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# Polytope of Type {6,24,4}

Atlas Canonical Name : {6,24,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97536)
Rank : 4
Schlafli Type : {6,24,4}
Number of vertices, edges, etc : 6, 72, 48, 4
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 : {6,24,2}*576c, {6,12,4}*576c
3-fold quotients : {6,8,4}*384a
4-fold quotients : {6,6,4}*288c, {6,12,2}*288c
6-fold quotients : {6,4,4}*192, {6,8,2}*192
8-fold quotients : {3,6,4}*144, {6,6,2}*144c
9-fold quotients : {2,8,4}*128a
12-fold quotients : {6,2,4}*96, {6,4,2}*96a
16-fold quotients : {3,6,2}*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, 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 := (  1,362)(  2,361)(  3,363)(  4,368)(  5,367)(  6,369)(  7,365)(  8,364)
(  9,366)( 10,371)( 11,370)( 12,372)( 13,377)( 14,376)( 15,378)( 16,374)
( 17,373)( 18,375)( 19,380)( 20,379)( 21,381)( 22,386)( 23,385)( 24,387)
( 25,383)( 26,382)( 27,384)( 28,389)( 29,388)( 30,390)( 31,395)( 32,394)
( 33,396)( 34,392)( 35,391)( 36,393)( 37,407)( 38,406)( 39,408)( 40,413)
( 41,412)( 42,414)( 43,410)( 44,409)( 45,411)( 46,398)( 47,397)( 48,399)
( 49,404)( 50,403)( 51,405)( 52,401)( 53,400)( 54,402)( 55,425)( 56,424)
( 57,426)( 58,431)( 59,430)( 60,432)( 61,428)( 62,427)( 63,429)( 64,416)
( 65,415)( 66,417)( 67,422)( 68,421)( 69,423)( 70,419)( 71,418)( 72,420)
( 73,290)( 74,289)( 75,291)( 76,296)( 77,295)( 78,297)( 79,293)( 80,292)
( 81,294)( 82,299)( 83,298)( 84,300)( 85,305)( 86,304)( 87,306)( 88,302)
( 89,301)( 90,303)( 91,308)( 92,307)( 93,309)( 94,314)( 95,313)( 96,315)
( 97,311)( 98,310)( 99,312)(100,317)(101,316)(102,318)(103,323)(104,322)
(105,324)(106,320)(107,319)(108,321)(109,335)(110,334)(111,336)(112,341)
(113,340)(114,342)(115,338)(116,337)(117,339)(118,326)(119,325)(120,327)
(121,332)(122,331)(123,333)(124,329)(125,328)(126,330)(127,353)(128,352)
(129,354)(130,359)(131,358)(132,360)(133,356)(134,355)(135,357)(136,344)
(137,343)(138,345)(139,350)(140,349)(141,351)(142,347)(143,346)(144,348)
(145,506)(146,505)(147,507)(148,512)(149,511)(150,513)(151,509)(152,508)
(153,510)(154,515)(155,514)(156,516)(157,521)(158,520)(159,522)(160,518)
(161,517)(162,519)(163,524)(164,523)(165,525)(166,530)(167,529)(168,531)
(169,527)(170,526)(171,528)(172,533)(173,532)(174,534)(175,539)(176,538)
(177,540)(178,536)(179,535)(180,537)(181,551)(182,550)(183,552)(184,557)
(185,556)(186,558)(187,554)(188,553)(189,555)(190,542)(191,541)(192,543)
(193,548)(194,547)(195,549)(196,545)(197,544)(198,546)(199,569)(200,568)
(201,570)(202,575)(203,574)(204,576)(205,572)(206,571)(207,573)(208,560)
(209,559)(210,561)(211,566)(212,565)(213,567)(214,563)(215,562)(216,564)
(217,434)(218,433)(219,435)(220,440)(221,439)(222,441)(223,437)(224,436)
(225,438)(226,443)(227,442)(228,444)(229,449)(230,448)(231,450)(232,446)
(233,445)(234,447)(235,452)(236,451)(237,453)(238,458)(239,457)(240,459)
(241,455)(242,454)(243,456)(244,461)(245,460)(246,462)(247,467)(248,466)
(249,468)(250,464)(251,463)(252,465)(253,479)(254,478)(255,480)(256,485)
(257,484)(258,486)(259,482)(260,481)(261,483)(262,470)(263,469)(264,471)
(265,476)(266,475)(267,477)(268,473)(269,472)(270,474)(271,497)(272,496)
(273,498)(274,503)(275,502)(276,504)(277,500)(278,499)(279,501)(280,488)
(281,487)(282,489)(283,494)(284,493)(285,495)(286,491)(287,490)(288,492);;
s2 := (  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)( 40, 49)
( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)( 57, 71)
( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 74, 78)( 75, 80)
( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)(101,105)
(102,107)(104,108)(109,118)(110,123)(111,125)(112,121)(113,126)(114,119)
(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)(131,144)
(132,137)(133,142)(134,138)(135,140)(145,163)(146,168)(147,170)(148,166)
(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)(156,179)
(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,208)(182,213)
(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)(190,199)
(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)(198,203)
(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)(224,237)
(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)(232,250)
(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)(258,281)
(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)(266,279)
(267,272)(268,277)(269,273)(270,275)(289,325)(290,330)(291,332)(292,328)
(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)(300,341)
(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)(308,348)
(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)(316,352)
(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)(324,356)
(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)(368,399)
(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)(376,412)
(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)(384,416)
(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)(392,432)
(393,425)(394,430)(395,426)(396,428)(433,487)(434,492)(435,494)(436,490)
(437,495)(438,488)(439,493)(440,489)(441,491)(442,496)(443,501)(444,503)
(445,499)(446,504)(447,497)(448,502)(449,498)(450,500)(451,469)(452,474)
(453,476)(454,472)(455,477)(456,470)(457,475)(458,471)(459,473)(460,478)
(461,483)(462,485)(463,481)(464,486)(465,479)(466,484)(467,480)(468,482)
(505,559)(506,564)(507,566)(508,562)(509,567)(510,560)(511,565)(512,561)
(513,563)(514,568)(515,573)(516,575)(517,571)(518,576)(519,569)(520,574)
(521,570)(522,572)(523,541)(524,546)(525,548)(526,544)(527,549)(528,542)
(529,547)(530,543)(531,545)(532,550)(533,555)(534,557)(535,553)(536,558)
(537,551)(538,556)(539,552)(540,554);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
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)!(  1,362)(  2,361)(  3,363)(  4,368)(  5,367)(  6,369)(  7,365)
(  8,364)(  9,366)( 10,371)( 11,370)( 12,372)( 13,377)( 14,376)( 15,378)
( 16,374)( 17,373)( 18,375)( 19,380)( 20,379)( 21,381)( 22,386)( 23,385)
( 24,387)( 25,383)( 26,382)( 27,384)( 28,389)( 29,388)( 30,390)( 31,395)
( 32,394)( 33,396)( 34,392)( 35,391)( 36,393)( 37,407)( 38,406)( 39,408)
( 40,413)( 41,412)( 42,414)( 43,410)( 44,409)( 45,411)( 46,398)( 47,397)
( 48,399)( 49,404)( 50,403)( 51,405)( 52,401)( 53,400)( 54,402)( 55,425)
( 56,424)( 57,426)( 58,431)( 59,430)( 60,432)( 61,428)( 62,427)( 63,429)
( 64,416)( 65,415)( 66,417)( 67,422)( 68,421)( 69,423)( 70,419)( 71,418)
( 72,420)( 73,290)( 74,289)( 75,291)( 76,296)( 77,295)( 78,297)( 79,293)
( 80,292)( 81,294)( 82,299)( 83,298)( 84,300)( 85,305)( 86,304)( 87,306)
( 88,302)( 89,301)( 90,303)( 91,308)( 92,307)( 93,309)( 94,314)( 95,313)
( 96,315)( 97,311)( 98,310)( 99,312)(100,317)(101,316)(102,318)(103,323)
(104,322)(105,324)(106,320)(107,319)(108,321)(109,335)(110,334)(111,336)
(112,341)(113,340)(114,342)(115,338)(116,337)(117,339)(118,326)(119,325)
(120,327)(121,332)(122,331)(123,333)(124,329)(125,328)(126,330)(127,353)
(128,352)(129,354)(130,359)(131,358)(132,360)(133,356)(134,355)(135,357)
(136,344)(137,343)(138,345)(139,350)(140,349)(141,351)(142,347)(143,346)
(144,348)(145,506)(146,505)(147,507)(148,512)(149,511)(150,513)(151,509)
(152,508)(153,510)(154,515)(155,514)(156,516)(157,521)(158,520)(159,522)
(160,518)(161,517)(162,519)(163,524)(164,523)(165,525)(166,530)(167,529)
(168,531)(169,527)(170,526)(171,528)(172,533)(173,532)(174,534)(175,539)
(176,538)(177,540)(178,536)(179,535)(180,537)(181,551)(182,550)(183,552)
(184,557)(185,556)(186,558)(187,554)(188,553)(189,555)(190,542)(191,541)
(192,543)(193,548)(194,547)(195,549)(196,545)(197,544)(198,546)(199,569)
(200,568)(201,570)(202,575)(203,574)(204,576)(205,572)(206,571)(207,573)
(208,560)(209,559)(210,561)(211,566)(212,565)(213,567)(214,563)(215,562)
(216,564)(217,434)(218,433)(219,435)(220,440)(221,439)(222,441)(223,437)
(224,436)(225,438)(226,443)(227,442)(228,444)(229,449)(230,448)(231,450)
(232,446)(233,445)(234,447)(235,452)(236,451)(237,453)(238,458)(239,457)
(240,459)(241,455)(242,454)(243,456)(244,461)(245,460)(246,462)(247,467)
(248,466)(249,468)(250,464)(251,463)(252,465)(253,479)(254,478)(255,480)
(256,485)(257,484)(258,486)(259,482)(260,481)(261,483)(262,470)(263,469)
(264,471)(265,476)(266,475)(267,477)(268,473)(269,472)(270,474)(271,497)
(272,496)(273,498)(274,503)(275,502)(276,504)(277,500)(278,499)(279,501)
(280,488)(281,487)(282,489)(283,494)(284,493)(285,495)(286,491)(287,490)
(288,492);
s2 := Sym(576)!(  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)
( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)
( 40, 49)( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)
( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 74, 78)
( 75, 80)( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)
(101,105)(102,107)(104,108)(109,118)(110,123)(111,125)(112,121)(113,126)
(114,119)(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)
(131,144)(132,137)(133,142)(134,138)(135,140)(145,163)(146,168)(147,170)
(148,166)(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)
(156,179)(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,208)
(182,213)(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)
(190,199)(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)
(198,203)(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)
(224,237)(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)
(232,250)(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)
(258,281)(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)
(266,279)(267,272)(268,277)(269,273)(270,275)(289,325)(290,330)(291,332)
(292,328)(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)
(300,341)(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)
(308,348)(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)
(316,352)(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)
(324,356)(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)
(368,399)(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)
(376,412)(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)
(384,416)(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)
(392,432)(393,425)(394,430)(395,426)(396,428)(433,487)(434,492)(435,494)
(436,490)(437,495)(438,488)(439,493)(440,489)(441,491)(442,496)(443,501)
(444,503)(445,499)(446,504)(447,497)(448,502)(449,498)(450,500)(451,469)
(452,474)(453,476)(454,472)(455,477)(456,470)(457,475)(458,471)(459,473)
(460,478)(461,483)(462,485)(463,481)(464,486)(465,479)(466,484)(467,480)
(468,482)(505,559)(506,564)(507,566)(508,562)(509,567)(510,560)(511,565)
(512,561)(513,563)(514,568)(515,573)(516,575)(517,571)(518,576)(519,569)
(520,574)(521,570)(522,572)(523,541)(524,546)(525,548)(526,544)(527,549)
(528,542)(529,547)(530,543)(531,545)(532,550)(533,555)(534,557)(535,553)
(536,558)(537,551)(538,556)(539,552)(540,554);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >;

```
References : None.
to this polytope