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