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Polytope of Type {4,4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,18}*1152d
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 4
Schlafli Type : {4,4,18}
Number of vertices, edges, etc : 4, 16, 72, 36
Order of s0s1s2s3 : 36
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 : {4,4,9}*576b, {2,4,18}*576
   3-fold quotients : {4,4,6}*384d
   4-fold quotients : {4,2,18}*288, {2,4,9}*288, {2,4,18}*288b, {2,4,18}*288c
   6-fold quotients : {4,4,3}*192b, {2,4,6}*192
   8-fold quotients : {4,2,9}*144, {2,4,9}*144, {2,2,18}*144
   12-fold quotients : {4,2,6}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {2,2,9}*72
   24-fold quotients : {4,2,3}*48, {2,4,3}*48, {2,2,6}*48
   36-fold quotients : {4,2,2}*32
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)(  8,152)
(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)( 96,276)
( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)
(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)(112,220)
(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)(120,228)
(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)(128,236)
(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)(136,244)
(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)(144,252)
(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)
(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)
(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)
(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)
(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)(328,472)
(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)
(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)
(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)
(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)
(361,541)(362,542)(363,543)(364,544)(365,545)(366,546)(367,547)(368,548)
(369,549)(370,550)(371,551)(372,552)(373,553)(374,554)(375,555)(376,556)
(377,557)(378,558)(379,559)(380,560)(381,561)(382,562)(383,563)(384,564)
(385,565)(386,566)(387,567)(388,568)(389,569)(390,570)(391,571)(392,572)
(393,573)(394,574)(395,575)(396,576)(397,505)(398,506)(399,507)(400,508)
(401,509)(402,510)(403,511)(404,512)(405,513)(406,514)(407,515)(408,516)
(409,517)(410,518)(411,519)(412,520)(413,521)(414,522)(415,523)(416,524)
(417,525)(418,526)(419,527)(420,528)(421,529)(422,530)(423,531)(424,532)
(425,533)(426,534)(427,535)(428,536)(429,537)(430,538)(431,539)(432,540);;
s1 := (  1, 75)(  2, 76)(  3, 73)(  4, 74)(  5, 79)(  6, 80)(  7, 77)(  8, 78)
(  9, 83)( 10, 84)( 11, 81)( 12, 82)( 13, 87)( 14, 88)( 15, 85)( 16, 86)
( 17, 91)( 18, 92)( 19, 89)( 20, 90)( 21, 95)( 22, 96)( 23, 93)( 24, 94)
( 25, 99)( 26,100)( 27, 97)( 28, 98)( 29,103)( 30,104)( 31,101)( 32,102)
( 33,107)( 34,108)( 35,105)( 36,106)( 37,111)( 38,112)( 39,109)( 40,110)
( 41,115)( 42,116)( 43,113)( 44,114)( 45,119)( 46,120)( 47,117)( 48,118)
( 49,123)( 50,124)( 51,121)( 52,122)( 53,127)( 54,128)( 55,125)( 56,126)
( 57,131)( 58,132)( 59,129)( 60,130)( 61,135)( 62,136)( 63,133)( 64,134)
( 65,139)( 66,140)( 67,137)( 68,138)( 69,143)( 70,144)( 71,141)( 72,142)
(145,219)(146,220)(147,217)(148,218)(149,223)(150,224)(151,221)(152,222)
(153,227)(154,228)(155,225)(156,226)(157,231)(158,232)(159,229)(160,230)
(161,235)(162,236)(163,233)(164,234)(165,239)(166,240)(167,237)(168,238)
(169,243)(170,244)(171,241)(172,242)(173,247)(174,248)(175,245)(176,246)
(177,251)(178,252)(179,249)(180,250)(181,255)(182,256)(183,253)(184,254)
(185,259)(186,260)(187,257)(188,258)(189,263)(190,264)(191,261)(192,262)
(193,267)(194,268)(195,265)(196,266)(197,271)(198,272)(199,269)(200,270)
(201,275)(202,276)(203,273)(204,274)(205,279)(206,280)(207,277)(208,278)
(209,283)(210,284)(211,281)(212,282)(213,287)(214,288)(215,285)(216,286)
(289,363)(290,364)(291,361)(292,362)(293,367)(294,368)(295,365)(296,366)
(297,371)(298,372)(299,369)(300,370)(301,375)(302,376)(303,373)(304,374)
(305,379)(306,380)(307,377)(308,378)(309,383)(310,384)(311,381)(312,382)
(313,387)(314,388)(315,385)(316,386)(317,391)(318,392)(319,389)(320,390)
(321,395)(322,396)(323,393)(324,394)(325,399)(326,400)(327,397)(328,398)
(329,403)(330,404)(331,401)(332,402)(333,407)(334,408)(335,405)(336,406)
(337,411)(338,412)(339,409)(340,410)(341,415)(342,416)(343,413)(344,414)
(345,419)(346,420)(347,417)(348,418)(349,423)(350,424)(351,421)(352,422)
(353,427)(354,428)(355,425)(356,426)(357,431)(358,432)(359,429)(360,430)
(433,507)(434,508)(435,505)(436,506)(437,511)(438,512)(439,509)(440,510)
(441,515)(442,516)(443,513)(444,514)(445,519)(446,520)(447,517)(448,518)
(449,523)(450,524)(451,521)(452,522)(453,527)(454,528)(455,525)(456,526)
(457,531)(458,532)(459,529)(460,530)(461,535)(462,536)(463,533)(464,534)
(465,539)(466,540)(467,537)(468,538)(469,543)(470,544)(471,541)(472,542)
(473,547)(474,548)(475,545)(476,546)(477,551)(478,552)(479,549)(480,550)
(481,555)(482,556)(483,553)(484,554)(485,559)(486,560)(487,557)(488,558)
(489,563)(490,564)(491,561)(492,562)(493,567)(494,568)(495,565)(496,566)
(497,571)(498,572)(499,569)(500,570)(501,575)(502,576)(503,573)(504,574);;
s2 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 69)( 50, 70)
( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)
( 59, 64)( 60, 63)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 85,105)
( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)( 93, 97)
( 94, 98)( 95,100)( 96, 99)(111,112)(113,117)(114,118)(115,120)(116,119)
(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)
(129,133)(130,134)(131,136)(132,135)(147,148)(149,153)(150,154)(151,156)
(152,155)(157,177)(158,178)(159,180)(160,179)(161,173)(162,174)(163,176)
(164,175)(165,169)(166,170)(167,172)(168,171)(183,184)(185,189)(186,190)
(187,192)(188,191)(193,213)(194,214)(195,216)(196,215)(197,209)(198,210)
(199,212)(200,211)(201,205)(202,206)(203,208)(204,207)(219,220)(221,225)
(222,226)(223,228)(224,227)(229,249)(230,250)(231,252)(232,251)(233,245)
(234,246)(235,248)(236,247)(237,241)(238,242)(239,244)(240,243)(255,256)
(257,261)(258,262)(259,264)(260,263)(265,285)(266,286)(267,288)(268,287)
(269,281)(270,282)(271,284)(272,283)(273,277)(274,278)(275,280)(276,279)
(291,292)(293,297)(294,298)(295,300)(296,299)(301,321)(302,322)(303,324)
(304,323)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)
(312,315)(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)
(339,360)(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)
(347,352)(348,351)(363,364)(365,369)(366,370)(367,372)(368,371)(373,393)
(374,394)(375,396)(376,395)(377,389)(378,390)(379,392)(380,391)(381,385)
(382,386)(383,388)(384,387)(399,400)(401,405)(402,406)(403,408)(404,407)
(409,429)(410,430)(411,432)(412,431)(413,425)(414,426)(415,428)(416,427)
(417,421)(418,422)(419,424)(420,423)(435,436)(437,441)(438,442)(439,444)
(440,443)(445,465)(446,466)(447,468)(448,467)(449,461)(450,462)(451,464)
(452,463)(453,457)(454,458)(455,460)(456,459)(471,472)(473,477)(474,478)
(475,480)(476,479)(481,501)(482,502)(483,504)(484,503)(485,497)(486,498)
(487,500)(488,499)(489,493)(490,494)(491,496)(492,495)(507,508)(509,513)
(510,514)(511,516)(512,515)(517,537)(518,538)(519,540)(520,539)(521,533)
(522,534)(523,536)(524,535)(525,529)(526,530)(527,532)(528,531)(543,544)
(545,549)(546,550)(547,552)(548,551)(553,573)(554,574)(555,576)(556,575)
(557,569)(558,570)(559,572)(560,571)(561,565)(562,566)(563,568)(564,567);;
s3 := (  1,301)(  2,304)(  3,303)(  4,302)(  5,309)(  6,312)(  7,311)(  8,310)
(  9,305)( 10,308)( 11,307)( 12,306)( 13,289)( 14,292)( 15,291)( 16,290)
( 17,297)( 18,300)( 19,299)( 20,298)( 21,293)( 22,296)( 23,295)( 24,294)
( 25,321)( 26,324)( 27,323)( 28,322)( 29,317)( 30,320)( 31,319)( 32,318)
( 33,313)( 34,316)( 35,315)( 36,314)( 37,337)( 38,340)( 39,339)( 40,338)
( 41,345)( 42,348)( 43,347)( 44,346)( 45,341)( 46,344)( 47,343)( 48,342)
( 49,325)( 50,328)( 51,327)( 52,326)( 53,333)( 54,336)( 55,335)( 56,334)
( 57,329)( 58,332)( 59,331)( 60,330)( 61,357)( 62,360)( 63,359)( 64,358)
( 65,353)( 66,356)( 67,355)( 68,354)( 69,349)( 70,352)( 71,351)( 72,350)
( 73,373)( 74,376)( 75,375)( 76,374)( 77,381)( 78,384)( 79,383)( 80,382)
( 81,377)( 82,380)( 83,379)( 84,378)( 85,361)( 86,364)( 87,363)( 88,362)
( 89,369)( 90,372)( 91,371)( 92,370)( 93,365)( 94,368)( 95,367)( 96,366)
( 97,393)( 98,396)( 99,395)(100,394)(101,389)(102,392)(103,391)(104,390)
(105,385)(106,388)(107,387)(108,386)(109,409)(110,412)(111,411)(112,410)
(113,417)(114,420)(115,419)(116,418)(117,413)(118,416)(119,415)(120,414)
(121,397)(122,400)(123,399)(124,398)(125,405)(126,408)(127,407)(128,406)
(129,401)(130,404)(131,403)(132,402)(133,429)(134,432)(135,431)(136,430)
(137,425)(138,428)(139,427)(140,426)(141,421)(142,424)(143,423)(144,422)
(145,445)(146,448)(147,447)(148,446)(149,453)(150,456)(151,455)(152,454)
(153,449)(154,452)(155,451)(156,450)(157,433)(158,436)(159,435)(160,434)
(161,441)(162,444)(163,443)(164,442)(165,437)(166,440)(167,439)(168,438)
(169,465)(170,468)(171,467)(172,466)(173,461)(174,464)(175,463)(176,462)
(177,457)(178,460)(179,459)(180,458)(181,481)(182,484)(183,483)(184,482)
(185,489)(186,492)(187,491)(188,490)(189,485)(190,488)(191,487)(192,486)
(193,469)(194,472)(195,471)(196,470)(197,477)(198,480)(199,479)(200,478)
(201,473)(202,476)(203,475)(204,474)(205,501)(206,504)(207,503)(208,502)
(209,497)(210,500)(211,499)(212,498)(213,493)(214,496)(215,495)(216,494)
(217,517)(218,520)(219,519)(220,518)(221,525)(222,528)(223,527)(224,526)
(225,521)(226,524)(227,523)(228,522)(229,505)(230,508)(231,507)(232,506)
(233,513)(234,516)(235,515)(236,514)(237,509)(238,512)(239,511)(240,510)
(241,537)(242,540)(243,539)(244,538)(245,533)(246,536)(247,535)(248,534)
(249,529)(250,532)(251,531)(252,530)(253,553)(254,556)(255,555)(256,554)
(257,561)(258,564)(259,563)(260,562)(261,557)(262,560)(263,559)(264,558)
(265,541)(266,544)(267,543)(268,542)(269,549)(270,552)(271,551)(272,550)
(273,545)(274,548)(275,547)(276,546)(277,573)(278,576)(279,575)(280,574)
(281,569)(282,572)(283,571)(284,570)(285,565)(286,568)(287,567)(288,566);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)
(  8,152)(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)
( 96,276)( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)
(104,284)(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)
(112,220)(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)
(120,228)(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)
(128,236)(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)
(136,244)(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)
(144,252)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)
(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)
(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)
(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)
(320,464)(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)
(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)
(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)
(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)
(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)
(360,504)(361,541)(362,542)(363,543)(364,544)(365,545)(366,546)(367,547)
(368,548)(369,549)(370,550)(371,551)(372,552)(373,553)(374,554)(375,555)
(376,556)(377,557)(378,558)(379,559)(380,560)(381,561)(382,562)(383,563)
(384,564)(385,565)(386,566)(387,567)(388,568)(389,569)(390,570)(391,571)
(392,572)(393,573)(394,574)(395,575)(396,576)(397,505)(398,506)(399,507)
(400,508)(401,509)(402,510)(403,511)(404,512)(405,513)(406,514)(407,515)
(408,516)(409,517)(410,518)(411,519)(412,520)(413,521)(414,522)(415,523)
(416,524)(417,525)(418,526)(419,527)(420,528)(421,529)(422,530)(423,531)
(424,532)(425,533)(426,534)(427,535)(428,536)(429,537)(430,538)(431,539)
(432,540);
s1 := Sym(576)!(  1, 75)(  2, 76)(  3, 73)(  4, 74)(  5, 79)(  6, 80)(  7, 77)
(  8, 78)(  9, 83)( 10, 84)( 11, 81)( 12, 82)( 13, 87)( 14, 88)( 15, 85)
( 16, 86)( 17, 91)( 18, 92)( 19, 89)( 20, 90)( 21, 95)( 22, 96)( 23, 93)
( 24, 94)( 25, 99)( 26,100)( 27, 97)( 28, 98)( 29,103)( 30,104)( 31,101)
( 32,102)( 33,107)( 34,108)( 35,105)( 36,106)( 37,111)( 38,112)( 39,109)
( 40,110)( 41,115)( 42,116)( 43,113)( 44,114)( 45,119)( 46,120)( 47,117)
( 48,118)( 49,123)( 50,124)( 51,121)( 52,122)( 53,127)( 54,128)( 55,125)
( 56,126)( 57,131)( 58,132)( 59,129)( 60,130)( 61,135)( 62,136)( 63,133)
( 64,134)( 65,139)( 66,140)( 67,137)( 68,138)( 69,143)( 70,144)( 71,141)
( 72,142)(145,219)(146,220)(147,217)(148,218)(149,223)(150,224)(151,221)
(152,222)(153,227)(154,228)(155,225)(156,226)(157,231)(158,232)(159,229)
(160,230)(161,235)(162,236)(163,233)(164,234)(165,239)(166,240)(167,237)
(168,238)(169,243)(170,244)(171,241)(172,242)(173,247)(174,248)(175,245)
(176,246)(177,251)(178,252)(179,249)(180,250)(181,255)(182,256)(183,253)
(184,254)(185,259)(186,260)(187,257)(188,258)(189,263)(190,264)(191,261)
(192,262)(193,267)(194,268)(195,265)(196,266)(197,271)(198,272)(199,269)
(200,270)(201,275)(202,276)(203,273)(204,274)(205,279)(206,280)(207,277)
(208,278)(209,283)(210,284)(211,281)(212,282)(213,287)(214,288)(215,285)
(216,286)(289,363)(290,364)(291,361)(292,362)(293,367)(294,368)(295,365)
(296,366)(297,371)(298,372)(299,369)(300,370)(301,375)(302,376)(303,373)
(304,374)(305,379)(306,380)(307,377)(308,378)(309,383)(310,384)(311,381)
(312,382)(313,387)(314,388)(315,385)(316,386)(317,391)(318,392)(319,389)
(320,390)(321,395)(322,396)(323,393)(324,394)(325,399)(326,400)(327,397)
(328,398)(329,403)(330,404)(331,401)(332,402)(333,407)(334,408)(335,405)
(336,406)(337,411)(338,412)(339,409)(340,410)(341,415)(342,416)(343,413)
(344,414)(345,419)(346,420)(347,417)(348,418)(349,423)(350,424)(351,421)
(352,422)(353,427)(354,428)(355,425)(356,426)(357,431)(358,432)(359,429)
(360,430)(433,507)(434,508)(435,505)(436,506)(437,511)(438,512)(439,509)
(440,510)(441,515)(442,516)(443,513)(444,514)(445,519)(446,520)(447,517)
(448,518)(449,523)(450,524)(451,521)(452,522)(453,527)(454,528)(455,525)
(456,526)(457,531)(458,532)(459,529)(460,530)(461,535)(462,536)(463,533)
(464,534)(465,539)(466,540)(467,537)(468,538)(469,543)(470,544)(471,541)
(472,542)(473,547)(474,548)(475,545)(476,546)(477,551)(478,552)(479,549)
(480,550)(481,555)(482,556)(483,553)(484,554)(485,559)(486,560)(487,557)
(488,558)(489,563)(490,564)(491,561)(492,562)(493,567)(494,568)(495,565)
(496,566)(497,571)(498,572)(499,569)(500,570)(501,575)(502,576)(503,573)
(504,574);
s2 := Sym(576)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 69)
( 50, 70)( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)
( 58, 62)( 59, 64)( 60, 63)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)
( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)
( 93, 97)( 94, 98)( 95,100)( 96, 99)(111,112)(113,117)(114,118)(115,120)
(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)
(128,139)(129,133)(130,134)(131,136)(132,135)(147,148)(149,153)(150,154)
(151,156)(152,155)(157,177)(158,178)(159,180)(160,179)(161,173)(162,174)
(163,176)(164,175)(165,169)(166,170)(167,172)(168,171)(183,184)(185,189)
(186,190)(187,192)(188,191)(193,213)(194,214)(195,216)(196,215)(197,209)
(198,210)(199,212)(200,211)(201,205)(202,206)(203,208)(204,207)(219,220)
(221,225)(222,226)(223,228)(224,227)(229,249)(230,250)(231,252)(232,251)
(233,245)(234,246)(235,248)(236,247)(237,241)(238,242)(239,244)(240,243)
(255,256)(257,261)(258,262)(259,264)(260,263)(265,285)(266,286)(267,288)
(268,287)(269,281)(270,282)(271,284)(272,283)(273,277)(274,278)(275,280)
(276,279)(291,292)(293,297)(294,298)(295,300)(296,299)(301,321)(302,322)
(303,324)(304,323)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)
(311,316)(312,315)(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)
(338,358)(339,360)(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)
(346,350)(347,352)(348,351)(363,364)(365,369)(366,370)(367,372)(368,371)
(373,393)(374,394)(375,396)(376,395)(377,389)(378,390)(379,392)(380,391)
(381,385)(382,386)(383,388)(384,387)(399,400)(401,405)(402,406)(403,408)
(404,407)(409,429)(410,430)(411,432)(412,431)(413,425)(414,426)(415,428)
(416,427)(417,421)(418,422)(419,424)(420,423)(435,436)(437,441)(438,442)
(439,444)(440,443)(445,465)(446,466)(447,468)(448,467)(449,461)(450,462)
(451,464)(452,463)(453,457)(454,458)(455,460)(456,459)(471,472)(473,477)
(474,478)(475,480)(476,479)(481,501)(482,502)(483,504)(484,503)(485,497)
(486,498)(487,500)(488,499)(489,493)(490,494)(491,496)(492,495)(507,508)
(509,513)(510,514)(511,516)(512,515)(517,537)(518,538)(519,540)(520,539)
(521,533)(522,534)(523,536)(524,535)(525,529)(526,530)(527,532)(528,531)
(543,544)(545,549)(546,550)(547,552)(548,551)(553,573)(554,574)(555,576)
(556,575)(557,569)(558,570)(559,572)(560,571)(561,565)(562,566)(563,568)
(564,567);
s3 := Sym(576)!(  1,301)(  2,304)(  3,303)(  4,302)(  5,309)(  6,312)(  7,311)
(  8,310)(  9,305)( 10,308)( 11,307)( 12,306)( 13,289)( 14,292)( 15,291)
( 16,290)( 17,297)( 18,300)( 19,299)( 20,298)( 21,293)( 22,296)( 23,295)
( 24,294)( 25,321)( 26,324)( 27,323)( 28,322)( 29,317)( 30,320)( 31,319)
( 32,318)( 33,313)( 34,316)( 35,315)( 36,314)( 37,337)( 38,340)( 39,339)
( 40,338)( 41,345)( 42,348)( 43,347)( 44,346)( 45,341)( 46,344)( 47,343)
( 48,342)( 49,325)( 50,328)( 51,327)( 52,326)( 53,333)( 54,336)( 55,335)
( 56,334)( 57,329)( 58,332)( 59,331)( 60,330)( 61,357)( 62,360)( 63,359)
( 64,358)( 65,353)( 66,356)( 67,355)( 68,354)( 69,349)( 70,352)( 71,351)
( 72,350)( 73,373)( 74,376)( 75,375)( 76,374)( 77,381)( 78,384)( 79,383)
( 80,382)( 81,377)( 82,380)( 83,379)( 84,378)( 85,361)( 86,364)( 87,363)
( 88,362)( 89,369)( 90,372)( 91,371)( 92,370)( 93,365)( 94,368)( 95,367)
( 96,366)( 97,393)( 98,396)( 99,395)(100,394)(101,389)(102,392)(103,391)
(104,390)(105,385)(106,388)(107,387)(108,386)(109,409)(110,412)(111,411)
(112,410)(113,417)(114,420)(115,419)(116,418)(117,413)(118,416)(119,415)
(120,414)(121,397)(122,400)(123,399)(124,398)(125,405)(126,408)(127,407)
(128,406)(129,401)(130,404)(131,403)(132,402)(133,429)(134,432)(135,431)
(136,430)(137,425)(138,428)(139,427)(140,426)(141,421)(142,424)(143,423)
(144,422)(145,445)(146,448)(147,447)(148,446)(149,453)(150,456)(151,455)
(152,454)(153,449)(154,452)(155,451)(156,450)(157,433)(158,436)(159,435)
(160,434)(161,441)(162,444)(163,443)(164,442)(165,437)(166,440)(167,439)
(168,438)(169,465)(170,468)(171,467)(172,466)(173,461)(174,464)(175,463)
(176,462)(177,457)(178,460)(179,459)(180,458)(181,481)(182,484)(183,483)
(184,482)(185,489)(186,492)(187,491)(188,490)(189,485)(190,488)(191,487)
(192,486)(193,469)(194,472)(195,471)(196,470)(197,477)(198,480)(199,479)
(200,478)(201,473)(202,476)(203,475)(204,474)(205,501)(206,504)(207,503)
(208,502)(209,497)(210,500)(211,499)(212,498)(213,493)(214,496)(215,495)
(216,494)(217,517)(218,520)(219,519)(220,518)(221,525)(222,528)(223,527)
(224,526)(225,521)(226,524)(227,523)(228,522)(229,505)(230,508)(231,507)
(232,506)(233,513)(234,516)(235,515)(236,514)(237,509)(238,512)(239,511)
(240,510)(241,537)(242,540)(243,539)(244,538)(245,533)(246,536)(247,535)
(248,534)(249,529)(250,532)(251,531)(252,530)(253,553)(254,556)(255,555)
(256,554)(257,561)(258,564)(259,563)(260,562)(261,557)(262,560)(263,559)
(264,558)(265,541)(266,544)(267,543)(268,542)(269,549)(270,552)(271,551)
(272,550)(273,545)(274,548)(275,547)(276,546)(277,573)(278,576)(279,575)
(280,574)(281,569)(282,572)(283,571)(284,570)(285,565)(286,568)(287,567)
(288,566);
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope