Polytope of Type {6,4,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,4,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,43028)
Rank : 5
Schlafli Type : {6,4,4,4}
Number of vertices, edges, etc : 9, 18, 12, 8, 4
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
Non-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 : {6,4,2,4}*576, {6,4,4,2}*576
4-fold quotients : {6,4,2,2}*288
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 10)( 2, 12)( 3, 11)( 4, 16)( 5, 18)( 6, 17)( 7, 13)( 8, 15)
( 9, 14)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)
( 26, 33)( 27, 32)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)
( 43, 49)( 44, 51)( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)
( 60, 71)( 61, 67)( 62, 69)( 63, 68)( 73, 82)( 74, 84)( 75, 83)( 76, 88)
( 77, 90)( 78, 89)( 79, 85)( 80, 87)( 81, 86)( 91,100)( 92,102)( 93,101)
( 94,106)( 95,108)( 96,107)( 97,103)( 98,105)( 99,104)(109,118)(110,120)
(111,119)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(127,136)
(128,138)(129,137)(130,142)(131,144)(132,143)(133,139)(134,141)(135,140)
(145,154)(146,156)(147,155)(148,160)(149,162)(150,161)(151,157)(152,159)
(153,158)(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)
(170,177)(171,176)(181,190)(182,192)(183,191)(184,196)(185,198)(186,197)
(187,193)(188,195)(189,194)(199,208)(200,210)(201,209)(202,214)(203,216)
(204,215)(205,211)(206,213)(207,212)(217,226)(218,228)(219,227)(220,232)
(221,234)(222,233)(223,229)(224,231)(225,230)(235,244)(236,246)(237,245)
(238,250)(239,252)(240,251)(241,247)(242,249)(243,248)(253,262)(254,264)
(255,263)(256,268)(257,270)(258,269)(259,265)(260,267)(261,266)(271,280)
(272,282)(273,281)(274,286)(275,288)(276,287)(277,283)(278,285)(279,284)
(289,298)(290,300)(291,299)(292,304)(293,306)(294,305)(295,301)(296,303)
(297,302)(307,316)(308,318)(309,317)(310,322)(311,324)(312,323)(313,319)
(314,321)(315,320)(325,334)(326,336)(327,335)(328,340)(329,342)(330,341)
(331,337)(332,339)(333,338)(343,352)(344,354)(345,353)(346,358)(347,360)
(348,359)(349,355)(350,357)(351,356)(361,370)(362,372)(363,371)(364,376)
(365,378)(366,377)(367,373)(368,375)(369,374)(379,388)(380,390)(381,389)
(382,394)(383,396)(384,395)(385,391)(386,393)(387,392)(397,406)(398,408)
(399,407)(400,412)(401,414)(402,413)(403,409)(404,411)(405,410)(415,424)
(416,426)(417,425)(418,430)(419,432)(420,431)(421,427)(422,429)(423,428)
(433,442)(434,444)(435,443)(436,448)(437,450)(438,449)(439,445)(440,447)
(441,446)(451,460)(452,462)(453,461)(454,466)(455,468)(456,467)(457,463)
(458,465)(459,464)(469,478)(470,480)(471,479)(472,484)(473,486)(474,485)
(475,481)(476,483)(477,482)(487,496)(488,498)(489,497)(490,502)(491,504)
(492,503)(493,499)(494,501)(495,500)(505,514)(506,516)(507,515)(508,520)
(509,522)(510,521)(511,517)(512,519)(513,518)(523,532)(524,534)(525,533)
(526,538)(527,540)(528,539)(529,535)(530,537)(531,536)(541,550)(542,552)
(543,551)(544,556)(545,558)(546,557)(547,553)(548,555)(549,554)(559,568)
(560,570)(561,569)(562,574)(563,576)(564,575)(565,571)(566,573)(567,572);;
s1 := ( 1,373)( 2,371)( 3,378)( 4,370)( 5,377)( 6,375)( 7,376)( 8,374)
( 9,372)( 10,364)( 11,362)( 12,369)( 13,361)( 14,368)( 15,366)( 16,367)
( 17,365)( 18,363)( 19,391)( 20,389)( 21,396)( 22,388)( 23,395)( 24,393)
( 25,394)( 26,392)( 27,390)( 28,382)( 29,380)( 30,387)( 31,379)( 32,386)
( 33,384)( 34,385)( 35,383)( 36,381)( 37,409)( 38,407)( 39,414)( 40,406)
( 41,413)( 42,411)( 43,412)( 44,410)( 45,408)( 46,400)( 47,398)( 48,405)
( 49,397)( 50,404)( 51,402)( 52,403)( 53,401)( 54,399)( 55,427)( 56,425)
( 57,432)( 58,424)( 59,431)( 60,429)( 61,430)( 62,428)( 63,426)( 64,418)
( 65,416)( 66,423)( 67,415)( 68,422)( 69,420)( 70,421)( 71,419)( 72,417)
( 73,301)( 74,299)( 75,306)( 76,298)( 77,305)( 78,303)( 79,304)( 80,302)
( 81,300)( 82,292)( 83,290)( 84,297)( 85,289)( 86,296)( 87,294)( 88,295)
( 89,293)( 90,291)( 91,319)( 92,317)( 93,324)( 94,316)( 95,323)( 96,321)
( 97,322)( 98,320)( 99,318)(100,310)(101,308)(102,315)(103,307)(104,314)
(105,312)(106,313)(107,311)(108,309)(109,337)(110,335)(111,342)(112,334)
(113,341)(114,339)(115,340)(116,338)(117,336)(118,328)(119,326)(120,333)
(121,325)(122,332)(123,330)(124,331)(125,329)(126,327)(127,355)(128,353)
(129,360)(130,352)(131,359)(132,357)(133,358)(134,356)(135,354)(136,346)
(137,344)(138,351)(139,343)(140,350)(141,348)(142,349)(143,347)(144,345)
(145,508)(146,506)(147,513)(148,505)(149,512)(150,510)(151,511)(152,509)
(153,507)(154,517)(155,515)(156,522)(157,514)(158,521)(159,519)(160,520)
(161,518)(162,516)(163,526)(164,524)(165,531)(166,523)(167,530)(168,528)
(169,529)(170,527)(171,525)(172,535)(173,533)(174,540)(175,532)(176,539)
(177,537)(178,538)(179,536)(180,534)(181,544)(182,542)(183,549)(184,541)
(185,548)(186,546)(187,547)(188,545)(189,543)(190,553)(191,551)(192,558)
(193,550)(194,557)(195,555)(196,556)(197,554)(198,552)(199,562)(200,560)
(201,567)(202,559)(203,566)(204,564)(205,565)(206,563)(207,561)(208,571)
(209,569)(210,576)(211,568)(212,575)(213,573)(214,574)(215,572)(216,570)
(217,436)(218,434)(219,441)(220,433)(221,440)(222,438)(223,439)(224,437)
(225,435)(226,445)(227,443)(228,450)(229,442)(230,449)(231,447)(232,448)
(233,446)(234,444)(235,454)(236,452)(237,459)(238,451)(239,458)(240,456)
(241,457)(242,455)(243,453)(244,463)(245,461)(246,468)(247,460)(248,467)
(249,465)(250,466)(251,464)(252,462)(253,472)(254,470)(255,477)(256,469)
(257,476)(258,474)(259,475)(260,473)(261,471)(262,481)(263,479)(264,486)
(265,478)(266,485)(267,483)(268,484)(269,482)(270,480)(271,490)(272,488)
(273,495)(274,487)(275,494)(276,492)(277,493)(278,491)(279,489)(280,499)
(281,497)(282,504)(283,496)(284,503)(285,501)(286,502)(287,500)(288,498);;
s2 := ( 1,145)( 2,147)( 3,146)( 4,149)( 5,148)( 6,150)( 7,153)( 8,152)
( 9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)( 16,162)
( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)( 24,168)
( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,183)( 39,182)( 40,185)
( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)( 48,191)
( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)( 56,201)
( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)( 64,208)
( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)( 72,214)
( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)( 80,224)
( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)( 88,234)
( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)( 96,240)
( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)(104,247)
(105,249)(106,252)(107,251)(108,250)(109,253)(110,255)(111,254)(112,257)
(113,256)(114,258)(115,261)(116,260)(117,259)(118,262)(119,264)(120,263)
(121,266)(122,265)(123,267)(124,270)(125,269)(126,268)(127,271)(128,273)
(129,272)(130,275)(131,274)(132,276)(133,279)(134,278)(135,277)(136,280)
(137,282)(138,281)(139,284)(140,283)(141,285)(142,288)(143,287)(144,286)
(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)(296,440)
(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)(304,450)
(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)(312,456)
(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)(320,463)
(321,465)(322,468)(323,467)(324,466)(325,469)(326,471)(327,470)(328,473)
(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)(336,479)
(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)(344,489)
(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)(352,496)
(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)(360,502)
(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)(368,512)
(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)(376,522)
(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)(384,528)
(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)(392,535)
(393,537)(394,540)(395,539)(396,538)(397,541)(398,543)(399,542)(400,545)
(401,544)(402,546)(403,549)(404,548)(405,547)(406,550)(407,552)(408,551)
(409,554)(410,553)(411,555)(412,558)(413,557)(414,556)(415,559)(416,561)
(417,560)(418,563)(419,562)(420,564)(421,567)(422,566)(423,565)(424,568)
(425,570)(426,569)(427,572)(428,571)(429,573)(430,576)(431,575)(432,574);;
s3 := ( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)
( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)
( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)
(105,141)(106,142)(107,143)(108,144)(145,163)(146,164)(147,165)(148,166)
(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)(156,174)
(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,199)(182,200)
(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)(189,207)(190,208)
(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)(197,215)(198,216)
(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)(224,278)
(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)(232,286)
(233,287)(234,288)(235,253)(236,254)(237,255)(238,256)(239,257)(240,258)
(241,259)(242,260)(243,261)(244,262)(245,263)(246,264)(247,265)(248,266)
(249,267)(250,268)(251,269)(252,270)(289,325)(290,326)(291,327)(292,328)
(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)
(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)(308,344)
(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)(316,352)
(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)(324,360)
(433,487)(434,488)(435,489)(436,490)(437,491)(438,492)(439,493)(440,494)
(441,495)(442,496)(443,497)(444,498)(445,499)(446,500)(447,501)(448,502)
(449,503)(450,504)(451,469)(452,470)(453,471)(454,472)(455,473)(456,474)
(457,475)(458,476)(459,477)(460,478)(461,479)(462,480)(463,481)(464,482)
(465,483)(466,484)(467,485)(468,486)(505,523)(506,524)(507,525)(508,526)
(509,527)(510,528)(511,529)(512,530)(513,531)(514,532)(515,533)(516,534)
(517,535)(518,536)(519,537)(520,538)(521,539)(522,540)(541,559)(542,560)
(543,561)(544,562)(545,563)(546,564)(547,565)(548,566)(549,567)(550,568)
(551,569)(552,570)(553,571)(554,572)(555,573)(556,574)(557,575)(558,576);;
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)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)
(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)
(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288)
(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)(296,368)
(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)(304,376)
(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)(312,384)
(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)(320,392)
(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)
(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)(336,408)
(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)(344,416)
(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)(352,424)
(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)(360,432)
(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)(440,512)
(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)(448,520)
(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)(456,528)
(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)(464,536)
(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)(472,544)
(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)(480,552)
(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)(488,560)
(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)(496,568)
(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)(504,576);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1, 10)( 2, 12)( 3, 11)( 4, 16)( 5, 18)( 6, 17)( 7, 13)
( 8, 15)( 9, 14)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)
( 25, 31)( 26, 33)( 27, 32)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)
( 42, 53)( 43, 49)( 44, 51)( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)
( 59, 72)( 60, 71)( 61, 67)( 62, 69)( 63, 68)( 73, 82)( 74, 84)( 75, 83)
( 76, 88)( 77, 90)( 78, 89)( 79, 85)( 80, 87)( 81, 86)( 91,100)( 92,102)
( 93,101)( 94,106)( 95,108)( 96,107)( 97,103)( 98,105)( 99,104)(109,118)
(110,120)(111,119)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)
(127,136)(128,138)(129,137)(130,142)(131,144)(132,143)(133,139)(134,141)
(135,140)(145,154)(146,156)(147,155)(148,160)(149,162)(150,161)(151,157)
(152,159)(153,158)(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)
(169,175)(170,177)(171,176)(181,190)(182,192)(183,191)(184,196)(185,198)
(186,197)(187,193)(188,195)(189,194)(199,208)(200,210)(201,209)(202,214)
(203,216)(204,215)(205,211)(206,213)(207,212)(217,226)(218,228)(219,227)
(220,232)(221,234)(222,233)(223,229)(224,231)(225,230)(235,244)(236,246)
(237,245)(238,250)(239,252)(240,251)(241,247)(242,249)(243,248)(253,262)
(254,264)(255,263)(256,268)(257,270)(258,269)(259,265)(260,267)(261,266)
(271,280)(272,282)(273,281)(274,286)(275,288)(276,287)(277,283)(278,285)
(279,284)(289,298)(290,300)(291,299)(292,304)(293,306)(294,305)(295,301)
(296,303)(297,302)(307,316)(308,318)(309,317)(310,322)(311,324)(312,323)
(313,319)(314,321)(315,320)(325,334)(326,336)(327,335)(328,340)(329,342)
(330,341)(331,337)(332,339)(333,338)(343,352)(344,354)(345,353)(346,358)
(347,360)(348,359)(349,355)(350,357)(351,356)(361,370)(362,372)(363,371)
(364,376)(365,378)(366,377)(367,373)(368,375)(369,374)(379,388)(380,390)
(381,389)(382,394)(383,396)(384,395)(385,391)(386,393)(387,392)(397,406)
(398,408)(399,407)(400,412)(401,414)(402,413)(403,409)(404,411)(405,410)
(415,424)(416,426)(417,425)(418,430)(419,432)(420,431)(421,427)(422,429)
(423,428)(433,442)(434,444)(435,443)(436,448)(437,450)(438,449)(439,445)
(440,447)(441,446)(451,460)(452,462)(453,461)(454,466)(455,468)(456,467)
(457,463)(458,465)(459,464)(469,478)(470,480)(471,479)(472,484)(473,486)
(474,485)(475,481)(476,483)(477,482)(487,496)(488,498)(489,497)(490,502)
(491,504)(492,503)(493,499)(494,501)(495,500)(505,514)(506,516)(507,515)
(508,520)(509,522)(510,521)(511,517)(512,519)(513,518)(523,532)(524,534)
(525,533)(526,538)(527,540)(528,539)(529,535)(530,537)(531,536)(541,550)
(542,552)(543,551)(544,556)(545,558)(546,557)(547,553)(548,555)(549,554)
(559,568)(560,570)(561,569)(562,574)(563,576)(564,575)(565,571)(566,573)
(567,572);
s1 := Sym(576)!( 1,373)( 2,371)( 3,378)( 4,370)( 5,377)( 6,375)( 7,376)
( 8,374)( 9,372)( 10,364)( 11,362)( 12,369)( 13,361)( 14,368)( 15,366)
( 16,367)( 17,365)( 18,363)( 19,391)( 20,389)( 21,396)( 22,388)( 23,395)
( 24,393)( 25,394)( 26,392)( 27,390)( 28,382)( 29,380)( 30,387)( 31,379)
( 32,386)( 33,384)( 34,385)( 35,383)( 36,381)( 37,409)( 38,407)( 39,414)
( 40,406)( 41,413)( 42,411)( 43,412)( 44,410)( 45,408)( 46,400)( 47,398)
( 48,405)( 49,397)( 50,404)( 51,402)( 52,403)( 53,401)( 54,399)( 55,427)
( 56,425)( 57,432)( 58,424)( 59,431)( 60,429)( 61,430)( 62,428)( 63,426)
( 64,418)( 65,416)( 66,423)( 67,415)( 68,422)( 69,420)( 70,421)( 71,419)
( 72,417)( 73,301)( 74,299)( 75,306)( 76,298)( 77,305)( 78,303)( 79,304)
( 80,302)( 81,300)( 82,292)( 83,290)( 84,297)( 85,289)( 86,296)( 87,294)
( 88,295)( 89,293)( 90,291)( 91,319)( 92,317)( 93,324)( 94,316)( 95,323)
( 96,321)( 97,322)( 98,320)( 99,318)(100,310)(101,308)(102,315)(103,307)
(104,314)(105,312)(106,313)(107,311)(108,309)(109,337)(110,335)(111,342)
(112,334)(113,341)(114,339)(115,340)(116,338)(117,336)(118,328)(119,326)
(120,333)(121,325)(122,332)(123,330)(124,331)(125,329)(126,327)(127,355)
(128,353)(129,360)(130,352)(131,359)(132,357)(133,358)(134,356)(135,354)
(136,346)(137,344)(138,351)(139,343)(140,350)(141,348)(142,349)(143,347)
(144,345)(145,508)(146,506)(147,513)(148,505)(149,512)(150,510)(151,511)
(152,509)(153,507)(154,517)(155,515)(156,522)(157,514)(158,521)(159,519)
(160,520)(161,518)(162,516)(163,526)(164,524)(165,531)(166,523)(167,530)
(168,528)(169,529)(170,527)(171,525)(172,535)(173,533)(174,540)(175,532)
(176,539)(177,537)(178,538)(179,536)(180,534)(181,544)(182,542)(183,549)
(184,541)(185,548)(186,546)(187,547)(188,545)(189,543)(190,553)(191,551)
(192,558)(193,550)(194,557)(195,555)(196,556)(197,554)(198,552)(199,562)
(200,560)(201,567)(202,559)(203,566)(204,564)(205,565)(206,563)(207,561)
(208,571)(209,569)(210,576)(211,568)(212,575)(213,573)(214,574)(215,572)
(216,570)(217,436)(218,434)(219,441)(220,433)(221,440)(222,438)(223,439)
(224,437)(225,435)(226,445)(227,443)(228,450)(229,442)(230,449)(231,447)
(232,448)(233,446)(234,444)(235,454)(236,452)(237,459)(238,451)(239,458)
(240,456)(241,457)(242,455)(243,453)(244,463)(245,461)(246,468)(247,460)
(248,467)(249,465)(250,466)(251,464)(252,462)(253,472)(254,470)(255,477)
(256,469)(257,476)(258,474)(259,475)(260,473)(261,471)(262,481)(263,479)
(264,486)(265,478)(266,485)(267,483)(268,484)(269,482)(270,480)(271,490)
(272,488)(273,495)(274,487)(275,494)(276,492)(277,493)(278,491)(279,489)
(280,499)(281,497)(282,504)(283,496)(284,503)(285,501)(286,502)(287,500)
(288,498);
s2 := Sym(576)!( 1,145)( 2,147)( 3,146)( 4,149)( 5,148)( 6,150)( 7,153)
( 8,152)( 9,151)( 10,154)( 11,156)( 12,155)( 13,158)( 14,157)( 15,159)
( 16,162)( 17,161)( 18,160)( 19,163)( 20,165)( 21,164)( 22,167)( 23,166)
( 24,168)( 25,171)( 26,170)( 27,169)( 28,172)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,183)( 39,182)
( 40,185)( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)
( 48,191)( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)
( 56,201)( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)
( 64,208)( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,217)( 74,219)( 75,218)( 76,221)( 77,220)( 78,222)( 79,225)
( 80,224)( 81,223)( 82,226)( 83,228)( 84,227)( 85,230)( 86,229)( 87,231)
( 88,234)( 89,233)( 90,232)( 91,235)( 92,237)( 93,236)( 94,239)( 95,238)
( 96,240)( 97,243)( 98,242)( 99,241)(100,244)(101,246)(102,245)(103,248)
(104,247)(105,249)(106,252)(107,251)(108,250)(109,253)(110,255)(111,254)
(112,257)(113,256)(114,258)(115,261)(116,260)(117,259)(118,262)(119,264)
(120,263)(121,266)(122,265)(123,267)(124,270)(125,269)(126,268)(127,271)
(128,273)(129,272)(130,275)(131,274)(132,276)(133,279)(134,278)(135,277)
(136,280)(137,282)(138,281)(139,284)(140,283)(141,285)(142,288)(143,287)
(144,286)(289,433)(290,435)(291,434)(292,437)(293,436)(294,438)(295,441)
(296,440)(297,439)(298,442)(299,444)(300,443)(301,446)(302,445)(303,447)
(304,450)(305,449)(306,448)(307,451)(308,453)(309,452)(310,455)(311,454)
(312,456)(313,459)(314,458)(315,457)(316,460)(317,462)(318,461)(319,464)
(320,463)(321,465)(322,468)(323,467)(324,466)(325,469)(326,471)(327,470)
(328,473)(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)
(336,479)(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)
(344,489)(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)
(352,496)(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)
(360,502)(361,505)(362,507)(363,506)(364,509)(365,508)(366,510)(367,513)
(368,512)(369,511)(370,514)(371,516)(372,515)(373,518)(374,517)(375,519)
(376,522)(377,521)(378,520)(379,523)(380,525)(381,524)(382,527)(383,526)
(384,528)(385,531)(386,530)(387,529)(388,532)(389,534)(390,533)(391,536)
(392,535)(393,537)(394,540)(395,539)(396,538)(397,541)(398,543)(399,542)
(400,545)(401,544)(402,546)(403,549)(404,548)(405,547)(406,550)(407,552)
(408,551)(409,554)(410,553)(411,555)(412,558)(413,557)(414,556)(415,559)
(416,561)(417,560)(418,563)(419,562)(420,564)(421,567)(422,566)(423,565)
(424,568)(425,570)(426,569)(427,572)(428,571)(429,573)(430,576)(431,575)
(432,574);
s3 := Sym(576)!( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)
( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)
( 96,132)( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)
(104,140)(105,141)(106,142)(107,143)(108,144)(145,163)(146,164)(147,165)
(148,166)(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)
(156,174)(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,199)
(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)(189,207)
(190,208)(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)(197,215)
(198,216)(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)
(224,278)(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)
(232,286)(233,287)(234,288)(235,253)(236,254)(237,255)(238,256)(239,257)
(240,258)(241,259)(242,260)(243,261)(244,262)(245,263)(246,264)(247,265)
(248,266)(249,267)(250,268)(251,269)(252,270)(289,325)(290,326)(291,327)
(292,328)(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)
(300,336)(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)
(308,344)(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)
(316,352)(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)
(324,360)(433,487)(434,488)(435,489)(436,490)(437,491)(438,492)(439,493)
(440,494)(441,495)(442,496)(443,497)(444,498)(445,499)(446,500)(447,501)
(448,502)(449,503)(450,504)(451,469)(452,470)(453,471)(454,472)(455,473)
(456,474)(457,475)(458,476)(459,477)(460,478)(461,479)(462,480)(463,481)
(464,482)(465,483)(466,484)(467,485)(468,486)(505,523)(506,524)(507,525)
(508,526)(509,527)(510,528)(511,529)(512,530)(513,531)(514,532)(515,533)
(516,534)(517,535)(518,536)(519,537)(520,538)(521,539)(522,540)(541,559)
(542,560)(543,561)(544,562)(545,563)(546,564)(547,565)(548,566)(549,567)
(550,568)(551,569)(552,570)(553,571)(554,572)(555,573)(556,574)(557,575)
(558,576);
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)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)
(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)
(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)
(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)
(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)
(216,288)(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)
(296,368)(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)
(304,376)(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)
(312,384)(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)
(320,392)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)
(328,400)(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)
(336,408)(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)
(344,416)(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)
(352,424)(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)
(360,432)(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)
(440,512)(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)
(448,520)(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)
(456,528)(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)
(464,536)(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)
(472,544)(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)
(480,552)(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)
(488,560)(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)
(496,568)(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)
(504,576);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1 >;
References : None.
to this polytope