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# Polytope of Type {24,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,119761)
Rank : 4
Schlafli Type : {24,6,4}
Number of vertices, edges, etc : 24, 72, 12, 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 : {24,6,2}*576c, {12,6,4}*576c
3-fold quotients : {8,6,4}*384a
4-fold quotients : {6,6,4}*288b, {12,6,2}*288c
6-fold quotients : {4,6,4}*192a, {8,6,2}*192
8-fold quotients : {6,6,2}*144b
9-fold quotients : {8,2,4}*128
12-fold quotients : {2,6,4}*96a, {4,6,2}*96a
16-fold quotients : {6,3,2}*72
18-fold quotients : {4,2,4}*64, {8,2,2}*64
24-fold quotients : {2,6,2}*48
36-fold quotients : {2,2,4}*32, {4,2,2}*32
48-fold quotients : {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  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)( 19,307)( 20,312)( 21,314)( 22,310)( 23,315)( 24,308)
( 25,313)( 26,309)( 27,311)( 28,316)( 29,321)( 30,323)( 31,319)( 32,324)
( 33,317)( 34,322)( 35,318)( 36,320)( 37,334)( 38,339)( 39,341)( 40,337)
( 41,342)( 42,335)( 43,340)( 44,336)( 45,338)( 46,325)( 47,330)( 48,332)
( 49,328)( 50,333)( 51,326)( 52,331)( 53,327)( 54,329)( 55,352)( 56,357)
( 57,359)( 58,355)( 59,360)( 60,353)( 61,358)( 62,354)( 63,356)( 64,343)
( 65,348)( 66,350)( 67,346)( 68,351)( 69,344)( 70,349)( 71,345)( 72,347)
( 73,397)( 74,402)( 75,404)( 76,400)( 77,405)( 78,398)( 79,403)( 80,399)
( 81,401)( 82,406)( 83,411)( 84,413)( 85,409)( 86,414)( 87,407)( 88,412)
( 89,408)( 90,410)( 91,415)( 92,420)( 93,422)( 94,418)( 95,423)( 96,416)
( 97,421)( 98,417)( 99,419)(100,424)(101,429)(102,431)(103,427)(104,432)
(105,425)(106,430)(107,426)(108,428)(109,361)(110,366)(111,368)(112,364)
(113,369)(114,362)(115,367)(116,363)(117,365)(118,370)(119,375)(120,377)
(121,373)(122,378)(123,371)(124,376)(125,372)(126,374)(127,379)(128,384)
(129,386)(130,382)(131,387)(132,380)(133,385)(134,381)(135,383)(136,388)
(137,393)(138,395)(139,391)(140,396)(141,389)(142,394)(143,390)(144,392)
(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)(163,451)(164,456)(165,458)(166,454)(167,459)(168,452)
(169,457)(170,453)(171,455)(172,460)(173,465)(174,467)(175,463)(176,468)
(177,461)(178,466)(179,462)(180,464)(181,478)(182,483)(183,485)(184,481)
(185,486)(186,479)(187,484)(188,480)(189,482)(190,469)(191,474)(192,476)
(193,472)(194,477)(195,470)(196,475)(197,471)(198,473)(199,496)(200,501)
(201,503)(202,499)(203,504)(204,497)(205,502)(206,498)(207,500)(208,487)
(209,492)(210,494)(211,490)(212,495)(213,488)(214,493)(215,489)(216,491)
(217,541)(218,546)(219,548)(220,544)(221,549)(222,542)(223,547)(224,543)
(225,545)(226,550)(227,555)(228,557)(229,553)(230,558)(231,551)(232,556)
(233,552)(234,554)(235,559)(236,564)(237,566)(238,562)(239,567)(240,560)
(241,565)(242,561)(243,563)(244,568)(245,573)(246,575)(247,571)(248,576)
(249,569)(250,574)(251,570)(252,572)(253,505)(254,510)(255,512)(256,508)
(257,513)(258,506)(259,511)(260,507)(261,509)(262,514)(263,519)(264,521)
(265,517)(266,522)(267,515)(268,520)(269,516)(270,518)(271,523)(272,528)
(273,530)(274,526)(275,531)(276,524)(277,529)(278,525)(279,527)(280,532)
(281,537)(282,539)(283,535)(284,540)(285,533)(286,538)(287,534)(288,536);;
s1 := (  1, 74)(  2, 73)(  3, 75)(  4, 80)(  5, 79)(  6, 81)(  7, 77)(  8, 76)
(  9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)
( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)( 24, 99)
( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)( 32,106)
( 33,108)( 34,104)( 35,103)( 36,105)( 37,119)( 38,118)( 39,120)( 40,125)
( 41,124)( 42,126)( 43,122)( 44,121)( 45,123)( 46,110)( 47,109)( 48,111)
( 49,116)( 50,115)( 51,117)( 52,113)( 53,112)( 54,114)( 55,137)( 56,136)
( 57,138)( 58,143)( 59,142)( 60,144)( 61,140)( 62,139)( 63,141)( 64,128)
( 65,127)( 66,129)( 67,134)( 68,133)( 69,135)( 70,131)( 71,130)( 72,132)
(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)(152,220)
(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)(160,230)
(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)(168,243)
(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)(176,250)
(177,252)(178,248)(179,247)(180,249)(181,263)(182,262)(183,264)(184,269)
(185,268)(186,270)(187,266)(188,265)(189,267)(190,254)(191,253)(192,255)
(193,260)(194,259)(195,261)(196,257)(197,256)(198,258)(199,281)(200,280)
(201,282)(202,287)(203,286)(204,288)(205,284)(206,283)(207,285)(208,272)
(209,271)(210,273)(211,278)(212,277)(213,279)(214,275)(215,274)(216,276)
(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)
(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)
(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)
(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)
(321,396)(322,392)(323,391)(324,393)(325,407)(326,406)(327,408)(328,413)
(329,412)(330,414)(331,410)(332,409)(333,411)(334,398)(335,397)(336,399)
(337,404)(338,403)(339,405)(340,401)(341,400)(342,402)(343,425)(344,424)
(345,426)(346,431)(347,430)(348,432)(349,428)(350,427)(351,429)(352,416)
(353,415)(354,417)(355,422)(356,421)(357,423)(358,419)(359,418)(360,420)
(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)(440,508)
(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)(448,518)
(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)(456,531)
(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)(464,538)
(465,540)(466,536)(467,535)(468,537)(469,551)(470,550)(471,552)(472,557)
(473,556)(474,558)(475,554)(476,553)(477,555)(478,542)(479,541)(480,543)
(481,548)(482,547)(483,549)(484,545)(485,544)(486,546)(487,569)(488,568)
(489,570)(490,575)(491,574)(492,576)(493,572)(494,571)(495,573)(496,560)
(497,559)(498,561)(499,566)(500,565)(501,567)(502,563)(503,562)(504,564);;
s2 := (  1,109)(  2,111)(  3,110)(  4,115)(  5,117)(  6,116)(  7,112)(  8,114)
(  9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)( 16,121)
( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)( 24,134)
( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)( 32,144)
( 33,143)( 34,139)( 35,141)( 36,140)( 37, 82)( 38, 84)( 39, 83)( 40, 88)
( 41, 90)( 42, 89)( 43, 85)( 44, 87)( 45, 86)( 46, 73)( 47, 75)( 48, 74)
( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)( 55,100)( 56,102)
( 57,101)( 58,106)( 59,108)( 60,107)( 61,103)( 62,105)( 63,104)( 64, 91)
( 65, 93)( 66, 92)( 67, 97)( 68, 99)( 69, 98)( 70, 94)( 71, 96)( 72, 95)
(145,271)(146,273)(147,272)(148,277)(149,279)(150,278)(151,274)(152,276)
(153,275)(154,280)(155,282)(156,281)(157,286)(158,288)(159,287)(160,283)
(161,285)(162,284)(163,253)(164,255)(165,254)(166,259)(167,261)(168,260)
(169,256)(170,258)(171,257)(172,262)(173,264)(174,263)(175,268)(176,270)
(177,269)(178,265)(179,267)(180,266)(181,244)(182,246)(183,245)(184,250)
(185,252)(186,251)(187,247)(188,249)(189,248)(190,235)(191,237)(192,236)
(193,241)(194,243)(195,242)(196,238)(197,240)(198,239)(199,226)(200,228)
(201,227)(202,232)(203,234)(204,233)(205,229)(206,231)(207,230)(208,217)
(209,219)(210,218)(211,223)(212,225)(213,224)(214,220)(215,222)(216,221)
(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)
(433,523)(434,525)(435,524)(436,529)(437,531)(438,530)(439,526)(440,528)
(441,527)(442,532)(443,534)(444,533)(445,538)(446,540)(447,539)(448,535)
(449,537)(450,536)(451,505)(452,507)(453,506)(454,511)(455,513)(456,512)
(457,508)(458,510)(459,509)(460,514)(461,516)(462,515)(463,520)(464,522)
(465,521)(466,517)(467,519)(468,518)(469,559)(470,561)(471,560)(472,565)
(473,567)(474,566)(475,562)(476,564)(477,563)(478,568)(479,570)(480,569)
(481,574)(482,576)(483,575)(484,571)(485,573)(486,572)(487,541)(488,543)
(489,542)(490,547)(491,549)(492,548)(493,544)(494,546)(495,545)(496,550)
(497,552)(498,551)(499,556)(500,558)(501,557)(502,553)(503,555)(504,554);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope