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Polytope of Type {4,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,8}*1152
Also Known As : {{4,4}6,{4,8|2}}. if this polytope has another name.
Group : SmallGroup(1152,119790)
Rank : 4
Schlafli Type : {4,4,8}
Number of vertices, edges, etc : 18, 36, 72, 8
Order of s0s1s2s3 : 24
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 : {4,4,4}*576a
   4-fold quotients : {4,4,2}*288
   8-fold quotients : {4,4,2}*144
   18-fold quotients : {2,2,8}*64
   36-fold quotients : {2,2,4}*32
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,145)(  2,147)(  3,146)(  4,149)(  5,148)(  6,150)(  7,153)(  8,152)
(  9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)( 16,162)
( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)( 24,168)
( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,183)( 39,182)( 40,185)
( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)( 48,191)
( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)( 56,201)
( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)( 64,208)
( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)( 72,214)
( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)( 80,224)
( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)( 88,234)
( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)( 96,240)
( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)(104,247)
(105,249)(106,252)(107,251)(108,250)(109,253)(110,255)(111,254)(112,257)
(113,256)(114,258)(115,261)(116,260)(117,259)(118,262)(119,264)(120,263)
(121,266)(122,265)(123,267)(124,270)(125,269)(126,268)(127,271)(128,273)
(129,272)(130,275)(131,274)(132,276)(133,279)(134,278)(135,277)(136,280)
(137,282)(138,281)(139,284)(140,283)(141,285)(142,288)(143,287)(144,286)
(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)(296,440)
(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)(304,450)
(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)(312,456)
(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)(320,463)
(321,465)(322,468)(323,467)(324,466)(325,469)(326,471)(327,470)(328,473)
(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)(336,479)
(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)(344,489)
(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)(352,496)
(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)(360,502)
(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)(368,512)
(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)(376,522)
(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)(384,528)
(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)(392,535)
(393,537)(394,540)(395,539)(396,538)(397,541)(398,543)(399,542)(400,545)
(401,544)(402,546)(403,549)(404,548)(405,547)(406,550)(407,552)(408,551)
(409,554)(410,553)(411,555)(412,558)(413,557)(414,556)(415,559)(416,561)
(417,560)(418,563)(419,562)(420,564)(421,567)(422,566)(423,565)(424,568)
(425,570)(426,569)(427,572)(428,571)(429,573)(430,576)(431,575)(432,574);;
s1 := (  1,109)(  2,114)(  3,116)(  4,112)(  5,117)(  6,110)(  7,115)(  8,111)
(  9,113)( 10,118)( 11,123)( 12,125)( 13,121)( 14,126)( 15,119)( 16,124)
( 17,120)( 18,122)( 19,127)( 20,132)( 21,134)( 22,130)( 23,135)( 24,128)
( 25,133)( 26,129)( 27,131)( 28,136)( 29,141)( 30,143)( 31,139)( 32,144)
( 33,137)( 34,142)( 35,138)( 36,140)( 37, 82)( 38, 87)( 39, 89)( 40, 85)
( 41, 90)( 42, 83)( 43, 88)( 44, 84)( 45, 86)( 46, 73)( 47, 78)( 48, 80)
( 49, 76)( 50, 81)( 51, 74)( 52, 79)( 53, 75)( 54, 77)( 55,100)( 56,105)
( 57,107)( 58,103)( 59,108)( 60,101)( 61,106)( 62,102)( 63,104)( 64, 91)
( 65, 96)( 66, 98)( 67, 94)( 68, 99)( 69, 92)( 70, 97)( 71, 93)( 72, 95)
(145,271)(146,276)(147,278)(148,274)(149,279)(150,272)(151,277)(152,273)
(153,275)(154,280)(155,285)(156,287)(157,283)(158,288)(159,281)(160,286)
(161,282)(162,284)(163,253)(164,258)(165,260)(166,256)(167,261)(168,254)
(169,259)(170,255)(171,257)(172,262)(173,267)(174,269)(175,265)(176,270)
(177,263)(178,268)(179,264)(180,266)(181,244)(182,249)(183,251)(184,247)
(185,252)(186,245)(187,250)(188,246)(189,248)(190,235)(191,240)(192,242)
(193,238)(194,243)(195,236)(196,241)(197,237)(198,239)(199,226)(200,231)
(201,233)(202,229)(203,234)(204,227)(205,232)(206,228)(207,230)(208,217)
(209,222)(210,224)(211,220)(212,225)(213,218)(214,223)(215,219)(216,221)
(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)(295,367)(296,363)
(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)(303,371)(304,376)
(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)(311,387)(312,380)
(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)(319,391)(320,396)
(321,389)(322,394)(323,390)(324,392)(325,397)(326,402)(327,404)(328,400)
(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)(336,413)
(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)(344,420)
(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)(352,424)
(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)(360,428)
(433,523)(434,528)(435,530)(436,526)(437,531)(438,524)(439,529)(440,525)
(441,527)(442,532)(443,537)(444,539)(445,535)(446,540)(447,533)(448,538)
(449,534)(450,536)(451,505)(452,510)(453,512)(454,508)(455,513)(456,506)
(457,511)(458,507)(459,509)(460,514)(461,519)(462,521)(463,517)(464,522)
(465,515)(466,520)(467,516)(468,518)(469,559)(470,564)(471,566)(472,562)
(473,567)(474,560)(475,565)(476,561)(477,563)(478,568)(479,573)(480,575)
(481,571)(482,576)(483,569)(484,574)(485,570)(486,572)(487,541)(488,546)
(489,548)(490,544)(491,549)(492,542)(493,547)(494,543)(495,545)(496,550)
(497,555)(498,557)(499,553)(500,558)(501,551)(502,556)(503,552)(504,554);;
s2 := (  1,458)(  2,459)(  3,457)(  4,454)(  5,455)(  6,456)(  7,453)(  8,451)
(  9,452)( 10,467)( 11,468)( 12,466)( 13,463)( 14,464)( 15,465)( 16,462)
( 17,460)( 18,461)( 19,440)( 20,441)( 21,439)( 22,436)( 23,437)( 24,438)
( 25,435)( 26,433)( 27,434)( 28,449)( 29,450)( 30,448)( 31,445)( 32,446)
( 33,447)( 34,444)( 35,442)( 36,443)( 37,503)( 38,504)( 39,502)( 40,499)
( 41,500)( 42,501)( 43,498)( 44,496)( 45,497)( 46,494)( 47,495)( 48,493)
( 49,490)( 50,491)( 51,492)( 52,489)( 53,487)( 54,488)( 55,485)( 56,486)
( 57,484)( 58,481)( 59,482)( 60,483)( 61,480)( 62,478)( 63,479)( 64,476)
( 65,477)( 66,475)( 67,472)( 68,473)( 69,474)( 70,471)( 71,469)( 72,470)
( 73,566)( 74,567)( 75,565)( 76,562)( 77,563)( 78,564)( 79,561)( 80,559)
( 81,560)( 82,575)( 83,576)( 84,574)( 85,571)( 86,572)( 87,573)( 88,570)
( 89,568)( 90,569)( 91,548)( 92,549)( 93,547)( 94,544)( 95,545)( 96,546)
( 97,543)( 98,541)( 99,542)(100,557)(101,558)(102,556)(103,553)(104,554)
(105,555)(106,552)(107,550)(108,551)(109,530)(110,531)(111,529)(112,526)
(113,527)(114,528)(115,525)(116,523)(117,524)(118,539)(119,540)(120,538)
(121,535)(122,536)(123,537)(124,534)(125,532)(126,533)(127,512)(128,513)
(129,511)(130,508)(131,509)(132,510)(133,507)(134,505)(135,506)(136,521)
(137,522)(138,520)(139,517)(140,518)(141,519)(142,516)(143,514)(144,515)
(145,314)(146,315)(147,313)(148,310)(149,311)(150,312)(151,309)(152,307)
(153,308)(154,323)(155,324)(156,322)(157,319)(158,320)(159,321)(160,318)
(161,316)(162,317)(163,296)(164,297)(165,295)(166,292)(167,293)(168,294)
(169,291)(170,289)(171,290)(172,305)(173,306)(174,304)(175,301)(176,302)
(177,303)(178,300)(179,298)(180,299)(181,359)(182,360)(183,358)(184,355)
(185,356)(186,357)(187,354)(188,352)(189,353)(190,350)(191,351)(192,349)
(193,346)(194,347)(195,348)(196,345)(197,343)(198,344)(199,341)(200,342)
(201,340)(202,337)(203,338)(204,339)(205,336)(206,334)(207,335)(208,332)
(209,333)(210,331)(211,328)(212,329)(213,330)(214,327)(215,325)(216,326)
(217,422)(218,423)(219,421)(220,418)(221,419)(222,420)(223,417)(224,415)
(225,416)(226,431)(227,432)(228,430)(229,427)(230,428)(231,429)(232,426)
(233,424)(234,425)(235,404)(236,405)(237,403)(238,400)(239,401)(240,402)
(241,399)(242,397)(243,398)(244,413)(245,414)(246,412)(247,409)(248,410)
(249,411)(250,408)(251,406)(252,407)(253,386)(254,387)(255,385)(256,382)
(257,383)(258,384)(259,381)(260,379)(261,380)(262,395)(263,396)(264,394)
(265,391)(266,392)(267,393)(268,390)(269,388)(270,389)(271,368)(272,369)
(273,367)(274,364)(275,365)(276,366)(277,363)(278,361)(279,362)(280,377)
(281,378)(282,376)(283,373)(284,374)(285,375)(286,372)(287,370)(288,371);;
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)( 37,118)( 38,119)( 39,120)( 40,121)
( 41,122)( 42,123)( 43,124)( 44,125)( 45,126)( 46,109)( 47,110)( 48,111)
( 49,112)( 50,113)( 51,114)( 52,115)( 53,116)( 54,117)( 55,136)( 56,137)
( 57,138)( 58,139)( 59,140)( 60,141)( 61,142)( 62,143)( 63,144)( 64,127)
( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)( 72,135)
(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)(181,262)(182,263)(183,264)(184,265)
(185,266)(186,267)(187,268)(188,269)(189,270)(190,253)(191,254)(192,255)
(193,256)(194,257)(195,258)(196,259)(197,260)(198,261)(199,280)(200,281)
(201,282)(202,283)(203,284)(204,285)(205,286)(206,287)(207,288)(208,271)
(209,272)(210,273)(211,274)(212,275)(213,276)(214,277)(215,278)(216,279)
(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)(325,406)(326,407)(327,408)(328,409)
(329,410)(330,411)(331,412)(332,413)(333,414)(334,397)(335,398)(336,399)
(337,400)(338,401)(339,402)(340,403)(341,404)(342,405)(343,424)(344,425)
(345,426)(346,427)(347,428)(348,429)(349,430)(350,431)(351,432)(352,415)
(353,416)(354,417)(355,418)(356,419)(357,420)(358,421)(359,422)(360,423)
(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)(469,550)(470,551)(471,552)(472,553)
(473,554)(474,555)(475,556)(476,557)(477,558)(478,541)(479,542)(480,543)
(481,544)(482,545)(483,546)(484,547)(485,548)(486,549)(487,568)(488,569)
(489,570)(490,571)(491,572)(492,573)(493,574)(494,575)(495,576)(496,559)
(497,560)(498,561)(499,562)(500,563)(501,564)(502,565)(503,566)(504,567);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,145)(  2,147)(  3,146)(  4,149)(  5,148)(  6,150)(  7,153)
(  8,152)(  9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)
( 16,162)( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)
( 24,168)( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,183)( 39,182)
( 40,185)( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)
( 48,191)( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)
( 56,201)( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)
( 64,208)( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)
( 80,224)( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)
( 88,234)( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)
( 96,240)( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)
(104,247)(105,249)(106,252)(107,251)(108,250)(109,253)(110,255)(111,254)
(112,257)(113,256)(114,258)(115,261)(116,260)(117,259)(118,262)(119,264)
(120,263)(121,266)(122,265)(123,267)(124,270)(125,269)(126,268)(127,271)
(128,273)(129,272)(130,275)(131,274)(132,276)(133,279)(134,278)(135,277)
(136,280)(137,282)(138,281)(139,284)(140,283)(141,285)(142,288)(143,287)
(144,286)(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)
(296,440)(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)
(304,450)(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)
(312,456)(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)
(320,463)(321,465)(322,468)(323,467)(324,466)(325,469)(326,471)(327,470)
(328,473)(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)
(336,479)(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)
(344,489)(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)
(352,496)(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)
(360,502)(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)
(368,512)(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)
(376,522)(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)
(384,528)(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)
(392,535)(393,537)(394,540)(395,539)(396,538)(397,541)(398,543)(399,542)
(400,545)(401,544)(402,546)(403,549)(404,548)(405,547)(406,550)(407,552)
(408,551)(409,554)(410,553)(411,555)(412,558)(413,557)(414,556)(415,559)
(416,561)(417,560)(418,563)(419,562)(420,564)(421,567)(422,566)(423,565)
(424,568)(425,570)(426,569)(427,572)(428,571)(429,573)(430,576)(431,575)
(432,574);
s1 := Sym(576)!(  1,109)(  2,114)(  3,116)(  4,112)(  5,117)(  6,110)(  7,115)
(  8,111)(  9,113)( 10,118)( 11,123)( 12,125)( 13,121)( 14,126)( 15,119)
( 16,124)( 17,120)( 18,122)( 19,127)( 20,132)( 21,134)( 22,130)( 23,135)
( 24,128)( 25,133)( 26,129)( 27,131)( 28,136)( 29,141)( 30,143)( 31,139)
( 32,144)( 33,137)( 34,142)( 35,138)( 36,140)( 37, 82)( 38, 87)( 39, 89)
( 40, 85)( 41, 90)( 42, 83)( 43, 88)( 44, 84)( 45, 86)( 46, 73)( 47, 78)
( 48, 80)( 49, 76)( 50, 81)( 51, 74)( 52, 79)( 53, 75)( 54, 77)( 55,100)
( 56,105)( 57,107)( 58,103)( 59,108)( 60,101)( 61,106)( 62,102)( 63,104)
( 64, 91)( 65, 96)( 66, 98)( 67, 94)( 68, 99)( 69, 92)( 70, 97)( 71, 93)
( 72, 95)(145,271)(146,276)(147,278)(148,274)(149,279)(150,272)(151,277)
(152,273)(153,275)(154,280)(155,285)(156,287)(157,283)(158,288)(159,281)
(160,286)(161,282)(162,284)(163,253)(164,258)(165,260)(166,256)(167,261)
(168,254)(169,259)(170,255)(171,257)(172,262)(173,267)(174,269)(175,265)
(176,270)(177,263)(178,268)(179,264)(180,266)(181,244)(182,249)(183,251)
(184,247)(185,252)(186,245)(187,250)(188,246)(189,248)(190,235)(191,240)
(192,242)(193,238)(194,243)(195,236)(196,241)(197,237)(198,239)(199,226)
(200,231)(201,233)(202,229)(203,234)(204,227)(205,232)(206,228)(207,230)
(208,217)(209,222)(210,224)(211,220)(212,225)(213,218)(214,223)(215,219)
(216,221)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)(295,367)
(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)(303,371)
(304,376)(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)(311,387)
(312,380)(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)(319,391)
(320,396)(321,389)(322,394)(323,390)(324,392)(325,397)(326,402)(327,404)
(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)
(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)
(344,420)(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)
(352,424)(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)
(360,428)(433,523)(434,528)(435,530)(436,526)(437,531)(438,524)(439,529)
(440,525)(441,527)(442,532)(443,537)(444,539)(445,535)(446,540)(447,533)
(448,538)(449,534)(450,536)(451,505)(452,510)(453,512)(454,508)(455,513)
(456,506)(457,511)(458,507)(459,509)(460,514)(461,519)(462,521)(463,517)
(464,522)(465,515)(466,520)(467,516)(468,518)(469,559)(470,564)(471,566)
(472,562)(473,567)(474,560)(475,565)(476,561)(477,563)(478,568)(479,573)
(480,575)(481,571)(482,576)(483,569)(484,574)(485,570)(486,572)(487,541)
(488,546)(489,548)(490,544)(491,549)(492,542)(493,547)(494,543)(495,545)
(496,550)(497,555)(498,557)(499,553)(500,558)(501,551)(502,556)(503,552)
(504,554);
s2 := Sym(576)!(  1,458)(  2,459)(  3,457)(  4,454)(  5,455)(  6,456)(  7,453)
(  8,451)(  9,452)( 10,467)( 11,468)( 12,466)( 13,463)( 14,464)( 15,465)
( 16,462)( 17,460)( 18,461)( 19,440)( 20,441)( 21,439)( 22,436)( 23,437)
( 24,438)( 25,435)( 26,433)( 27,434)( 28,449)( 29,450)( 30,448)( 31,445)
( 32,446)( 33,447)( 34,444)( 35,442)( 36,443)( 37,503)( 38,504)( 39,502)
( 40,499)( 41,500)( 42,501)( 43,498)( 44,496)( 45,497)( 46,494)( 47,495)
( 48,493)( 49,490)( 50,491)( 51,492)( 52,489)( 53,487)( 54,488)( 55,485)
( 56,486)( 57,484)( 58,481)( 59,482)( 60,483)( 61,480)( 62,478)( 63,479)
( 64,476)( 65,477)( 66,475)( 67,472)( 68,473)( 69,474)( 70,471)( 71,469)
( 72,470)( 73,566)( 74,567)( 75,565)( 76,562)( 77,563)( 78,564)( 79,561)
( 80,559)( 81,560)( 82,575)( 83,576)( 84,574)( 85,571)( 86,572)( 87,573)
( 88,570)( 89,568)( 90,569)( 91,548)( 92,549)( 93,547)( 94,544)( 95,545)
( 96,546)( 97,543)( 98,541)( 99,542)(100,557)(101,558)(102,556)(103,553)
(104,554)(105,555)(106,552)(107,550)(108,551)(109,530)(110,531)(111,529)
(112,526)(113,527)(114,528)(115,525)(116,523)(117,524)(118,539)(119,540)
(120,538)(121,535)(122,536)(123,537)(124,534)(125,532)(126,533)(127,512)
(128,513)(129,511)(130,508)(131,509)(132,510)(133,507)(134,505)(135,506)
(136,521)(137,522)(138,520)(139,517)(140,518)(141,519)(142,516)(143,514)
(144,515)(145,314)(146,315)(147,313)(148,310)(149,311)(150,312)(151,309)
(152,307)(153,308)(154,323)(155,324)(156,322)(157,319)(158,320)(159,321)
(160,318)(161,316)(162,317)(163,296)(164,297)(165,295)(166,292)(167,293)
(168,294)(169,291)(170,289)(171,290)(172,305)(173,306)(174,304)(175,301)
(176,302)(177,303)(178,300)(179,298)(180,299)(181,359)(182,360)(183,358)
(184,355)(185,356)(186,357)(187,354)(188,352)(189,353)(190,350)(191,351)
(192,349)(193,346)(194,347)(195,348)(196,345)(197,343)(198,344)(199,341)
(200,342)(201,340)(202,337)(203,338)(204,339)(205,336)(206,334)(207,335)
(208,332)(209,333)(210,331)(211,328)(212,329)(213,330)(214,327)(215,325)
(216,326)(217,422)(218,423)(219,421)(220,418)(221,419)(222,420)(223,417)
(224,415)(225,416)(226,431)(227,432)(228,430)(229,427)(230,428)(231,429)
(232,426)(233,424)(234,425)(235,404)(236,405)(237,403)(238,400)(239,401)
(240,402)(241,399)(242,397)(243,398)(244,413)(245,414)(246,412)(247,409)
(248,410)(249,411)(250,408)(251,406)(252,407)(253,386)(254,387)(255,385)
(256,382)(257,383)(258,384)(259,381)(260,379)(261,380)(262,395)(263,396)
(264,394)(265,391)(266,392)(267,393)(268,390)(269,388)(270,389)(271,368)
(272,369)(273,367)(274,364)(275,365)(276,366)(277,363)(278,361)(279,362)
(280,377)(281,378)(282,376)(283,373)(284,374)(285,375)(286,372)(287,370)
(288,371);
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)( 37,118)( 38,119)( 39,120)
( 40,121)( 41,122)( 42,123)( 43,124)( 44,125)( 45,126)( 46,109)( 47,110)
( 48,111)( 49,112)( 50,113)( 51,114)( 52,115)( 53,116)( 54,117)( 55,136)
( 56,137)( 57,138)( 58,139)( 59,140)( 60,141)( 61,142)( 62,143)( 63,144)
( 64,127)( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)
( 72,135)(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)(181,262)(182,263)(183,264)
(184,265)(185,266)(186,267)(187,268)(188,269)(189,270)(190,253)(191,254)
(192,255)(193,256)(194,257)(195,258)(196,259)(197,260)(198,261)(199,280)
(200,281)(201,282)(202,283)(203,284)(204,285)(205,286)(206,287)(207,288)
(208,271)(209,272)(210,273)(211,274)(212,275)(213,276)(214,277)(215,278)
(216,279)(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)(325,406)(326,407)(327,408)
(328,409)(329,410)(330,411)(331,412)(332,413)(333,414)(334,397)(335,398)
(336,399)(337,400)(338,401)(339,402)(340,403)(341,404)(342,405)(343,424)
(344,425)(345,426)(346,427)(347,428)(348,429)(349,430)(350,431)(351,432)
(352,415)(353,416)(354,417)(355,418)(356,419)(357,420)(358,421)(359,422)
(360,423)(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)(469,550)(470,551)(471,552)
(472,553)(473,554)(474,555)(475,556)(476,557)(477,558)(478,541)(479,542)
(480,543)(481,544)(482,545)(483,546)(484,547)(485,548)(486,549)(487,568)
(488,569)(489,570)(490,571)(491,572)(492,573)(493,574)(494,575)(495,576)
(496,559)(497,560)(498,561)(499,562)(500,563)(501,564)(502,565)(503,566)
(504,567);
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*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 
References : None.
to this polytope