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

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