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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4,6}*1152a
Also Known As : {{4,6|2},{6,4|2},{4,6|2}}. if this polytope has another name.
Group : SmallGroup(1152,136336)
Rank : 5
Schlafli Type : {4,6,4,6}
Number of vertices, edges, etc : 4, 12, 12, 12, 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 : {2,6,4,6}*576, {4,6,2,6}*576a
   3-fold quotients : {4,6,4,2}*384a, {4,2,4,6}*384a
   4-fold quotients : {4,6,2,3}*288a, {2,6,2,6}*288
   6-fold quotients : {2,2,4,6}*192a, {2,6,4,2}*192a, {4,2,2,6}*192, {4,6,2,2}*192a
   8-fold quotients : {2,3,2,6}*144, {2,6,2,3}*144
   9-fold quotients : {4,2,4,2}*128
   12-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96, {2,6,2,2}*96
   16-fold quotients : {2,3,2,3}*72
   18-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   24-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1,289)(  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 := (  1,109)(  2,116)(  3,114)(  4,115)(  5,113)(  6,111)(  7,112)(  8,110)
(  9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)( 16,121)
( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)( 24,129)
( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)( 32,140)
( 33,138)( 34,139)( 35,137)( 36,144)( 37, 73)( 38, 80)( 39, 78)( 40, 79)
( 41, 77)( 42, 75)( 43, 76)( 44, 74)( 45, 81)( 46, 82)( 47, 89)( 48, 87)
( 49, 88)( 50, 86)( 51, 84)( 52, 85)( 53, 83)( 54, 90)( 55, 91)( 56, 98)
( 57, 96)( 58, 97)( 59, 95)( 60, 93)( 61, 94)( 62, 92)( 63, 99)( 64,100)
( 65,107)( 66,105)( 67,106)( 68,104)( 69,102)( 70,103)( 71,101)( 72,108)
(145,253)(146,260)(147,258)(148,259)(149,257)(150,255)(151,256)(152,254)
(153,261)(154,262)(155,269)(156,267)(157,268)(158,266)(159,264)(160,265)
(161,263)(162,270)(163,271)(164,278)(165,276)(166,277)(167,275)(168,273)
(169,274)(170,272)(171,279)(172,280)(173,287)(174,285)(175,286)(176,284)
(177,282)(178,283)(179,281)(180,288)(181,217)(182,224)(183,222)(184,223)
(185,221)(186,219)(187,220)(188,218)(189,225)(190,226)(191,233)(192,231)
(193,232)(194,230)(195,228)(196,229)(197,227)(198,234)(199,235)(200,242)
(201,240)(202,241)(203,239)(204,237)(205,238)(206,236)(207,243)(208,244)
(209,251)(210,249)(211,250)(212,248)(213,246)(214,247)(215,245)(216,252)
(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)
(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)
(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)
(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)
(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)
(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)
(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)
(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)
(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)
(433,541)(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)(440,542)
(441,549)(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)(448,553)
(449,551)(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)(456,561)
(457,562)(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)(464,572)
(465,570)(466,571)(467,569)(468,576)(469,505)(470,512)(471,510)(472,511)
(473,509)(474,507)(475,508)(476,506)(477,513)(478,514)(479,521)(480,519)
(481,520)(482,518)(483,516)(484,517)(485,515)(486,522)(487,523)(488,530)
(489,528)(490,529)(491,527)(492,525)(493,526)(494,524)(495,531)(496,532)
(497,539)(498,537)(499,538)(500,536)(501,534)(502,535)(503,533)(504,540);;
s2 := (  1,112)(  2,110)(  3,117)(  4,109)(  5,116)(  6,114)(  7,115)(  8,113)
(  9,111)( 10,121)( 11,119)( 12,126)( 13,118)( 14,125)( 15,123)( 16,124)
( 17,122)( 18,120)( 19,130)( 20,128)( 21,135)( 22,127)( 23,134)( 24,132)
( 25,133)( 26,131)( 27,129)( 28,139)( 29,137)( 30,144)( 31,136)( 32,143)
( 33,141)( 34,142)( 35,140)( 36,138)( 37, 76)( 38, 74)( 39, 81)( 40, 73)
( 41, 80)( 42, 78)( 43, 79)( 44, 77)( 45, 75)( 46, 85)( 47, 83)( 48, 90)
( 49, 82)( 50, 89)( 51, 87)( 52, 88)( 53, 86)( 54, 84)( 55, 94)( 56, 92)
( 57, 99)( 58, 91)( 59, 98)( 60, 96)( 61, 97)( 62, 95)( 63, 93)( 64,103)
( 65,101)( 66,108)( 67,100)( 68,107)( 69,105)( 70,106)( 71,104)( 72,102)
(145,265)(146,263)(147,270)(148,262)(149,269)(150,267)(151,268)(152,266)
(153,264)(154,256)(155,254)(156,261)(157,253)(158,260)(159,258)(160,259)
(161,257)(162,255)(163,283)(164,281)(165,288)(166,280)(167,287)(168,285)
(169,286)(170,284)(171,282)(172,274)(173,272)(174,279)(175,271)(176,278)
(177,276)(178,277)(179,275)(180,273)(181,229)(182,227)(183,234)(184,226)
(185,233)(186,231)(187,232)(188,230)(189,228)(190,220)(191,218)(192,225)
(193,217)(194,224)(195,222)(196,223)(197,221)(198,219)(199,247)(200,245)
(201,252)(202,244)(203,251)(204,249)(205,250)(206,248)(207,246)(208,238)
(209,236)(210,243)(211,235)(212,242)(213,240)(214,241)(215,239)(216,237)
(289,418)(290,416)(291,423)(292,415)(293,422)(294,420)(295,421)(296,419)
(297,417)(298,427)(299,425)(300,432)(301,424)(302,431)(303,429)(304,430)
(305,428)(306,426)(307,400)(308,398)(309,405)(310,397)(311,404)(312,402)
(313,403)(314,401)(315,399)(316,409)(317,407)(318,414)(319,406)(320,413)
(321,411)(322,412)(323,410)(324,408)(325,382)(326,380)(327,387)(328,379)
(329,386)(330,384)(331,385)(332,383)(333,381)(334,391)(335,389)(336,396)
(337,388)(338,395)(339,393)(340,394)(341,392)(342,390)(343,364)(344,362)
(345,369)(346,361)(347,368)(348,366)(349,367)(350,365)(351,363)(352,373)
(353,371)(354,378)(355,370)(356,377)(357,375)(358,376)(359,374)(360,372)
(433,571)(434,569)(435,576)(436,568)(437,575)(438,573)(439,574)(440,572)
(441,570)(442,562)(443,560)(444,567)(445,559)(446,566)(447,564)(448,565)
(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)(455,557)(456,555)
(457,556)(458,554)(459,552)(460,544)(461,542)(462,549)(463,541)(464,548)
(465,546)(466,547)(467,545)(468,543)(469,535)(470,533)(471,540)(472,532)
(473,539)(474,537)(475,538)(476,536)(477,534)(478,526)(479,524)(480,531)
(481,523)(482,530)(483,528)(484,529)(485,527)(486,525)(487,517)(488,515)
(489,522)(490,514)(491,521)(492,519)(493,520)(494,518)(495,516)(496,508)
(497,506)(498,513)(499,505)(500,512)(501,510)(502,511)(503,509)(504,507);;
s3 := (  1,181)(  2,186)(  3,188)(  4,184)(  5,189)(  6,182)(  7,187)(  8,183)
(  9,185)( 10,190)( 11,195)( 12,197)( 13,193)( 14,198)( 15,191)( 16,196)
( 17,192)( 18,194)( 19,199)( 20,204)( 21,206)( 22,202)( 23,207)( 24,200)
( 25,205)( 26,201)( 27,203)( 28,208)( 29,213)( 30,215)( 31,211)( 32,216)
( 33,209)( 34,214)( 35,210)( 36,212)( 37,145)( 38,150)( 39,152)( 40,148)
( 41,153)( 42,146)( 43,151)( 44,147)( 45,149)( 46,154)( 47,159)( 48,161)
( 49,157)( 50,162)( 51,155)( 52,160)( 53,156)( 54,158)( 55,163)( 56,168)
( 57,170)( 58,166)( 59,171)( 60,164)( 61,169)( 62,165)( 63,167)( 64,172)
( 65,177)( 66,179)( 67,175)( 68,180)( 69,173)( 70,178)( 71,174)( 72,176)
( 73,253)( 74,258)( 75,260)( 76,256)( 77,261)( 78,254)( 79,259)( 80,255)
( 81,257)( 82,262)( 83,267)( 84,269)( 85,265)( 86,270)( 87,263)( 88,268)
( 89,264)( 90,266)( 91,271)( 92,276)( 93,278)( 94,274)( 95,279)( 96,272)
( 97,277)( 98,273)( 99,275)(100,280)(101,285)(102,287)(103,283)(104,288)
(105,281)(106,286)(107,282)(108,284)(109,217)(110,222)(111,224)(112,220)
(113,225)(114,218)(115,223)(116,219)(117,221)(118,226)(119,231)(120,233)
(121,229)(122,234)(123,227)(124,232)(125,228)(126,230)(127,235)(128,240)
(129,242)(130,238)(131,243)(132,236)(133,241)(134,237)(135,239)(136,244)
(137,249)(138,251)(139,247)(140,252)(141,245)(142,250)(143,246)(144,248)
(289,469)(290,474)(291,476)(292,472)(293,477)(294,470)(295,475)(296,471)
(297,473)(298,478)(299,483)(300,485)(301,481)(302,486)(303,479)(304,484)
(305,480)(306,482)(307,487)(308,492)(309,494)(310,490)(311,495)(312,488)
(313,493)(314,489)(315,491)(316,496)(317,501)(318,503)(319,499)(320,504)
(321,497)(322,502)(323,498)(324,500)(325,433)(326,438)(327,440)(328,436)
(329,441)(330,434)(331,439)(332,435)(333,437)(334,442)(335,447)(336,449)
(337,445)(338,450)(339,443)(340,448)(341,444)(342,446)(343,451)(344,456)
(345,458)(346,454)(347,459)(348,452)(349,457)(350,453)(351,455)(352,460)
(353,465)(354,467)(355,463)(356,468)(357,461)(358,466)(359,462)(360,464)
(361,541)(362,546)(363,548)(364,544)(365,549)(366,542)(367,547)(368,543)
(369,545)(370,550)(371,555)(372,557)(373,553)(374,558)(375,551)(376,556)
(377,552)(378,554)(379,559)(380,564)(381,566)(382,562)(383,567)(384,560)
(385,565)(386,561)(387,563)(388,568)(389,573)(390,575)(391,571)(392,576)
(393,569)(394,574)(395,570)(396,572)(397,505)(398,510)(399,512)(400,508)
(401,513)(402,506)(403,511)(404,507)(405,509)(406,514)(407,519)(408,521)
(409,517)(410,522)(411,515)(412,520)(413,516)(414,518)(415,523)(416,528)
(417,530)(418,526)(419,531)(420,524)(421,529)(422,525)(423,527)(424,532)
(425,537)(426,539)(427,535)(428,540)(429,533)(430,538)(431,534)(432,536);;
s4 := (  1, 41)(  2, 43)(  3, 39)(  4, 44)(  5, 37)(  6, 42)(  7, 38)(  8, 40)
(  9, 45)( 10, 50)( 11, 52)( 12, 48)( 13, 53)( 14, 46)( 15, 51)( 16, 47)
( 17, 49)( 18, 54)( 19, 59)( 20, 61)( 21, 57)( 22, 62)( 23, 55)( 24, 60)
( 25, 56)( 26, 58)( 27, 63)( 28, 68)( 29, 70)( 30, 66)( 31, 71)( 32, 64)
( 33, 69)( 34, 65)( 35, 67)( 36, 72)( 73,113)( 74,115)( 75,111)( 76,116)
( 77,109)( 78,114)( 79,110)( 80,112)( 81,117)( 82,122)( 83,124)( 84,120)
( 85,125)( 86,118)( 87,123)( 88,119)( 89,121)( 90,126)( 91,131)( 92,133)
( 93,129)( 94,134)( 95,127)( 96,132)( 97,128)( 98,130)( 99,135)(100,140)
(101,142)(102,138)(103,143)(104,136)(105,141)(106,137)(107,139)(108,144)
(145,185)(146,187)(147,183)(148,188)(149,181)(150,186)(151,182)(152,184)
(153,189)(154,194)(155,196)(156,192)(157,197)(158,190)(159,195)(160,191)
(161,193)(162,198)(163,203)(164,205)(165,201)(166,206)(167,199)(168,204)
(169,200)(170,202)(171,207)(172,212)(173,214)(174,210)(175,215)(176,208)
(177,213)(178,209)(179,211)(180,216)(217,257)(218,259)(219,255)(220,260)
(221,253)(222,258)(223,254)(224,256)(225,261)(226,266)(227,268)(228,264)
(229,269)(230,262)(231,267)(232,263)(233,265)(234,270)(235,275)(236,277)
(237,273)(238,278)(239,271)(240,276)(241,272)(242,274)(243,279)(244,284)
(245,286)(246,282)(247,287)(248,280)(249,285)(250,281)(251,283)(252,288)
(289,329)(290,331)(291,327)(292,332)(293,325)(294,330)(295,326)(296,328)
(297,333)(298,338)(299,340)(300,336)(301,341)(302,334)(303,339)(304,335)
(305,337)(306,342)(307,347)(308,349)(309,345)(310,350)(311,343)(312,348)
(313,344)(314,346)(315,351)(316,356)(317,358)(318,354)(319,359)(320,352)
(321,357)(322,353)(323,355)(324,360)(361,401)(362,403)(363,399)(364,404)
(365,397)(366,402)(367,398)(368,400)(369,405)(370,410)(371,412)(372,408)
(373,413)(374,406)(375,411)(376,407)(377,409)(378,414)(379,419)(380,421)
(381,417)(382,422)(383,415)(384,420)(385,416)(386,418)(387,423)(388,428)
(389,430)(390,426)(391,431)(392,424)(393,429)(394,425)(395,427)(396,432)
(433,473)(434,475)(435,471)(436,476)(437,469)(438,474)(439,470)(440,472)
(441,477)(442,482)(443,484)(444,480)(445,485)(446,478)(447,483)(448,479)
(449,481)(450,486)(451,491)(452,493)(453,489)(454,494)(455,487)(456,492)
(457,488)(458,490)(459,495)(460,500)(461,502)(462,498)(463,503)(464,496)
(465,501)(466,497)(467,499)(468,504)(505,545)(506,547)(507,543)(508,548)
(509,541)(510,546)(511,542)(512,544)(513,549)(514,554)(515,556)(516,552)
(517,557)(518,550)(519,555)(520,551)(521,553)(522,558)(523,563)(524,565)
(525,561)(526,566)(527,559)(528,564)(529,560)(530,562)(531,567)(532,572)
(533,574)(534,570)(535,575)(536,568)(537,573)(538,569)(539,571)(540,576);;
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*s0*s1*s0*s1*s0*s1, 
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)( 73,379)( 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)!(  1,109)(  2,116)(  3,114)(  4,115)(  5,113)(  6,111)(  7,112)
(  8,110)(  9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)
( 16,121)( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)
( 24,129)( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)
( 32,140)( 33,138)( 34,139)( 35,137)( 36,144)( 37, 73)( 38, 80)( 39, 78)
( 40, 79)( 41, 77)( 42, 75)( 43, 76)( 44, 74)( 45, 81)( 46, 82)( 47, 89)
( 48, 87)( 49, 88)( 50, 86)( 51, 84)( 52, 85)( 53, 83)( 54, 90)( 55, 91)
( 56, 98)( 57, 96)( 58, 97)( 59, 95)( 60, 93)( 61, 94)( 62, 92)( 63, 99)
( 64,100)( 65,107)( 66,105)( 67,106)( 68,104)( 69,102)( 70,103)( 71,101)
( 72,108)(145,253)(146,260)(147,258)(148,259)(149,257)(150,255)(151,256)
(152,254)(153,261)(154,262)(155,269)(156,267)(157,268)(158,266)(159,264)
(160,265)(161,263)(162,270)(163,271)(164,278)(165,276)(166,277)(167,275)
(168,273)(169,274)(170,272)(171,279)(172,280)(173,287)(174,285)(175,286)
(176,284)(177,282)(178,283)(179,281)(180,288)(181,217)(182,224)(183,222)
(184,223)(185,221)(186,219)(187,220)(188,218)(189,225)(190,226)(191,233)
(192,231)(193,232)(194,230)(195,228)(196,229)(197,227)(198,234)(199,235)
(200,242)(201,240)(202,241)(203,239)(204,237)(205,238)(206,236)(207,243)
(208,244)(209,251)(210,249)(211,250)(212,248)(213,246)(214,247)(215,245)
(216,252)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)
(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)
(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)
(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)
(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)
(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)
(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)
(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)
(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)
(360,396)(433,541)(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)
(440,542)(441,549)(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)
(448,553)(449,551)(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)
(456,561)(457,562)(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)
(464,572)(465,570)(466,571)(467,569)(468,576)(469,505)(470,512)(471,510)
(472,511)(473,509)(474,507)(475,508)(476,506)(477,513)(478,514)(479,521)
(480,519)(481,520)(482,518)(483,516)(484,517)(485,515)(486,522)(487,523)
(488,530)(489,528)(490,529)(491,527)(492,525)(493,526)(494,524)(495,531)
(496,532)(497,539)(498,537)(499,538)(500,536)(501,534)(502,535)(503,533)
(504,540);
s2 := Sym(576)!(  1,112)(  2,110)(  3,117)(  4,109)(  5,116)(  6,114)(  7,115)
(  8,113)(  9,111)( 10,121)( 11,119)( 12,126)( 13,118)( 14,125)( 15,123)
( 16,124)( 17,122)( 18,120)( 19,130)( 20,128)( 21,135)( 22,127)( 23,134)
( 24,132)( 25,133)( 26,131)( 27,129)( 28,139)( 29,137)( 30,144)( 31,136)
( 32,143)( 33,141)( 34,142)( 35,140)( 36,138)( 37, 76)( 38, 74)( 39, 81)
( 40, 73)( 41, 80)( 42, 78)( 43, 79)( 44, 77)( 45, 75)( 46, 85)( 47, 83)
( 48, 90)( 49, 82)( 50, 89)( 51, 87)( 52, 88)( 53, 86)( 54, 84)( 55, 94)
( 56, 92)( 57, 99)( 58, 91)( 59, 98)( 60, 96)( 61, 97)( 62, 95)( 63, 93)
( 64,103)( 65,101)( 66,108)( 67,100)( 68,107)( 69,105)( 70,106)( 71,104)
( 72,102)(145,265)(146,263)(147,270)(148,262)(149,269)(150,267)(151,268)
(152,266)(153,264)(154,256)(155,254)(156,261)(157,253)(158,260)(159,258)
(160,259)(161,257)(162,255)(163,283)(164,281)(165,288)(166,280)(167,287)
(168,285)(169,286)(170,284)(171,282)(172,274)(173,272)(174,279)(175,271)
(176,278)(177,276)(178,277)(179,275)(180,273)(181,229)(182,227)(183,234)
(184,226)(185,233)(186,231)(187,232)(188,230)(189,228)(190,220)(191,218)
(192,225)(193,217)(194,224)(195,222)(196,223)(197,221)(198,219)(199,247)
(200,245)(201,252)(202,244)(203,251)(204,249)(205,250)(206,248)(207,246)
(208,238)(209,236)(210,243)(211,235)(212,242)(213,240)(214,241)(215,239)
(216,237)(289,418)(290,416)(291,423)(292,415)(293,422)(294,420)(295,421)
(296,419)(297,417)(298,427)(299,425)(300,432)(301,424)(302,431)(303,429)
(304,430)(305,428)(306,426)(307,400)(308,398)(309,405)(310,397)(311,404)
(312,402)(313,403)(314,401)(315,399)(316,409)(317,407)(318,414)(319,406)
(320,413)(321,411)(322,412)(323,410)(324,408)(325,382)(326,380)(327,387)
(328,379)(329,386)(330,384)(331,385)(332,383)(333,381)(334,391)(335,389)
(336,396)(337,388)(338,395)(339,393)(340,394)(341,392)(342,390)(343,364)
(344,362)(345,369)(346,361)(347,368)(348,366)(349,367)(350,365)(351,363)
(352,373)(353,371)(354,378)(355,370)(356,377)(357,375)(358,376)(359,374)
(360,372)(433,571)(434,569)(435,576)(436,568)(437,575)(438,573)(439,574)
(440,572)(441,570)(442,562)(443,560)(444,567)(445,559)(446,566)(447,564)
(448,565)(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)(455,557)
(456,555)(457,556)(458,554)(459,552)(460,544)(461,542)(462,549)(463,541)
(464,548)(465,546)(466,547)(467,545)(468,543)(469,535)(470,533)(471,540)
(472,532)(473,539)(474,537)(475,538)(476,536)(477,534)(478,526)(479,524)
(480,531)(481,523)(482,530)(483,528)(484,529)(485,527)(486,525)(487,517)
(488,515)(489,522)(490,514)(491,521)(492,519)(493,520)(494,518)(495,516)
(496,508)(497,506)(498,513)(499,505)(500,512)(501,510)(502,511)(503,509)
(504,507);
s3 := Sym(576)!(  1,181)(  2,186)(  3,188)(  4,184)(  5,189)(  6,182)(  7,187)
(  8,183)(  9,185)( 10,190)( 11,195)( 12,197)( 13,193)( 14,198)( 15,191)
( 16,196)( 17,192)( 18,194)( 19,199)( 20,204)( 21,206)( 22,202)( 23,207)
( 24,200)( 25,205)( 26,201)( 27,203)( 28,208)( 29,213)( 30,215)( 31,211)
( 32,216)( 33,209)( 34,214)( 35,210)( 36,212)( 37,145)( 38,150)( 39,152)
( 40,148)( 41,153)( 42,146)( 43,151)( 44,147)( 45,149)( 46,154)( 47,159)
( 48,161)( 49,157)( 50,162)( 51,155)( 52,160)( 53,156)( 54,158)( 55,163)
( 56,168)( 57,170)( 58,166)( 59,171)( 60,164)( 61,169)( 62,165)( 63,167)
( 64,172)( 65,177)( 66,179)( 67,175)( 68,180)( 69,173)( 70,178)( 71,174)
( 72,176)( 73,253)( 74,258)( 75,260)( 76,256)( 77,261)( 78,254)( 79,259)
( 80,255)( 81,257)( 82,262)( 83,267)( 84,269)( 85,265)( 86,270)( 87,263)
( 88,268)( 89,264)( 90,266)( 91,271)( 92,276)( 93,278)( 94,274)( 95,279)
( 96,272)( 97,277)( 98,273)( 99,275)(100,280)(101,285)(102,287)(103,283)
(104,288)(105,281)(106,286)(107,282)(108,284)(109,217)(110,222)(111,224)
(112,220)(113,225)(114,218)(115,223)(116,219)(117,221)(118,226)(119,231)
(120,233)(121,229)(122,234)(123,227)(124,232)(125,228)(126,230)(127,235)
(128,240)(129,242)(130,238)(131,243)(132,236)(133,241)(134,237)(135,239)
(136,244)(137,249)(138,251)(139,247)(140,252)(141,245)(142,250)(143,246)
(144,248)(289,469)(290,474)(291,476)(292,472)(293,477)(294,470)(295,475)
(296,471)(297,473)(298,478)(299,483)(300,485)(301,481)(302,486)(303,479)
(304,484)(305,480)(306,482)(307,487)(308,492)(309,494)(310,490)(311,495)
(312,488)(313,493)(314,489)(315,491)(316,496)(317,501)(318,503)(319,499)
(320,504)(321,497)(322,502)(323,498)(324,500)(325,433)(326,438)(327,440)
(328,436)(329,441)(330,434)(331,439)(332,435)(333,437)(334,442)(335,447)
(336,449)(337,445)(338,450)(339,443)(340,448)(341,444)(342,446)(343,451)
(344,456)(345,458)(346,454)(347,459)(348,452)(349,457)(350,453)(351,455)
(352,460)(353,465)(354,467)(355,463)(356,468)(357,461)(358,466)(359,462)
(360,464)(361,541)(362,546)(363,548)(364,544)(365,549)(366,542)(367,547)
(368,543)(369,545)(370,550)(371,555)(372,557)(373,553)(374,558)(375,551)
(376,556)(377,552)(378,554)(379,559)(380,564)(381,566)(382,562)(383,567)
(384,560)(385,565)(386,561)(387,563)(388,568)(389,573)(390,575)(391,571)
(392,576)(393,569)(394,574)(395,570)(396,572)(397,505)(398,510)(399,512)
(400,508)(401,513)(402,506)(403,511)(404,507)(405,509)(406,514)(407,519)
(408,521)(409,517)(410,522)(411,515)(412,520)(413,516)(414,518)(415,523)
(416,528)(417,530)(418,526)(419,531)(420,524)(421,529)(422,525)(423,527)
(424,532)(425,537)(426,539)(427,535)(428,540)(429,533)(430,538)(431,534)
(432,536);
s4 := Sym(576)!(  1, 41)(  2, 43)(  3, 39)(  4, 44)(  5, 37)(  6, 42)(  7, 38)
(  8, 40)(  9, 45)( 10, 50)( 11, 52)( 12, 48)( 13, 53)( 14, 46)( 15, 51)
( 16, 47)( 17, 49)( 18, 54)( 19, 59)( 20, 61)( 21, 57)( 22, 62)( 23, 55)
( 24, 60)( 25, 56)( 26, 58)( 27, 63)( 28, 68)( 29, 70)( 30, 66)( 31, 71)
( 32, 64)( 33, 69)( 34, 65)( 35, 67)( 36, 72)( 73,113)( 74,115)( 75,111)
( 76,116)( 77,109)( 78,114)( 79,110)( 80,112)( 81,117)( 82,122)( 83,124)
( 84,120)( 85,125)( 86,118)( 87,123)( 88,119)( 89,121)( 90,126)( 91,131)
( 92,133)( 93,129)( 94,134)( 95,127)( 96,132)( 97,128)( 98,130)( 99,135)
(100,140)(101,142)(102,138)(103,143)(104,136)(105,141)(106,137)(107,139)
(108,144)(145,185)(146,187)(147,183)(148,188)(149,181)(150,186)(151,182)
(152,184)(153,189)(154,194)(155,196)(156,192)(157,197)(158,190)(159,195)
(160,191)(161,193)(162,198)(163,203)(164,205)(165,201)(166,206)(167,199)
(168,204)(169,200)(170,202)(171,207)(172,212)(173,214)(174,210)(175,215)
(176,208)(177,213)(178,209)(179,211)(180,216)(217,257)(218,259)(219,255)
(220,260)(221,253)(222,258)(223,254)(224,256)(225,261)(226,266)(227,268)
(228,264)(229,269)(230,262)(231,267)(232,263)(233,265)(234,270)(235,275)
(236,277)(237,273)(238,278)(239,271)(240,276)(241,272)(242,274)(243,279)
(244,284)(245,286)(246,282)(247,287)(248,280)(249,285)(250,281)(251,283)
(252,288)(289,329)(290,331)(291,327)(292,332)(293,325)(294,330)(295,326)
(296,328)(297,333)(298,338)(299,340)(300,336)(301,341)(302,334)(303,339)
(304,335)(305,337)(306,342)(307,347)(308,349)(309,345)(310,350)(311,343)
(312,348)(313,344)(314,346)(315,351)(316,356)(317,358)(318,354)(319,359)
(320,352)(321,357)(322,353)(323,355)(324,360)(361,401)(362,403)(363,399)
(364,404)(365,397)(366,402)(367,398)(368,400)(369,405)(370,410)(371,412)
(372,408)(373,413)(374,406)(375,411)(376,407)(377,409)(378,414)(379,419)
(380,421)(381,417)(382,422)(383,415)(384,420)(385,416)(386,418)(387,423)
(388,428)(389,430)(390,426)(391,431)(392,424)(393,429)(394,425)(395,427)
(396,432)(433,473)(434,475)(435,471)(436,476)(437,469)(438,474)(439,470)
(440,472)(441,477)(442,482)(443,484)(444,480)(445,485)(446,478)(447,483)
(448,479)(449,481)(450,486)(451,491)(452,493)(453,489)(454,494)(455,487)
(456,492)(457,488)(458,490)(459,495)(460,500)(461,502)(462,498)(463,503)
(464,496)(465,501)(466,497)(467,499)(468,504)(505,545)(506,547)(507,543)
(508,548)(509,541)(510,546)(511,542)(512,544)(513,549)(514,554)(515,556)
(516,552)(517,557)(518,550)(519,555)(520,551)(521,553)(522,558)(523,563)
(524,565)(525,561)(526,566)(527,559)(528,564)(529,560)(530,562)(531,567)
(532,572)(533,574)(534,570)(535,575)(536,568)(537,573)(538,569)(539,571)
(540,576);
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*s0*s1*s0*s1*s0*s1, 
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope