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Polytope of Type {18,4,8}

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