Polytope of Type {8,9,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,9,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,155437)
Rank : 4
Schlafli Type : {8,9,4}
Number of vertices, edges, etc : 16, 72, 36, 4
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 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 : {4,9,4}*576b
3-fold quotients : {8,3,4}*384
4-fold quotients : {4,9,4}*288
6-fold quotients : {4,3,4}*192b
8-fold quotients : {2,9,4}*144
12-fold quotients : {4,3,4}*96
24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,293)( 2,294)( 3,296)( 4,295)( 5,290)( 6,289)( 7,291)( 8,292)
( 9,301)( 10,302)( 11,304)( 12,303)( 13,298)( 14,297)( 15,299)( 16,300)
( 17,309)( 18,310)( 19,312)( 20,311)( 21,306)( 22,305)( 23,307)( 24,308)
( 25,317)( 26,318)( 27,320)( 28,319)( 29,314)( 30,313)( 31,315)( 32,316)
( 33,325)( 34,326)( 35,328)( 36,327)( 37,322)( 38,321)( 39,323)( 40,324)
( 41,333)( 42,334)( 43,336)( 44,335)( 45,330)( 46,329)( 47,331)( 48,332)
( 49,341)( 50,342)( 51,344)( 52,343)( 53,338)( 54,337)( 55,339)( 56,340)
( 57,349)( 58,350)( 59,352)( 60,351)( 61,346)( 62,345)( 63,347)( 64,348)
( 65,357)( 66,358)( 67,360)( 68,359)( 69,354)( 70,353)( 71,355)( 72,356)
( 73,365)( 74,366)( 75,368)( 76,367)( 77,362)( 78,361)( 79,363)( 80,364)
( 81,373)( 82,374)( 83,376)( 84,375)( 85,370)( 86,369)( 87,371)( 88,372)
( 89,381)( 90,382)( 91,384)( 92,383)( 93,378)( 94,377)( 95,379)( 96,380)
( 97,389)( 98,390)( 99,392)(100,391)(101,386)(102,385)(103,387)(104,388)
(105,397)(106,398)(107,400)(108,399)(109,394)(110,393)(111,395)(112,396)
(113,405)(114,406)(115,408)(116,407)(117,402)(118,401)(119,403)(120,404)
(121,413)(122,414)(123,416)(124,415)(125,410)(126,409)(127,411)(128,412)
(129,421)(130,422)(131,424)(132,423)(133,418)(134,417)(135,419)(136,420)
(137,429)(138,430)(139,432)(140,431)(141,426)(142,425)(143,427)(144,428)
(145,437)(146,438)(147,440)(148,439)(149,434)(150,433)(151,435)(152,436)
(153,445)(154,446)(155,448)(156,447)(157,442)(158,441)(159,443)(160,444)
(161,453)(162,454)(163,456)(164,455)(165,450)(166,449)(167,451)(168,452)
(169,461)(170,462)(171,464)(172,463)(173,458)(174,457)(175,459)(176,460)
(177,469)(178,470)(179,472)(180,471)(181,466)(182,465)(183,467)(184,468)
(185,477)(186,478)(187,480)(188,479)(189,474)(190,473)(191,475)(192,476)
(193,485)(194,486)(195,488)(196,487)(197,482)(198,481)(199,483)(200,484)
(201,493)(202,494)(203,496)(204,495)(205,490)(206,489)(207,491)(208,492)
(209,501)(210,502)(211,504)(212,503)(213,498)(214,497)(215,499)(216,500)
(217,509)(218,510)(219,512)(220,511)(221,506)(222,505)(223,507)(224,508)
(225,517)(226,518)(227,520)(228,519)(229,514)(230,513)(231,515)(232,516)
(233,525)(234,526)(235,528)(236,527)(237,522)(238,521)(239,523)(240,524)
(241,533)(242,534)(243,536)(244,535)(245,530)(246,529)(247,531)(248,532)
(249,541)(250,542)(251,544)(252,543)(253,538)(254,537)(255,539)(256,540)
(257,549)(258,550)(259,552)(260,551)(261,546)(262,545)(263,547)(264,548)
(265,557)(266,558)(267,560)(268,559)(269,554)(270,553)(271,555)(272,556)
(273,565)(274,566)(275,568)(276,567)(277,562)(278,561)(279,563)(280,564)
(281,573)(282,574)(283,576)(284,575)(285,570)(286,569)(287,571)(288,572);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 17, 25)( 18, 26)
( 19, 28)( 20, 27)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)( 34, 66)
( 35, 68)( 36, 67)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)( 42, 74)
( 43, 76)( 44, 75)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)( 50, 90)
( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)( 58, 82)
( 59, 84)( 60, 83)( 61, 87)( 62, 88)( 63, 85)( 64, 86)( 97,257)( 98,258)
( 99,260)(100,259)(101,263)(102,264)(103,261)(104,262)(105,265)(106,266)
(107,268)(108,267)(109,271)(110,272)(111,269)(112,270)(113,281)(114,282)
(115,284)(116,283)(117,287)(118,288)(119,285)(120,286)(121,273)(122,274)
(123,276)(124,275)(125,279)(126,280)(127,277)(128,278)(129,225)(130,226)
(131,228)(132,227)(133,231)(134,232)(135,229)(136,230)(137,233)(138,234)
(139,236)(140,235)(141,239)(142,240)(143,237)(144,238)(145,249)(146,250)
(147,252)(148,251)(149,255)(150,256)(151,253)(152,254)(153,241)(154,242)
(155,244)(156,243)(157,247)(158,248)(159,245)(160,246)(161,193)(162,194)
(163,196)(164,195)(165,199)(166,200)(167,197)(168,198)(169,201)(170,202)
(171,204)(172,203)(173,207)(174,208)(175,205)(176,206)(177,217)(178,218)
(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,209)(186,210)
(187,212)(188,211)(189,215)(190,216)(191,213)(192,214)(289,290)(293,296)
(294,295)(297,298)(301,304)(302,303)(305,314)(306,313)(307,315)(308,316)
(309,320)(310,319)(311,318)(312,317)(321,354)(322,353)(323,355)(324,356)
(325,360)(326,359)(327,358)(328,357)(329,362)(330,361)(331,363)(332,364)
(333,368)(334,367)(335,366)(336,365)(337,378)(338,377)(339,379)(340,380)
(341,384)(342,383)(343,382)(344,381)(345,370)(346,369)(347,371)(348,372)
(349,376)(350,375)(351,374)(352,373)(385,546)(386,545)(387,547)(388,548)
(389,552)(390,551)(391,550)(392,549)(393,554)(394,553)(395,555)(396,556)
(397,560)(398,559)(399,558)(400,557)(401,570)(402,569)(403,571)(404,572)
(405,576)(406,575)(407,574)(408,573)(409,562)(410,561)(411,563)(412,564)
(413,568)(414,567)(415,566)(416,565)(417,514)(418,513)(419,515)(420,516)
(421,520)(422,519)(423,518)(424,517)(425,522)(426,521)(427,523)(428,524)
(429,528)(430,527)(431,526)(432,525)(433,538)(434,537)(435,539)(436,540)
(437,544)(438,543)(439,542)(440,541)(441,530)(442,529)(443,531)(444,532)
(445,536)(446,535)(447,534)(448,533)(449,482)(450,481)(451,483)(452,484)
(453,488)(454,487)(455,486)(456,485)(457,490)(458,489)(459,491)(460,492)
(461,496)(462,495)(463,494)(464,493)(465,506)(466,505)(467,507)(468,508)
(469,512)(470,511)(471,510)(472,509)(473,498)(474,497)(475,499)(476,500)
(477,504)(478,503)(479,502)(480,501);;
s2 := ( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)( 8,100)
( 9,121)( 10,122)( 11,127)( 12,128)( 13,126)( 14,125)( 15,123)( 16,124)
( 17,113)( 18,114)( 19,119)( 20,120)( 21,118)( 22,117)( 23,115)( 24,116)
( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)( 32,108)
( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)( 40,164)
( 41,185)( 42,186)( 43,191)( 44,192)( 45,190)( 46,189)( 47,187)( 48,188)
( 49,177)( 50,178)( 51,183)( 52,184)( 53,182)( 54,181)( 55,179)( 56,180)
( 57,169)( 58,170)( 59,175)( 60,176)( 61,174)( 62,173)( 63,171)( 64,172)
( 65,129)( 66,130)( 67,135)( 68,136)( 69,134)( 70,133)( 71,131)( 72,132)
( 73,153)( 74,154)( 75,159)( 76,160)( 77,158)( 78,157)( 79,155)( 80,156)
( 81,145)( 82,146)( 83,151)( 84,152)( 85,150)( 86,149)( 87,147)( 88,148)
( 89,137)( 90,138)( 91,143)( 92,144)( 93,142)( 94,141)( 95,139)( 96,140)
(193,257)(194,258)(195,263)(196,264)(197,262)(198,261)(199,259)(200,260)
(201,281)(202,282)(203,287)(204,288)(205,286)(206,285)(207,283)(208,284)
(209,273)(210,274)(211,279)(212,280)(213,278)(214,277)(215,275)(216,276)
(217,265)(218,266)(219,271)(220,272)(221,270)(222,269)(223,267)(224,268)
(227,231)(228,232)(229,230)(233,249)(234,250)(235,255)(236,256)(237,254)
(238,253)(239,251)(240,252)(243,247)(244,248)(245,246)(289,386)(290,385)
(291,392)(292,391)(293,389)(294,390)(295,388)(296,387)(297,410)(298,409)
(299,416)(300,415)(301,413)(302,414)(303,412)(304,411)(305,402)(306,401)
(307,408)(308,407)(309,405)(310,406)(311,404)(312,403)(313,394)(314,393)
(315,400)(316,399)(317,397)(318,398)(319,396)(320,395)(321,450)(322,449)
(323,456)(324,455)(325,453)(326,454)(327,452)(328,451)(329,474)(330,473)
(331,480)(332,479)(333,477)(334,478)(335,476)(336,475)(337,466)(338,465)
(339,472)(340,471)(341,469)(342,470)(343,468)(344,467)(345,458)(346,457)
(347,464)(348,463)(349,461)(350,462)(351,460)(352,459)(353,418)(354,417)
(355,424)(356,423)(357,421)(358,422)(359,420)(360,419)(361,442)(362,441)
(363,448)(364,447)(365,445)(366,446)(367,444)(368,443)(369,434)(370,433)
(371,440)(372,439)(373,437)(374,438)(375,436)(376,435)(377,426)(378,425)
(379,432)(380,431)(381,429)(382,430)(383,428)(384,427)(481,546)(482,545)
(483,552)(484,551)(485,549)(486,550)(487,548)(488,547)(489,570)(490,569)
(491,576)(492,575)(493,573)(494,574)(495,572)(496,571)(497,562)(498,561)
(499,568)(500,567)(501,565)(502,566)(503,564)(504,563)(505,554)(506,553)
(507,560)(508,559)(509,557)(510,558)(511,556)(512,555)(513,514)(515,520)
(516,519)(521,538)(522,537)(523,544)(524,543)(525,541)(526,542)(527,540)
(528,539)(529,530)(531,536)(532,535);;
s3 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)
(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)
(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)
(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)
(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480)
(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)(488,496)
(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)(504,512)
(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)(520,528)
(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)(536,544)
(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)(552,560)
(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)(568,576);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,293)( 2,294)( 3,296)( 4,295)( 5,290)( 6,289)( 7,291)
( 8,292)( 9,301)( 10,302)( 11,304)( 12,303)( 13,298)( 14,297)( 15,299)
( 16,300)( 17,309)( 18,310)( 19,312)( 20,311)( 21,306)( 22,305)( 23,307)
( 24,308)( 25,317)( 26,318)( 27,320)( 28,319)( 29,314)( 30,313)( 31,315)
( 32,316)( 33,325)( 34,326)( 35,328)( 36,327)( 37,322)( 38,321)( 39,323)
( 40,324)( 41,333)( 42,334)( 43,336)( 44,335)( 45,330)( 46,329)( 47,331)
( 48,332)( 49,341)( 50,342)( 51,344)( 52,343)( 53,338)( 54,337)( 55,339)
( 56,340)( 57,349)( 58,350)( 59,352)( 60,351)( 61,346)( 62,345)( 63,347)
( 64,348)( 65,357)( 66,358)( 67,360)( 68,359)( 69,354)( 70,353)( 71,355)
( 72,356)( 73,365)( 74,366)( 75,368)( 76,367)( 77,362)( 78,361)( 79,363)
( 80,364)( 81,373)( 82,374)( 83,376)( 84,375)( 85,370)( 86,369)( 87,371)
( 88,372)( 89,381)( 90,382)( 91,384)( 92,383)( 93,378)( 94,377)( 95,379)
( 96,380)( 97,389)( 98,390)( 99,392)(100,391)(101,386)(102,385)(103,387)
(104,388)(105,397)(106,398)(107,400)(108,399)(109,394)(110,393)(111,395)
(112,396)(113,405)(114,406)(115,408)(116,407)(117,402)(118,401)(119,403)
(120,404)(121,413)(122,414)(123,416)(124,415)(125,410)(126,409)(127,411)
(128,412)(129,421)(130,422)(131,424)(132,423)(133,418)(134,417)(135,419)
(136,420)(137,429)(138,430)(139,432)(140,431)(141,426)(142,425)(143,427)
(144,428)(145,437)(146,438)(147,440)(148,439)(149,434)(150,433)(151,435)
(152,436)(153,445)(154,446)(155,448)(156,447)(157,442)(158,441)(159,443)
(160,444)(161,453)(162,454)(163,456)(164,455)(165,450)(166,449)(167,451)
(168,452)(169,461)(170,462)(171,464)(172,463)(173,458)(174,457)(175,459)
(176,460)(177,469)(178,470)(179,472)(180,471)(181,466)(182,465)(183,467)
(184,468)(185,477)(186,478)(187,480)(188,479)(189,474)(190,473)(191,475)
(192,476)(193,485)(194,486)(195,488)(196,487)(197,482)(198,481)(199,483)
(200,484)(201,493)(202,494)(203,496)(204,495)(205,490)(206,489)(207,491)
(208,492)(209,501)(210,502)(211,504)(212,503)(213,498)(214,497)(215,499)
(216,500)(217,509)(218,510)(219,512)(220,511)(221,506)(222,505)(223,507)
(224,508)(225,517)(226,518)(227,520)(228,519)(229,514)(230,513)(231,515)
(232,516)(233,525)(234,526)(235,528)(236,527)(237,522)(238,521)(239,523)
(240,524)(241,533)(242,534)(243,536)(244,535)(245,530)(246,529)(247,531)
(248,532)(249,541)(250,542)(251,544)(252,543)(253,538)(254,537)(255,539)
(256,540)(257,549)(258,550)(259,552)(260,551)(261,546)(262,545)(263,547)
(264,548)(265,557)(266,558)(267,560)(268,559)(269,554)(270,553)(271,555)
(272,556)(273,565)(274,566)(275,568)(276,567)(277,562)(278,561)(279,563)
(280,564)(281,573)(282,574)(283,576)(284,575)(285,570)(286,569)(287,571)
(288,572);
s1 := Sym(576)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 17, 25)
( 18, 26)( 19, 28)( 20, 27)( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 33, 65)
( 34, 66)( 35, 68)( 36, 67)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 73)
( 42, 74)( 43, 76)( 44, 75)( 45, 79)( 46, 80)( 47, 77)( 48, 78)( 49, 89)
( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 81)
( 58, 82)( 59, 84)( 60, 83)( 61, 87)( 62, 88)( 63, 85)( 64, 86)( 97,257)
( 98,258)( 99,260)(100,259)(101,263)(102,264)(103,261)(104,262)(105,265)
(106,266)(107,268)(108,267)(109,271)(110,272)(111,269)(112,270)(113,281)
(114,282)(115,284)(116,283)(117,287)(118,288)(119,285)(120,286)(121,273)
(122,274)(123,276)(124,275)(125,279)(126,280)(127,277)(128,278)(129,225)
(130,226)(131,228)(132,227)(133,231)(134,232)(135,229)(136,230)(137,233)
(138,234)(139,236)(140,235)(141,239)(142,240)(143,237)(144,238)(145,249)
(146,250)(147,252)(148,251)(149,255)(150,256)(151,253)(152,254)(153,241)
(154,242)(155,244)(156,243)(157,247)(158,248)(159,245)(160,246)(161,193)
(162,194)(163,196)(164,195)(165,199)(166,200)(167,197)(168,198)(169,201)
(170,202)(171,204)(172,203)(173,207)(174,208)(175,205)(176,206)(177,217)
(178,218)(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,209)
(186,210)(187,212)(188,211)(189,215)(190,216)(191,213)(192,214)(289,290)
(293,296)(294,295)(297,298)(301,304)(302,303)(305,314)(306,313)(307,315)
(308,316)(309,320)(310,319)(311,318)(312,317)(321,354)(322,353)(323,355)
(324,356)(325,360)(326,359)(327,358)(328,357)(329,362)(330,361)(331,363)
(332,364)(333,368)(334,367)(335,366)(336,365)(337,378)(338,377)(339,379)
(340,380)(341,384)(342,383)(343,382)(344,381)(345,370)(346,369)(347,371)
(348,372)(349,376)(350,375)(351,374)(352,373)(385,546)(386,545)(387,547)
(388,548)(389,552)(390,551)(391,550)(392,549)(393,554)(394,553)(395,555)
(396,556)(397,560)(398,559)(399,558)(400,557)(401,570)(402,569)(403,571)
(404,572)(405,576)(406,575)(407,574)(408,573)(409,562)(410,561)(411,563)
(412,564)(413,568)(414,567)(415,566)(416,565)(417,514)(418,513)(419,515)
(420,516)(421,520)(422,519)(423,518)(424,517)(425,522)(426,521)(427,523)
(428,524)(429,528)(430,527)(431,526)(432,525)(433,538)(434,537)(435,539)
(436,540)(437,544)(438,543)(439,542)(440,541)(441,530)(442,529)(443,531)
(444,532)(445,536)(446,535)(447,534)(448,533)(449,482)(450,481)(451,483)
(452,484)(453,488)(454,487)(455,486)(456,485)(457,490)(458,489)(459,491)
(460,492)(461,496)(462,495)(463,494)(464,493)(465,506)(466,505)(467,507)
(468,508)(469,512)(470,511)(471,510)(472,509)(473,498)(474,497)(475,499)
(476,500)(477,504)(478,503)(479,502)(480,501);
s2 := Sym(576)!( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)
( 8,100)( 9,121)( 10,122)( 11,127)( 12,128)( 13,126)( 14,125)( 15,123)
( 16,124)( 17,113)( 18,114)( 19,119)( 20,120)( 21,118)( 22,117)( 23,115)
( 24,116)( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)
( 32,108)( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)
( 40,164)( 41,185)( 42,186)( 43,191)( 44,192)( 45,190)( 46,189)( 47,187)
( 48,188)( 49,177)( 50,178)( 51,183)( 52,184)( 53,182)( 54,181)( 55,179)
( 56,180)( 57,169)( 58,170)( 59,175)( 60,176)( 61,174)( 62,173)( 63,171)
( 64,172)( 65,129)( 66,130)( 67,135)( 68,136)( 69,134)( 70,133)( 71,131)
( 72,132)( 73,153)( 74,154)( 75,159)( 76,160)( 77,158)( 78,157)( 79,155)
( 80,156)( 81,145)( 82,146)( 83,151)( 84,152)( 85,150)( 86,149)( 87,147)
( 88,148)( 89,137)( 90,138)( 91,143)( 92,144)( 93,142)( 94,141)( 95,139)
( 96,140)(193,257)(194,258)(195,263)(196,264)(197,262)(198,261)(199,259)
(200,260)(201,281)(202,282)(203,287)(204,288)(205,286)(206,285)(207,283)
(208,284)(209,273)(210,274)(211,279)(212,280)(213,278)(214,277)(215,275)
(216,276)(217,265)(218,266)(219,271)(220,272)(221,270)(222,269)(223,267)
(224,268)(227,231)(228,232)(229,230)(233,249)(234,250)(235,255)(236,256)
(237,254)(238,253)(239,251)(240,252)(243,247)(244,248)(245,246)(289,386)
(290,385)(291,392)(292,391)(293,389)(294,390)(295,388)(296,387)(297,410)
(298,409)(299,416)(300,415)(301,413)(302,414)(303,412)(304,411)(305,402)
(306,401)(307,408)(308,407)(309,405)(310,406)(311,404)(312,403)(313,394)
(314,393)(315,400)(316,399)(317,397)(318,398)(319,396)(320,395)(321,450)
(322,449)(323,456)(324,455)(325,453)(326,454)(327,452)(328,451)(329,474)
(330,473)(331,480)(332,479)(333,477)(334,478)(335,476)(336,475)(337,466)
(338,465)(339,472)(340,471)(341,469)(342,470)(343,468)(344,467)(345,458)
(346,457)(347,464)(348,463)(349,461)(350,462)(351,460)(352,459)(353,418)
(354,417)(355,424)(356,423)(357,421)(358,422)(359,420)(360,419)(361,442)
(362,441)(363,448)(364,447)(365,445)(366,446)(367,444)(368,443)(369,434)
(370,433)(371,440)(372,439)(373,437)(374,438)(375,436)(376,435)(377,426)
(378,425)(379,432)(380,431)(381,429)(382,430)(383,428)(384,427)(481,546)
(482,545)(483,552)(484,551)(485,549)(486,550)(487,548)(488,547)(489,570)
(490,569)(491,576)(492,575)(493,573)(494,574)(495,572)(496,571)(497,562)
(498,561)(499,568)(500,567)(501,565)(502,566)(503,564)(504,563)(505,554)
(506,553)(507,560)(508,559)(509,557)(510,558)(511,556)(512,555)(513,514)
(515,520)(516,519)(521,538)(522,537)(523,544)(524,543)(525,541)(526,542)
(527,540)(528,539)(529,530)(531,536)(532,535);
s3 := Sym(576)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)
(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)
(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)
(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)
(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)
(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)
(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)
(472,480)(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)
(488,496)(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)
(504,512)(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)
(520,528)(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)
(536,544)(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)
(552,560)(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)
(568,576);
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,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope