Polytope of Type {144,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {144,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,154003)
Rank : 3
Schlafli Type : {144,4}
Number of vertices, edges, etc : 144, 288, 4
Order of s0s1s2 : 144
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {72,4}*576c
3-fold quotients : {48,4}*384c
4-fold quotients : {36,4}*288b
6-fold quotients : {24,4}*192c
8-fold quotients : {18,4}*144b
12-fold quotients : {12,4}*96b
16-fold quotients : {9,4}*72
24-fold quotients : {6,4}*48c
48-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 69)( 50, 70)
( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)
( 59, 64)( 60, 63)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)( 78,118)
( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,141)( 86,142)
( 87,144)( 88,143)( 89,137)( 90,138)( 91,140)( 92,139)( 93,133)( 94,134)
( 95,136)( 96,135)( 97,129)( 98,130)( 99,132)(100,131)(101,125)(102,126)
(103,128)(104,127)(105,121)(106,122)(107,124)(108,123)(145,217)(146,218)
(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)(154,222)
(155,224)(156,223)(157,249)(158,250)(159,252)(160,251)(161,245)(162,246)
(163,248)(164,247)(165,241)(166,242)(167,244)(168,243)(169,237)(170,238)
(171,240)(172,239)(173,233)(174,234)(175,236)(176,235)(177,229)(178,230)
(179,232)(180,231)(181,253)(182,254)(183,256)(184,255)(185,261)(186,262)
(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,285)(194,286)
(195,288)(196,287)(197,281)(198,282)(199,284)(200,283)(201,277)(202,278)
(203,280)(204,279)(205,273)(206,274)(207,276)(208,275)(209,269)(210,270)
(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)(289,433)(290,434)
(291,436)(292,435)(293,441)(294,442)(295,444)(296,443)(297,437)(298,438)
(299,440)(300,439)(301,465)(302,466)(303,468)(304,467)(305,461)(306,462)
(307,464)(308,463)(309,457)(310,458)(311,460)(312,459)(313,453)(314,454)
(315,456)(316,455)(317,449)(318,450)(319,452)(320,451)(321,445)(322,446)
(323,448)(324,447)(325,469)(326,470)(327,472)(328,471)(329,477)(330,478)
(331,480)(332,479)(333,473)(334,474)(335,476)(336,475)(337,501)(338,502)
(339,504)(340,503)(341,497)(342,498)(343,500)(344,499)(345,493)(346,494)
(347,496)(348,495)(349,489)(350,490)(351,492)(352,491)(353,485)(354,486)
(355,488)(356,487)(357,481)(358,482)(359,484)(360,483)(361,541)(362,542)
(363,544)(364,543)(365,549)(366,550)(367,552)(368,551)(369,545)(370,546)
(371,548)(372,547)(373,573)(374,574)(375,576)(376,575)(377,569)(378,570)
(379,572)(380,571)(381,565)(382,566)(383,568)(384,567)(385,561)(386,562)
(387,564)(388,563)(389,557)(390,558)(391,560)(392,559)(393,553)(394,554)
(395,556)(396,555)(397,505)(398,506)(399,508)(400,507)(401,513)(402,514)
(403,516)(404,515)(405,509)(406,510)(407,512)(408,511)(409,537)(410,538)
(411,540)(412,539)(413,533)(414,534)(415,536)(416,535)(417,529)(418,530)
(419,532)(420,531)(421,525)(422,526)(423,528)(424,527)(425,521)(426,522)
(427,524)(428,523)(429,517)(430,518)(431,520)(432,519);;
s1 := ( 1,301)( 2,304)( 3,303)( 4,302)( 5,309)( 6,312)( 7,311)( 8,310)
( 9,305)( 10,308)( 11,307)( 12,306)( 13,289)( 14,292)( 15,291)( 16,290)
( 17,297)( 18,300)( 19,299)( 20,298)( 21,293)( 22,296)( 23,295)( 24,294)
( 25,321)( 26,324)( 27,323)( 28,322)( 29,317)( 30,320)( 31,319)( 32,318)
( 33,313)( 34,316)( 35,315)( 36,314)( 37,337)( 38,340)( 39,339)( 40,338)
( 41,345)( 42,348)( 43,347)( 44,346)( 45,341)( 46,344)( 47,343)( 48,342)
( 49,325)( 50,328)( 51,327)( 52,326)( 53,333)( 54,336)( 55,335)( 56,334)
( 57,329)( 58,332)( 59,331)( 60,330)( 61,357)( 62,360)( 63,359)( 64,358)
( 65,353)( 66,356)( 67,355)( 68,354)( 69,349)( 70,352)( 71,351)( 72,350)
( 73,409)( 74,412)( 75,411)( 76,410)( 77,417)( 78,420)( 79,419)( 80,418)
( 81,413)( 82,416)( 83,415)( 84,414)( 85,397)( 86,400)( 87,399)( 88,398)
( 89,405)( 90,408)( 91,407)( 92,406)( 93,401)( 94,404)( 95,403)( 96,402)
( 97,429)( 98,432)( 99,431)(100,430)(101,425)(102,428)(103,427)(104,426)
(105,421)(106,424)(107,423)(108,422)(109,373)(110,376)(111,375)(112,374)
(113,381)(114,384)(115,383)(116,382)(117,377)(118,380)(119,379)(120,378)
(121,361)(122,364)(123,363)(124,362)(125,369)(126,372)(127,371)(128,370)
(129,365)(130,368)(131,367)(132,366)(133,393)(134,396)(135,395)(136,394)
(137,389)(138,392)(139,391)(140,390)(141,385)(142,388)(143,387)(144,386)
(145,517)(146,520)(147,519)(148,518)(149,525)(150,528)(151,527)(152,526)
(153,521)(154,524)(155,523)(156,522)(157,505)(158,508)(159,507)(160,506)
(161,513)(162,516)(163,515)(164,514)(165,509)(166,512)(167,511)(168,510)
(169,537)(170,540)(171,539)(172,538)(173,533)(174,536)(175,535)(176,534)
(177,529)(178,532)(179,531)(180,530)(181,553)(182,556)(183,555)(184,554)
(185,561)(186,564)(187,563)(188,562)(189,557)(190,560)(191,559)(192,558)
(193,541)(194,544)(195,543)(196,542)(197,549)(198,552)(199,551)(200,550)
(201,545)(202,548)(203,547)(204,546)(205,573)(206,576)(207,575)(208,574)
(209,569)(210,572)(211,571)(212,570)(213,565)(214,568)(215,567)(216,566)
(217,445)(218,448)(219,447)(220,446)(221,453)(222,456)(223,455)(224,454)
(225,449)(226,452)(227,451)(228,450)(229,433)(230,436)(231,435)(232,434)
(233,441)(234,444)(235,443)(236,442)(237,437)(238,440)(239,439)(240,438)
(241,465)(242,468)(243,467)(244,466)(245,461)(246,464)(247,463)(248,462)
(249,457)(250,460)(251,459)(252,458)(253,481)(254,484)(255,483)(256,482)
(257,489)(258,492)(259,491)(260,490)(261,485)(262,488)(263,487)(264,486)
(265,469)(266,472)(267,471)(268,470)(269,477)(270,480)(271,479)(272,478)
(273,473)(274,476)(275,475)(276,474)(277,501)(278,504)(279,503)(280,502)
(281,497)(282,500)(283,499)(284,498)(285,493)(286,496)(287,495)(288,494);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)
(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)
(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)
(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)
(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)
(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)
(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 69)
( 50, 70)( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)
( 58, 62)( 59, 64)( 60, 63)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)
( 78,118)( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,141)
( 86,142)( 87,144)( 88,143)( 89,137)( 90,138)( 91,140)( 92,139)( 93,133)
( 94,134)( 95,136)( 96,135)( 97,129)( 98,130)( 99,132)(100,131)(101,125)
(102,126)(103,128)(104,127)(105,121)(106,122)(107,124)(108,123)(145,217)
(146,218)(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)
(154,222)(155,224)(156,223)(157,249)(158,250)(159,252)(160,251)(161,245)
(162,246)(163,248)(164,247)(165,241)(166,242)(167,244)(168,243)(169,237)
(170,238)(171,240)(172,239)(173,233)(174,234)(175,236)(176,235)(177,229)
(178,230)(179,232)(180,231)(181,253)(182,254)(183,256)(184,255)(185,261)
(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,285)
(194,286)(195,288)(196,287)(197,281)(198,282)(199,284)(200,283)(201,277)
(202,278)(203,280)(204,279)(205,273)(206,274)(207,276)(208,275)(209,269)
(210,270)(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)(289,433)
(290,434)(291,436)(292,435)(293,441)(294,442)(295,444)(296,443)(297,437)
(298,438)(299,440)(300,439)(301,465)(302,466)(303,468)(304,467)(305,461)
(306,462)(307,464)(308,463)(309,457)(310,458)(311,460)(312,459)(313,453)
(314,454)(315,456)(316,455)(317,449)(318,450)(319,452)(320,451)(321,445)
(322,446)(323,448)(324,447)(325,469)(326,470)(327,472)(328,471)(329,477)
(330,478)(331,480)(332,479)(333,473)(334,474)(335,476)(336,475)(337,501)
(338,502)(339,504)(340,503)(341,497)(342,498)(343,500)(344,499)(345,493)
(346,494)(347,496)(348,495)(349,489)(350,490)(351,492)(352,491)(353,485)
(354,486)(355,488)(356,487)(357,481)(358,482)(359,484)(360,483)(361,541)
(362,542)(363,544)(364,543)(365,549)(366,550)(367,552)(368,551)(369,545)
(370,546)(371,548)(372,547)(373,573)(374,574)(375,576)(376,575)(377,569)
(378,570)(379,572)(380,571)(381,565)(382,566)(383,568)(384,567)(385,561)
(386,562)(387,564)(388,563)(389,557)(390,558)(391,560)(392,559)(393,553)
(394,554)(395,556)(396,555)(397,505)(398,506)(399,508)(400,507)(401,513)
(402,514)(403,516)(404,515)(405,509)(406,510)(407,512)(408,511)(409,537)
(410,538)(411,540)(412,539)(413,533)(414,534)(415,536)(416,535)(417,529)
(418,530)(419,532)(420,531)(421,525)(422,526)(423,528)(424,527)(425,521)
(426,522)(427,524)(428,523)(429,517)(430,518)(431,520)(432,519);
s1 := Sym(576)!( 1,301)( 2,304)( 3,303)( 4,302)( 5,309)( 6,312)( 7,311)
( 8,310)( 9,305)( 10,308)( 11,307)( 12,306)( 13,289)( 14,292)( 15,291)
( 16,290)( 17,297)( 18,300)( 19,299)( 20,298)( 21,293)( 22,296)( 23,295)
( 24,294)( 25,321)( 26,324)( 27,323)( 28,322)( 29,317)( 30,320)( 31,319)
( 32,318)( 33,313)( 34,316)( 35,315)( 36,314)( 37,337)( 38,340)( 39,339)
( 40,338)( 41,345)( 42,348)( 43,347)( 44,346)( 45,341)( 46,344)( 47,343)
( 48,342)( 49,325)( 50,328)( 51,327)( 52,326)( 53,333)( 54,336)( 55,335)
( 56,334)( 57,329)( 58,332)( 59,331)( 60,330)( 61,357)( 62,360)( 63,359)
( 64,358)( 65,353)( 66,356)( 67,355)( 68,354)( 69,349)( 70,352)( 71,351)
( 72,350)( 73,409)( 74,412)( 75,411)( 76,410)( 77,417)( 78,420)( 79,419)
( 80,418)( 81,413)( 82,416)( 83,415)( 84,414)( 85,397)( 86,400)( 87,399)
( 88,398)( 89,405)( 90,408)( 91,407)( 92,406)( 93,401)( 94,404)( 95,403)
( 96,402)( 97,429)( 98,432)( 99,431)(100,430)(101,425)(102,428)(103,427)
(104,426)(105,421)(106,424)(107,423)(108,422)(109,373)(110,376)(111,375)
(112,374)(113,381)(114,384)(115,383)(116,382)(117,377)(118,380)(119,379)
(120,378)(121,361)(122,364)(123,363)(124,362)(125,369)(126,372)(127,371)
(128,370)(129,365)(130,368)(131,367)(132,366)(133,393)(134,396)(135,395)
(136,394)(137,389)(138,392)(139,391)(140,390)(141,385)(142,388)(143,387)
(144,386)(145,517)(146,520)(147,519)(148,518)(149,525)(150,528)(151,527)
(152,526)(153,521)(154,524)(155,523)(156,522)(157,505)(158,508)(159,507)
(160,506)(161,513)(162,516)(163,515)(164,514)(165,509)(166,512)(167,511)
(168,510)(169,537)(170,540)(171,539)(172,538)(173,533)(174,536)(175,535)
(176,534)(177,529)(178,532)(179,531)(180,530)(181,553)(182,556)(183,555)
(184,554)(185,561)(186,564)(187,563)(188,562)(189,557)(190,560)(191,559)
(192,558)(193,541)(194,544)(195,543)(196,542)(197,549)(198,552)(199,551)
(200,550)(201,545)(202,548)(203,547)(204,546)(205,573)(206,576)(207,575)
(208,574)(209,569)(210,572)(211,571)(212,570)(213,565)(214,568)(215,567)
(216,566)(217,445)(218,448)(219,447)(220,446)(221,453)(222,456)(223,455)
(224,454)(225,449)(226,452)(227,451)(228,450)(229,433)(230,436)(231,435)
(232,434)(233,441)(234,444)(235,443)(236,442)(237,437)(238,440)(239,439)
(240,438)(241,465)(242,468)(243,467)(244,466)(245,461)(246,464)(247,463)
(248,462)(249,457)(250,460)(251,459)(252,458)(253,481)(254,484)(255,483)
(256,482)(257,489)(258,492)(259,491)(260,490)(261,485)(262,488)(263,487)
(264,486)(265,469)(266,472)(267,471)(268,470)(269,477)(270,480)(271,479)
(272,478)(273,473)(274,476)(275,475)(276,474)(277,501)(278,504)(279,503)
(280,502)(281,497)(282,500)(283,499)(284,498)(285,493)(286,496)(287,495)
(288,494);
s2 := Sym(576)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)
(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)
(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)
(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)
(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)
(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)
(575,576);
poly := sub<Sym(576)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope