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Polytope of Type {4,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,4}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157449)
Rank : 4
Schlafli Type : {4,18,4}
Number of vertices, edges, etc : 8, 72, 72, 4
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Non-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 : {4,9,4}*576b, {4,18,4}*576e, {4,18,4}*576g
   3-fold quotients : {4,6,4}*384e
   4-fold quotients : {2,18,4}*288c, {4,9,4}*288
   6-fold quotients : {4,3,4}*192b, {4,6,4}*192e, {4,6,4}*192g
   8-fold quotients : {2,9,4}*144
   12-fold quotients : {2,6,4}*96b, {4,3,4}*96
   24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,297)(  2,298)(  3,299)(  4,300)(  5,301)(  6,302)(  7,303)(  8,304)
(  9,289)( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,296)
( 17,313)( 18,314)( 19,315)( 20,316)( 21,317)( 22,318)( 23,319)( 24,320)
( 25,305)( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)
( 33,329)( 34,330)( 35,331)( 36,332)( 37,333)( 38,334)( 39,335)( 40,336)
( 41,321)( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)( 48,328)
( 49,345)( 50,346)( 51,347)( 52,348)( 53,349)( 54,350)( 55,351)( 56,352)
( 57,337)( 58,338)( 59,339)( 60,340)( 61,341)( 62,342)( 63,343)( 64,344)
( 65,361)( 66,362)( 67,363)( 68,364)( 69,365)( 70,366)( 71,367)( 72,368)
( 73,353)( 74,354)( 75,355)( 76,356)( 77,357)( 78,358)( 79,359)( 80,360)
( 81,377)( 82,378)( 83,379)( 84,380)( 85,381)( 86,382)( 87,383)( 88,384)
( 89,369)( 90,370)( 91,371)( 92,372)( 93,373)( 94,374)( 95,375)( 96,376)
( 97,393)( 98,394)( 99,395)(100,396)(101,397)(102,398)(103,399)(104,400)
(105,385)(106,386)(107,387)(108,388)(109,389)(110,390)(111,391)(112,392)
(113,409)(114,410)(115,411)(116,412)(117,413)(118,414)(119,415)(120,416)
(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)(128,408)
(129,425)(130,426)(131,427)(132,428)(133,429)(134,430)(135,431)(136,432)
(137,417)(138,418)(139,419)(140,420)(141,421)(142,422)(143,423)(144,424)
(145,441)(146,442)(147,443)(148,444)(149,445)(150,446)(151,447)(152,448)
(153,433)(154,434)(155,435)(156,436)(157,437)(158,438)(159,439)(160,440)
(161,457)(162,458)(163,459)(164,460)(165,461)(166,462)(167,463)(168,464)
(169,449)(170,450)(171,451)(172,452)(173,453)(174,454)(175,455)(176,456)
(177,473)(178,474)(179,475)(180,476)(181,477)(182,478)(183,479)(184,480)
(185,465)(186,466)(187,467)(188,468)(189,469)(190,470)(191,471)(192,472)
(193,489)(194,490)(195,491)(196,492)(197,493)(198,494)(199,495)(200,496)
(201,481)(202,482)(203,483)(204,484)(205,485)(206,486)(207,487)(208,488)
(209,505)(210,506)(211,507)(212,508)(213,509)(214,510)(215,511)(216,512)
(217,497)(218,498)(219,499)(220,500)(221,501)(222,502)(223,503)(224,504)
(225,521)(226,522)(227,523)(228,524)(229,525)(230,526)(231,527)(232,528)
(233,513)(234,514)(235,515)(236,516)(237,517)(238,518)(239,519)(240,520)
(241,537)(242,538)(243,539)(244,540)(245,541)(246,542)(247,543)(248,544)
(249,529)(250,530)(251,531)(252,532)(253,533)(254,534)(255,535)(256,536)
(257,553)(258,554)(259,555)(260,556)(261,557)(262,558)(263,559)(264,560)
(265,545)(266,546)(267,547)(268,548)(269,549)(270,550)(271,551)(272,552)
(273,569)(274,570)(275,571)(276,572)(277,573)(278,574)(279,575)(280,576)
(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)(288,568);;
s1 := (  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);;
s2 := (  1,193)(  2,196)(  3,195)(  4,194)(  5,205)(  6,208)(  7,207)(  8,206)
(  9,201)( 10,204)( 11,203)( 12,202)( 13,197)( 14,200)( 15,199)( 16,198)
( 17,225)( 18,228)( 19,227)( 20,226)( 21,237)( 22,240)( 23,239)( 24,238)
( 25,233)( 26,236)( 27,235)( 28,234)( 29,229)( 30,232)( 31,231)( 32,230)
( 33,209)( 34,212)( 35,211)( 36,210)( 37,221)( 38,224)( 39,223)( 40,222)
( 41,217)( 42,220)( 43,219)( 44,218)( 45,213)( 46,216)( 47,215)( 48,214)
( 49,145)( 50,148)( 51,147)( 52,146)( 53,157)( 54,160)( 55,159)( 56,158)
( 57,153)( 58,156)( 59,155)( 60,154)( 61,149)( 62,152)( 63,151)( 64,150)
( 65,177)( 66,180)( 67,179)( 68,178)( 69,189)( 70,192)( 71,191)( 72,190)
( 73,185)( 74,188)( 75,187)( 76,186)( 77,181)( 78,184)( 79,183)( 80,182)
( 81,161)( 82,164)( 83,163)( 84,162)( 85,173)( 86,176)( 87,175)( 88,174)
( 89,169)( 90,172)( 91,171)( 92,170)( 93,165)( 94,168)( 95,167)( 96,166)
( 97,273)( 98,276)( 99,275)(100,274)(101,285)(102,288)(103,287)(104,286)
(105,281)(106,284)(107,283)(108,282)(109,277)(110,280)(111,279)(112,278)
(113,257)(114,260)(115,259)(116,258)(117,269)(118,272)(119,271)(120,270)
(121,265)(122,268)(123,267)(124,266)(125,261)(126,264)(127,263)(128,262)
(129,241)(130,244)(131,243)(132,242)(133,253)(134,256)(135,255)(136,254)
(137,249)(138,252)(139,251)(140,250)(141,245)(142,248)(143,247)(144,246)
(289,481)(290,484)(291,483)(292,482)(293,493)(294,496)(295,495)(296,494)
(297,489)(298,492)(299,491)(300,490)(301,485)(302,488)(303,487)(304,486)
(305,513)(306,516)(307,515)(308,514)(309,525)(310,528)(311,527)(312,526)
(313,521)(314,524)(315,523)(316,522)(317,517)(318,520)(319,519)(320,518)
(321,497)(322,500)(323,499)(324,498)(325,509)(326,512)(327,511)(328,510)
(329,505)(330,508)(331,507)(332,506)(333,501)(334,504)(335,503)(336,502)
(337,433)(338,436)(339,435)(340,434)(341,445)(342,448)(343,447)(344,446)
(345,441)(346,444)(347,443)(348,442)(349,437)(350,440)(351,439)(352,438)
(353,465)(354,468)(355,467)(356,466)(357,477)(358,480)(359,479)(360,478)
(361,473)(362,476)(363,475)(364,474)(365,469)(366,472)(367,471)(368,470)
(369,449)(370,452)(371,451)(372,450)(373,461)(374,464)(375,463)(376,462)
(377,457)(378,460)(379,459)(380,458)(381,453)(382,456)(383,455)(384,454)
(385,561)(386,564)(387,563)(388,562)(389,573)(390,576)(391,575)(392,574)
(393,569)(394,572)(395,571)(396,570)(397,565)(398,568)(399,567)(400,566)
(401,545)(402,548)(403,547)(404,546)(405,557)(406,560)(407,559)(408,558)
(409,553)(410,556)(411,555)(412,554)(413,549)(414,552)(415,551)(416,550)
(417,529)(418,532)(419,531)(420,530)(421,541)(422,544)(423,543)(424,542)
(425,537)(426,540)(427,539)(428,538)(429,533)(430,536)(431,535)(432,534);;
s3 := (  1,146)(  2,145)(  3,148)(  4,147)(  5,150)(  6,149)(  7,152)(  8,151)
(  9,154)( 10,153)( 11,156)( 12,155)( 13,158)( 14,157)( 15,160)( 16,159)
( 17,162)( 18,161)( 19,164)( 20,163)( 21,166)( 22,165)( 23,168)( 24,167)
( 25,170)( 26,169)( 27,172)( 28,171)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,178)( 34,177)( 35,180)( 36,179)( 37,182)( 38,181)( 39,184)( 40,183)
( 41,186)( 42,185)( 43,188)( 44,187)( 45,190)( 46,189)( 47,192)( 48,191)
( 49,194)( 50,193)( 51,196)( 52,195)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,202)( 58,201)( 59,204)( 60,203)( 61,206)( 62,205)( 63,208)( 64,207)
( 65,210)( 66,209)( 67,212)( 68,211)( 69,214)( 70,213)( 71,216)( 72,215)
( 73,218)( 74,217)( 75,220)( 76,219)( 77,222)( 78,221)( 79,224)( 80,223)
( 81,226)( 82,225)( 83,228)( 84,227)( 85,230)( 86,229)( 87,232)( 88,231)
( 89,234)( 90,233)( 91,236)( 92,235)( 93,238)( 94,237)( 95,240)( 96,239)
( 97,242)( 98,241)( 99,244)(100,243)(101,246)(102,245)(103,248)(104,247)
(105,250)(106,249)(107,252)(108,251)(109,254)(110,253)(111,256)(112,255)
(113,258)(114,257)(115,260)(116,259)(117,262)(118,261)(119,264)(120,263)
(121,266)(122,265)(123,268)(124,267)(125,270)(126,269)(127,272)(128,271)
(129,274)(130,273)(131,276)(132,275)(133,278)(134,277)(135,280)(136,279)
(137,282)(138,281)(139,284)(140,283)(141,286)(142,285)(143,288)(144,287)
(289,434)(290,433)(291,436)(292,435)(293,438)(294,437)(295,440)(296,439)
(297,442)(298,441)(299,444)(300,443)(301,446)(302,445)(303,448)(304,447)
(305,450)(306,449)(307,452)(308,451)(309,454)(310,453)(311,456)(312,455)
(313,458)(314,457)(315,460)(316,459)(317,462)(318,461)(319,464)(320,463)
(321,466)(322,465)(323,468)(324,467)(325,470)(326,469)(327,472)(328,471)
(329,474)(330,473)(331,476)(332,475)(333,478)(334,477)(335,480)(336,479)
(337,482)(338,481)(339,484)(340,483)(341,486)(342,485)(343,488)(344,487)
(345,490)(346,489)(347,492)(348,491)(349,494)(350,493)(351,496)(352,495)
(353,498)(354,497)(355,500)(356,499)(357,502)(358,501)(359,504)(360,503)
(361,506)(362,505)(363,508)(364,507)(365,510)(366,509)(367,512)(368,511)
(369,514)(370,513)(371,516)(372,515)(373,518)(374,517)(375,520)(376,519)
(377,522)(378,521)(379,524)(380,523)(381,526)(382,525)(383,528)(384,527)
(385,530)(386,529)(387,532)(388,531)(389,534)(390,533)(391,536)(392,535)
(393,538)(394,537)(395,540)(396,539)(397,542)(398,541)(399,544)(400,543)
(401,546)(402,545)(403,548)(404,547)(405,550)(406,549)(407,552)(408,551)
(409,554)(410,553)(411,556)(412,555)(413,558)(414,557)(415,560)(416,559)
(417,562)(418,561)(419,564)(420,563)(421,566)(422,565)(423,568)(424,567)
(425,570)(426,569)(427,572)(428,571)(429,574)(430,573)(431,576)(432,575);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,297)(  2,298)(  3,299)(  4,300)(  5,301)(  6,302)(  7,303)
(  8,304)(  9,289)( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)
( 16,296)( 17,313)( 18,314)( 19,315)( 20,316)( 21,317)( 22,318)( 23,319)
( 24,320)( 25,305)( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)
( 32,312)( 33,329)( 34,330)( 35,331)( 36,332)( 37,333)( 38,334)( 39,335)
( 40,336)( 41,321)( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)
( 48,328)( 49,345)( 50,346)( 51,347)( 52,348)( 53,349)( 54,350)( 55,351)
( 56,352)( 57,337)( 58,338)( 59,339)( 60,340)( 61,341)( 62,342)( 63,343)
( 64,344)( 65,361)( 66,362)( 67,363)( 68,364)( 69,365)( 70,366)( 71,367)
( 72,368)( 73,353)( 74,354)( 75,355)( 76,356)( 77,357)( 78,358)( 79,359)
( 80,360)( 81,377)( 82,378)( 83,379)( 84,380)( 85,381)( 86,382)( 87,383)
( 88,384)( 89,369)( 90,370)( 91,371)( 92,372)( 93,373)( 94,374)( 95,375)
( 96,376)( 97,393)( 98,394)( 99,395)(100,396)(101,397)(102,398)(103,399)
(104,400)(105,385)(106,386)(107,387)(108,388)(109,389)(110,390)(111,391)
(112,392)(113,409)(114,410)(115,411)(116,412)(117,413)(118,414)(119,415)
(120,416)(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)
(128,408)(129,425)(130,426)(131,427)(132,428)(133,429)(134,430)(135,431)
(136,432)(137,417)(138,418)(139,419)(140,420)(141,421)(142,422)(143,423)
(144,424)(145,441)(146,442)(147,443)(148,444)(149,445)(150,446)(151,447)
(152,448)(153,433)(154,434)(155,435)(156,436)(157,437)(158,438)(159,439)
(160,440)(161,457)(162,458)(163,459)(164,460)(165,461)(166,462)(167,463)
(168,464)(169,449)(170,450)(171,451)(172,452)(173,453)(174,454)(175,455)
(176,456)(177,473)(178,474)(179,475)(180,476)(181,477)(182,478)(183,479)
(184,480)(185,465)(186,466)(187,467)(188,468)(189,469)(190,470)(191,471)
(192,472)(193,489)(194,490)(195,491)(196,492)(197,493)(198,494)(199,495)
(200,496)(201,481)(202,482)(203,483)(204,484)(205,485)(206,486)(207,487)
(208,488)(209,505)(210,506)(211,507)(212,508)(213,509)(214,510)(215,511)
(216,512)(217,497)(218,498)(219,499)(220,500)(221,501)(222,502)(223,503)
(224,504)(225,521)(226,522)(227,523)(228,524)(229,525)(230,526)(231,527)
(232,528)(233,513)(234,514)(235,515)(236,516)(237,517)(238,518)(239,519)
(240,520)(241,537)(242,538)(243,539)(244,540)(245,541)(246,542)(247,543)
(248,544)(249,529)(250,530)(251,531)(252,532)(253,533)(254,534)(255,535)
(256,536)(257,553)(258,554)(259,555)(260,556)(261,557)(262,558)(263,559)
(264,560)(265,545)(266,546)(267,547)(268,548)(269,549)(270,550)(271,551)
(272,552)(273,569)(274,570)(275,571)(276,572)(277,573)(278,574)(279,575)
(280,576)(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)
(288,568);
s1 := 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);
s2 := Sym(576)!(  1,193)(  2,196)(  3,195)(  4,194)(  5,205)(  6,208)(  7,207)
(  8,206)(  9,201)( 10,204)( 11,203)( 12,202)( 13,197)( 14,200)( 15,199)
( 16,198)( 17,225)( 18,228)( 19,227)( 20,226)( 21,237)( 22,240)( 23,239)
( 24,238)( 25,233)( 26,236)( 27,235)( 28,234)( 29,229)( 30,232)( 31,231)
( 32,230)( 33,209)( 34,212)( 35,211)( 36,210)( 37,221)( 38,224)( 39,223)
( 40,222)( 41,217)( 42,220)( 43,219)( 44,218)( 45,213)( 46,216)( 47,215)
( 48,214)( 49,145)( 50,148)( 51,147)( 52,146)( 53,157)( 54,160)( 55,159)
( 56,158)( 57,153)( 58,156)( 59,155)( 60,154)( 61,149)( 62,152)( 63,151)
( 64,150)( 65,177)( 66,180)( 67,179)( 68,178)( 69,189)( 70,192)( 71,191)
( 72,190)( 73,185)( 74,188)( 75,187)( 76,186)( 77,181)( 78,184)( 79,183)
( 80,182)( 81,161)( 82,164)( 83,163)( 84,162)( 85,173)( 86,176)( 87,175)
( 88,174)( 89,169)( 90,172)( 91,171)( 92,170)( 93,165)( 94,168)( 95,167)
( 96,166)( 97,273)( 98,276)( 99,275)(100,274)(101,285)(102,288)(103,287)
(104,286)(105,281)(106,284)(107,283)(108,282)(109,277)(110,280)(111,279)
(112,278)(113,257)(114,260)(115,259)(116,258)(117,269)(118,272)(119,271)
(120,270)(121,265)(122,268)(123,267)(124,266)(125,261)(126,264)(127,263)
(128,262)(129,241)(130,244)(131,243)(132,242)(133,253)(134,256)(135,255)
(136,254)(137,249)(138,252)(139,251)(140,250)(141,245)(142,248)(143,247)
(144,246)(289,481)(290,484)(291,483)(292,482)(293,493)(294,496)(295,495)
(296,494)(297,489)(298,492)(299,491)(300,490)(301,485)(302,488)(303,487)
(304,486)(305,513)(306,516)(307,515)(308,514)(309,525)(310,528)(311,527)
(312,526)(313,521)(314,524)(315,523)(316,522)(317,517)(318,520)(319,519)
(320,518)(321,497)(322,500)(323,499)(324,498)(325,509)(326,512)(327,511)
(328,510)(329,505)(330,508)(331,507)(332,506)(333,501)(334,504)(335,503)
(336,502)(337,433)(338,436)(339,435)(340,434)(341,445)(342,448)(343,447)
(344,446)(345,441)(346,444)(347,443)(348,442)(349,437)(350,440)(351,439)
(352,438)(353,465)(354,468)(355,467)(356,466)(357,477)(358,480)(359,479)
(360,478)(361,473)(362,476)(363,475)(364,474)(365,469)(366,472)(367,471)
(368,470)(369,449)(370,452)(371,451)(372,450)(373,461)(374,464)(375,463)
(376,462)(377,457)(378,460)(379,459)(380,458)(381,453)(382,456)(383,455)
(384,454)(385,561)(386,564)(387,563)(388,562)(389,573)(390,576)(391,575)
(392,574)(393,569)(394,572)(395,571)(396,570)(397,565)(398,568)(399,567)
(400,566)(401,545)(402,548)(403,547)(404,546)(405,557)(406,560)(407,559)
(408,558)(409,553)(410,556)(411,555)(412,554)(413,549)(414,552)(415,551)
(416,550)(417,529)(418,532)(419,531)(420,530)(421,541)(422,544)(423,543)
(424,542)(425,537)(426,540)(427,539)(428,538)(429,533)(430,536)(431,535)
(432,534);
s3 := Sym(576)!(  1,146)(  2,145)(  3,148)(  4,147)(  5,150)(  6,149)(  7,152)
(  8,151)(  9,154)( 10,153)( 11,156)( 12,155)( 13,158)( 14,157)( 15,160)
( 16,159)( 17,162)( 18,161)( 19,164)( 20,163)( 21,166)( 22,165)( 23,168)
( 24,167)( 25,170)( 26,169)( 27,172)( 28,171)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,178)( 34,177)( 35,180)( 36,179)( 37,182)( 38,181)( 39,184)
( 40,183)( 41,186)( 42,185)( 43,188)( 44,187)( 45,190)( 46,189)( 47,192)
( 48,191)( 49,194)( 50,193)( 51,196)( 52,195)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,202)( 58,201)( 59,204)( 60,203)( 61,206)( 62,205)( 63,208)
( 64,207)( 65,210)( 66,209)( 67,212)( 68,211)( 69,214)( 70,213)( 71,216)
( 72,215)( 73,218)( 74,217)( 75,220)( 76,219)( 77,222)( 78,221)( 79,224)
( 80,223)( 81,226)( 82,225)( 83,228)( 84,227)( 85,230)( 86,229)( 87,232)
( 88,231)( 89,234)( 90,233)( 91,236)( 92,235)( 93,238)( 94,237)( 95,240)
( 96,239)( 97,242)( 98,241)( 99,244)(100,243)(101,246)(102,245)(103,248)
(104,247)(105,250)(106,249)(107,252)(108,251)(109,254)(110,253)(111,256)
(112,255)(113,258)(114,257)(115,260)(116,259)(117,262)(118,261)(119,264)
(120,263)(121,266)(122,265)(123,268)(124,267)(125,270)(126,269)(127,272)
(128,271)(129,274)(130,273)(131,276)(132,275)(133,278)(134,277)(135,280)
(136,279)(137,282)(138,281)(139,284)(140,283)(141,286)(142,285)(143,288)
(144,287)(289,434)(290,433)(291,436)(292,435)(293,438)(294,437)(295,440)
(296,439)(297,442)(298,441)(299,444)(300,443)(301,446)(302,445)(303,448)
(304,447)(305,450)(306,449)(307,452)(308,451)(309,454)(310,453)(311,456)
(312,455)(313,458)(314,457)(315,460)(316,459)(317,462)(318,461)(319,464)
(320,463)(321,466)(322,465)(323,468)(324,467)(325,470)(326,469)(327,472)
(328,471)(329,474)(330,473)(331,476)(332,475)(333,478)(334,477)(335,480)
(336,479)(337,482)(338,481)(339,484)(340,483)(341,486)(342,485)(343,488)
(344,487)(345,490)(346,489)(347,492)(348,491)(349,494)(350,493)(351,496)
(352,495)(353,498)(354,497)(355,500)(356,499)(357,502)(358,501)(359,504)
(360,503)(361,506)(362,505)(363,508)(364,507)(365,510)(366,509)(367,512)
(368,511)(369,514)(370,513)(371,516)(372,515)(373,518)(374,517)(375,520)
(376,519)(377,522)(378,521)(379,524)(380,523)(381,526)(382,525)(383,528)
(384,527)(385,530)(386,529)(387,532)(388,531)(389,534)(390,533)(391,536)
(392,535)(393,538)(394,537)(395,540)(396,539)(397,542)(398,541)(399,544)
(400,543)(401,546)(402,545)(403,548)(404,547)(405,550)(406,549)(407,552)
(408,551)(409,554)(410,553)(411,556)(412,555)(413,558)(414,557)(415,560)
(416,559)(417,562)(418,561)(419,564)(420,563)(421,566)(422,565)(423,568)
(424,567)(425,570)(426,569)(427,572)(428,571)(429,574)(430,573)(431,576)
(432,575);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s3 >; 
 
References : None.
to this polytope