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}*1152a
Also Known As : {{4,6|2},{6,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,136337)
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
   Self-Dual
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}*576a, {4,6,6,2}*576a
   3-fold quotients : {4,2,6,4}*384a, {4,6,2,4}*384a
   4-fold quotients : {2,6,6,2}*288a
   6-fold quotients : {2,2,6,4}*192a, {2,6,2,4}*192, {4,2,6,2}*192, {4,6,2,2}*192a
   9-fold quotients : {4,2,2,4}*128
   12-fold quotients : {2,3,2,4}*96, {4,2,3,2}*96, {2,2,6,2}*96, {2,6,2,2}*96
   18-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   24-fold quotients : {2,2,3,2}*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, 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 := (  1,109)(  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)
(145,262)(146,269)(147,267)(148,268)(149,266)(150,264)(151,265)(152,263)
(153,270)(154,253)(155,260)(156,258)(157,259)(158,257)(159,255)(160,256)
(161,254)(162,261)(163,280)(164,287)(165,285)(166,286)(167,284)(168,282)
(169,283)(170,281)(171,288)(172,271)(173,278)(174,276)(175,277)(176,275)
(177,273)(178,274)(179,272)(180,279)(181,226)(182,233)(183,231)(184,232)
(185,230)(186,228)(187,229)(188,227)(189,234)(190,217)(191,224)(192,222)
(193,223)(194,221)(195,219)(196,220)(197,218)(198,225)(199,244)(200,251)
(201,249)(202,250)(203,248)(204,246)(205,247)(206,245)(207,252)(208,235)
(209,242)(210,240)(211,241)(212,239)(213,237)(214,238)(215,236)(216,243)
(289,415)(290,422)(291,420)(292,421)(293,419)(294,417)(295,418)(296,416)
(297,423)(298,424)(299,431)(300,429)(301,430)(302,428)(303,426)(304,427)
(305,425)(306,432)(307,397)(308,404)(309,402)(310,403)(311,401)(312,399)
(313,400)(314,398)(315,405)(316,406)(317,413)(318,411)(319,412)(320,410)
(321,408)(322,409)(323,407)(324,414)(325,379)(326,386)(327,384)(328,385)
(329,383)(330,381)(331,382)(332,380)(333,387)(334,388)(335,395)(336,393)
(337,394)(338,392)(339,390)(340,391)(341,389)(342,396)(343,361)(344,368)
(345,366)(346,367)(347,365)(348,363)(349,364)(350,362)(351,369)(352,370)
(353,377)(354,375)(355,376)(356,374)(357,372)(358,373)(359,371)(360,378)
(433,568)(434,575)(435,573)(436,574)(437,572)(438,570)(439,571)(440,569)
(441,576)(442,559)(443,566)(444,564)(445,565)(446,563)(447,561)(448,562)
(449,560)(450,567)(451,550)(452,557)(453,555)(454,556)(455,554)(456,552)
(457,553)(458,551)(459,558)(460,541)(461,548)(462,546)(463,547)(464,545)
(465,543)(466,544)(467,542)(468,549)(469,532)(470,539)(471,537)(472,538)
(473,536)(474,534)(475,535)(476,533)(477,540)(478,523)(479,530)(480,528)
(481,529)(482,527)(483,525)(484,526)(485,524)(486,531)(487,514)(488,521)
(489,519)(490,520)(491,518)(492,516)(493,517)(494,515)(495,522)(496,505)
(497,512)(498,510)(499,511)(500,509)(501,507)(502,508)(503,506)(504,513);;
s4 := (  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)(  8,152)
(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)
( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)(104,248)
(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)(112,256)
(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)
(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)
(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)
(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)
(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)
(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)
(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)
(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)
(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)(328,472)
(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)
(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)
(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)
(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)
(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)(368,512)
(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)(376,520)
(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)(384,528)
(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)(392,536)
(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)(400,544)
(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)
(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)
(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)
(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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)!(  1,109)(  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)(145,262)(146,269)(147,267)(148,268)(149,266)(150,264)(151,265)
(152,263)(153,270)(154,253)(155,260)(156,258)(157,259)(158,257)(159,255)
(160,256)(161,254)(162,261)(163,280)(164,287)(165,285)(166,286)(167,284)
(168,282)(169,283)(170,281)(171,288)(172,271)(173,278)(174,276)(175,277)
(176,275)(177,273)(178,274)(179,272)(180,279)(181,226)(182,233)(183,231)
(184,232)(185,230)(186,228)(187,229)(188,227)(189,234)(190,217)(191,224)
(192,222)(193,223)(194,221)(195,219)(196,220)(197,218)(198,225)(199,244)
(200,251)(201,249)(202,250)(203,248)(204,246)(205,247)(206,245)(207,252)
(208,235)(209,242)(210,240)(211,241)(212,239)(213,237)(214,238)(215,236)
(216,243)(289,415)(290,422)(291,420)(292,421)(293,419)(294,417)(295,418)
(296,416)(297,423)(298,424)(299,431)(300,429)(301,430)(302,428)(303,426)
(304,427)(305,425)(306,432)(307,397)(308,404)(309,402)(310,403)(311,401)
(312,399)(313,400)(314,398)(315,405)(316,406)(317,413)(318,411)(319,412)
(320,410)(321,408)(322,409)(323,407)(324,414)(325,379)(326,386)(327,384)
(328,385)(329,383)(330,381)(331,382)(332,380)(333,387)(334,388)(335,395)
(336,393)(337,394)(338,392)(339,390)(340,391)(341,389)(342,396)(343,361)
(344,368)(345,366)(346,367)(347,365)(348,363)(349,364)(350,362)(351,369)
(352,370)(353,377)(354,375)(355,376)(356,374)(357,372)(358,373)(359,371)
(360,378)(433,568)(434,575)(435,573)(436,574)(437,572)(438,570)(439,571)
(440,569)(441,576)(442,559)(443,566)(444,564)(445,565)(446,563)(447,561)
(448,562)(449,560)(450,567)(451,550)(452,557)(453,555)(454,556)(455,554)
(456,552)(457,553)(458,551)(459,558)(460,541)(461,548)(462,546)(463,547)
(464,545)(465,543)(466,544)(467,542)(468,549)(469,532)(470,539)(471,537)
(472,538)(473,536)(474,534)(475,535)(476,533)(477,540)(478,523)(479,530)
(480,528)(481,529)(482,527)(483,525)(484,526)(485,524)(486,531)(487,514)
(488,521)(489,519)(490,520)(491,518)(492,516)(493,517)(494,515)(495,522)
(496,505)(497,512)(498,510)(499,511)(500,509)(501,507)(502,508)(503,506)
(504,513);
s4 := Sym(576)!(  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)
(  8,152)(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)
( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)
( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)
( 96,240)( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)
(104,248)(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)
(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)
(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)
(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)
(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)
(144,288)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)
(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)
(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)
(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)
(320,464)(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)
(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)
(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)
(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)
(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)
(360,504)(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)
(368,512)(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)
(376,520)(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)
(384,528)(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)
(392,536)(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)
(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)
(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)
(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)
(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)
(432,576);
poly := sub<Sym(576)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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