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Polytope of Type {6,6,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,4,4}*1152b
Also Known As : {{6,6|2},{6,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,134261)
Rank : 5
Schlafli Type : {6,6,4,4}
Number of vertices, edges, etc : 6, 18, 12, 8, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 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 : {6,6,2,4}*576a, {6,6,4,2}*576a
   3-fold quotients : {2,6,4,4}*384, {6,2,4,4}*384
   4-fold quotients : {6,6,2,2}*288a
   6-fold quotients : {3,2,4,4}*192, {2,6,2,4}*192, {2,6,4,2}*192a, {6,2,2,4}*192, {6,2,4,2}*192
   9-fold quotients : {2,2,4,4}*128
   12-fold quotients : {2,3,2,4}*96, {3,2,2,4}*96, {3,2,4,2}*96, {2,6,2,2}*96, {6,2,2,2}*96
   18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   24-fold quotients : {2,3,2,2}*48, {3,2,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 37)(  2, 42)(  3, 44)(  4, 40)(  5, 45)(  6, 38)(  7, 43)(  8, 39)
(  9, 41)( 10, 46)( 11, 51)( 12, 53)( 13, 49)( 14, 54)( 15, 47)( 16, 52)
( 17, 48)( 18, 50)( 19, 55)( 20, 60)( 21, 62)( 22, 58)( 23, 63)( 24, 56)
( 25, 61)( 26, 57)( 27, 59)( 28, 64)( 29, 69)( 30, 71)( 31, 67)( 32, 72)
( 33, 65)( 34, 70)( 35, 66)( 36, 68)( 73,109)( 74,114)( 75,116)( 76,112)
( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)
( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,127)( 92,132)
( 93,134)( 94,130)( 95,135)( 96,128)( 97,133)( 98,129)( 99,131)(100,136)
(101,141)(102,143)(103,139)(104,144)(105,137)(106,142)(107,138)(108,140)
(145,181)(146,186)(147,188)(148,184)(149,189)(150,182)(151,187)(152,183)
(153,185)(154,190)(155,195)(156,197)(157,193)(158,198)(159,191)(160,196)
(161,192)(162,194)(163,199)(164,204)(165,206)(166,202)(167,207)(168,200)
(169,205)(170,201)(171,203)(172,208)(173,213)(174,215)(175,211)(176,216)
(177,209)(178,214)(179,210)(180,212)(217,253)(218,258)(219,260)(220,256)
(221,261)(222,254)(223,259)(224,255)(225,257)(226,262)(227,267)(228,269)
(229,265)(230,270)(231,263)(232,268)(233,264)(234,266)(235,271)(236,276)
(237,278)(238,274)(239,279)(240,272)(241,277)(242,273)(243,275)(244,280)
(245,285)(246,287)(247,283)(248,288)(249,281)(250,286)(251,282)(252,284)
(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)
(433,469)(434,474)(435,476)(436,472)(437,477)(438,470)(439,475)(440,471)
(441,473)(442,478)(443,483)(444,485)(445,481)(446,486)(447,479)(448,484)
(449,480)(450,482)(451,487)(452,492)(453,494)(454,490)(455,495)(456,488)
(457,493)(458,489)(459,491)(460,496)(461,501)(462,503)(463,499)(464,504)
(465,497)(466,502)(467,498)(468,500)(505,541)(506,546)(507,548)(508,544)
(509,549)(510,542)(511,547)(512,543)(513,545)(514,550)(515,555)(516,557)
(517,553)(518,558)(519,551)(520,556)(521,552)(522,554)(523,559)(524,564)
(525,566)(526,562)(527,567)(528,560)(529,565)(530,561)(531,563)(532,568)
(533,573)(534,575)(535,571)(536,576)(537,569)(538,574)(539,570)(540,572);;
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)( 37,110)( 38,109)( 39,111)( 40,116)
( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)( 48,120)
( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)( 56,127)
( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)
( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141)
(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)(181,254)(182,253)(183,255)(184,260)
(185,259)(186,261)(187,257)(188,256)(189,258)(190,263)(191,262)(192,264)
(193,269)(194,268)(195,270)(196,266)(197,265)(198,267)(199,272)(200,271)
(201,273)(202,278)(203,277)(204,279)(205,275)(206,274)(207,276)(208,281)
(209,280)(210,282)(211,287)(212,286)(213,288)(214,284)(215,283)(216,285)
(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)(325,398)(326,397)(327,399)(328,404)
(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)(336,408)
(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)(344,415)
(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)(352,425)
(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)(360,429)
(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)(469,542)(470,541)(471,543)(472,548)
(473,547)(474,549)(475,545)(476,544)(477,546)(478,551)(479,550)(480,552)
(481,557)(482,556)(483,558)(484,554)(485,553)(486,555)(487,560)(488,559)
(489,561)(490,566)(491,565)(492,567)(493,563)(494,562)(495,564)(496,569)
(497,568)(498,570)(499,575)(500,574)(501,576)(502,572)(503,571)(504,573);;
s2 := (  1,397)(  2,404)(  3,402)(  4,403)(  5,401)(  6,399)(  7,400)(  8,398)
(  9,405)( 10,406)( 11,413)( 12,411)( 13,412)( 14,410)( 15,408)( 16,409)
( 17,407)( 18,414)( 19,415)( 20,422)( 21,420)( 22,421)( 23,419)( 24,417)
( 25,418)( 26,416)( 27,423)( 28,424)( 29,431)( 30,429)( 31,430)( 32,428)
( 33,426)( 34,427)( 35,425)( 36,432)( 37,361)( 38,368)( 39,366)( 40,367)
( 41,365)( 42,363)( 43,364)( 44,362)( 45,369)( 46,370)( 47,377)( 48,375)
( 49,376)( 50,374)( 51,372)( 52,373)( 53,371)( 54,378)( 55,379)( 56,386)
( 57,384)( 58,385)( 59,383)( 60,381)( 61,382)( 62,380)( 63,387)( 64,388)
( 65,395)( 66,393)( 67,394)( 68,392)( 69,390)( 70,391)( 71,389)( 72,396)
( 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)
(145,541)(146,548)(147,546)(148,547)(149,545)(150,543)(151,544)(152,542)
(153,549)(154,550)(155,557)(156,555)(157,556)(158,554)(159,552)(160,553)
(161,551)(162,558)(163,559)(164,566)(165,564)(166,565)(167,563)(168,561)
(169,562)(170,560)(171,567)(172,568)(173,575)(174,573)(175,574)(176,572)
(177,570)(178,571)(179,569)(180,576)(181,505)(182,512)(183,510)(184,511)
(185,509)(186,507)(187,508)(188,506)(189,513)(190,514)(191,521)(192,519)
(193,520)(194,518)(195,516)(196,517)(197,515)(198,522)(199,523)(200,530)
(201,528)(202,529)(203,527)(204,525)(205,526)(206,524)(207,531)(208,532)
(209,539)(210,537)(211,538)(212,536)(213,534)(214,535)(215,533)(216,540)
(217,469)(218,476)(219,474)(220,475)(221,473)(222,471)(223,472)(224,470)
(225,477)(226,478)(227,485)(228,483)(229,484)(230,482)(231,480)(232,481)
(233,479)(234,486)(235,487)(236,494)(237,492)(238,493)(239,491)(240,489)
(241,490)(242,488)(243,495)(244,496)(245,503)(246,501)(247,502)(248,500)
(249,498)(250,499)(251,497)(252,504)(253,433)(254,440)(255,438)(256,439)
(257,437)(258,435)(259,436)(260,434)(261,441)(262,442)(263,449)(264,447)
(265,448)(266,446)(267,444)(268,445)(269,443)(270,450)(271,451)(272,458)
(273,456)(274,457)(275,455)(276,453)(277,454)(278,452)(279,459)(280,460)
(281,467)(282,465)(283,466)(284,464)(285,462)(286,463)(287,461)(288,468);;
s3 := (145,154)(146,155)(147,156)(148,157)(149,158)(150,159)(151,160)(152,161)
(153,162)(163,172)(164,173)(165,174)(166,175)(167,176)(168,177)(169,178)
(170,179)(171,180)(181,190)(182,191)(183,192)(184,193)(185,194)(186,195)
(187,196)(188,197)(189,198)(199,208)(200,209)(201,210)(202,211)(203,212)
(204,213)(205,214)(206,215)(207,216)(217,226)(218,227)(219,228)(220,229)
(221,230)(222,231)(223,232)(224,233)(225,234)(235,244)(236,245)(237,246)
(238,247)(239,248)(240,249)(241,250)(242,251)(243,252)(253,262)(254,263)
(255,264)(256,265)(257,266)(258,267)(259,268)(260,269)(261,270)(271,280)
(272,281)(273,282)(274,283)(275,284)(276,285)(277,286)(278,287)(279,288)
(289,307)(290,308)(291,309)(292,310)(293,311)(294,312)(295,313)(296,314)
(297,315)(298,316)(299,317)(300,318)(301,319)(302,320)(303,321)(304,322)
(305,323)(306,324)(325,343)(326,344)(327,345)(328,346)(329,347)(330,348)
(331,349)(332,350)(333,351)(334,352)(335,353)(336,354)(337,355)(338,356)
(339,357)(340,358)(341,359)(342,360)(361,379)(362,380)(363,381)(364,382)
(365,383)(366,384)(367,385)(368,386)(369,387)(370,388)(371,389)(372,390)
(373,391)(374,392)(375,393)(376,394)(377,395)(378,396)(397,415)(398,416)
(399,417)(400,418)(401,419)(402,420)(403,421)(404,422)(405,423)(406,424)
(407,425)(408,426)(409,427)(410,428)(411,429)(412,430)(413,431)(414,432)
(433,460)(434,461)(435,462)(436,463)(437,464)(438,465)(439,466)(440,467)
(441,468)(442,451)(443,452)(444,453)(445,454)(446,455)(447,456)(448,457)
(449,458)(450,459)(469,496)(470,497)(471,498)(472,499)(473,500)(474,501)
(475,502)(476,503)(477,504)(478,487)(479,488)(480,489)(481,490)(482,491)
(483,492)(484,493)(485,494)(486,495)(505,532)(506,533)(507,534)(508,535)
(509,536)(510,537)(511,538)(512,539)(513,540)(514,523)(515,524)(516,525)
(517,526)(518,527)(519,528)(520,529)(521,530)(522,531)(541,568)(542,569)
(543,570)(544,571)(545,572)(546,573)(547,574)(548,575)(549,576)(550,559)
(551,560)(552,561)(553,562)(554,563)(555,564)(556,565)(557,566)(558,567);;
s4 := (  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,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1, 37)(  2, 42)(  3, 44)(  4, 40)(  5, 45)(  6, 38)(  7, 43)
(  8, 39)(  9, 41)( 10, 46)( 11, 51)( 12, 53)( 13, 49)( 14, 54)( 15, 47)
( 16, 52)( 17, 48)( 18, 50)( 19, 55)( 20, 60)( 21, 62)( 22, 58)( 23, 63)
( 24, 56)( 25, 61)( 26, 57)( 27, 59)( 28, 64)( 29, 69)( 30, 71)( 31, 67)
( 32, 72)( 33, 65)( 34, 70)( 35, 66)( 36, 68)( 73,109)( 74,114)( 75,116)
( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)
( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,127)
( 92,132)( 93,134)( 94,130)( 95,135)( 96,128)( 97,133)( 98,129)( 99,131)
(100,136)(101,141)(102,143)(103,139)(104,144)(105,137)(106,142)(107,138)
(108,140)(145,181)(146,186)(147,188)(148,184)(149,189)(150,182)(151,187)
(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)(158,198)(159,191)
(160,196)(161,192)(162,194)(163,199)(164,204)(165,206)(166,202)(167,207)
(168,200)(169,205)(170,201)(171,203)(172,208)(173,213)(174,215)(175,211)
(176,216)(177,209)(178,214)(179,210)(180,212)(217,253)(218,258)(219,260)
(220,256)(221,261)(222,254)(223,259)(224,255)(225,257)(226,262)(227,267)
(228,269)(229,265)(230,270)(231,263)(232,268)(233,264)(234,266)(235,271)
(236,276)(237,278)(238,274)(239,279)(240,272)(241,277)(242,273)(243,275)
(244,280)(245,285)(246,287)(247,283)(248,288)(249,281)(250,286)(251,282)
(252,284)(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)(433,469)(434,474)(435,476)(436,472)(437,477)(438,470)(439,475)
(440,471)(441,473)(442,478)(443,483)(444,485)(445,481)(446,486)(447,479)
(448,484)(449,480)(450,482)(451,487)(452,492)(453,494)(454,490)(455,495)
(456,488)(457,493)(458,489)(459,491)(460,496)(461,501)(462,503)(463,499)
(464,504)(465,497)(466,502)(467,498)(468,500)(505,541)(506,546)(507,548)
(508,544)(509,549)(510,542)(511,547)(512,543)(513,545)(514,550)(515,555)
(516,557)(517,553)(518,558)(519,551)(520,556)(521,552)(522,554)(523,559)
(524,564)(525,566)(526,562)(527,567)(528,560)(529,565)(530,561)(531,563)
(532,568)(533,573)(534,575)(535,571)(536,576)(537,569)(538,574)(539,570)
(540,572);
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)( 37,110)( 38,109)( 39,111)
( 40,116)( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)
( 48,120)( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)
( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)
( 64,137)( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)
( 72,141)(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)(181,254)(182,253)(183,255)
(184,260)(185,259)(186,261)(187,257)(188,256)(189,258)(190,263)(191,262)
(192,264)(193,269)(194,268)(195,270)(196,266)(197,265)(198,267)(199,272)
(200,271)(201,273)(202,278)(203,277)(204,279)(205,275)(206,274)(207,276)
(208,281)(209,280)(210,282)(211,287)(212,286)(213,288)(214,284)(215,283)
(216,285)(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)(325,398)(326,397)(327,399)
(328,404)(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)
(336,408)(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)
(344,415)(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)
(352,425)(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)
(360,429)(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)(469,542)(470,541)(471,543)
(472,548)(473,547)(474,549)(475,545)(476,544)(477,546)(478,551)(479,550)
(480,552)(481,557)(482,556)(483,558)(484,554)(485,553)(486,555)(487,560)
(488,559)(489,561)(490,566)(491,565)(492,567)(493,563)(494,562)(495,564)
(496,569)(497,568)(498,570)(499,575)(500,574)(501,576)(502,572)(503,571)
(504,573);
s2 := Sym(576)!(  1,397)(  2,404)(  3,402)(  4,403)(  5,401)(  6,399)(  7,400)
(  8,398)(  9,405)( 10,406)( 11,413)( 12,411)( 13,412)( 14,410)( 15,408)
( 16,409)( 17,407)( 18,414)( 19,415)( 20,422)( 21,420)( 22,421)( 23,419)
( 24,417)( 25,418)( 26,416)( 27,423)( 28,424)( 29,431)( 30,429)( 31,430)
( 32,428)( 33,426)( 34,427)( 35,425)( 36,432)( 37,361)( 38,368)( 39,366)
( 40,367)( 41,365)( 42,363)( 43,364)( 44,362)( 45,369)( 46,370)( 47,377)
( 48,375)( 49,376)( 50,374)( 51,372)( 52,373)( 53,371)( 54,378)( 55,379)
( 56,386)( 57,384)( 58,385)( 59,383)( 60,381)( 61,382)( 62,380)( 63,387)
( 64,388)( 65,395)( 66,393)( 67,394)( 68,392)( 69,390)( 70,391)( 71,389)
( 72,396)( 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)(145,541)(146,548)(147,546)(148,547)(149,545)(150,543)(151,544)
(152,542)(153,549)(154,550)(155,557)(156,555)(157,556)(158,554)(159,552)
(160,553)(161,551)(162,558)(163,559)(164,566)(165,564)(166,565)(167,563)
(168,561)(169,562)(170,560)(171,567)(172,568)(173,575)(174,573)(175,574)
(176,572)(177,570)(178,571)(179,569)(180,576)(181,505)(182,512)(183,510)
(184,511)(185,509)(186,507)(187,508)(188,506)(189,513)(190,514)(191,521)
(192,519)(193,520)(194,518)(195,516)(196,517)(197,515)(198,522)(199,523)
(200,530)(201,528)(202,529)(203,527)(204,525)(205,526)(206,524)(207,531)
(208,532)(209,539)(210,537)(211,538)(212,536)(213,534)(214,535)(215,533)
(216,540)(217,469)(218,476)(219,474)(220,475)(221,473)(222,471)(223,472)
(224,470)(225,477)(226,478)(227,485)(228,483)(229,484)(230,482)(231,480)
(232,481)(233,479)(234,486)(235,487)(236,494)(237,492)(238,493)(239,491)
(240,489)(241,490)(242,488)(243,495)(244,496)(245,503)(246,501)(247,502)
(248,500)(249,498)(250,499)(251,497)(252,504)(253,433)(254,440)(255,438)
(256,439)(257,437)(258,435)(259,436)(260,434)(261,441)(262,442)(263,449)
(264,447)(265,448)(266,446)(267,444)(268,445)(269,443)(270,450)(271,451)
(272,458)(273,456)(274,457)(275,455)(276,453)(277,454)(278,452)(279,459)
(280,460)(281,467)(282,465)(283,466)(284,464)(285,462)(286,463)(287,461)
(288,468);
s3 := Sym(576)!(145,154)(146,155)(147,156)(148,157)(149,158)(150,159)(151,160)
(152,161)(153,162)(163,172)(164,173)(165,174)(166,175)(167,176)(168,177)
(169,178)(170,179)(171,180)(181,190)(182,191)(183,192)(184,193)(185,194)
(186,195)(187,196)(188,197)(189,198)(199,208)(200,209)(201,210)(202,211)
(203,212)(204,213)(205,214)(206,215)(207,216)(217,226)(218,227)(219,228)
(220,229)(221,230)(222,231)(223,232)(224,233)(225,234)(235,244)(236,245)
(237,246)(238,247)(239,248)(240,249)(241,250)(242,251)(243,252)(253,262)
(254,263)(255,264)(256,265)(257,266)(258,267)(259,268)(260,269)(261,270)
(271,280)(272,281)(273,282)(274,283)(275,284)(276,285)(277,286)(278,287)
(279,288)(289,307)(290,308)(291,309)(292,310)(293,311)(294,312)(295,313)
(296,314)(297,315)(298,316)(299,317)(300,318)(301,319)(302,320)(303,321)
(304,322)(305,323)(306,324)(325,343)(326,344)(327,345)(328,346)(329,347)
(330,348)(331,349)(332,350)(333,351)(334,352)(335,353)(336,354)(337,355)
(338,356)(339,357)(340,358)(341,359)(342,360)(361,379)(362,380)(363,381)
(364,382)(365,383)(366,384)(367,385)(368,386)(369,387)(370,388)(371,389)
(372,390)(373,391)(374,392)(375,393)(376,394)(377,395)(378,396)(397,415)
(398,416)(399,417)(400,418)(401,419)(402,420)(403,421)(404,422)(405,423)
(406,424)(407,425)(408,426)(409,427)(410,428)(411,429)(412,430)(413,431)
(414,432)(433,460)(434,461)(435,462)(436,463)(437,464)(438,465)(439,466)
(440,467)(441,468)(442,451)(443,452)(444,453)(445,454)(446,455)(447,456)
(448,457)(449,458)(450,459)(469,496)(470,497)(471,498)(472,499)(473,500)
(474,501)(475,502)(476,503)(477,504)(478,487)(479,488)(480,489)(481,490)
(482,491)(483,492)(484,493)(485,494)(486,495)(505,532)(506,533)(507,534)
(508,535)(509,536)(510,537)(511,538)(512,539)(513,540)(514,523)(515,524)
(516,525)(517,526)(518,527)(519,528)(520,529)(521,530)(522,531)(541,568)
(542,569)(543,570)(544,571)(545,572)(546,573)(547,574)(548,575)(549,576)
(550,559)(551,560)(552,561)(553,562)(554,563)(555,564)(556,565)(557,566)
(558,567);
s4 := 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,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope