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