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}*1152c
if this polytope has a name.
Group : SmallGroup(1152,134263)
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 : {4,4,6,3}*576, {4,2,6,6}*576b, {2,4,6,6}*576c
   3-fold quotients : {4,4,2,6}*384
   4-fold quotients : {4,2,6,3}*288, {2,4,6,3}*288, {2,2,6,6}*288b
   6-fold quotients : {4,4,2,3}*192, {2,4,2,6}*192, {4,2,2,6}*192
   8-fold quotients : {2,2,6,3}*144
   9-fold quotients : {4,4,2,2}*128
   12-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96, {2,2,2,6}*96
   18-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   24-fold quotients : {2,2,2,3}*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 := (  1,145)(  2,150)(  3,152)(  4,148)(  5,153)(  6,146)(  7,151)(  8,147)
(  9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)
( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)
( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)
( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)( 40,184)
( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)
( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)
( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)
( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)
( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)( 80,219)
( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)( 88,232)
( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)( 96,236)
( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)(104,252)
(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)(112,256)
(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)
(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)
(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)
(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)
(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)
(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)
(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)
(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)
(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)(328,472)
(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)
(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)
(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)
(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)
(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)(368,507)
(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)(376,520)
(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)(384,524)
(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)(392,540)
(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)(400,544)
(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)
(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)
(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)
(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);;
s3 := (  1, 38)(  2, 37)(  3, 39)(  4, 44)(  5, 43)(  6, 45)(  7, 41)(  8, 40)
(  9, 42)( 10, 47)( 11, 46)( 12, 48)( 13, 53)( 14, 52)( 15, 54)( 16, 50)
( 17, 49)( 18, 51)( 19, 56)( 20, 55)( 21, 57)( 22, 62)( 23, 61)( 24, 63)
( 25, 59)( 26, 58)( 27, 60)( 28, 65)( 29, 64)( 30, 66)( 31, 71)( 32, 70)
( 33, 72)( 34, 68)( 35, 67)( 36, 69)( 73,110)( 74,109)( 75,111)( 76,116)
( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)
( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,128)( 92,127)
( 93,129)( 94,134)( 95,133)( 96,135)( 97,131)( 98,130)( 99,132)(100,137)
(101,136)(102,138)(103,143)(104,142)(105,144)(106,140)(107,139)(108,141)
(145,182)(146,181)(147,183)(148,188)(149,187)(150,189)(151,185)(152,184)
(153,186)(154,191)(155,190)(156,192)(157,197)(158,196)(159,198)(160,194)
(161,193)(162,195)(163,200)(164,199)(165,201)(166,206)(167,205)(168,207)
(169,203)(170,202)(171,204)(172,209)(173,208)(174,210)(175,215)(176,214)
(177,216)(178,212)(179,211)(180,213)(217,254)(218,253)(219,255)(220,260)
(221,259)(222,261)(223,257)(224,256)(225,258)(226,263)(227,262)(228,264)
(229,269)(230,268)(231,270)(232,266)(233,265)(234,267)(235,272)(236,271)
(237,273)(238,278)(239,277)(240,279)(241,275)(242,274)(243,276)(244,281)
(245,280)(246,282)(247,287)(248,286)(249,288)(250,284)(251,283)(252,285)
(289,326)(290,325)(291,327)(292,332)(293,331)(294,333)(295,329)(296,328)
(297,330)(298,335)(299,334)(300,336)(301,341)(302,340)(303,342)(304,338)
(305,337)(306,339)(307,344)(308,343)(309,345)(310,350)(311,349)(312,351)
(313,347)(314,346)(315,348)(316,353)(317,352)(318,354)(319,359)(320,358)
(321,360)(322,356)(323,355)(324,357)(361,398)(362,397)(363,399)(364,404)
(365,403)(366,405)(367,401)(368,400)(369,402)(370,407)(371,406)(372,408)
(373,413)(374,412)(375,414)(376,410)(377,409)(378,411)(379,416)(380,415)
(381,417)(382,422)(383,421)(384,423)(385,419)(386,418)(387,420)(388,425)
(389,424)(390,426)(391,431)(392,430)(393,432)(394,428)(395,427)(396,429)
(433,470)(434,469)(435,471)(436,476)(437,475)(438,477)(439,473)(440,472)
(441,474)(442,479)(443,478)(444,480)(445,485)(446,484)(447,486)(448,482)
(449,481)(450,483)(451,488)(452,487)(453,489)(454,494)(455,493)(456,495)
(457,491)(458,490)(459,492)(460,497)(461,496)(462,498)(463,503)(464,502)
(465,504)(466,500)(467,499)(468,501)(505,542)(506,541)(507,543)(508,548)
(509,547)(510,549)(511,545)(512,544)(513,546)(514,551)(515,550)(516,552)
(517,557)(518,556)(519,558)(520,554)(521,553)(522,555)(523,560)(524,559)
(525,561)(526,566)(527,565)(528,567)(529,563)(530,562)(531,564)(532,569)
(533,568)(534,570)(535,575)(536,574)(537,576)(538,572)(539,571)(540,573);;
s4 := (  1,109)(  2,111)(  3,110)(  4,115)(  5,117)(  6,116)(  7,112)(  8,114)
(  9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)( 16,121)
( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)( 24,134)
( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)( 32,144)
( 33,143)( 34,139)( 35,141)( 36,140)( 37, 73)( 38, 75)( 39, 74)( 40, 79)
( 41, 81)( 42, 80)( 43, 76)( 44, 78)( 45, 77)( 46, 82)( 47, 84)( 48, 83)
( 49, 88)( 50, 90)( 51, 89)( 52, 85)( 53, 87)( 54, 86)( 55, 91)( 56, 93)
( 57, 92)( 58, 97)( 59, 99)( 60, 98)( 61, 94)( 62, 96)( 63, 95)( 64,100)
( 65,102)( 66,101)( 67,106)( 68,108)( 69,107)( 70,103)( 71,105)( 72,104)
(145,253)(146,255)(147,254)(148,259)(149,261)(150,260)(151,256)(152,258)
(153,257)(154,262)(155,264)(156,263)(157,268)(158,270)(159,269)(160,265)
(161,267)(162,266)(163,271)(164,273)(165,272)(166,277)(167,279)(168,278)
(169,274)(170,276)(171,275)(172,280)(173,282)(174,281)(175,286)(176,288)
(177,287)(178,283)(179,285)(180,284)(181,217)(182,219)(183,218)(184,223)
(185,225)(186,224)(187,220)(188,222)(189,221)(190,226)(191,228)(192,227)
(193,232)(194,234)(195,233)(196,229)(197,231)(198,230)(199,235)(200,237)
(201,236)(202,241)(203,243)(204,242)(205,238)(206,240)(207,239)(208,244)
(209,246)(210,245)(211,250)(212,252)(213,251)(214,247)(215,249)(216,248)
(289,397)(290,399)(291,398)(292,403)(293,405)(294,404)(295,400)(296,402)
(297,401)(298,406)(299,408)(300,407)(301,412)(302,414)(303,413)(304,409)
(305,411)(306,410)(307,415)(308,417)(309,416)(310,421)(311,423)(312,422)
(313,418)(314,420)(315,419)(316,424)(317,426)(318,425)(319,430)(320,432)
(321,431)(322,427)(323,429)(324,428)(325,361)(326,363)(327,362)(328,367)
(329,369)(330,368)(331,364)(332,366)(333,365)(334,370)(335,372)(336,371)
(337,376)(338,378)(339,377)(340,373)(341,375)(342,374)(343,379)(344,381)
(345,380)(346,385)(347,387)(348,386)(349,382)(350,384)(351,383)(352,388)
(353,390)(354,389)(355,394)(356,396)(357,395)(358,391)(359,393)(360,392)
(433,541)(434,543)(435,542)(436,547)(437,549)(438,548)(439,544)(440,546)
(441,545)(442,550)(443,552)(444,551)(445,556)(446,558)(447,557)(448,553)
(449,555)(450,554)(451,559)(452,561)(453,560)(454,565)(455,567)(456,566)
(457,562)(458,564)(459,563)(460,568)(461,570)(462,569)(463,574)(464,576)
(465,575)(466,571)(467,573)(468,572)(469,505)(470,507)(471,506)(472,511)
(473,513)(474,512)(475,508)(476,510)(477,509)(478,514)(479,516)(480,515)
(481,520)(482,522)(483,521)(484,517)(485,519)(486,518)(487,523)(488,525)
(489,524)(490,529)(491,531)(492,530)(493,526)(494,528)(495,527)(496,532)
(497,534)(498,533)(499,538)(500,540)(501,539)(502,535)(503,537)(504,536);;
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*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)!(  1,145)(  2,150)(  3,152)(  4,148)(  5,153)(  6,146)(  7,151)
(  8,147)(  9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)
( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)
( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)
( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)
( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)
( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)
( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)
( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)
( 72,212)( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)
( 80,219)( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)
( 88,232)( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)
( 96,236)( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)
(104,252)(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)
(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)
(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)
(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)
(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)
(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)
(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)
(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)
(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)
(320,468)(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)
(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)
(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)
(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)
(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)
(360,500)(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)
(368,507)(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)
(376,520)(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)
(384,524)(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)
(392,540)(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)
(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)
(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)
(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)
(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)
(432,572);
s3 := Sym(576)!(  1, 38)(  2, 37)(  3, 39)(  4, 44)(  5, 43)(  6, 45)(  7, 41)
(  8, 40)(  9, 42)( 10, 47)( 11, 46)( 12, 48)( 13, 53)( 14, 52)( 15, 54)
( 16, 50)( 17, 49)( 18, 51)( 19, 56)( 20, 55)( 21, 57)( 22, 62)( 23, 61)
( 24, 63)( 25, 59)( 26, 58)( 27, 60)( 28, 65)( 29, 64)( 30, 66)( 31, 71)
( 32, 70)( 33, 72)( 34, 68)( 35, 67)( 36, 69)( 73,110)( 74,109)( 75,111)
( 76,116)( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)
( 84,120)( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,128)
( 92,127)( 93,129)( 94,134)( 95,133)( 96,135)( 97,131)( 98,130)( 99,132)
(100,137)(101,136)(102,138)(103,143)(104,142)(105,144)(106,140)(107,139)
(108,141)(145,182)(146,181)(147,183)(148,188)(149,187)(150,189)(151,185)
(152,184)(153,186)(154,191)(155,190)(156,192)(157,197)(158,196)(159,198)
(160,194)(161,193)(162,195)(163,200)(164,199)(165,201)(166,206)(167,205)
(168,207)(169,203)(170,202)(171,204)(172,209)(173,208)(174,210)(175,215)
(176,214)(177,216)(178,212)(179,211)(180,213)(217,254)(218,253)(219,255)
(220,260)(221,259)(222,261)(223,257)(224,256)(225,258)(226,263)(227,262)
(228,264)(229,269)(230,268)(231,270)(232,266)(233,265)(234,267)(235,272)
(236,271)(237,273)(238,278)(239,277)(240,279)(241,275)(242,274)(243,276)
(244,281)(245,280)(246,282)(247,287)(248,286)(249,288)(250,284)(251,283)
(252,285)(289,326)(290,325)(291,327)(292,332)(293,331)(294,333)(295,329)
(296,328)(297,330)(298,335)(299,334)(300,336)(301,341)(302,340)(303,342)
(304,338)(305,337)(306,339)(307,344)(308,343)(309,345)(310,350)(311,349)
(312,351)(313,347)(314,346)(315,348)(316,353)(317,352)(318,354)(319,359)
(320,358)(321,360)(322,356)(323,355)(324,357)(361,398)(362,397)(363,399)
(364,404)(365,403)(366,405)(367,401)(368,400)(369,402)(370,407)(371,406)
(372,408)(373,413)(374,412)(375,414)(376,410)(377,409)(378,411)(379,416)
(380,415)(381,417)(382,422)(383,421)(384,423)(385,419)(386,418)(387,420)
(388,425)(389,424)(390,426)(391,431)(392,430)(393,432)(394,428)(395,427)
(396,429)(433,470)(434,469)(435,471)(436,476)(437,475)(438,477)(439,473)
(440,472)(441,474)(442,479)(443,478)(444,480)(445,485)(446,484)(447,486)
(448,482)(449,481)(450,483)(451,488)(452,487)(453,489)(454,494)(455,493)
(456,495)(457,491)(458,490)(459,492)(460,497)(461,496)(462,498)(463,503)
(464,502)(465,504)(466,500)(467,499)(468,501)(505,542)(506,541)(507,543)
(508,548)(509,547)(510,549)(511,545)(512,544)(513,546)(514,551)(515,550)
(516,552)(517,557)(518,556)(519,558)(520,554)(521,553)(522,555)(523,560)
(524,559)(525,561)(526,566)(527,565)(528,567)(529,563)(530,562)(531,564)
(532,569)(533,568)(534,570)(535,575)(536,574)(537,576)(538,572)(539,571)
(540,573);
s4 := Sym(576)!(  1,109)(  2,111)(  3,110)(  4,115)(  5,117)(  6,116)(  7,112)
(  8,114)(  9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)
( 16,121)( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)
( 24,134)( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)
( 32,144)( 33,143)( 34,139)( 35,141)( 36,140)( 37, 73)( 38, 75)( 39, 74)
( 40, 79)( 41, 81)( 42, 80)( 43, 76)( 44, 78)( 45, 77)( 46, 82)( 47, 84)
( 48, 83)( 49, 88)( 50, 90)( 51, 89)( 52, 85)( 53, 87)( 54, 86)( 55, 91)
( 56, 93)( 57, 92)( 58, 97)( 59, 99)( 60, 98)( 61, 94)( 62, 96)( 63, 95)
( 64,100)( 65,102)( 66,101)( 67,106)( 68,108)( 69,107)( 70,103)( 71,105)
( 72,104)(145,253)(146,255)(147,254)(148,259)(149,261)(150,260)(151,256)
(152,258)(153,257)(154,262)(155,264)(156,263)(157,268)(158,270)(159,269)
(160,265)(161,267)(162,266)(163,271)(164,273)(165,272)(166,277)(167,279)
(168,278)(169,274)(170,276)(171,275)(172,280)(173,282)(174,281)(175,286)
(176,288)(177,287)(178,283)(179,285)(180,284)(181,217)(182,219)(183,218)
(184,223)(185,225)(186,224)(187,220)(188,222)(189,221)(190,226)(191,228)
(192,227)(193,232)(194,234)(195,233)(196,229)(197,231)(198,230)(199,235)
(200,237)(201,236)(202,241)(203,243)(204,242)(205,238)(206,240)(207,239)
(208,244)(209,246)(210,245)(211,250)(212,252)(213,251)(214,247)(215,249)
(216,248)(289,397)(290,399)(291,398)(292,403)(293,405)(294,404)(295,400)
(296,402)(297,401)(298,406)(299,408)(300,407)(301,412)(302,414)(303,413)
(304,409)(305,411)(306,410)(307,415)(308,417)(309,416)(310,421)(311,423)
(312,422)(313,418)(314,420)(315,419)(316,424)(317,426)(318,425)(319,430)
(320,432)(321,431)(322,427)(323,429)(324,428)(325,361)(326,363)(327,362)
(328,367)(329,369)(330,368)(331,364)(332,366)(333,365)(334,370)(335,372)
(336,371)(337,376)(338,378)(339,377)(340,373)(341,375)(342,374)(343,379)
(344,381)(345,380)(346,385)(347,387)(348,386)(349,382)(350,384)(351,383)
(352,388)(353,390)(354,389)(355,394)(356,396)(357,395)(358,391)(359,393)
(360,392)(433,541)(434,543)(435,542)(436,547)(437,549)(438,548)(439,544)
(440,546)(441,545)(442,550)(443,552)(444,551)(445,556)(446,558)(447,557)
(448,553)(449,555)(450,554)(451,559)(452,561)(453,560)(454,565)(455,567)
(456,566)(457,562)(458,564)(459,563)(460,568)(461,570)(462,569)(463,574)
(464,576)(465,575)(466,571)(467,573)(468,572)(469,505)(470,507)(471,506)
(472,511)(473,513)(474,512)(475,508)(476,510)(477,509)(478,514)(479,516)
(480,515)(481,520)(482,522)(483,521)(484,517)(485,519)(486,518)(487,523)
(488,525)(489,524)(490,529)(491,531)(492,530)(493,526)(494,528)(495,527)
(496,532)(497,534)(498,533)(499,538)(500,540)(501,539)(502,535)(503,537)
(504,536);
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*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope