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