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Polytope of Type {18,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,8,4}*1152a
Also Known As : {{18,8|2},{8,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,97511)
Rank : 4
Schlafli Type : {18,8,4}
Number of vertices, edges, etc : 18, 72, 16, 4
Order of s0s1s2s3 : 72
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 : {18,4,4}*576, {18,8,2}*576
   3-fold quotients : {6,8,4}*384a
   4-fold quotients : {18,2,4}*288, {18,4,2}*288a
   6-fold quotients : {6,4,4}*192, {6,8,2}*192
   8-fold quotients : {9,2,4}*144, {18,2,2}*144
   9-fold quotients : {2,8,4}*128a
   12-fold quotients : {6,2,4}*96, {6,4,2}*96a
   16-fold quotients : {9,2,2}*72
   18-fold quotients : {2,4,4}*64, {2,8,2}*64
   24-fold quotients : {3,2,4}*48, {6,2,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   48-fold quotients : {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 73)(  2, 75)(  3, 74)(  4, 81)(  5, 80)(  6, 79)(  7, 78)(  8, 77)
(  9, 76)( 10, 82)( 11, 84)( 12, 83)( 13, 90)( 14, 89)( 15, 88)( 16, 87)
( 17, 86)( 18, 85)( 19, 91)( 20, 93)( 21, 92)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28,100)( 29,102)( 30,101)( 31,108)( 32,107)
( 33,106)( 34,105)( 35,104)( 36,103)( 37,109)( 38,111)( 39,110)( 40,117)
( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,118)( 47,120)( 48,119)
( 49,126)( 50,125)( 51,124)( 52,123)( 53,122)( 54,121)( 55,127)( 56,129)
( 57,128)( 58,135)( 59,134)( 60,133)( 61,132)( 62,131)( 63,130)( 64,136)
( 65,138)( 66,137)( 67,144)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139)
(145,217)(146,219)(147,218)(148,225)(149,224)(150,223)(151,222)(152,221)
(153,220)(154,226)(155,228)(156,227)(157,234)(158,233)(159,232)(160,231)
(161,230)(162,229)(163,235)(164,237)(165,236)(166,243)(167,242)(168,241)
(169,240)(170,239)(171,238)(172,244)(173,246)(174,245)(175,252)(176,251)
(177,250)(178,249)(179,248)(180,247)(181,253)(182,255)(183,254)(184,261)
(185,260)(186,259)(187,258)(188,257)(189,256)(190,262)(191,264)(192,263)
(193,270)(194,269)(195,268)(196,267)(197,266)(198,265)(199,271)(200,273)
(201,272)(202,279)(203,278)(204,277)(205,276)(206,275)(207,274)(208,280)
(209,282)(210,281)(211,288)(212,287)(213,286)(214,285)(215,284)(216,283)
(289,361)(290,363)(291,362)(292,369)(293,368)(294,367)(295,366)(296,365)
(297,364)(298,370)(299,372)(300,371)(301,378)(302,377)(303,376)(304,375)
(305,374)(306,373)(307,379)(308,381)(309,380)(310,387)(311,386)(312,385)
(313,384)(314,383)(315,382)(316,388)(317,390)(318,389)(319,396)(320,395)
(321,394)(322,393)(323,392)(324,391)(325,397)(326,399)(327,398)(328,405)
(329,404)(330,403)(331,402)(332,401)(333,400)(334,406)(335,408)(336,407)
(337,414)(338,413)(339,412)(340,411)(341,410)(342,409)(343,415)(344,417)
(345,416)(346,423)(347,422)(348,421)(349,420)(350,419)(351,418)(352,424)
(353,426)(354,425)(355,432)(356,431)(357,430)(358,429)(359,428)(360,427)
(433,505)(434,507)(435,506)(436,513)(437,512)(438,511)(439,510)(440,509)
(441,508)(442,514)(443,516)(444,515)(445,522)(446,521)(447,520)(448,519)
(449,518)(450,517)(451,523)(452,525)(453,524)(454,531)(455,530)(456,529)
(457,528)(458,527)(459,526)(460,532)(461,534)(462,533)(463,540)(464,539)
(465,538)(466,537)(467,536)(468,535)(469,541)(470,543)(471,542)(472,549)
(473,548)(474,547)(475,546)(476,545)(477,544)(478,550)(479,552)(480,551)
(481,558)(482,557)(483,556)(484,555)(485,554)(486,553)(487,559)(488,561)
(489,560)(490,567)(491,566)(492,565)(493,564)(494,563)(495,562)(496,568)
(497,570)(498,569)(499,576)(500,575)(501,574)(502,573)(503,572)(504,571);;
s1 := (  1,364)(  2,366)(  3,365)(  4,361)(  5,363)(  6,362)(  7,369)(  8,368)
(  9,367)( 10,373)( 11,375)( 12,374)( 13,370)( 14,372)( 15,371)( 16,378)
( 17,377)( 18,376)( 19,382)( 20,384)( 21,383)( 22,379)( 23,381)( 24,380)
( 25,387)( 26,386)( 27,385)( 28,391)( 29,393)( 30,392)( 31,388)( 32,390)
( 33,389)( 34,396)( 35,395)( 36,394)( 37,409)( 38,411)( 39,410)( 40,406)
( 41,408)( 42,407)( 43,414)( 44,413)( 45,412)( 46,400)( 47,402)( 48,401)
( 49,397)( 50,399)( 51,398)( 52,405)( 53,404)( 54,403)( 55,427)( 56,429)
( 57,428)( 58,424)( 59,426)( 60,425)( 61,432)( 62,431)( 63,430)( 64,418)
( 65,420)( 66,419)( 67,415)( 68,417)( 69,416)( 70,423)( 71,422)( 72,421)
( 73,292)( 74,294)( 75,293)( 76,289)( 77,291)( 78,290)( 79,297)( 80,296)
( 81,295)( 82,301)( 83,303)( 84,302)( 85,298)( 86,300)( 87,299)( 88,306)
( 89,305)( 90,304)( 91,310)( 92,312)( 93,311)( 94,307)( 95,309)( 96,308)
( 97,315)( 98,314)( 99,313)(100,319)(101,321)(102,320)(103,316)(104,318)
(105,317)(106,324)(107,323)(108,322)(109,337)(110,339)(111,338)(112,334)
(113,336)(114,335)(115,342)(116,341)(117,340)(118,328)(119,330)(120,329)
(121,325)(122,327)(123,326)(124,333)(125,332)(126,331)(127,355)(128,357)
(129,356)(130,352)(131,354)(132,353)(133,360)(134,359)(135,358)(136,346)
(137,348)(138,347)(139,343)(140,345)(141,344)(142,351)(143,350)(144,349)
(145,508)(146,510)(147,509)(148,505)(149,507)(150,506)(151,513)(152,512)
(153,511)(154,517)(155,519)(156,518)(157,514)(158,516)(159,515)(160,522)
(161,521)(162,520)(163,526)(164,528)(165,527)(166,523)(167,525)(168,524)
(169,531)(170,530)(171,529)(172,535)(173,537)(174,536)(175,532)(176,534)
(177,533)(178,540)(179,539)(180,538)(181,553)(182,555)(183,554)(184,550)
(185,552)(186,551)(187,558)(188,557)(189,556)(190,544)(191,546)(192,545)
(193,541)(194,543)(195,542)(196,549)(197,548)(198,547)(199,571)(200,573)
(201,572)(202,568)(203,570)(204,569)(205,576)(206,575)(207,574)(208,562)
(209,564)(210,563)(211,559)(212,561)(213,560)(214,567)(215,566)(216,565)
(217,436)(218,438)(219,437)(220,433)(221,435)(222,434)(223,441)(224,440)
(225,439)(226,445)(227,447)(228,446)(229,442)(230,444)(231,443)(232,450)
(233,449)(234,448)(235,454)(236,456)(237,455)(238,451)(239,453)(240,452)
(241,459)(242,458)(243,457)(244,463)(245,465)(246,464)(247,460)(248,462)
(249,461)(250,468)(251,467)(252,466)(253,481)(254,483)(255,482)(256,478)
(257,480)(258,479)(259,486)(260,485)(261,484)(262,472)(263,474)(264,473)
(265,469)(266,471)(267,470)(268,477)(269,476)(270,475)(271,499)(272,501)
(273,500)(274,496)(275,498)(276,497)(277,504)(278,503)(279,502)(280,490)
(281,492)(282,491)(283,487)(284,489)(285,488)(286,495)(287,494)(288,493);;
s2 := ( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)
( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)
( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)(114,123)
(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)(131,140)
(132,141)(133,142)(134,143)(135,144)(145,163)(146,164)(147,165)(148,166)
(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)(156,174)
(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,208)(182,209)
(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)(190,199)
(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)(198,207)
(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)(224,242)
(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)(232,250)
(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)(258,285)
(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)(266,275)
(267,276)(268,277)(269,278)(270,279)(289,325)(290,326)(291,327)(292,328)
(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)
(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)(308,344)
(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)(316,352)
(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)(324,360)
(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)(368,404)
(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)(376,412)
(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)(384,420)
(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)(392,428)
(393,429)(394,430)(395,431)(396,432)(433,487)(434,488)(435,489)(436,490)
(437,491)(438,492)(439,493)(440,494)(441,495)(442,496)(443,497)(444,498)
(445,499)(446,500)(447,501)(448,502)(449,503)(450,504)(451,469)(452,470)
(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)(460,478)
(461,479)(462,480)(463,481)(464,482)(465,483)(466,484)(467,485)(468,486)
(505,559)(506,560)(507,561)(508,562)(509,563)(510,564)(511,565)(512,566)
(513,567)(514,568)(515,569)(516,570)(517,571)(518,572)(519,573)(520,574)
(521,575)(522,576)(523,541)(524,542)(525,543)(526,544)(527,545)(528,546)
(529,547)(530,548)(531,549)(532,550)(533,551)(534,552)(535,553)(536,554)
(537,555)(538,556)(539,557)(540,558);;
s3 := (  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)
( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)
( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)(104,248)
(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)(112,256)
(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)
(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)
(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)
(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)
(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)
(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)(368,512)
(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)(376,520)
(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)(384,528)
(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)(392,536)
(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)(400,544)
(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)
(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)
(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)
(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1, 73)(  2, 75)(  3, 74)(  4, 81)(  5, 80)(  6, 79)(  7, 78)
(  8, 77)(  9, 76)( 10, 82)( 11, 84)( 12, 83)( 13, 90)( 14, 89)( 15, 88)
( 16, 87)( 17, 86)( 18, 85)( 19, 91)( 20, 93)( 21, 92)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28,100)( 29,102)( 30,101)( 31,108)
( 32,107)( 33,106)( 34,105)( 35,104)( 36,103)( 37,109)( 38,111)( 39,110)
( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,118)( 47,120)
( 48,119)( 49,126)( 50,125)( 51,124)( 52,123)( 53,122)( 54,121)( 55,127)
( 56,129)( 57,128)( 58,135)( 59,134)( 60,133)( 61,132)( 62,131)( 63,130)
( 64,136)( 65,138)( 66,137)( 67,144)( 68,143)( 69,142)( 70,141)( 71,140)
( 72,139)(145,217)(146,219)(147,218)(148,225)(149,224)(150,223)(151,222)
(152,221)(153,220)(154,226)(155,228)(156,227)(157,234)(158,233)(159,232)
(160,231)(161,230)(162,229)(163,235)(164,237)(165,236)(166,243)(167,242)
(168,241)(169,240)(170,239)(171,238)(172,244)(173,246)(174,245)(175,252)
(176,251)(177,250)(178,249)(179,248)(180,247)(181,253)(182,255)(183,254)
(184,261)(185,260)(186,259)(187,258)(188,257)(189,256)(190,262)(191,264)
(192,263)(193,270)(194,269)(195,268)(196,267)(197,266)(198,265)(199,271)
(200,273)(201,272)(202,279)(203,278)(204,277)(205,276)(206,275)(207,274)
(208,280)(209,282)(210,281)(211,288)(212,287)(213,286)(214,285)(215,284)
(216,283)(289,361)(290,363)(291,362)(292,369)(293,368)(294,367)(295,366)
(296,365)(297,364)(298,370)(299,372)(300,371)(301,378)(302,377)(303,376)
(304,375)(305,374)(306,373)(307,379)(308,381)(309,380)(310,387)(311,386)
(312,385)(313,384)(314,383)(315,382)(316,388)(317,390)(318,389)(319,396)
(320,395)(321,394)(322,393)(323,392)(324,391)(325,397)(326,399)(327,398)
(328,405)(329,404)(330,403)(331,402)(332,401)(333,400)(334,406)(335,408)
(336,407)(337,414)(338,413)(339,412)(340,411)(341,410)(342,409)(343,415)
(344,417)(345,416)(346,423)(347,422)(348,421)(349,420)(350,419)(351,418)
(352,424)(353,426)(354,425)(355,432)(356,431)(357,430)(358,429)(359,428)
(360,427)(433,505)(434,507)(435,506)(436,513)(437,512)(438,511)(439,510)
(440,509)(441,508)(442,514)(443,516)(444,515)(445,522)(446,521)(447,520)
(448,519)(449,518)(450,517)(451,523)(452,525)(453,524)(454,531)(455,530)
(456,529)(457,528)(458,527)(459,526)(460,532)(461,534)(462,533)(463,540)
(464,539)(465,538)(466,537)(467,536)(468,535)(469,541)(470,543)(471,542)
(472,549)(473,548)(474,547)(475,546)(476,545)(477,544)(478,550)(479,552)
(480,551)(481,558)(482,557)(483,556)(484,555)(485,554)(486,553)(487,559)
(488,561)(489,560)(490,567)(491,566)(492,565)(493,564)(494,563)(495,562)
(496,568)(497,570)(498,569)(499,576)(500,575)(501,574)(502,573)(503,572)
(504,571);
s1 := Sym(576)!(  1,364)(  2,366)(  3,365)(  4,361)(  5,363)(  6,362)(  7,369)
(  8,368)(  9,367)( 10,373)( 11,375)( 12,374)( 13,370)( 14,372)( 15,371)
( 16,378)( 17,377)( 18,376)( 19,382)( 20,384)( 21,383)( 22,379)( 23,381)
( 24,380)( 25,387)( 26,386)( 27,385)( 28,391)( 29,393)( 30,392)( 31,388)
( 32,390)( 33,389)( 34,396)( 35,395)( 36,394)( 37,409)( 38,411)( 39,410)
( 40,406)( 41,408)( 42,407)( 43,414)( 44,413)( 45,412)( 46,400)( 47,402)
( 48,401)( 49,397)( 50,399)( 51,398)( 52,405)( 53,404)( 54,403)( 55,427)
( 56,429)( 57,428)( 58,424)( 59,426)( 60,425)( 61,432)( 62,431)( 63,430)
( 64,418)( 65,420)( 66,419)( 67,415)( 68,417)( 69,416)( 70,423)( 71,422)
( 72,421)( 73,292)( 74,294)( 75,293)( 76,289)( 77,291)( 78,290)( 79,297)
( 80,296)( 81,295)( 82,301)( 83,303)( 84,302)( 85,298)( 86,300)( 87,299)
( 88,306)( 89,305)( 90,304)( 91,310)( 92,312)( 93,311)( 94,307)( 95,309)
( 96,308)( 97,315)( 98,314)( 99,313)(100,319)(101,321)(102,320)(103,316)
(104,318)(105,317)(106,324)(107,323)(108,322)(109,337)(110,339)(111,338)
(112,334)(113,336)(114,335)(115,342)(116,341)(117,340)(118,328)(119,330)
(120,329)(121,325)(122,327)(123,326)(124,333)(125,332)(126,331)(127,355)
(128,357)(129,356)(130,352)(131,354)(132,353)(133,360)(134,359)(135,358)
(136,346)(137,348)(138,347)(139,343)(140,345)(141,344)(142,351)(143,350)
(144,349)(145,508)(146,510)(147,509)(148,505)(149,507)(150,506)(151,513)
(152,512)(153,511)(154,517)(155,519)(156,518)(157,514)(158,516)(159,515)
(160,522)(161,521)(162,520)(163,526)(164,528)(165,527)(166,523)(167,525)
(168,524)(169,531)(170,530)(171,529)(172,535)(173,537)(174,536)(175,532)
(176,534)(177,533)(178,540)(179,539)(180,538)(181,553)(182,555)(183,554)
(184,550)(185,552)(186,551)(187,558)(188,557)(189,556)(190,544)(191,546)
(192,545)(193,541)(194,543)(195,542)(196,549)(197,548)(198,547)(199,571)
(200,573)(201,572)(202,568)(203,570)(204,569)(205,576)(206,575)(207,574)
(208,562)(209,564)(210,563)(211,559)(212,561)(213,560)(214,567)(215,566)
(216,565)(217,436)(218,438)(219,437)(220,433)(221,435)(222,434)(223,441)
(224,440)(225,439)(226,445)(227,447)(228,446)(229,442)(230,444)(231,443)
(232,450)(233,449)(234,448)(235,454)(236,456)(237,455)(238,451)(239,453)
(240,452)(241,459)(242,458)(243,457)(244,463)(245,465)(246,464)(247,460)
(248,462)(249,461)(250,468)(251,467)(252,466)(253,481)(254,483)(255,482)
(256,478)(257,480)(258,479)(259,486)(260,485)(261,484)(262,472)(263,474)
(264,473)(265,469)(266,471)(267,470)(268,477)(269,476)(270,475)(271,499)
(272,501)(273,500)(274,496)(275,498)(276,497)(277,504)(278,503)(279,502)
(280,490)(281,492)(282,491)(283,487)(284,489)(285,488)(286,495)(287,494)
(288,493);
s2 := Sym(576)!( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)
( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)
( 61, 70)( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)
(114,123)(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)
(131,140)(132,141)(133,142)(134,143)(135,144)(145,163)(146,164)(147,165)
(148,166)(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)
(156,174)(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,208)
(182,209)(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)
(190,199)(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)
(198,207)(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)
(224,242)(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)
(232,250)(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)
(258,285)(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)
(266,275)(267,276)(268,277)(269,278)(270,279)(289,325)(290,326)(291,327)
(292,328)(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)
(300,336)(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)
(308,344)(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)
(316,352)(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)
(324,360)(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)
(368,404)(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)
(376,412)(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)
(384,420)(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)
(392,428)(393,429)(394,430)(395,431)(396,432)(433,487)(434,488)(435,489)
(436,490)(437,491)(438,492)(439,493)(440,494)(441,495)(442,496)(443,497)
(444,498)(445,499)(446,500)(447,501)(448,502)(449,503)(450,504)(451,469)
(452,470)(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)
(460,478)(461,479)(462,480)(463,481)(464,482)(465,483)(466,484)(467,485)
(468,486)(505,559)(506,560)(507,561)(508,562)(509,563)(510,564)(511,565)
(512,566)(513,567)(514,568)(515,569)(516,570)(517,571)(518,572)(519,573)
(520,574)(521,575)(522,576)(523,541)(524,542)(525,543)(526,544)(527,545)
(528,546)(529,547)(530,548)(531,549)(532,550)(533,551)(534,552)(535,553)
(536,554)(537,555)(538,556)(539,557)(540,558);
s3 := 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)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)
( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)
( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)
( 96,240)( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)
(104,248)(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)
(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)
(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)
(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)
(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)
(144,288)(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)(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)
(368,512)(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)
(376,520)(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)
(384,528)(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)
(392,536)(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)
(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)
(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)
(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)
(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)
(432,576);
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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope