Polytope of Type {4,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,8}*1152a
Also Known As : {{4,6}4,{6,8|2}}. if this polytope has another name.
Group : SmallGroup(1152,119790)
Rank : 4
Schlafli Type : {4,6,8}
Number of vertices, edges, etc : 12, 36, 72, 8
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 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 : {4,6,4}*576a
4-fold quotients : {4,6,2}*288
8-fold quotients : {4,6,2}*144
9-fold quotients : {4,2,8}*128
18-fold quotients : {4,2,4}*64, {2,2,8}*64
36-fold quotients : {2,2,4}*32, {4,2,2}*32
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1,109)( 2,114)( 3,116)( 4,112)( 5,117)( 6,110)( 7,115)( 8,111)
( 9,113)( 10,118)( 11,123)( 12,125)( 13,121)( 14,126)( 15,119)( 16,124)
( 17,120)( 18,122)( 19,127)( 20,132)( 21,134)( 22,130)( 23,135)( 24,128)
( 25,133)( 26,129)( 27,131)( 28,136)( 29,141)( 30,143)( 31,139)( 32,144)
( 33,137)( 34,142)( 35,138)( 36,140)( 37, 82)( 38, 87)( 39, 89)( 40, 85)
( 41, 90)( 42, 83)( 43, 88)( 44, 84)( 45, 86)( 46, 73)( 47, 78)( 48, 80)
( 49, 76)( 50, 81)( 51, 74)( 52, 79)( 53, 75)( 54, 77)( 55,100)( 56,105)
( 57,107)( 58,103)( 59,108)( 60,101)( 61,106)( 62,102)( 63,104)( 64, 91)
( 65, 96)( 66, 98)( 67, 94)( 68, 99)( 69, 92)( 70, 97)( 71, 93)( 72, 95)
(145,271)(146,276)(147,278)(148,274)(149,279)(150,272)(151,277)(152,273)
(153,275)(154,280)(155,285)(156,287)(157,283)(158,288)(159,281)(160,286)
(161,282)(162,284)(163,253)(164,258)(165,260)(166,256)(167,261)(168,254)
(169,259)(170,255)(171,257)(172,262)(173,267)(174,269)(175,265)(176,270)
(177,263)(178,268)(179,264)(180,266)(181,244)(182,249)(183,251)(184,247)
(185,252)(186,245)(187,250)(188,246)(189,248)(190,235)(191,240)(192,242)
(193,238)(194,243)(195,236)(196,241)(197,237)(198,239)(199,226)(200,231)
(201,233)(202,229)(203,234)(204,227)(205,232)(206,228)(207,230)(208,217)
(209,222)(210,224)(211,220)(212,225)(213,218)(214,223)(215,219)(216,221)
(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)
(433,523)(434,528)(435,530)(436,526)(437,531)(438,524)(439,529)(440,525)
(441,527)(442,532)(443,537)(444,539)(445,535)(446,540)(447,533)(448,538)
(449,534)(450,536)(451,505)(452,510)(453,512)(454,508)(455,513)(456,506)
(457,511)(458,507)(459,509)(460,514)(461,519)(462,521)(463,517)(464,522)
(465,515)(466,520)(467,516)(468,518)(469,559)(470,564)(471,566)(472,562)
(473,567)(474,560)(475,565)(476,561)(477,563)(478,568)(479,573)(480,575)
(481,571)(482,576)(483,569)(484,574)(485,570)(486,572)(487,541)(488,546)
(489,548)(490,544)(491,549)(492,542)(493,547)(494,543)(495,545)(496,550)
(497,555)(498,557)(499,553)(500,558)(501,551)(502,556)(503,552)(504,554);;
s2 := ( 1,314)( 2,313)( 3,315)( 4,311)( 5,310)( 6,312)( 7,308)( 8,307)
( 9,309)( 10,323)( 11,322)( 12,324)( 13,320)( 14,319)( 15,321)( 16,317)
( 17,316)( 18,318)( 19,296)( 20,295)( 21,297)( 22,293)( 23,292)( 24,294)
( 25,290)( 26,289)( 27,291)( 28,305)( 29,304)( 30,306)( 31,302)( 32,301)
( 33,303)( 34,299)( 35,298)( 36,300)( 37,359)( 38,358)( 39,360)( 40,356)
( 41,355)( 42,357)( 43,353)( 44,352)( 45,354)( 46,350)( 47,349)( 48,351)
( 49,347)( 50,346)( 51,348)( 52,344)( 53,343)( 54,345)( 55,341)( 56,340)
( 57,342)( 58,338)( 59,337)( 60,339)( 61,335)( 62,334)( 63,336)( 64,332)
( 65,331)( 66,333)( 67,329)( 68,328)( 69,330)( 70,326)( 71,325)( 72,327)
( 73,422)( 74,421)( 75,423)( 76,419)( 77,418)( 78,420)( 79,416)( 80,415)
( 81,417)( 82,431)( 83,430)( 84,432)( 85,428)( 86,427)( 87,429)( 88,425)
( 89,424)( 90,426)( 91,404)( 92,403)( 93,405)( 94,401)( 95,400)( 96,402)
( 97,398)( 98,397)( 99,399)(100,413)(101,412)(102,414)(103,410)(104,409)
(105,411)(106,407)(107,406)(108,408)(109,386)(110,385)(111,387)(112,383)
(113,382)(114,384)(115,380)(116,379)(117,381)(118,395)(119,394)(120,396)
(121,392)(122,391)(123,393)(124,389)(125,388)(126,390)(127,368)(128,367)
(129,369)(130,365)(131,364)(132,366)(133,362)(134,361)(135,363)(136,377)
(137,376)(138,378)(139,374)(140,373)(141,375)(142,371)(143,370)(144,372)
(145,458)(146,457)(147,459)(148,455)(149,454)(150,456)(151,452)(152,451)
(153,453)(154,467)(155,466)(156,468)(157,464)(158,463)(159,465)(160,461)
(161,460)(162,462)(163,440)(164,439)(165,441)(166,437)(167,436)(168,438)
(169,434)(170,433)(171,435)(172,449)(173,448)(174,450)(175,446)(176,445)
(177,447)(178,443)(179,442)(180,444)(181,503)(182,502)(183,504)(184,500)
(185,499)(186,501)(187,497)(188,496)(189,498)(190,494)(191,493)(192,495)
(193,491)(194,490)(195,492)(196,488)(197,487)(198,489)(199,485)(200,484)
(201,486)(202,482)(203,481)(204,483)(205,479)(206,478)(207,480)(208,476)
(209,475)(210,477)(211,473)(212,472)(213,474)(214,470)(215,469)(216,471)
(217,566)(218,565)(219,567)(220,563)(221,562)(222,564)(223,560)(224,559)
(225,561)(226,575)(227,574)(228,576)(229,572)(230,571)(231,573)(232,569)
(233,568)(234,570)(235,548)(236,547)(237,549)(238,545)(239,544)(240,546)
(241,542)(242,541)(243,543)(244,557)(245,556)(246,558)(247,554)(248,553)
(249,555)(250,551)(251,550)(252,552)(253,530)(254,529)(255,531)(256,527)
(257,526)(258,528)(259,524)(260,523)(261,525)(262,539)(263,538)(264,540)
(265,536)(266,535)(267,537)(268,533)(269,532)(270,534)(271,512)(272,511)
(273,513)(274,509)(275,508)(276,510)(277,506)(278,505)(279,507)(280,521)
(281,520)(282,522)(283,518)(284,517)(285,519)(286,515)(287,514)(288,516);;
s3 := ( 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)( 37,118)( 38,119)( 39,120)( 40,121)
( 41,122)( 42,123)( 43,124)( 44,125)( 45,126)( 46,109)( 47,110)( 48,111)
( 49,112)( 50,113)( 51,114)( 52,115)( 53,116)( 54,117)( 55,136)( 56,137)
( 57,138)( 58,139)( 59,140)( 60,141)( 61,142)( 62,143)( 63,144)( 64,127)
( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)( 72,135)
(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)(181,262)(182,263)(183,264)(184,265)
(185,266)(186,267)(187,268)(188,269)(189,270)(190,253)(191,254)(192,255)
(193,256)(194,257)(195,258)(196,259)(197,260)(198,261)(199,280)(200,281)
(201,282)(202,283)(203,284)(204,285)(205,286)(206,287)(207,288)(208,271)
(209,272)(210,273)(211,274)(212,275)(213,276)(214,277)(215,278)(216,279)
(289,361)(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)(325,406)(326,407)(327,408)(328,409)
(329,410)(330,411)(331,412)(332,413)(333,414)(334,397)(335,398)(336,399)
(337,400)(338,401)(339,402)(340,403)(341,404)(342,405)(343,424)(344,425)
(345,426)(346,427)(347,428)(348,429)(349,430)(350,431)(351,432)(352,415)
(353,416)(354,417)(355,418)(356,419)(357,420)(358,421)(359,422)(360,423)
(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)(469,550)(470,551)(471,552)(472,553)
(473,554)(474,555)(475,556)(476,557)(477,558)(478,541)(479,542)(480,543)
(481,544)(482,545)(483,546)(484,547)(485,548)(486,549)(487,568)(488,569)
(489,570)(490,571)(491,572)(492,573)(493,574)(494,575)(495,576)(496,559)
(497,560)(498,561)(499,562)(500,563)(501,564)(502,565)(503,566)(504,567);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(576)!( 1,109)( 2,114)( 3,116)( 4,112)( 5,117)( 6,110)( 7,115)
( 8,111)( 9,113)( 10,118)( 11,123)( 12,125)( 13,121)( 14,126)( 15,119)
( 16,124)( 17,120)( 18,122)( 19,127)( 20,132)( 21,134)( 22,130)( 23,135)
( 24,128)( 25,133)( 26,129)( 27,131)( 28,136)( 29,141)( 30,143)( 31,139)
( 32,144)( 33,137)( 34,142)( 35,138)( 36,140)( 37, 82)( 38, 87)( 39, 89)
( 40, 85)( 41, 90)( 42, 83)( 43, 88)( 44, 84)( 45, 86)( 46, 73)( 47, 78)
( 48, 80)( 49, 76)( 50, 81)( 51, 74)( 52, 79)( 53, 75)( 54, 77)( 55,100)
( 56,105)( 57,107)( 58,103)( 59,108)( 60,101)( 61,106)( 62,102)( 63,104)
( 64, 91)( 65, 96)( 66, 98)( 67, 94)( 68, 99)( 69, 92)( 70, 97)( 71, 93)
( 72, 95)(145,271)(146,276)(147,278)(148,274)(149,279)(150,272)(151,277)
(152,273)(153,275)(154,280)(155,285)(156,287)(157,283)(158,288)(159,281)
(160,286)(161,282)(162,284)(163,253)(164,258)(165,260)(166,256)(167,261)
(168,254)(169,259)(170,255)(171,257)(172,262)(173,267)(174,269)(175,265)
(176,270)(177,263)(178,268)(179,264)(180,266)(181,244)(182,249)(183,251)
(184,247)(185,252)(186,245)(187,250)(188,246)(189,248)(190,235)(191,240)
(192,242)(193,238)(194,243)(195,236)(196,241)(197,237)(198,239)(199,226)
(200,231)(201,233)(202,229)(203,234)(204,227)(205,232)(206,228)(207,230)
(208,217)(209,222)(210,224)(211,220)(212,225)(213,218)(214,223)(215,219)
(216,221)(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)(433,523)(434,528)(435,530)(436,526)(437,531)(438,524)(439,529)
(440,525)(441,527)(442,532)(443,537)(444,539)(445,535)(446,540)(447,533)
(448,538)(449,534)(450,536)(451,505)(452,510)(453,512)(454,508)(455,513)
(456,506)(457,511)(458,507)(459,509)(460,514)(461,519)(462,521)(463,517)
(464,522)(465,515)(466,520)(467,516)(468,518)(469,559)(470,564)(471,566)
(472,562)(473,567)(474,560)(475,565)(476,561)(477,563)(478,568)(479,573)
(480,575)(481,571)(482,576)(483,569)(484,574)(485,570)(486,572)(487,541)
(488,546)(489,548)(490,544)(491,549)(492,542)(493,547)(494,543)(495,545)
(496,550)(497,555)(498,557)(499,553)(500,558)(501,551)(502,556)(503,552)
(504,554);
s2 := Sym(576)!( 1,314)( 2,313)( 3,315)( 4,311)( 5,310)( 6,312)( 7,308)
( 8,307)( 9,309)( 10,323)( 11,322)( 12,324)( 13,320)( 14,319)( 15,321)
( 16,317)( 17,316)( 18,318)( 19,296)( 20,295)( 21,297)( 22,293)( 23,292)
( 24,294)( 25,290)( 26,289)( 27,291)( 28,305)( 29,304)( 30,306)( 31,302)
( 32,301)( 33,303)( 34,299)( 35,298)( 36,300)( 37,359)( 38,358)( 39,360)
( 40,356)( 41,355)( 42,357)( 43,353)( 44,352)( 45,354)( 46,350)( 47,349)
( 48,351)( 49,347)( 50,346)( 51,348)( 52,344)( 53,343)( 54,345)( 55,341)
( 56,340)( 57,342)( 58,338)( 59,337)( 60,339)( 61,335)( 62,334)( 63,336)
( 64,332)( 65,331)( 66,333)( 67,329)( 68,328)( 69,330)( 70,326)( 71,325)
( 72,327)( 73,422)( 74,421)( 75,423)( 76,419)( 77,418)( 78,420)( 79,416)
( 80,415)( 81,417)( 82,431)( 83,430)( 84,432)( 85,428)( 86,427)( 87,429)
( 88,425)( 89,424)( 90,426)( 91,404)( 92,403)( 93,405)( 94,401)( 95,400)
( 96,402)( 97,398)( 98,397)( 99,399)(100,413)(101,412)(102,414)(103,410)
(104,409)(105,411)(106,407)(107,406)(108,408)(109,386)(110,385)(111,387)
(112,383)(113,382)(114,384)(115,380)(116,379)(117,381)(118,395)(119,394)
(120,396)(121,392)(122,391)(123,393)(124,389)(125,388)(126,390)(127,368)
(128,367)(129,369)(130,365)(131,364)(132,366)(133,362)(134,361)(135,363)
(136,377)(137,376)(138,378)(139,374)(140,373)(141,375)(142,371)(143,370)
(144,372)(145,458)(146,457)(147,459)(148,455)(149,454)(150,456)(151,452)
(152,451)(153,453)(154,467)(155,466)(156,468)(157,464)(158,463)(159,465)
(160,461)(161,460)(162,462)(163,440)(164,439)(165,441)(166,437)(167,436)
(168,438)(169,434)(170,433)(171,435)(172,449)(173,448)(174,450)(175,446)
(176,445)(177,447)(178,443)(179,442)(180,444)(181,503)(182,502)(183,504)
(184,500)(185,499)(186,501)(187,497)(188,496)(189,498)(190,494)(191,493)
(192,495)(193,491)(194,490)(195,492)(196,488)(197,487)(198,489)(199,485)
(200,484)(201,486)(202,482)(203,481)(204,483)(205,479)(206,478)(207,480)
(208,476)(209,475)(210,477)(211,473)(212,472)(213,474)(214,470)(215,469)
(216,471)(217,566)(218,565)(219,567)(220,563)(221,562)(222,564)(223,560)
(224,559)(225,561)(226,575)(227,574)(228,576)(229,572)(230,571)(231,573)
(232,569)(233,568)(234,570)(235,548)(236,547)(237,549)(238,545)(239,544)
(240,546)(241,542)(242,541)(243,543)(244,557)(245,556)(246,558)(247,554)
(248,553)(249,555)(250,551)(251,550)(252,552)(253,530)(254,529)(255,531)
(256,527)(257,526)(258,528)(259,524)(260,523)(261,525)(262,539)(263,538)
(264,540)(265,536)(266,535)(267,537)(268,533)(269,532)(270,534)(271,512)
(272,511)(273,513)(274,509)(275,508)(276,510)(277,506)(278,505)(279,507)
(280,521)(281,520)(282,522)(283,518)(284,517)(285,519)(286,515)(287,514)
(288,516);
s3 := 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)( 37,118)( 38,119)( 39,120)
( 40,121)( 41,122)( 42,123)( 43,124)( 44,125)( 45,126)( 46,109)( 47,110)
( 48,111)( 49,112)( 50,113)( 51,114)( 52,115)( 53,116)( 54,117)( 55,136)
( 56,137)( 57,138)( 58,139)( 59,140)( 60,141)( 61,142)( 62,143)( 63,144)
( 64,127)( 65,128)( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)
( 72,135)(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)(181,262)(182,263)(183,264)
(184,265)(185,266)(186,267)(187,268)(188,269)(189,270)(190,253)(191,254)
(192,255)(193,256)(194,257)(195,258)(196,259)(197,260)(198,261)(199,280)
(200,281)(201,282)(202,283)(203,284)(204,285)(205,286)(206,287)(207,288)
(208,271)(209,272)(210,273)(211,274)(212,275)(213,276)(214,277)(215,278)
(216,279)(289,361)(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)(325,406)(326,407)(327,408)
(328,409)(329,410)(330,411)(331,412)(332,413)(333,414)(334,397)(335,398)
(336,399)(337,400)(338,401)(339,402)(340,403)(341,404)(342,405)(343,424)
(344,425)(345,426)(346,427)(347,428)(348,429)(349,430)(350,431)(351,432)
(352,415)(353,416)(354,417)(355,418)(356,419)(357,420)(358,421)(359,422)
(360,423)(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)(469,550)(470,551)(471,552)
(472,553)(473,554)(474,555)(475,556)(476,557)(477,558)(478,541)(479,542)
(480,543)(481,544)(482,545)(483,546)(484,547)(485,548)(486,549)(487,568)
(488,569)(489,570)(490,571)(491,572)(492,573)(493,574)(494,575)(495,576)
(496,559)(497,560)(498,561)(499,562)(500,563)(501,564)(502,565)(503,566)
(504,567);
poly := sub<Sym(576)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope