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Polytope of Type {6,6,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,16}*1152c
if this polytope has a name.
Group : SmallGroup(1152,133450)
Rank : 4
Schlafli Type : {6,6,16}
Number of vertices, edges, etc : 6, 18, 48, 16
Order of s0s1s2s3 : 48
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 : {3,6,16}*576, {6,6,8}*576c
   3-fold quotients : {6,2,16}*384
   4-fold quotients : {3,6,8}*288, {6,6,4}*288c
   6-fold quotients : {3,2,16}*192, {6,2,8}*192
   8-fold quotients : {3,6,4}*144, {6,6,2}*144c
   9-fold quotients : {2,2,16}*128
   12-fold quotients : {3,2,8}*96, {6,2,4}*96
   16-fold quotients : {3,6,2}*72
   18-fold quotients : {2,2,8}*64
   24-fold quotients : {3,2,4}*48, {6,2,2}*48
   36-fold quotients : {2,2,4}*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, 79)(  5, 81)(  6, 80)(  7, 76)(  8, 78)
(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)( 16, 85)
( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)
( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)
( 33,107)( 34,103)( 35,105)( 36,104)( 37,109)( 38,111)( 39,110)( 40,115)
( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)( 48,119)
( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)( 56,129)
( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)( 64,136)
( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)( 72,140)
(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)(152,222)
(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)(160,229)
(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)(168,242)
(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)(176,252)
(177,251)(178,247)(179,249)(180,248)(181,253)(182,255)(183,254)(184,259)
(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)(192,263)
(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)(200,273)
(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)(208,280)
(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)(216,284)
(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)(296,366)
(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)(304,373)
(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)(312,386)
(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)(320,396)
(321,395)(322,391)(323,393)(324,392)(325,397)(326,399)(327,398)(328,403)
(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)(336,407)
(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)(344,417)
(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)(352,424)
(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)(360,428)
(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)(440,510)
(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)(448,517)
(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)(456,530)
(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)(464,540)
(465,539)(466,535)(467,537)(468,536)(469,541)(470,543)(471,542)(472,547)
(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)(480,551)
(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)(488,561)
(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)(496,568)
(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)(504,572);;
s1 := (  1,218)(  2,217)(  3,219)(  4,224)(  5,223)(  6,225)(  7,221)(  8,220)
(  9,222)( 10,227)( 11,226)( 12,228)( 13,233)( 14,232)( 15,234)( 16,230)
( 17,229)( 18,231)( 19,236)( 20,235)( 21,237)( 22,242)( 23,241)( 24,243)
( 25,239)( 26,238)( 27,240)( 28,245)( 29,244)( 30,246)( 31,251)( 32,250)
( 33,252)( 34,248)( 35,247)( 36,249)( 37,254)( 38,253)( 39,255)( 40,260)
( 41,259)( 42,261)( 43,257)( 44,256)( 45,258)( 46,263)( 47,262)( 48,264)
( 49,269)( 50,268)( 51,270)( 52,266)( 53,265)( 54,267)( 55,272)( 56,271)
( 57,273)( 58,278)( 59,277)( 60,279)( 61,275)( 62,274)( 63,276)( 64,281)
( 65,280)( 66,282)( 67,287)( 68,286)( 69,288)( 70,284)( 71,283)( 72,285)
( 73,146)( 74,145)( 75,147)( 76,152)( 77,151)( 78,153)( 79,149)( 80,148)
( 81,150)( 82,155)( 83,154)( 84,156)( 85,161)( 86,160)( 87,162)( 88,158)
( 89,157)( 90,159)( 91,164)( 92,163)( 93,165)( 94,170)( 95,169)( 96,171)
( 97,167)( 98,166)( 99,168)(100,173)(101,172)(102,174)(103,179)(104,178)
(105,180)(106,176)(107,175)(108,177)(109,182)(110,181)(111,183)(112,188)
(113,187)(114,189)(115,185)(116,184)(117,186)(118,191)(119,190)(120,192)
(121,197)(122,196)(123,198)(124,194)(125,193)(126,195)(127,200)(128,199)
(129,201)(130,206)(131,205)(132,207)(133,203)(134,202)(135,204)(136,209)
(137,208)(138,210)(139,215)(140,214)(141,216)(142,212)(143,211)(144,213)
(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)(296,508)
(297,510)(298,515)(299,514)(300,516)(301,521)(302,520)(303,522)(304,518)
(305,517)(306,519)(307,524)(308,523)(309,525)(310,530)(311,529)(312,531)
(313,527)(314,526)(315,528)(316,533)(317,532)(318,534)(319,539)(320,538)
(321,540)(322,536)(323,535)(324,537)(325,542)(326,541)(327,543)(328,548)
(329,547)(330,549)(331,545)(332,544)(333,546)(334,551)(335,550)(336,552)
(337,557)(338,556)(339,558)(340,554)(341,553)(342,555)(343,560)(344,559)
(345,561)(346,566)(347,565)(348,567)(349,563)(350,562)(351,564)(352,569)
(353,568)(354,570)(355,575)(356,574)(357,576)(358,572)(359,571)(360,573)
(361,434)(362,433)(363,435)(364,440)(365,439)(366,441)(367,437)(368,436)
(369,438)(370,443)(371,442)(372,444)(373,449)(374,448)(375,450)(376,446)
(377,445)(378,447)(379,452)(380,451)(381,453)(382,458)(383,457)(384,459)
(385,455)(386,454)(387,456)(388,461)(389,460)(390,462)(391,467)(392,466)
(393,468)(394,464)(395,463)(396,465)(397,470)(398,469)(399,471)(400,476)
(401,475)(402,477)(403,473)(404,472)(405,474)(406,479)(407,478)(408,480)
(409,485)(410,484)(411,486)(412,482)(413,481)(414,483)(415,488)(416,487)
(417,489)(418,494)(419,493)(420,495)(421,491)(422,490)(423,492)(424,497)
(425,496)(426,498)(427,503)(428,502)(429,504)(430,500)(431,499)(432,501);;
s2 := (  1,289)(  2,294)(  3,296)(  4,292)(  5,297)(  6,290)(  7,295)(  8,291)
(  9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)( 16,304)
( 17,300)( 18,302)( 19,316)( 20,321)( 21,323)( 22,319)( 23,324)( 24,317)
( 25,322)( 26,318)( 27,320)( 28,307)( 29,312)( 30,314)( 31,310)( 32,315)
( 33,308)( 34,313)( 35,309)( 36,311)( 37,343)( 38,348)( 39,350)( 40,346)
( 41,351)( 42,344)( 43,349)( 44,345)( 45,347)( 46,352)( 47,357)( 48,359)
( 49,355)( 50,360)( 51,353)( 52,358)( 53,354)( 54,356)( 55,325)( 56,330)
( 57,332)( 58,328)( 59,333)( 60,326)( 61,331)( 62,327)( 63,329)( 64,334)
( 65,339)( 66,341)( 67,337)( 68,342)( 69,335)( 70,340)( 71,336)( 72,338)
( 73,361)( 74,366)( 75,368)( 76,364)( 77,369)( 78,362)( 79,367)( 80,363)
( 81,365)( 82,370)( 83,375)( 84,377)( 85,373)( 86,378)( 87,371)( 88,376)
( 89,372)( 90,374)( 91,388)( 92,393)( 93,395)( 94,391)( 95,396)( 96,389)
( 97,394)( 98,390)( 99,392)(100,379)(101,384)(102,386)(103,382)(104,387)
(105,380)(106,385)(107,381)(108,383)(109,415)(110,420)(111,422)(112,418)
(113,423)(114,416)(115,421)(116,417)(117,419)(118,424)(119,429)(120,431)
(121,427)(122,432)(123,425)(124,430)(125,426)(126,428)(127,397)(128,402)
(129,404)(130,400)(131,405)(132,398)(133,403)(134,399)(135,401)(136,406)
(137,411)(138,413)(139,409)(140,414)(141,407)(142,412)(143,408)(144,410)
(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)(152,435)
(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)(160,448)
(161,444)(162,446)(163,460)(164,465)(165,467)(166,463)(167,468)(168,461)
(169,466)(170,462)(171,464)(172,451)(173,456)(174,458)(175,454)(176,459)
(177,452)(178,457)(179,453)(180,455)(181,487)(182,492)(183,494)(184,490)
(185,495)(186,488)(187,493)(188,489)(189,491)(190,496)(191,501)(192,503)
(193,499)(194,504)(195,497)(196,502)(197,498)(198,500)(199,469)(200,474)
(201,476)(202,472)(203,477)(204,470)(205,475)(206,471)(207,473)(208,478)
(209,483)(210,485)(211,481)(212,486)(213,479)(214,484)(215,480)(216,482)
(217,505)(218,510)(219,512)(220,508)(221,513)(222,506)(223,511)(224,507)
(225,509)(226,514)(227,519)(228,521)(229,517)(230,522)(231,515)(232,520)
(233,516)(234,518)(235,532)(236,537)(237,539)(238,535)(239,540)(240,533)
(241,538)(242,534)(243,536)(244,523)(245,528)(246,530)(247,526)(248,531)
(249,524)(250,529)(251,525)(252,527)(253,559)(254,564)(255,566)(256,562)
(257,567)(258,560)(259,565)(260,561)(261,563)(262,568)(263,573)(264,575)
(265,571)(266,576)(267,569)(268,574)(269,570)(270,572)(271,541)(272,546)
(273,548)(274,544)(275,549)(276,542)(277,547)(278,543)(279,545)(280,550)
(281,555)(282,557)(283,553)(284,558)(285,551)(286,556)(287,552)(288,554);;
s3 := ( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)
( 27, 36)( 37, 55)( 38, 56)( 39, 57)( 40, 58)( 41, 59)( 42, 60)( 43, 61)
( 44, 62)( 45, 63)( 46, 64)( 47, 65)( 48, 66)( 49, 67)( 50, 68)( 51, 69)
( 52, 70)( 53, 71)( 54, 72)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)
( 96,105)( 97,106)( 98,107)( 99,108)(109,127)(110,128)(111,129)(112,130)
(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138)
(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(163,172)(164,173)
(165,174)(166,175)(167,176)(168,177)(169,178)(170,179)(171,180)(181,199)
(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)(189,207)
(190,208)(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)(197,215)
(198,216)(235,244)(236,245)(237,246)(238,247)(239,248)(240,249)(241,250)
(242,251)(243,252)(253,271)(254,272)(255,273)(256,274)(257,275)(258,276)
(259,277)(260,278)(261,279)(262,280)(263,281)(264,282)(265,283)(266,284)
(267,285)(268,286)(269,287)(270,288)(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)(307,352)(308,353)
(309,354)(310,355)(311,356)(312,357)(313,358)(314,359)(315,360)(316,343)
(317,344)(318,345)(319,346)(320,347)(321,348)(322,349)(323,350)(324,351)
(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)(379,424)(380,425)(381,426)(382,427)(383,428)(384,429)
(385,430)(386,431)(387,432)(388,415)(389,416)(390,417)(391,418)(392,419)
(393,420)(394,421)(395,422)(396,423)(433,469)(434,470)(435,471)(436,472)
(437,473)(438,474)(439,475)(440,476)(441,477)(442,478)(443,479)(444,480)
(445,481)(446,482)(447,483)(448,484)(449,485)(450,486)(451,496)(452,497)
(453,498)(454,499)(455,500)(456,501)(457,502)(458,503)(459,504)(460,487)
(461,488)(462,489)(463,490)(464,491)(465,492)(466,493)(467,494)(468,495)
(505,541)(506,542)(507,543)(508,544)(509,545)(510,546)(511,547)(512,548)
(513,549)(514,550)(515,551)(516,552)(517,553)(518,554)(519,555)(520,556)
(521,557)(522,558)(523,568)(524,569)(525,570)(526,571)(527,572)(528,573)
(529,574)(530,575)(531,576)(532,559)(533,560)(534,561)(535,562)(536,563)
(537,564)(538,565)(539,566)(540,567);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)
(  8, 78)(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)
( 16, 85)( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)
( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)
( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,109)( 38,111)( 39,110)
( 40,115)( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)
( 48,119)( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)
( 56,129)( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)
( 64,136)( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)
( 72,140)(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)
(152,222)(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)
(160,229)(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)
(168,242)(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)
(176,252)(177,251)(178,247)(179,249)(180,248)(181,253)(182,255)(183,254)
(184,259)(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)
(192,263)(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)
(200,273)(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)
(208,280)(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)
(216,284)(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)
(296,366)(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)
(304,373)(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)
(312,386)(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)
(320,396)(321,395)(322,391)(323,393)(324,392)(325,397)(326,399)(327,398)
(328,403)(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)
(336,407)(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)
(344,417)(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)
(352,424)(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)
(360,428)(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)
(440,510)(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)
(448,517)(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)
(456,530)(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)
(464,540)(465,539)(466,535)(467,537)(468,536)(469,541)(470,543)(471,542)
(472,547)(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)
(480,551)(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)
(488,561)(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)
(496,568)(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)
(504,572);
s1 := Sym(576)!(  1,218)(  2,217)(  3,219)(  4,224)(  5,223)(  6,225)(  7,221)
(  8,220)(  9,222)( 10,227)( 11,226)( 12,228)( 13,233)( 14,232)( 15,234)
( 16,230)( 17,229)( 18,231)( 19,236)( 20,235)( 21,237)( 22,242)( 23,241)
( 24,243)( 25,239)( 26,238)( 27,240)( 28,245)( 29,244)( 30,246)( 31,251)
( 32,250)( 33,252)( 34,248)( 35,247)( 36,249)( 37,254)( 38,253)( 39,255)
( 40,260)( 41,259)( 42,261)( 43,257)( 44,256)( 45,258)( 46,263)( 47,262)
( 48,264)( 49,269)( 50,268)( 51,270)( 52,266)( 53,265)( 54,267)( 55,272)
( 56,271)( 57,273)( 58,278)( 59,277)( 60,279)( 61,275)( 62,274)( 63,276)
( 64,281)( 65,280)( 66,282)( 67,287)( 68,286)( 69,288)( 70,284)( 71,283)
( 72,285)( 73,146)( 74,145)( 75,147)( 76,152)( 77,151)( 78,153)( 79,149)
( 80,148)( 81,150)( 82,155)( 83,154)( 84,156)( 85,161)( 86,160)( 87,162)
( 88,158)( 89,157)( 90,159)( 91,164)( 92,163)( 93,165)( 94,170)( 95,169)
( 96,171)( 97,167)( 98,166)( 99,168)(100,173)(101,172)(102,174)(103,179)
(104,178)(105,180)(106,176)(107,175)(108,177)(109,182)(110,181)(111,183)
(112,188)(113,187)(114,189)(115,185)(116,184)(117,186)(118,191)(119,190)
(120,192)(121,197)(122,196)(123,198)(124,194)(125,193)(126,195)(127,200)
(128,199)(129,201)(130,206)(131,205)(132,207)(133,203)(134,202)(135,204)
(136,209)(137,208)(138,210)(139,215)(140,214)(141,216)(142,212)(143,211)
(144,213)(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)
(296,508)(297,510)(298,515)(299,514)(300,516)(301,521)(302,520)(303,522)
(304,518)(305,517)(306,519)(307,524)(308,523)(309,525)(310,530)(311,529)
(312,531)(313,527)(314,526)(315,528)(316,533)(317,532)(318,534)(319,539)
(320,538)(321,540)(322,536)(323,535)(324,537)(325,542)(326,541)(327,543)
(328,548)(329,547)(330,549)(331,545)(332,544)(333,546)(334,551)(335,550)
(336,552)(337,557)(338,556)(339,558)(340,554)(341,553)(342,555)(343,560)
(344,559)(345,561)(346,566)(347,565)(348,567)(349,563)(350,562)(351,564)
(352,569)(353,568)(354,570)(355,575)(356,574)(357,576)(358,572)(359,571)
(360,573)(361,434)(362,433)(363,435)(364,440)(365,439)(366,441)(367,437)
(368,436)(369,438)(370,443)(371,442)(372,444)(373,449)(374,448)(375,450)
(376,446)(377,445)(378,447)(379,452)(380,451)(381,453)(382,458)(383,457)
(384,459)(385,455)(386,454)(387,456)(388,461)(389,460)(390,462)(391,467)
(392,466)(393,468)(394,464)(395,463)(396,465)(397,470)(398,469)(399,471)
(400,476)(401,475)(402,477)(403,473)(404,472)(405,474)(406,479)(407,478)
(408,480)(409,485)(410,484)(411,486)(412,482)(413,481)(414,483)(415,488)
(416,487)(417,489)(418,494)(419,493)(420,495)(421,491)(422,490)(423,492)
(424,497)(425,496)(426,498)(427,503)(428,502)(429,504)(430,500)(431,499)
(432,501);
s2 := Sym(576)!(  1,289)(  2,294)(  3,296)(  4,292)(  5,297)(  6,290)(  7,295)
(  8,291)(  9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)
( 16,304)( 17,300)( 18,302)( 19,316)( 20,321)( 21,323)( 22,319)( 23,324)
( 24,317)( 25,322)( 26,318)( 27,320)( 28,307)( 29,312)( 30,314)( 31,310)
( 32,315)( 33,308)( 34,313)( 35,309)( 36,311)( 37,343)( 38,348)( 39,350)
( 40,346)( 41,351)( 42,344)( 43,349)( 44,345)( 45,347)( 46,352)( 47,357)
( 48,359)( 49,355)( 50,360)( 51,353)( 52,358)( 53,354)( 54,356)( 55,325)
( 56,330)( 57,332)( 58,328)( 59,333)( 60,326)( 61,331)( 62,327)( 63,329)
( 64,334)( 65,339)( 66,341)( 67,337)( 68,342)( 69,335)( 70,340)( 71,336)
( 72,338)( 73,361)( 74,366)( 75,368)( 76,364)( 77,369)( 78,362)( 79,367)
( 80,363)( 81,365)( 82,370)( 83,375)( 84,377)( 85,373)( 86,378)( 87,371)
( 88,376)( 89,372)( 90,374)( 91,388)( 92,393)( 93,395)( 94,391)( 95,396)
( 96,389)( 97,394)( 98,390)( 99,392)(100,379)(101,384)(102,386)(103,382)
(104,387)(105,380)(106,385)(107,381)(108,383)(109,415)(110,420)(111,422)
(112,418)(113,423)(114,416)(115,421)(116,417)(117,419)(118,424)(119,429)
(120,431)(121,427)(122,432)(123,425)(124,430)(125,426)(126,428)(127,397)
(128,402)(129,404)(130,400)(131,405)(132,398)(133,403)(134,399)(135,401)
(136,406)(137,411)(138,413)(139,409)(140,414)(141,407)(142,412)(143,408)
(144,410)(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)
(152,435)(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)
(160,448)(161,444)(162,446)(163,460)(164,465)(165,467)(166,463)(167,468)
(168,461)(169,466)(170,462)(171,464)(172,451)(173,456)(174,458)(175,454)
(176,459)(177,452)(178,457)(179,453)(180,455)(181,487)(182,492)(183,494)
(184,490)(185,495)(186,488)(187,493)(188,489)(189,491)(190,496)(191,501)
(192,503)(193,499)(194,504)(195,497)(196,502)(197,498)(198,500)(199,469)
(200,474)(201,476)(202,472)(203,477)(204,470)(205,475)(206,471)(207,473)
(208,478)(209,483)(210,485)(211,481)(212,486)(213,479)(214,484)(215,480)
(216,482)(217,505)(218,510)(219,512)(220,508)(221,513)(222,506)(223,511)
(224,507)(225,509)(226,514)(227,519)(228,521)(229,517)(230,522)(231,515)
(232,520)(233,516)(234,518)(235,532)(236,537)(237,539)(238,535)(239,540)
(240,533)(241,538)(242,534)(243,536)(244,523)(245,528)(246,530)(247,526)
(248,531)(249,524)(250,529)(251,525)(252,527)(253,559)(254,564)(255,566)
(256,562)(257,567)(258,560)(259,565)(260,561)(261,563)(262,568)(263,573)
(264,575)(265,571)(266,576)(267,569)(268,574)(269,570)(270,572)(271,541)
(272,546)(273,548)(274,544)(275,549)(276,542)(277,547)(278,543)(279,545)
(280,550)(281,555)(282,557)(283,553)(284,558)(285,551)(286,556)(287,552)
(288,554);
s3 := Sym(576)!( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)
( 26, 35)( 27, 36)( 37, 55)( 38, 56)( 39, 57)( 40, 58)( 41, 59)( 42, 60)
( 43, 61)( 44, 62)( 45, 63)( 46, 64)( 47, 65)( 48, 66)( 49, 67)( 50, 68)
( 51, 69)( 52, 70)( 53, 71)( 54, 72)( 91,100)( 92,101)( 93,102)( 94,103)
( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(109,127)(110,128)(111,129)
(112,130)(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)
(120,138)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(163,172)
(164,173)(165,174)(166,175)(167,176)(168,177)(169,178)(170,179)(171,180)
(181,199)(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)
(189,207)(190,208)(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)
(197,215)(198,216)(235,244)(236,245)(237,246)(238,247)(239,248)(240,249)
(241,250)(242,251)(243,252)(253,271)(254,272)(255,273)(256,274)(257,275)
(258,276)(259,277)(260,278)(261,279)(262,280)(263,281)(264,282)(265,283)
(266,284)(267,285)(268,286)(269,287)(270,288)(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)(307,352)
(308,353)(309,354)(310,355)(311,356)(312,357)(313,358)(314,359)(315,360)
(316,343)(317,344)(318,345)(319,346)(320,347)(321,348)(322,349)(323,350)
(324,351)(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)(379,424)(380,425)(381,426)(382,427)(383,428)
(384,429)(385,430)(386,431)(387,432)(388,415)(389,416)(390,417)(391,418)
(392,419)(393,420)(394,421)(395,422)(396,423)(433,469)(434,470)(435,471)
(436,472)(437,473)(438,474)(439,475)(440,476)(441,477)(442,478)(443,479)
(444,480)(445,481)(446,482)(447,483)(448,484)(449,485)(450,486)(451,496)
(452,497)(453,498)(454,499)(455,500)(456,501)(457,502)(458,503)(459,504)
(460,487)(461,488)(462,489)(463,490)(464,491)(465,492)(466,493)(467,494)
(468,495)(505,541)(506,542)(507,543)(508,544)(509,545)(510,546)(511,547)
(512,548)(513,549)(514,550)(515,551)(516,552)(517,553)(518,554)(519,555)
(520,556)(521,557)(522,558)(523,568)(524,569)(525,570)(526,571)(527,572)
(528,573)(529,574)(530,575)(531,576)(532,559)(533,560)(534,561)(535,562)
(536,563)(537,564)(538,565)(539,566)(540,567);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope