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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,136339)
Rank : 5
Schlafli Type : {4,6,6,4}
Number of vertices, edges, etc : 4, 12, 18, 12, 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 : {2,6,6,4}*576b, {4,6,6,2}*576c
   3-fold quotients : {4,2,6,4}*384a
   4-fold quotients : {4,6,3,2}*288, {2,6,6,2}*288b
   6-fold quotients : {2,2,6,4}*192a, {4,2,6,2}*192
   8-fold quotients : {2,6,3,2}*144
   9-fold quotients : {4,2,2,4}*128
   12-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   18-fold quotients : {2,2,2,4}*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)
( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)( 80,386)
( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)( 88,394)
( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)( 96,366)
( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)(104,374)
(105,375)(106,376)(107,377)(108,378)(109,415)(110,416)(111,417)(112,418)
(113,419)(114,420)(115,421)(116,422)(117,423)(118,424)(119,425)(120,426)
(121,427)(122,428)(123,429)(124,430)(125,431)(126,432)(127,397)(128,398)
(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)
(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)(144,414)
(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)
(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)(224,530)
(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)(232,538)
(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)(240,510)
(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)(248,518)
(249,519)(250,520)(251,521)(252,522)(253,559)(254,560)(255,561)(256,562)
(257,563)(258,564)(259,565)(260,566)(261,567)(262,568)(263,569)(264,570)
(265,571)(266,572)(267,573)(268,574)(269,575)(270,576)(271,541)(272,542)
(273,543)(274,544)(275,545)(276,546)(277,547)(278,548)(279,549)(280,550)
(281,551)(282,552)(283,553)(284,554)(285,555)(286,556)(287,557)(288,558);;
s1 := (  1, 73)(  2, 78)(  3, 80)(  4, 76)(  5, 81)(  6, 74)(  7, 79)(  8, 75)
(  9, 77)( 10, 82)( 11, 87)( 12, 89)( 13, 85)( 14, 90)( 15, 83)( 16, 88)
( 17, 84)( 18, 86)( 19, 91)( 20, 96)( 21, 98)( 22, 94)( 23, 99)( 24, 92)
( 25, 97)( 26, 93)( 27, 95)( 28,100)( 29,105)( 30,107)( 31,103)( 32,108)
( 33,101)( 34,106)( 35,102)( 36,104)( 37,109)( 38,114)( 39,116)( 40,112)
( 41,117)( 42,110)( 43,115)( 44,111)( 45,113)( 46,118)( 47,123)( 48,125)
( 49,121)( 50,126)( 51,119)( 52,124)( 53,120)( 54,122)( 55,127)( 56,132)
( 57,134)( 58,130)( 59,135)( 60,128)( 61,133)( 62,129)( 63,131)( 64,136)
( 65,141)( 66,143)( 67,139)( 68,144)( 69,137)( 70,142)( 71,138)( 72,140)
(145,217)(146,222)(147,224)(148,220)(149,225)(150,218)(151,223)(152,219)
(153,221)(154,226)(155,231)(156,233)(157,229)(158,234)(159,227)(160,232)
(161,228)(162,230)(163,235)(164,240)(165,242)(166,238)(167,243)(168,236)
(169,241)(170,237)(171,239)(172,244)(173,249)(174,251)(175,247)(176,252)
(177,245)(178,250)(179,246)(180,248)(181,253)(182,258)(183,260)(184,256)
(185,261)(186,254)(187,259)(188,255)(189,257)(190,262)(191,267)(192,269)
(193,265)(194,270)(195,263)(196,268)(197,264)(198,266)(199,271)(200,276)
(201,278)(202,274)(203,279)(204,272)(205,277)(206,273)(207,275)(208,280)
(209,285)(210,287)(211,283)(212,288)(213,281)(214,286)(215,282)(216,284)
(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)(295,367)(296,363)
(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)(303,371)(304,376)
(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)(311,387)(312,380)
(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)(319,391)(320,396)
(321,389)(322,394)(323,390)(324,392)(325,397)(326,402)(327,404)(328,400)
(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)(336,413)
(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)(344,420)
(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)(352,424)
(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)(360,428)
(433,505)(434,510)(435,512)(436,508)(437,513)(438,506)(439,511)(440,507)
(441,509)(442,514)(443,519)(444,521)(445,517)(446,522)(447,515)(448,520)
(449,516)(450,518)(451,523)(452,528)(453,530)(454,526)(455,531)(456,524)
(457,529)(458,525)(459,527)(460,532)(461,537)(462,539)(463,535)(464,540)
(465,533)(466,538)(467,534)(468,536)(469,541)(470,546)(471,548)(472,544)
(473,549)(474,542)(475,547)(476,543)(477,545)(478,550)(479,555)(480,557)
(481,553)(482,558)(483,551)(484,556)(485,552)(486,554)(487,559)(488,564)
(489,566)(490,562)(491,567)(492,560)(493,565)(494,561)(495,563)(496,568)
(497,573)(498,575)(499,571)(500,576)(501,569)(502,574)(503,570)(504,572);;
s2 := (  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);;
s3 := (  1,181)(  2,183)(  3,182)(  4,187)(  5,189)(  6,188)(  7,184)(  8,186)
(  9,185)( 10,190)( 11,192)( 12,191)( 13,196)( 14,198)( 15,197)( 16,193)
( 17,195)( 18,194)( 19,199)( 20,201)( 21,200)( 22,205)( 23,207)( 24,206)
( 25,202)( 26,204)( 27,203)( 28,208)( 29,210)( 30,209)( 31,214)( 32,216)
( 33,215)( 34,211)( 35,213)( 36,212)( 37,145)( 38,147)( 39,146)( 40,151)
( 41,153)( 42,152)( 43,148)( 44,150)( 45,149)( 46,154)( 47,156)( 48,155)
( 49,160)( 50,162)( 51,161)( 52,157)( 53,159)( 54,158)( 55,163)( 56,165)
( 57,164)( 58,169)( 59,171)( 60,170)( 61,166)( 62,168)( 63,167)( 64,172)
( 65,174)( 66,173)( 67,178)( 68,180)( 69,179)( 70,175)( 71,177)( 72,176)
( 73,253)( 74,255)( 75,254)( 76,259)( 77,261)( 78,260)( 79,256)( 80,258)
( 81,257)( 82,262)( 83,264)( 84,263)( 85,268)( 86,270)( 87,269)( 88,265)
( 89,267)( 90,266)( 91,271)( 92,273)( 93,272)( 94,277)( 95,279)( 96,278)
( 97,274)( 98,276)( 99,275)(100,280)(101,282)(102,281)(103,286)(104,288)
(105,287)(106,283)(107,285)(108,284)(109,217)(110,219)(111,218)(112,223)
(113,225)(114,224)(115,220)(116,222)(117,221)(118,226)(119,228)(120,227)
(121,232)(122,234)(123,233)(124,229)(125,231)(126,230)(127,235)(128,237)
(129,236)(130,241)(131,243)(132,242)(133,238)(134,240)(135,239)(136,244)
(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)(144,248)
(289,469)(290,471)(291,470)(292,475)(293,477)(294,476)(295,472)(296,474)
(297,473)(298,478)(299,480)(300,479)(301,484)(302,486)(303,485)(304,481)
(305,483)(306,482)(307,487)(308,489)(309,488)(310,493)(311,495)(312,494)
(313,490)(314,492)(315,491)(316,496)(317,498)(318,497)(319,502)(320,504)
(321,503)(322,499)(323,501)(324,500)(325,433)(326,435)(327,434)(328,439)
(329,441)(330,440)(331,436)(332,438)(333,437)(334,442)(335,444)(336,443)
(337,448)(338,450)(339,449)(340,445)(341,447)(342,446)(343,451)(344,453)
(345,452)(346,457)(347,459)(348,458)(349,454)(350,456)(351,455)(352,460)
(353,462)(354,461)(355,466)(356,468)(357,467)(358,463)(359,465)(360,464)
(361,541)(362,543)(363,542)(364,547)(365,549)(366,548)(367,544)(368,546)
(369,545)(370,550)(371,552)(372,551)(373,556)(374,558)(375,557)(376,553)
(377,555)(378,554)(379,559)(380,561)(381,560)(382,565)(383,567)(384,566)
(385,562)(386,564)(387,563)(388,568)(389,570)(390,569)(391,574)(392,576)
(393,575)(394,571)(395,573)(396,572)(397,505)(398,507)(399,506)(400,511)
(401,513)(402,512)(403,508)(404,510)(405,509)(406,514)(407,516)(408,515)
(409,520)(410,522)(411,521)(412,517)(413,519)(414,518)(415,523)(416,525)
(417,524)(418,529)(419,531)(420,530)(421,526)(422,528)(423,527)(424,532)
(425,534)(426,533)(427,538)(428,540)(429,539)(430,535)(431,537)(432,536);;
s4 := (  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)
(145,226)(146,227)(147,228)(148,229)(149,230)(150,231)(151,232)(152,233)
(153,234)(154,217)(155,218)(156,219)(157,220)(158,221)(159,222)(160,223)
(161,224)(162,225)(163,244)(164,245)(165,246)(166,247)(167,248)(168,249)
(169,250)(170,251)(171,252)(172,235)(173,236)(174,237)(175,238)(176,239)
(177,240)(178,241)(179,242)(180,243)(181,262)(182,263)(183,264)(184,265)
(185,266)(186,267)(187,268)(188,269)(189,270)(190,253)(191,254)(192,255)
(193,256)(194,257)(195,258)(196,259)(197,260)(198,261)(199,280)(200,281)
(201,282)(202,283)(203,284)(204,285)(205,286)(206,287)(207,288)(208,271)
(209,272)(210,273)(211,274)(212,275)(213,276)(214,277)(215,278)(216,279)
(289,379)(290,380)(291,381)(292,382)(293,383)(294,384)(295,385)(296,386)
(297,387)(298,388)(299,389)(300,390)(301,391)(302,392)(303,393)(304,394)
(305,395)(306,396)(307,361)(308,362)(309,363)(310,364)(311,365)(312,366)
(313,367)(314,368)(315,369)(316,370)(317,371)(318,372)(319,373)(320,374)
(321,375)(322,376)(323,377)(324,378)(325,415)(326,416)(327,417)(328,418)
(329,419)(330,420)(331,421)(332,422)(333,423)(334,424)(335,425)(336,426)
(337,427)(338,428)(339,429)(340,430)(341,431)(342,432)(343,397)(344,398)
(345,399)(346,400)(347,401)(348,402)(349,403)(350,404)(351,405)(352,406)
(353,407)(354,408)(355,409)(356,410)(357,411)(358,412)(359,413)(360,414)
(433,532)(434,533)(435,534)(436,535)(437,536)(438,537)(439,538)(440,539)
(441,540)(442,523)(443,524)(444,525)(445,526)(446,527)(447,528)(448,529)
(449,530)(450,531)(451,514)(452,515)(453,516)(454,517)(455,518)(456,519)
(457,520)(458,521)(459,522)(460,505)(461,506)(462,507)(463,508)(464,509)
(465,510)(466,511)(467,512)(468,513)(469,568)(470,569)(471,570)(472,571)
(473,572)(474,573)(475,574)(476,575)(477,576)(478,559)(479,560)(480,561)
(481,562)(482,563)(483,564)(484,565)(485,566)(486,567)(487,550)(488,551)
(489,552)(490,553)(491,554)(492,555)(493,556)(494,557)(495,558)(496,541)
(497,542)(498,543)(499,544)(500,545)(501,546)(502,547)(503,548)(504,549);;
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)
( 80,386)( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)
( 88,394)( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)
( 96,366)( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)
(104,374)(105,375)(106,376)(107,377)(108,378)(109,415)(110,416)(111,417)
(112,418)(113,419)(114,420)(115,421)(116,422)(117,423)(118,424)(119,425)
(120,426)(121,427)(122,428)(123,429)(124,430)(125,431)(126,432)(127,397)
(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)
(136,406)(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)
(144,414)(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)(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)
(224,530)(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)
(232,538)(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)
(240,510)(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)
(248,518)(249,519)(250,520)(251,521)(252,522)(253,559)(254,560)(255,561)
(256,562)(257,563)(258,564)(259,565)(260,566)(261,567)(262,568)(263,569)
(264,570)(265,571)(266,572)(267,573)(268,574)(269,575)(270,576)(271,541)
(272,542)(273,543)(274,544)(275,545)(276,546)(277,547)(278,548)(279,549)
(280,550)(281,551)(282,552)(283,553)(284,554)(285,555)(286,556)(287,557)
(288,558);
s1 := Sym(576)!(  1, 73)(  2, 78)(  3, 80)(  4, 76)(  5, 81)(  6, 74)(  7, 79)
(  8, 75)(  9, 77)( 10, 82)( 11, 87)( 12, 89)( 13, 85)( 14, 90)( 15, 83)
( 16, 88)( 17, 84)( 18, 86)( 19, 91)( 20, 96)( 21, 98)( 22, 94)( 23, 99)
( 24, 92)( 25, 97)( 26, 93)( 27, 95)( 28,100)( 29,105)( 30,107)( 31,103)
( 32,108)( 33,101)( 34,106)( 35,102)( 36,104)( 37,109)( 38,114)( 39,116)
( 40,112)( 41,117)( 42,110)( 43,115)( 44,111)( 45,113)( 46,118)( 47,123)
( 48,125)( 49,121)( 50,126)( 51,119)( 52,124)( 53,120)( 54,122)( 55,127)
( 56,132)( 57,134)( 58,130)( 59,135)( 60,128)( 61,133)( 62,129)( 63,131)
( 64,136)( 65,141)( 66,143)( 67,139)( 68,144)( 69,137)( 70,142)( 71,138)
( 72,140)(145,217)(146,222)(147,224)(148,220)(149,225)(150,218)(151,223)
(152,219)(153,221)(154,226)(155,231)(156,233)(157,229)(158,234)(159,227)
(160,232)(161,228)(162,230)(163,235)(164,240)(165,242)(166,238)(167,243)
(168,236)(169,241)(170,237)(171,239)(172,244)(173,249)(174,251)(175,247)
(176,252)(177,245)(178,250)(179,246)(180,248)(181,253)(182,258)(183,260)
(184,256)(185,261)(186,254)(187,259)(188,255)(189,257)(190,262)(191,267)
(192,269)(193,265)(194,270)(195,263)(196,268)(197,264)(198,266)(199,271)
(200,276)(201,278)(202,274)(203,279)(204,272)(205,277)(206,273)(207,275)
(208,280)(209,285)(210,287)(211,283)(212,288)(213,281)(214,286)(215,282)
(216,284)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)(295,367)
(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)(303,371)
(304,376)(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)(311,387)
(312,380)(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)(319,391)
(320,396)(321,389)(322,394)(323,390)(324,392)(325,397)(326,402)(327,404)
(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)
(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)
(344,420)(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)
(352,424)(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)
(360,428)(433,505)(434,510)(435,512)(436,508)(437,513)(438,506)(439,511)
(440,507)(441,509)(442,514)(443,519)(444,521)(445,517)(446,522)(447,515)
(448,520)(449,516)(450,518)(451,523)(452,528)(453,530)(454,526)(455,531)
(456,524)(457,529)(458,525)(459,527)(460,532)(461,537)(462,539)(463,535)
(464,540)(465,533)(466,538)(467,534)(468,536)(469,541)(470,546)(471,548)
(472,544)(473,549)(474,542)(475,547)(476,543)(477,545)(478,550)(479,555)
(480,557)(481,553)(482,558)(483,551)(484,556)(485,552)(486,554)(487,559)
(488,564)(489,566)(490,562)(491,567)(492,560)(493,565)(494,561)(495,563)
(496,568)(497,573)(498,575)(499,571)(500,576)(501,569)(502,574)(503,570)
(504,572);
s2 := 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);
s3 := Sym(576)!(  1,181)(  2,183)(  3,182)(  4,187)(  5,189)(  6,188)(  7,184)
(  8,186)(  9,185)( 10,190)( 11,192)( 12,191)( 13,196)( 14,198)( 15,197)
( 16,193)( 17,195)( 18,194)( 19,199)( 20,201)( 21,200)( 22,205)( 23,207)
( 24,206)( 25,202)( 26,204)( 27,203)( 28,208)( 29,210)( 30,209)( 31,214)
( 32,216)( 33,215)( 34,211)( 35,213)( 36,212)( 37,145)( 38,147)( 39,146)
( 40,151)( 41,153)( 42,152)( 43,148)( 44,150)( 45,149)( 46,154)( 47,156)
( 48,155)( 49,160)( 50,162)( 51,161)( 52,157)( 53,159)( 54,158)( 55,163)
( 56,165)( 57,164)( 58,169)( 59,171)( 60,170)( 61,166)( 62,168)( 63,167)
( 64,172)( 65,174)( 66,173)( 67,178)( 68,180)( 69,179)( 70,175)( 71,177)
( 72,176)( 73,253)( 74,255)( 75,254)( 76,259)( 77,261)( 78,260)( 79,256)
( 80,258)( 81,257)( 82,262)( 83,264)( 84,263)( 85,268)( 86,270)( 87,269)
( 88,265)( 89,267)( 90,266)( 91,271)( 92,273)( 93,272)( 94,277)( 95,279)
( 96,278)( 97,274)( 98,276)( 99,275)(100,280)(101,282)(102,281)(103,286)
(104,288)(105,287)(106,283)(107,285)(108,284)(109,217)(110,219)(111,218)
(112,223)(113,225)(114,224)(115,220)(116,222)(117,221)(118,226)(119,228)
(120,227)(121,232)(122,234)(123,233)(124,229)(125,231)(126,230)(127,235)
(128,237)(129,236)(130,241)(131,243)(132,242)(133,238)(134,240)(135,239)
(136,244)(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)
(144,248)(289,469)(290,471)(291,470)(292,475)(293,477)(294,476)(295,472)
(296,474)(297,473)(298,478)(299,480)(300,479)(301,484)(302,486)(303,485)
(304,481)(305,483)(306,482)(307,487)(308,489)(309,488)(310,493)(311,495)
(312,494)(313,490)(314,492)(315,491)(316,496)(317,498)(318,497)(319,502)
(320,504)(321,503)(322,499)(323,501)(324,500)(325,433)(326,435)(327,434)
(328,439)(329,441)(330,440)(331,436)(332,438)(333,437)(334,442)(335,444)
(336,443)(337,448)(338,450)(339,449)(340,445)(341,447)(342,446)(343,451)
(344,453)(345,452)(346,457)(347,459)(348,458)(349,454)(350,456)(351,455)
(352,460)(353,462)(354,461)(355,466)(356,468)(357,467)(358,463)(359,465)
(360,464)(361,541)(362,543)(363,542)(364,547)(365,549)(366,548)(367,544)
(368,546)(369,545)(370,550)(371,552)(372,551)(373,556)(374,558)(375,557)
(376,553)(377,555)(378,554)(379,559)(380,561)(381,560)(382,565)(383,567)
(384,566)(385,562)(386,564)(387,563)(388,568)(389,570)(390,569)(391,574)
(392,576)(393,575)(394,571)(395,573)(396,572)(397,505)(398,507)(399,506)
(400,511)(401,513)(402,512)(403,508)(404,510)(405,509)(406,514)(407,516)
(408,515)(409,520)(410,522)(411,521)(412,517)(413,519)(414,518)(415,523)
(416,525)(417,524)(418,529)(419,531)(420,530)(421,526)(422,528)(423,527)
(424,532)(425,534)(426,533)(427,538)(428,540)(429,539)(430,535)(431,537)
(432,536);
s4 := 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)(145,226)(146,227)(147,228)(148,229)(149,230)(150,231)(151,232)
(152,233)(153,234)(154,217)(155,218)(156,219)(157,220)(158,221)(159,222)
(160,223)(161,224)(162,225)(163,244)(164,245)(165,246)(166,247)(167,248)
(168,249)(169,250)(170,251)(171,252)(172,235)(173,236)(174,237)(175,238)
(176,239)(177,240)(178,241)(179,242)(180,243)(181,262)(182,263)(183,264)
(184,265)(185,266)(186,267)(187,268)(188,269)(189,270)(190,253)(191,254)
(192,255)(193,256)(194,257)(195,258)(196,259)(197,260)(198,261)(199,280)
(200,281)(201,282)(202,283)(203,284)(204,285)(205,286)(206,287)(207,288)
(208,271)(209,272)(210,273)(211,274)(212,275)(213,276)(214,277)(215,278)
(216,279)(289,379)(290,380)(291,381)(292,382)(293,383)(294,384)(295,385)
(296,386)(297,387)(298,388)(299,389)(300,390)(301,391)(302,392)(303,393)
(304,394)(305,395)(306,396)(307,361)(308,362)(309,363)(310,364)(311,365)
(312,366)(313,367)(314,368)(315,369)(316,370)(317,371)(318,372)(319,373)
(320,374)(321,375)(322,376)(323,377)(324,378)(325,415)(326,416)(327,417)
(328,418)(329,419)(330,420)(331,421)(332,422)(333,423)(334,424)(335,425)
(336,426)(337,427)(338,428)(339,429)(340,430)(341,431)(342,432)(343,397)
(344,398)(345,399)(346,400)(347,401)(348,402)(349,403)(350,404)(351,405)
(352,406)(353,407)(354,408)(355,409)(356,410)(357,411)(358,412)(359,413)
(360,414)(433,532)(434,533)(435,534)(436,535)(437,536)(438,537)(439,538)
(440,539)(441,540)(442,523)(443,524)(444,525)(445,526)(446,527)(447,528)
(448,529)(449,530)(450,531)(451,514)(452,515)(453,516)(454,517)(455,518)
(456,519)(457,520)(458,521)(459,522)(460,505)(461,506)(462,507)(463,508)
(464,509)(465,510)(466,511)(467,512)(468,513)(469,568)(470,569)(471,570)
(472,571)(473,572)(474,573)(475,574)(476,575)(477,576)(478,559)(479,560)
(480,561)(481,562)(482,563)(483,564)(484,565)(485,566)(486,567)(487,550)
(488,551)(489,552)(490,553)(491,554)(492,555)(493,556)(494,557)(495,558)
(496,541)(497,542)(498,543)(499,544)(500,545)(501,546)(502,547)(503,548)
(504,549);
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope