333)(314,334)(315,336)(316,335)(317,329)
(318,330)(319,332)(320,331)(337,417)(338,418)(339,420)(340,419)(341,421)
(342,422)(343,424)(344,423)(345,429)(346,430)(347,432)(348,431)(349,425)
(350,426)(351,428)(352,427)(353,401)(354,402)(355,404)(356,403)(357,405)
(358,406)(359,408)(360,407)(361,413)(362,414)(363,416)(364,415)(365,409)
(366,410)(367,412)(368,411)(369,385)(370,386)(371,388)(372,387)(373,389)
(374,390)(375,392)(376,391)(377,397)(378,398)(379,400)(380,399)(381,393)
(382,394)(383,396)(384,395)(435,436)(439,440)(441,445)(442,446)(443,448)
(444,447)(449,465)(450,466)(451,468)(452,467)(453,469)(454,470)(455,472)
(456,471)(457,477)(458,478)(459,480)(460,479)(461,473)(462,474)(463,476)
(464,475)(481,561)(482,562)(483,564)(484,563)(485,565)(486,566)(487,568)
(488,567)(489,573)(490,574)(491,576)(492,575)(493,569)(494,570)(495,572)
(496,571)(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)(503,552)
(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)(511,556)
(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)(519,536)
(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)(527,540)
(528,539);
s1 := Sym(576)!(  1,193)(  2,196)(  3,195)(  4,194)(  5,208)(  6,205)(  7,206)
(  8,207)(  9,203)( 10,202)( 11,201)( 12,204)( 13,198)( 14,199)( 15,200)
( 16,197)( 17,225)( 18,228)( 19,227)( 20,226)( 21,240)( 22,237)( 23,238)
( 24,239)( 25,235)( 26,234)( 27,233)( 28,236)( 29,230)( 30,231)( 31,232)
( 32,229)( 33,209)( 34,212)( 35,211)( 36,210)( 37,224)( 38,221)( 39,222)
( 40,223)( 41,219)( 42,218)( 43,217)( 44,220)( 45,214)( 46,215)( 47,216)
( 48,213)( 49,145)( 50,148)( 51,147)( 52,146)( 53,160)( 54,157)( 55,158)
( 56,159)( 57,155)( 58,154)( 59,153)( 60,156)( 61,150)( 62,151)( 63,152)
( 64,149)( 65,177)( 66,180)( 67,179)( 68,178)( 69,192)( 70,189)( 71,190)
( 72,191)( 73,187)( 74,186)( 75,185)( 76,188)( 77,182)( 78,183)( 79,184)
( 80,181)( 81,161)( 82,164)( 83,163)( 84,162)( 85,176)( 86,173)( 87,174)
( 88,175)( 89,171)( 90,170)( 91,169)( 92,172)( 93,166)( 94,167)( 95,168)
( 96,165)( 97,273)( 98,276)( 99,275)(100,274)(101,288)(102,285)(103,286)
(104,287)(105,283)(106,282)(107,281)(108,284)(109,278)(110,279)(111,280)
(112,277)(113,257)(114,260)(115,259)(116,258)(117,272)(118,269)(119,270)
(120,271)(121,267)(122,266)(123,265)(124,268)(125,262)(126,263)(127,264)
(128,261)(129,241)(130,244)(131,243)(132,242)(133,256)(134,253)(135,254)
(136,255)(137,251)(138,250)(139,249)(140,252)(141,246)(142,247)(143,248)
(144,245)(289,481)(290,484)(291,483)(292,482)(293,496)(294,493)(295,494)
(296,495)(297,491)(298,490)(299,489)(300,492)(301,486)(302,487)(303,488)
(304,485)(305,513)(306,516)(307,515)(308,514)(309,528)(310,525)(311,526)
(312,527)(313,523)(314,522)(315,521)(316,524)(317,518)(318,519)(319,520)
(320,517)(321,497)(322,500)(323,499)(324,498)(325,512)(326,509)(327,510)
(328,511)(329,507)(330,506)(331,505)(332,508)(333,502)(334,503)(335,504)
(336,501)(337,433)(338,436)(339,435)(340,434)(341,448)(342,445)(343,446)
(344,447)(345,443)(346,442)(347,441)(348,444)(349,438)(350,439)(351,440)
(352,437)(353,465)(354,468)(355,467)(356,466)(357,480)(358,477)(359,478)
(360,479)(361,475)(362,474)(363,473)(364,476)(365,470)(366,471)(367,472)
(368,469)(369,449)(370,452)(371,451)(372,450)(373,464)(374,461)(375,462)
(376,463)(377,459)(378,458)(379,457)(380,460)(381,454)(382,455)(383,456)
(384,453)(385,561)(386,564)(387,563)(388,562)(389,576)(390,573)(391,574)
(392,575)(393,571)(394,570)(395,569)(396,572)(397,566)(398,567)(399,568)
(400,565)(401,545)(402,548)(403,547)(404,546)(405,560)(406,557)(407,558)
(408,559)(409,555)(410,554)(411,553)(412,556)(413,550)(414,551)(415,552)
(416,549)(417,529)(418,532)(419,531)(420,530)(421,544)(422,541)(423,542)
(424,543)(425,539)(426,538)(427,537)(428,540)(429,534)(430,535)(431,536)
(432,533);
s2 := Sym(576)!(  1,293)(  2,294)(  3,295)(  4,296)(  5,289)(  6,290)(  7,291)
(  8,292)(  9,301)( 10,302)( 11,303)( 12,304)( 13,297)( 14,298)( 15,299)
( 16,300)( 17,309)( 18,310)( 19,311)( 20,312)( 21,305)( 22,306)( 23,307)
( 24,308)( 25,317)( 26,318)( 27,319)( 28,320)( 29,313)( 30,314)( 31,315)
( 32,316)( 33,325)( 34,326)( 35,327)( 36,328)( 37,321)( 38,322)( 39,323)
( 40,324)( 41,333)( 42,334)( 43,335)( 44,336)( 45,329)( 46,330)( 47,331)
( 48,332)( 49,341)( 50,342)( 51,343)( 52,344)( 53,337)( 54,338)( 55,339)
( 56,340)( 57,349)( 58,350)( 59,351)( 60,352)( 61,345)( 62,346)( 63,347)
( 64,348)( 65,357)( 66,358)( 67,359)( 68,360)( 69,353)( 70,354)( 71,355)
( 72,356)( 73,365)( 74,366)( 75,367)( 76,368)( 77,361)( 78,362)( 79,363)
( 80,364)( 81,373)( 82,374)( 83,375)( 84,376)( 85,369)( 86,370)( 87,371)
( 88,372)( 89,381)( 90,382)( 91,383)( 92,384)( 93,377)( 94,378)( 95,379)
( 96,380)( 97,389)( 98,390)( 99,391)(100,392)(101,385)(102,386)(103,387)
(104,388)(105,397)(106,398)(107,399)(108,400)(109,393)(110,394)(111,395)
(112,396)(113,405)(114,406)(115,407)(116,408)(117,401)(118,402)(119,403)
(120,404)(121,413)(122,414)(123,415)(124,416)(125,409)(126,410)(127,411)
(128,412)(129,421)(130,422)(131,423)(132,424)(133,417)(134,418)(135,419)
(136,420)(137,429)(138,430)(139,431)(140,432)(141,425)(142,426)(143,427)
(144,428)(145,437)(146,438)(147,439)(148,440)(149,433)(150,434)(151,435)
(152,436)(153,445)(154,446)(155,447)(156,448)(157,441)(158,442)(159,443)
(160,444)(161,453)(162,454)(163,455)(164,456)(165,449)(166,450)(167,451)
(168,452)(169,461)(170,462)(171,463)(172,464)(173,457)(174,458)(175,459)
(176,460)(177,469)(178,470)(179,471)(180,472)(181,465)(182,466)(183,467)
(184,468)(185,477)(186,478)(187,479)(188,480)(189,473)(190,474)(191,475)
(192,476)(193,485)(194,486)(195,487)(196,488)(197,481)(198,482)(199,483)
(200,484)(201,493)(202,494)(203,495)(204,496)(205,489)(206,490)(207,491)
(208,492)(209,501)(210,502)(211,503)(212,504)(213,497)(214,498)(215,499)
(216,500)(217,509)(218,510)(219,511)(220,512)(221,505)(222,506)(223,507)
(224,508)(225,517)(226,518)(227,519)(228,520)(229,513)(230,514)(231,515)
(232,516)(233,525)(234,526)(235,527)(236,528)(237,521)(238,522)(239,523)
(240,524)(241,533)(242,534)(243,535)(244,536)(245,529)(246,530)(247,531)
(248,532)(249,541)(250,542)(251,543)(252,544)(253,537)(254,538)(255,539)
(256,540)(257,549)(258,550)(259,551)(260,552)(261,545)(262,546)(263,547)
(264,548)(265,557)(266,558)(267,559)(268,560)(269,553)(270,554)(271,555)
(272,556)(273,565)(274,566)(275,567)(276,568)(277,561)(278,562)(279,563)
(280,564)(281,573)(282,574)(283,575)(284,576)(285,569)(286,570)(287,571)
(288,572);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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