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