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Polytope of Type {4,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,12}*1152b
Also Known As : {{4,12|2},{12,12|2}}. if this polytope has another name.
Group : SmallGroup(1152,43022)
Rank : 4
Schlafli Type : {4,12,12}
Number of vertices, edges, etc : 4, 24, 72, 12
Order of s0s1s2s3 : 12
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 : {4,12,6}*576a, {4,6,12}*576a, {2,12,12}*576a
   3-fold quotients : {4,12,4}*384a, {4,4,12}*384
   4-fold quotients : {2,6,12}*288a, {2,12,6}*288a, {4,6,6}*288a
   6-fold quotients : {2,4,12}*192a, {2,12,4}*192a, {4,12,2}*192a, {4,2,12}*192, {4,4,6}*192, {4,6,4}*192a
   8-fold quotients : {2,6,6}*144a
   9-fold quotients : {4,4,4}*128
   12-fold quotients : {2,2,12}*96, {2,12,2}*96, {2,4,6}*96a, {2,6,4}*96a, {4,2,6}*96, {4,6,2}*96a
   18-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24, {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, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)(  8, 80)
(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)
( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)
( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)
( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)
( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)
(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)
(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288)
(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)(296,368)
(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)(304,376)
(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)(312,384)
(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)(320,392)
(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)
(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)(336,408)
(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)(344,416)
(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)(352,424)
(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)(360,432)
(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)(440,512)
(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)(448,520)
(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)(456,528)
(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)(464,536)
(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)(472,544)
(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)(480,552)
(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)(488,560)
(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)(496,568)
(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)(504,576);;
s1 := (  1,361)(  2,368)(  3,366)(  4,367)(  5,365)(  6,363)(  7,364)(  8,362)
(  9,369)( 10,370)( 11,377)( 12,375)( 13,376)( 14,374)( 15,372)( 16,373)
( 17,371)( 18,378)( 19,379)( 20,386)( 21,384)( 22,385)( 23,383)( 24,381)
( 25,382)( 26,380)( 27,387)( 28,388)( 29,395)( 30,393)( 31,394)( 32,392)
( 33,390)( 34,391)( 35,389)( 36,396)( 37,397)( 38,404)( 39,402)( 40,403)
( 41,401)( 42,399)( 43,400)( 44,398)( 45,405)( 46,406)( 47,413)( 48,411)
( 49,412)( 50,410)( 51,408)( 52,409)( 53,407)( 54,414)( 55,415)( 56,422)
( 57,420)( 58,421)( 59,419)( 60,417)( 61,418)( 62,416)( 63,423)( 64,424)
( 65,431)( 66,429)( 67,430)( 68,428)( 69,426)( 70,427)( 71,425)( 72,432)
( 73,325)( 74,332)( 75,330)( 76,331)( 77,329)( 78,327)( 79,328)( 80,326)
( 81,333)( 82,334)( 83,341)( 84,339)( 85,340)( 86,338)( 87,336)( 88,337)
( 89,335)( 90,342)( 91,343)( 92,350)( 93,348)( 94,349)( 95,347)( 96,345)
( 97,346)( 98,344)( 99,351)(100,352)(101,359)(102,357)(103,358)(104,356)
(105,354)(106,355)(107,353)(108,360)(109,289)(110,296)(111,294)(112,295)
(113,293)(114,291)(115,292)(116,290)(117,297)(118,298)(119,305)(120,303)
(121,304)(122,302)(123,300)(124,301)(125,299)(126,306)(127,307)(128,314)
(129,312)(130,313)(131,311)(132,309)(133,310)(134,308)(135,315)(136,316)
(137,323)(138,321)(139,322)(140,320)(141,318)(142,319)(143,317)(144,324)
(145,532)(146,539)(147,537)(148,538)(149,536)(150,534)(151,535)(152,533)
(153,540)(154,523)(155,530)(156,528)(157,529)(158,527)(159,525)(160,526)
(161,524)(162,531)(163,514)(164,521)(165,519)(166,520)(167,518)(168,516)
(169,517)(170,515)(171,522)(172,505)(173,512)(174,510)(175,511)(176,509)
(177,507)(178,508)(179,506)(180,513)(181,568)(182,575)(183,573)(184,574)
(185,572)(186,570)(187,571)(188,569)(189,576)(190,559)(191,566)(192,564)
(193,565)(194,563)(195,561)(196,562)(197,560)(198,567)(199,550)(200,557)
(201,555)(202,556)(203,554)(204,552)(205,553)(206,551)(207,558)(208,541)
(209,548)(210,546)(211,547)(212,545)(213,543)(214,544)(215,542)(216,549)
(217,496)(218,503)(219,501)(220,502)(221,500)(222,498)(223,499)(224,497)
(225,504)(226,487)(227,494)(228,492)(229,493)(230,491)(231,489)(232,490)
(233,488)(234,495)(235,478)(236,485)(237,483)(238,484)(239,482)(240,480)
(241,481)(242,479)(243,486)(244,469)(245,476)(246,474)(247,475)(248,473)
(249,471)(250,472)(251,470)(252,477)(253,460)(254,467)(255,465)(256,466)
(257,464)(258,462)(259,463)(260,461)(261,468)(262,451)(263,458)(264,456)
(265,457)(266,455)(267,453)(268,454)(269,452)(270,459)(271,442)(272,449)
(273,447)(274,448)(275,446)(276,444)(277,445)(278,443)(279,450)(280,433)
(281,440)(282,438)(283,439)(284,437)(285,435)(286,436)(287,434)(288,441);;
s2 := (  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,151)(  8,153)
(  9,152)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,160)
( 17,162)( 18,161)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)
( 25,169)( 26,171)( 27,170)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)
( 33,173)( 34,178)( 35,180)( 36,179)( 37,184)( 38,186)( 39,185)( 40,181)
( 41,183)( 42,182)( 43,187)( 44,189)( 45,188)( 46,193)( 47,195)( 48,194)
( 49,190)( 50,192)( 51,191)( 52,196)( 53,198)( 54,197)( 55,202)( 56,204)
( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)( 64,211)
( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,214)( 71,216)( 72,215)
( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,223)( 80,225)
( 81,224)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)( 88,232)
( 89,234)( 90,233)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)( 96,236)
( 97,241)( 98,243)( 99,242)(100,247)(101,249)(102,248)(103,244)(104,246)
(105,245)(106,250)(107,252)(108,251)(109,256)(110,258)(111,257)(112,253)
(113,255)(114,254)(115,259)(116,261)(117,260)(118,265)(119,267)(120,266)
(121,262)(122,264)(123,263)(124,268)(125,270)(126,269)(127,274)(128,276)
(129,275)(130,271)(131,273)(132,272)(133,277)(134,279)(135,278)(136,283)
(137,285)(138,284)(139,280)(140,282)(141,281)(142,286)(143,288)(144,287)
(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,439)(296,441)
(297,440)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,448)
(305,450)(306,449)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)
(313,457)(314,459)(315,458)(316,463)(317,465)(318,464)(319,460)(320,462)
(321,461)(322,466)(323,468)(324,467)(325,472)(326,474)(327,473)(328,469)
(329,471)(330,470)(331,475)(332,477)(333,476)(334,481)(335,483)(336,482)
(337,478)(338,480)(339,479)(340,484)(341,486)(342,485)(343,490)(344,492)
(345,491)(346,487)(347,489)(348,488)(349,493)(350,495)(351,494)(352,499)
(353,501)(354,500)(355,496)(356,498)(357,497)(358,502)(359,504)(360,503)
(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,511)(368,513)
(369,512)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)(376,520)
(377,522)(378,521)(379,526)(380,528)(381,527)(382,523)(383,525)(384,524)
(385,529)(386,531)(387,530)(388,535)(389,537)(390,536)(391,532)(392,534)
(393,533)(394,538)(395,540)(396,539)(397,544)(398,546)(399,545)(400,541)
(401,543)(402,542)(403,547)(404,549)(405,548)(406,553)(407,555)(408,554)
(409,550)(410,552)(411,551)(412,556)(413,558)(414,557)(415,562)(416,564)
(417,563)(418,559)(419,561)(420,560)(421,565)(422,567)(423,566)(424,571)
(425,573)(426,572)(427,568)(428,570)(429,569)(430,574)(431,576)(432,575);;
s3 := (  1,365)(  2,367)(  3,363)(  4,368)(  5,361)(  6,366)(  7,362)(  8,364)
(  9,369)( 10,374)( 11,376)( 12,372)( 13,377)( 14,370)( 15,375)( 16,371)
( 17,373)( 18,378)( 19,383)( 20,385)( 21,381)( 22,386)( 23,379)( 24,384)
( 25,380)( 26,382)( 27,387)( 28,392)( 29,394)( 30,390)( 31,395)( 32,388)
( 33,393)( 34,389)( 35,391)( 36,396)( 37,401)( 38,403)( 39,399)( 40,404)
( 41,397)( 42,402)( 43,398)( 44,400)( 45,405)( 46,410)( 47,412)( 48,408)
( 49,413)( 50,406)( 51,411)( 52,407)( 53,409)( 54,414)( 55,419)( 56,421)
( 57,417)( 58,422)( 59,415)( 60,420)( 61,416)( 62,418)( 63,423)( 64,428)
( 65,430)( 66,426)( 67,431)( 68,424)( 69,429)( 70,425)( 71,427)( 72,432)
( 73,293)( 74,295)( 75,291)( 76,296)( 77,289)( 78,294)( 79,290)( 80,292)
( 81,297)( 82,302)( 83,304)( 84,300)( 85,305)( 86,298)( 87,303)( 88,299)
( 89,301)( 90,306)( 91,311)( 92,313)( 93,309)( 94,314)( 95,307)( 96,312)
( 97,308)( 98,310)( 99,315)(100,320)(101,322)(102,318)(103,323)(104,316)
(105,321)(106,317)(107,319)(108,324)(109,329)(110,331)(111,327)(112,332)
(113,325)(114,330)(115,326)(116,328)(117,333)(118,338)(119,340)(120,336)
(121,341)(122,334)(123,339)(124,335)(125,337)(126,342)(127,347)(128,349)
(129,345)(130,350)(131,343)(132,348)(133,344)(134,346)(135,351)(136,356)
(137,358)(138,354)(139,359)(140,352)(141,357)(142,353)(143,355)(144,360)
(145,518)(146,520)(147,516)(148,521)(149,514)(150,519)(151,515)(152,517)
(153,522)(154,509)(155,511)(156,507)(157,512)(158,505)(159,510)(160,506)
(161,508)(162,513)(163,536)(164,538)(165,534)(166,539)(167,532)(168,537)
(169,533)(170,535)(171,540)(172,527)(173,529)(174,525)(175,530)(176,523)
(177,528)(178,524)(179,526)(180,531)(181,554)(182,556)(183,552)(184,557)
(185,550)(186,555)(187,551)(188,553)(189,558)(190,545)(191,547)(192,543)
(193,548)(194,541)(195,546)(196,542)(197,544)(198,549)(199,572)(200,574)
(201,570)(202,575)(203,568)(204,573)(205,569)(206,571)(207,576)(208,563)
(209,565)(210,561)(211,566)(212,559)(213,564)(214,560)(215,562)(216,567)
(217,446)(218,448)(219,444)(220,449)(221,442)(222,447)(223,443)(224,445)
(225,450)(226,437)(227,439)(228,435)(229,440)(230,433)(231,438)(232,434)
(233,436)(234,441)(235,464)(236,466)(237,462)(238,467)(239,460)(240,465)
(241,461)(242,463)(243,468)(244,455)(245,457)(246,453)(247,458)(248,451)
(249,456)(250,452)(251,454)(252,459)(253,482)(254,484)(255,480)(256,485)
(257,478)(258,483)(259,479)(260,481)(261,486)(262,473)(263,475)(264,471)
(265,476)(266,469)(267,474)(268,470)(269,472)(270,477)(271,500)(272,502)
(273,498)(274,503)(275,496)(276,501)(277,497)(278,499)(279,504)(280,491)
(281,493)(282,489)(283,494)(284,487)(285,492)(286,488)(287,490)(288,495);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)
(  8, 80)(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)
( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)
( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)
( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)
( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)
( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)
( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)
(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)
(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)
(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)
(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)
(216,288)(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)
(296,368)(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)
(304,376)(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)
(312,384)(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)
(320,392)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)
(328,400)(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)
(336,408)(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)
(344,416)(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)
(352,424)(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)
(360,432)(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)
(440,512)(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)
(448,520)(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)
(456,528)(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)
(464,536)(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)
(472,544)(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)
(480,552)(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)
(488,560)(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)
(496,568)(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)
(504,576);
s1 := Sym(576)!(  1,361)(  2,368)(  3,366)(  4,367)(  5,365)(  6,363)(  7,364)
(  8,362)(  9,369)( 10,370)( 11,377)( 12,375)( 13,376)( 14,374)( 15,372)
( 16,373)( 17,371)( 18,378)( 19,379)( 20,386)( 21,384)( 22,385)( 23,383)
( 24,381)( 25,382)( 26,380)( 27,387)( 28,388)( 29,395)( 30,393)( 31,394)
( 32,392)( 33,390)( 34,391)( 35,389)( 36,396)( 37,397)( 38,404)( 39,402)
( 40,403)( 41,401)( 42,399)( 43,400)( 44,398)( 45,405)( 46,406)( 47,413)
( 48,411)( 49,412)( 50,410)( 51,408)( 52,409)( 53,407)( 54,414)( 55,415)
( 56,422)( 57,420)( 58,421)( 59,419)( 60,417)( 61,418)( 62,416)( 63,423)
( 64,424)( 65,431)( 66,429)( 67,430)( 68,428)( 69,426)( 70,427)( 71,425)
( 72,432)( 73,325)( 74,332)( 75,330)( 76,331)( 77,329)( 78,327)( 79,328)
( 80,326)( 81,333)( 82,334)( 83,341)( 84,339)( 85,340)( 86,338)( 87,336)
( 88,337)( 89,335)( 90,342)( 91,343)( 92,350)( 93,348)( 94,349)( 95,347)
( 96,345)( 97,346)( 98,344)( 99,351)(100,352)(101,359)(102,357)(103,358)
(104,356)(105,354)(106,355)(107,353)(108,360)(109,289)(110,296)(111,294)
(112,295)(113,293)(114,291)(115,292)(116,290)(117,297)(118,298)(119,305)
(120,303)(121,304)(122,302)(123,300)(124,301)(125,299)(126,306)(127,307)
(128,314)(129,312)(130,313)(131,311)(132,309)(133,310)(134,308)(135,315)
(136,316)(137,323)(138,321)(139,322)(140,320)(141,318)(142,319)(143,317)
(144,324)(145,532)(146,539)(147,537)(148,538)(149,536)(150,534)(151,535)
(152,533)(153,540)(154,523)(155,530)(156,528)(157,529)(158,527)(159,525)
(160,526)(161,524)(162,531)(163,514)(164,521)(165,519)(166,520)(167,518)
(168,516)(169,517)(170,515)(171,522)(172,505)(173,512)(174,510)(175,511)
(176,509)(177,507)(178,508)(179,506)(180,513)(181,568)(182,575)(183,573)
(184,574)(185,572)(186,570)(187,571)(188,569)(189,576)(190,559)(191,566)
(192,564)(193,565)(194,563)(195,561)(196,562)(197,560)(198,567)(199,550)
(200,557)(201,555)(202,556)(203,554)(204,552)(205,553)(206,551)(207,558)
(208,541)(209,548)(210,546)(211,547)(212,545)(213,543)(214,544)(215,542)
(216,549)(217,496)(218,503)(219,501)(220,502)(221,500)(222,498)(223,499)
(224,497)(225,504)(226,487)(227,494)(228,492)(229,493)(230,491)(231,489)
(232,490)(233,488)(234,495)(235,478)(236,485)(237,483)(238,484)(239,482)
(240,480)(241,481)(242,479)(243,486)(244,469)(245,476)(246,474)(247,475)
(248,473)(249,471)(250,472)(251,470)(252,477)(253,460)(254,467)(255,465)
(256,466)(257,464)(258,462)(259,463)(260,461)(261,468)(262,451)(263,458)
(264,456)(265,457)(266,455)(267,453)(268,454)(269,452)(270,459)(271,442)
(272,449)(273,447)(274,448)(275,446)(276,444)(277,445)(278,443)(279,450)
(280,433)(281,440)(282,438)(283,439)(284,437)(285,435)(286,436)(287,434)
(288,441);
s2 := Sym(576)!(  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,151)
(  8,153)(  9,152)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)
( 16,160)( 17,162)( 18,161)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)
( 24,164)( 25,169)( 26,171)( 27,170)( 28,175)( 29,177)( 30,176)( 31,172)
( 32,174)( 33,173)( 34,178)( 35,180)( 36,179)( 37,184)( 38,186)( 39,185)
( 40,181)( 41,183)( 42,182)( 43,187)( 44,189)( 45,188)( 46,193)( 47,195)
( 48,194)( 49,190)( 50,192)( 51,191)( 52,196)( 53,198)( 54,197)( 55,202)
( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)
( 64,211)( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,214)( 71,216)
( 72,215)( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,223)
( 80,225)( 81,224)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)
( 88,232)( 89,234)( 90,233)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)
( 96,236)( 97,241)( 98,243)( 99,242)(100,247)(101,249)(102,248)(103,244)
(104,246)(105,245)(106,250)(107,252)(108,251)(109,256)(110,258)(111,257)
(112,253)(113,255)(114,254)(115,259)(116,261)(117,260)(118,265)(119,267)
(120,266)(121,262)(122,264)(123,263)(124,268)(125,270)(126,269)(127,274)
(128,276)(129,275)(130,271)(131,273)(132,272)(133,277)(134,279)(135,278)
(136,283)(137,285)(138,284)(139,280)(140,282)(141,281)(142,286)(143,288)
(144,287)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,439)
(296,441)(297,440)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)
(304,448)(305,450)(306,449)(307,454)(308,456)(309,455)(310,451)(311,453)
(312,452)(313,457)(314,459)(315,458)(316,463)(317,465)(318,464)(319,460)
(320,462)(321,461)(322,466)(323,468)(324,467)(325,472)(326,474)(327,473)
(328,469)(329,471)(330,470)(331,475)(332,477)(333,476)(334,481)(335,483)
(336,482)(337,478)(338,480)(339,479)(340,484)(341,486)(342,485)(343,490)
(344,492)(345,491)(346,487)(347,489)(348,488)(349,493)(350,495)(351,494)
(352,499)(353,501)(354,500)(355,496)(356,498)(357,497)(358,502)(359,504)
(360,503)(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,511)
(368,513)(369,512)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)
(376,520)(377,522)(378,521)(379,526)(380,528)(381,527)(382,523)(383,525)
(384,524)(385,529)(386,531)(387,530)(388,535)(389,537)(390,536)(391,532)
(392,534)(393,533)(394,538)(395,540)(396,539)(397,544)(398,546)(399,545)
(400,541)(401,543)(402,542)(403,547)(404,549)(405,548)(406,553)(407,555)
(408,554)(409,550)(410,552)(411,551)(412,556)(413,558)(414,557)(415,562)
(416,564)(417,563)(418,559)(419,561)(420,560)(421,565)(422,567)(423,566)
(424,571)(425,573)(426,572)(427,568)(428,570)(429,569)(430,574)(431,576)
(432,575);
s3 := Sym(576)!(  1,365)(  2,367)(  3,363)(  4,368)(  5,361)(  6,366)(  7,362)
(  8,364)(  9,369)( 10,374)( 11,376)( 12,372)( 13,377)( 14,370)( 15,375)
( 16,371)( 17,373)( 18,378)( 19,383)( 20,385)( 21,381)( 22,386)( 23,379)
( 24,384)( 25,380)( 26,382)( 27,387)( 28,392)( 29,394)( 30,390)( 31,395)
( 32,388)( 33,393)( 34,389)( 35,391)( 36,396)( 37,401)( 38,403)( 39,399)
( 40,404)( 41,397)( 42,402)( 43,398)( 44,400)( 45,405)( 46,410)( 47,412)
( 48,408)( 49,413)( 50,406)( 51,411)( 52,407)( 53,409)( 54,414)( 55,419)
( 56,421)( 57,417)( 58,422)( 59,415)( 60,420)( 61,416)( 62,418)( 63,423)
( 64,428)( 65,430)( 66,426)( 67,431)( 68,424)( 69,429)( 70,425)( 71,427)
( 72,432)( 73,293)( 74,295)( 75,291)( 76,296)( 77,289)( 78,294)( 79,290)
( 80,292)( 81,297)( 82,302)( 83,304)( 84,300)( 85,305)( 86,298)( 87,303)
( 88,299)( 89,301)( 90,306)( 91,311)( 92,313)( 93,309)( 94,314)( 95,307)
( 96,312)( 97,308)( 98,310)( 99,315)(100,320)(101,322)(102,318)(103,323)
(104,316)(105,321)(106,317)(107,319)(108,324)(109,329)(110,331)(111,327)
(112,332)(113,325)(114,330)(115,326)(116,328)(117,333)(118,338)(119,340)
(120,336)(121,341)(122,334)(123,339)(124,335)(125,337)(126,342)(127,347)
(128,349)(129,345)(130,350)(131,343)(132,348)(133,344)(134,346)(135,351)
(136,356)(137,358)(138,354)(139,359)(140,352)(141,357)(142,353)(143,355)
(144,360)(145,518)(146,520)(147,516)(148,521)(149,514)(150,519)(151,515)
(152,517)(153,522)(154,509)(155,511)(156,507)(157,512)(158,505)(159,510)
(160,506)(161,508)(162,513)(163,536)(164,538)(165,534)(166,539)(167,532)
(168,537)(169,533)(170,535)(171,540)(172,527)(173,529)(174,525)(175,530)
(176,523)(177,528)(178,524)(179,526)(180,531)(181,554)(182,556)(183,552)
(184,557)(185,550)(186,555)(187,551)(188,553)(189,558)(190,545)(191,547)
(192,543)(193,548)(194,541)(195,546)(196,542)(197,544)(198,549)(199,572)
(200,574)(201,570)(202,575)(203,568)(204,573)(205,569)(206,571)(207,576)
(208,563)(209,565)(210,561)(211,566)(212,559)(213,564)(214,560)(215,562)
(216,567)(217,446)(218,448)(219,444)(220,449)(221,442)(222,447)(223,443)
(224,445)(225,450)(226,437)(227,439)(228,435)(229,440)(230,433)(231,438)
(232,434)(233,436)(234,441)(235,464)(236,466)(237,462)(238,467)(239,460)
(240,465)(241,461)(242,463)(243,468)(244,455)(245,457)(246,453)(247,458)
(248,451)(249,456)(250,452)(251,454)(252,459)(253,482)(254,484)(255,480)
(256,485)(257,478)(258,483)(259,479)(260,481)(261,486)(262,473)(263,475)
(264,471)(265,476)(266,469)(267,474)(268,470)(269,472)(270,477)(271,500)
(272,502)(273,498)(274,503)(275,496)(276,501)(277,497)(278,499)(279,504)
(280,491)(281,493)(282,489)(283,494)(284,487)(285,492)(286,488)(287,490)
(288,495);
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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