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Polytope of Type {36,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,4,4}*1152
Also Known As : {{36,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,42999)
Rank : 4
Schlafli Type : {36,4,4}
Number of vertices, edges, etc : 36, 72, 8, 4
Order of s0s1s2s3 : 36
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 : {36,4,2}*576a, {36,2,4}*576, {18,4,4}*576
   3-fold quotients : {12,4,4}*384
   4-fold quotients : {36,2,2}*288, {18,2,4}*288, {18,4,2}*288a
   6-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192
   8-fold quotients : {9,2,4}*144, {18,2,2}*144
   9-fold quotients : {4,4,4}*128
   12-fold quotients : {12,2,2}*96, {6,2,4}*96, {6,4,2}*96a
   16-fold quotients : {9,2,2}*72
   18-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   24-fold quotients : {3,2,4}*48, {6,2,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*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 := (  1,361)(  2,363)(  3,362)(  4,369)(  5,368)(  6,367)(  7,366)(  8,365)
(  9,364)( 10,370)( 11,372)( 12,371)( 13,378)( 14,377)( 15,376)( 16,375)
( 17,374)( 18,373)( 19,379)( 20,381)( 21,380)( 22,387)( 23,386)( 24,385)
( 25,384)( 26,383)( 27,382)( 28,388)( 29,390)( 30,389)( 31,396)( 32,395)
( 33,394)( 34,393)( 35,392)( 36,391)( 37,397)( 38,399)( 39,398)( 40,405)
( 41,404)( 42,403)( 43,402)( 44,401)( 45,400)( 46,406)( 47,408)( 48,407)
( 49,414)( 50,413)( 51,412)( 52,411)( 53,410)( 54,409)( 55,415)( 56,417)
( 57,416)( 58,423)( 59,422)( 60,421)( 61,420)( 62,419)( 63,418)( 64,424)
( 65,426)( 66,425)( 67,432)( 68,431)( 69,430)( 70,429)( 71,428)( 72,427)
( 73,289)( 74,291)( 75,290)( 76,297)( 77,296)( 78,295)( 79,294)( 80,293)
( 81,292)( 82,298)( 83,300)( 84,299)( 85,306)( 86,305)( 87,304)( 88,303)
( 89,302)( 90,301)( 91,307)( 92,309)( 93,308)( 94,315)( 95,314)( 96,313)
( 97,312)( 98,311)( 99,310)(100,316)(101,318)(102,317)(103,324)(104,323)
(105,322)(106,321)(107,320)(108,319)(109,325)(110,327)(111,326)(112,333)
(113,332)(114,331)(115,330)(116,329)(117,328)(118,334)(119,336)(120,335)
(121,342)(122,341)(123,340)(124,339)(125,338)(126,337)(127,343)(128,345)
(129,344)(130,351)(131,350)(132,349)(133,348)(134,347)(135,346)(136,352)
(137,354)(138,353)(139,360)(140,359)(141,358)(142,357)(143,356)(144,355)
(145,514)(146,516)(147,515)(148,522)(149,521)(150,520)(151,519)(152,518)
(153,517)(154,505)(155,507)(156,506)(157,513)(158,512)(159,511)(160,510)
(161,509)(162,508)(163,532)(164,534)(165,533)(166,540)(167,539)(168,538)
(169,537)(170,536)(171,535)(172,523)(173,525)(174,524)(175,531)(176,530)
(177,529)(178,528)(179,527)(180,526)(181,550)(182,552)(183,551)(184,558)
(185,557)(186,556)(187,555)(188,554)(189,553)(190,541)(191,543)(192,542)
(193,549)(194,548)(195,547)(196,546)(197,545)(198,544)(199,568)(200,570)
(201,569)(202,576)(203,575)(204,574)(205,573)(206,572)(207,571)(208,559)
(209,561)(210,560)(211,567)(212,566)(213,565)(214,564)(215,563)(216,562)
(217,442)(218,444)(219,443)(220,450)(221,449)(222,448)(223,447)(224,446)
(225,445)(226,433)(227,435)(228,434)(229,441)(230,440)(231,439)(232,438)
(233,437)(234,436)(235,460)(236,462)(237,461)(238,468)(239,467)(240,466)
(241,465)(242,464)(243,463)(244,451)(245,453)(246,452)(247,459)(248,458)
(249,457)(250,456)(251,455)(252,454)(253,478)(254,480)(255,479)(256,486)
(257,485)(258,484)(259,483)(260,482)(261,481)(262,469)(263,471)(264,470)
(265,477)(266,476)(267,475)(268,474)(269,473)(270,472)(271,496)(272,498)
(273,497)(274,504)(275,503)(276,502)(277,501)(278,500)(279,499)(280,487)
(281,489)(282,488)(283,495)(284,494)(285,493)(286,492)(287,491)(288,490);;
s1 := (  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,153)(  8,152)
(  9,151)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,162)
( 17,161)( 18,160)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)
( 25,171)( 26,170)( 27,169)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)
( 33,173)( 34,180)( 35,179)( 36,178)( 37,184)( 38,186)( 39,185)( 40,181)
( 41,183)( 42,182)( 43,189)( 44,188)( 45,187)( 46,193)( 47,195)( 48,194)
( 49,190)( 50,192)( 51,191)( 52,198)( 53,197)( 54,196)( 55,202)( 56,204)
( 57,203)( 58,199)( 59,201)( 60,200)( 61,207)( 62,206)( 63,205)( 64,211)
( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,216)( 71,215)( 72,214)
( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,225)( 80,224)
( 81,223)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)( 88,234)
( 89,233)( 90,232)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)( 96,236)
( 97,243)( 98,242)( 99,241)(100,247)(101,249)(102,248)(103,244)(104,246)
(105,245)(106,252)(107,251)(108,250)(109,256)(110,258)(111,257)(112,253)
(113,255)(114,254)(115,261)(116,260)(117,259)(118,265)(119,267)(120,266)
(121,262)(122,264)(123,263)(124,270)(125,269)(126,268)(127,274)(128,276)
(129,275)(130,271)(131,273)(132,272)(133,279)(134,278)(135,277)(136,283)
(137,285)(138,284)(139,280)(140,282)(141,281)(142,288)(143,287)(144,286)
(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,441)(296,440)
(297,439)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,450)
(305,449)(306,448)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)
(313,459)(314,458)(315,457)(316,463)(317,465)(318,464)(319,460)(320,462)
(321,461)(322,468)(323,467)(324,466)(325,472)(326,474)(327,473)(328,469)
(329,471)(330,470)(331,477)(332,476)(333,475)(334,481)(335,483)(336,482)
(337,478)(338,480)(339,479)(340,486)(341,485)(342,484)(343,490)(344,492)
(345,491)(346,487)(347,489)(348,488)(349,495)(350,494)(351,493)(352,499)
(353,501)(354,500)(355,496)(356,498)(357,497)(358,504)(359,503)(360,502)
(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,513)(368,512)
(369,511)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)(376,522)
(377,521)(378,520)(379,526)(380,528)(381,527)(382,523)(383,525)(384,524)
(385,531)(386,530)(387,529)(388,535)(389,537)(390,536)(391,532)(392,534)
(393,533)(394,540)(395,539)(396,538)(397,544)(398,546)(399,545)(400,541)
(401,543)(402,542)(403,549)(404,548)(405,547)(406,553)(407,555)(408,554)
(409,550)(410,552)(411,551)(412,558)(413,557)(414,556)(415,562)(416,564)
(417,563)(418,559)(419,561)(420,560)(421,567)(422,566)(423,565)(424,571)
(425,573)(426,572)(427,568)(428,570)(429,569)(430,576)(431,575)(432,574);;
s2 := ( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)
( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)
( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)
(105,141)(106,142)(107,143)(108,144)(145,163)(146,164)(147,165)(148,166)
(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)(156,174)
(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,199)(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)
(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)(224,278)
(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)(232,286)
(233,287)(234,288)(235,253)(236,254)(237,255)(238,256)(239,257)(240,258)
(241,259)(242,260)(243,261)(244,262)(245,263)(246,264)(247,265)(248,266)
(249,267)(250,268)(251,269)(252,270)(289,325)(290,326)(291,327)(292,328)
(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)
(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)(308,344)
(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)(316,352)
(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)(324,360)
(433,487)(434,488)(435,489)(436,490)(437,491)(438,492)(439,493)(440,494)
(441,495)(442,496)(443,497)(444,498)(445,499)(446,500)(447,501)(448,502)
(449,503)(450,504)(451,469)(452,470)(453,471)(454,472)(455,473)(456,474)
(457,475)(458,476)(459,477)(460,478)(461,479)(462,480)(463,481)(464,482)
(465,483)(466,484)(467,485)(468,486)(505,523)(506,524)(507,525)(508,526)
(509,527)(510,528)(511,529)(512,530)(513,531)(514,532)(515,533)(516,534)
(517,535)(518,536)(519,537)(520,538)(521,539)(522,540)(541,559)(542,560)
(543,561)(544,562)(545,563)(546,564)(547,565)(548,566)(549,567)(550,568)
(551,569)(552,570)(553,571)(554,572)(555,573)(556,574)(557,575)(558,576);;
s3 := (  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);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,361)(  2,363)(  3,362)(  4,369)(  5,368)(  6,367)(  7,366)
(  8,365)(  9,364)( 10,370)( 11,372)( 12,371)( 13,378)( 14,377)( 15,376)
( 16,375)( 17,374)( 18,373)( 19,379)( 20,381)( 21,380)( 22,387)( 23,386)
( 24,385)( 25,384)( 26,383)( 27,382)( 28,388)( 29,390)( 30,389)( 31,396)
( 32,395)( 33,394)( 34,393)( 35,392)( 36,391)( 37,397)( 38,399)( 39,398)
( 40,405)( 41,404)( 42,403)( 43,402)( 44,401)( 45,400)( 46,406)( 47,408)
( 48,407)( 49,414)( 50,413)( 51,412)( 52,411)( 53,410)( 54,409)( 55,415)
( 56,417)( 57,416)( 58,423)( 59,422)( 60,421)( 61,420)( 62,419)( 63,418)
( 64,424)( 65,426)( 66,425)( 67,432)( 68,431)( 69,430)( 70,429)( 71,428)
( 72,427)( 73,289)( 74,291)( 75,290)( 76,297)( 77,296)( 78,295)( 79,294)
( 80,293)( 81,292)( 82,298)( 83,300)( 84,299)( 85,306)( 86,305)( 87,304)
( 88,303)( 89,302)( 90,301)( 91,307)( 92,309)( 93,308)( 94,315)( 95,314)
( 96,313)( 97,312)( 98,311)( 99,310)(100,316)(101,318)(102,317)(103,324)
(104,323)(105,322)(106,321)(107,320)(108,319)(109,325)(110,327)(111,326)
(112,333)(113,332)(114,331)(115,330)(116,329)(117,328)(118,334)(119,336)
(120,335)(121,342)(122,341)(123,340)(124,339)(125,338)(126,337)(127,343)
(128,345)(129,344)(130,351)(131,350)(132,349)(133,348)(134,347)(135,346)
(136,352)(137,354)(138,353)(139,360)(140,359)(141,358)(142,357)(143,356)
(144,355)(145,514)(146,516)(147,515)(148,522)(149,521)(150,520)(151,519)
(152,518)(153,517)(154,505)(155,507)(156,506)(157,513)(158,512)(159,511)
(160,510)(161,509)(162,508)(163,532)(164,534)(165,533)(166,540)(167,539)
(168,538)(169,537)(170,536)(171,535)(172,523)(173,525)(174,524)(175,531)
(176,530)(177,529)(178,528)(179,527)(180,526)(181,550)(182,552)(183,551)
(184,558)(185,557)(186,556)(187,555)(188,554)(189,553)(190,541)(191,543)
(192,542)(193,549)(194,548)(195,547)(196,546)(197,545)(198,544)(199,568)
(200,570)(201,569)(202,576)(203,575)(204,574)(205,573)(206,572)(207,571)
(208,559)(209,561)(210,560)(211,567)(212,566)(213,565)(214,564)(215,563)
(216,562)(217,442)(218,444)(219,443)(220,450)(221,449)(222,448)(223,447)
(224,446)(225,445)(226,433)(227,435)(228,434)(229,441)(230,440)(231,439)
(232,438)(233,437)(234,436)(235,460)(236,462)(237,461)(238,468)(239,467)
(240,466)(241,465)(242,464)(243,463)(244,451)(245,453)(246,452)(247,459)
(248,458)(249,457)(250,456)(251,455)(252,454)(253,478)(254,480)(255,479)
(256,486)(257,485)(258,484)(259,483)(260,482)(261,481)(262,469)(263,471)
(264,470)(265,477)(266,476)(267,475)(268,474)(269,473)(270,472)(271,496)
(272,498)(273,497)(274,504)(275,503)(276,502)(277,501)(278,500)(279,499)
(280,487)(281,489)(282,488)(283,495)(284,494)(285,493)(286,492)(287,491)
(288,490);
s1 := Sym(576)!(  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,153)
(  8,152)(  9,151)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)
( 16,162)( 17,161)( 18,160)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)
( 24,164)( 25,171)( 26,170)( 27,169)( 28,175)( 29,177)( 30,176)( 31,172)
( 32,174)( 33,173)( 34,180)( 35,179)( 36,178)( 37,184)( 38,186)( 39,185)
( 40,181)( 41,183)( 42,182)( 43,189)( 44,188)( 45,187)( 46,193)( 47,195)
( 48,194)( 49,190)( 50,192)( 51,191)( 52,198)( 53,197)( 54,196)( 55,202)
( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,207)( 62,206)( 63,205)
( 64,211)( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,216)( 71,215)
( 72,214)( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,225)
( 80,224)( 81,223)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)
( 88,234)( 89,233)( 90,232)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)
( 96,236)( 97,243)( 98,242)( 99,241)(100,247)(101,249)(102,248)(103,244)
(104,246)(105,245)(106,252)(107,251)(108,250)(109,256)(110,258)(111,257)
(112,253)(113,255)(114,254)(115,261)(116,260)(117,259)(118,265)(119,267)
(120,266)(121,262)(122,264)(123,263)(124,270)(125,269)(126,268)(127,274)
(128,276)(129,275)(130,271)(131,273)(132,272)(133,279)(134,278)(135,277)
(136,283)(137,285)(138,284)(139,280)(140,282)(141,281)(142,288)(143,287)
(144,286)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,441)
(296,440)(297,439)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)
(304,450)(305,449)(306,448)(307,454)(308,456)(309,455)(310,451)(311,453)
(312,452)(313,459)(314,458)(315,457)(316,463)(317,465)(318,464)(319,460)
(320,462)(321,461)(322,468)(323,467)(324,466)(325,472)(326,474)(327,473)
(328,469)(329,471)(330,470)(331,477)(332,476)(333,475)(334,481)(335,483)
(336,482)(337,478)(338,480)(339,479)(340,486)(341,485)(342,484)(343,490)
(344,492)(345,491)(346,487)(347,489)(348,488)(349,495)(350,494)(351,493)
(352,499)(353,501)(354,500)(355,496)(356,498)(357,497)(358,504)(359,503)
(360,502)(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,513)
(368,512)(369,511)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)
(376,522)(377,521)(378,520)(379,526)(380,528)(381,527)(382,523)(383,525)
(384,524)(385,531)(386,530)(387,529)(388,535)(389,537)(390,536)(391,532)
(392,534)(393,533)(394,540)(395,539)(396,538)(397,544)(398,546)(399,545)
(400,541)(401,543)(402,542)(403,549)(404,548)(405,547)(406,553)(407,555)
(408,554)(409,550)(410,552)(411,551)(412,558)(413,557)(414,556)(415,562)
(416,564)(417,563)(418,559)(419,561)(420,560)(421,567)(422,566)(423,565)
(424,571)(425,573)(426,572)(427,568)(428,570)(429,569)(430,576)(431,575)
(432,574);
s2 := Sym(576)!( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)
( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)
( 96,132)( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)
(104,140)(105,141)(106,142)(107,143)(108,144)(145,163)(146,164)(147,165)
(148,166)(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)
(156,174)(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,199)
(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)(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)
(224,278)(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)
(232,286)(233,287)(234,288)(235,253)(236,254)(237,255)(238,256)(239,257)
(240,258)(241,259)(242,260)(243,261)(244,262)(245,263)(246,264)(247,265)
(248,266)(249,267)(250,268)(251,269)(252,270)(289,325)(290,326)(291,327)
(292,328)(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)
(300,336)(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)
(308,344)(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)
(316,352)(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)
(324,360)(433,487)(434,488)(435,489)(436,490)(437,491)(438,492)(439,493)
(440,494)(441,495)(442,496)(443,497)(444,498)(445,499)(446,500)(447,501)
(448,502)(449,503)(450,504)(451,469)(452,470)(453,471)(454,472)(455,473)
(456,474)(457,475)(458,476)(459,477)(460,478)(461,479)(462,480)(463,481)
(464,482)(465,483)(466,484)(467,485)(468,486)(505,523)(506,524)(507,525)
(508,526)(509,527)(510,528)(511,529)(512,530)(513,531)(514,532)(515,533)
(516,534)(517,535)(518,536)(519,537)(520,538)(521,539)(522,540)(541,559)
(542,560)(543,561)(544,562)(545,563)(546,564)(547,565)(548,566)(549,567)
(550,568)(551,569)(552,570)(553,571)(554,572)(555,573)(556,574)(557,575)
(558,576);
s3 := 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);
poly := sub<Sym(576)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope