Polytope of Type {144,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {144,4}*1152d
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}*384d
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, 38)( 2, 37)( 3, 40)( 4, 39)( 5, 42)( 6, 41)( 7, 44)( 8, 43)
( 9, 46)( 10, 45)( 11, 48)( 12, 47)( 13, 50)( 14, 49)( 15, 52)( 16, 51)
( 17, 54)( 18, 53)( 19, 56)( 20, 55)( 21, 58)( 22, 57)( 23, 60)( 24, 59)
( 25, 62)( 26, 61)( 27, 64)( 28, 63)( 29, 66)( 30, 65)( 31, 68)( 32, 67)
( 33, 70)( 34, 69)( 35, 72)( 36, 71)( 73,110)( 74,109)( 75,112)( 76,111)
( 77,114)( 78,113)( 79,116)( 80,115)( 81,118)( 82,117)( 83,120)( 84,119)
( 85,122)( 86,121)( 87,124)( 88,123)( 89,126)( 90,125)( 91,128)( 92,127)
( 93,130)( 94,129)( 95,132)( 96,131)( 97,134)( 98,133)( 99,136)(100,135)
(101,138)(102,137)(103,140)(104,139)(105,142)(106,141)(107,144)(108,143)
(145,182)(146,181)(147,184)(148,183)(149,186)(150,185)(151,188)(152,187)
(153,190)(154,189)(155,192)(156,191)(157,194)(158,193)(159,196)(160,195)
(161,198)(162,197)(163,200)(164,199)(165,202)(166,201)(167,204)(168,203)
(169,206)(170,205)(171,208)(172,207)(173,210)(174,209)(175,212)(176,211)
(177,214)(178,213)(179,216)(180,215)(217,254)(218,253)(219,256)(220,255)
(221,258)(222,257)(223,260)(224,259)(225,262)(226,261)(227,264)(228,263)
(229,266)(230,265)(231,268)(232,267)(233,270)(234,269)(235,272)(236,271)
(237,274)(238,273)(239,276)(240,275)(241,278)(242,277)(243,280)(244,279)
(245,282)(246,281)(247,284)(248,283)(249,286)(250,285)(251,288)(252,287)
(289,326)(290,325)(291,328)(292,327)(293,330)(294,329)(295,332)(296,331)
(297,334)(298,333)(299,336)(300,335)(301,338)(302,337)(303,340)(304,339)
(305,342)(306,341)(307,344)(308,343)(309,346)(310,345)(311,348)(312,347)
(313,350)(314,349)(315,352)(316,351)(317,354)(318,353)(319,356)(320,355)
(321,358)(322,357)(323,360)(324,359)(361,398)(362,397)(363,400)(364,399)
(365,402)(366,401)(367,404)(368,403)(369,406)(370,405)(371,408)(372,407)
(373,410)(374,409)(375,412)(376,411)(377,414)(378,413)(379,416)(380,415)
(381,418)(382,417)(383,420)(384,419)(385,422)(386,421)(387,424)(388,423)
(389,426)(390,425)(391,428)(392,427)(393,430)(394,429)(395,432)(396,431)
(433,470)(434,469)(435,472)(436,471)(437,474)(438,473)(439,476)(440,475)
(441,478)(442,477)(443,480)(444,479)(445,482)(446,481)(447,484)(448,483)
(449,486)(450,485)(451,488)(452,487)(453,490)(454,489)(455,492)(456,491)
(457,494)(458,493)(459,496)(460,495)(461,498)(462,497)(463,500)(464,499)
(465,502)(466,501)(467,504)(468,503)(505,542)(506,541)(507,544)(508,543)
(509,546)(510,545)(511,548)(512,547)(513,550)(514,549)(515,552)(516,551)
(517,554)(518,553)(519,556)(520,555)(521,558)(522,557)(523,560)(524,559)
(525,562)(526,561)(527,564)(528,563)(529,566)(530,565)(531,568)(532,567)
(533,570)(534,569)(535,572)(536,571)(537,574)(538,573)(539,576)(540,575);;
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,
s0*s1*s2*s1*s0*s1*s0*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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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, 38)( 2, 37)( 3, 40)( 4, 39)( 5, 42)( 6, 41)( 7, 44)
( 8, 43)( 9, 46)( 10, 45)( 11, 48)( 12, 47)( 13, 50)( 14, 49)( 15, 52)
( 16, 51)( 17, 54)( 18, 53)( 19, 56)( 20, 55)( 21, 58)( 22, 57)( 23, 60)
( 24, 59)( 25, 62)( 26, 61)( 27, 64)( 28, 63)( 29, 66)( 30, 65)( 31, 68)
( 32, 67)( 33, 70)( 34, 69)( 35, 72)( 36, 71)( 73,110)( 74,109)( 75,112)
( 76,111)( 77,114)( 78,113)( 79,116)( 80,115)( 81,118)( 82,117)( 83,120)
( 84,119)( 85,122)( 86,121)( 87,124)( 88,123)( 89,126)( 90,125)( 91,128)
( 92,127)( 93,130)( 94,129)( 95,132)( 96,131)( 97,134)( 98,133)( 99,136)
(100,135)(101,138)(102,137)(103,140)(104,139)(105,142)(106,141)(107,144)
(108,143)(145,182)(146,181)(147,184)(148,183)(149,186)(150,185)(151,188)
(152,187)(153,190)(154,189)(155,192)(156,191)(157,194)(158,193)(159,196)
(160,195)(161,198)(162,197)(163,200)(164,199)(165,202)(166,201)(167,204)
(168,203)(169,206)(170,205)(171,208)(172,207)(173,210)(174,209)(175,212)
(176,211)(177,214)(178,213)(179,216)(180,215)(217,254)(218,253)(219,256)
(220,255)(221,258)(222,257)(223,260)(224,259)(225,262)(226,261)(227,264)
(228,263)(229,266)(230,265)(231,268)(232,267)(233,270)(234,269)(235,272)
(236,271)(237,274)(238,273)(239,276)(240,275)(241,278)(242,277)(243,280)
(244,279)(245,282)(246,281)(247,284)(248,283)(249,286)(250,285)(251,288)
(252,287)(289,326)(290,325)(291,328)(292,327)(293,330)(294,329)(295,332)
(296,331)(297,334)(298,333)(299,336)(300,335)(301,338)(302,337)(303,340)
(304,339)(305,342)(306,341)(307,344)(308,343)(309,346)(310,345)(311,348)
(312,347)(313,350)(314,349)(315,352)(316,351)(317,354)(318,353)(319,356)
(320,355)(321,358)(322,357)(323,360)(324,359)(361,398)(362,397)(363,400)
(364,399)(365,402)(366,401)(367,404)(368,403)(369,406)(370,405)(371,408)
(372,407)(373,410)(374,409)(375,412)(376,411)(377,414)(378,413)(379,416)
(380,415)(381,418)(382,417)(383,420)(384,419)(385,422)(386,421)(387,424)
(388,423)(389,426)(390,425)(391,428)(392,427)(393,430)(394,429)(395,432)
(396,431)(433,470)(434,469)(435,472)(436,471)(437,474)(438,473)(439,476)
(440,475)(441,478)(442,477)(443,480)(444,479)(445,482)(446,481)(447,484)
(448,483)(449,486)(450,485)(451,488)(452,487)(453,490)(454,489)(455,492)
(456,491)(457,494)(458,493)(459,496)(460,495)(461,498)(462,497)(463,500)
(464,499)(465,502)(466,501)(467,504)(468,503)(505,542)(506,541)(507,544)
(508,543)(509,546)(510,545)(511,548)(512,547)(513,550)(514,549)(515,552)
(516,551)(517,554)(518,553)(519,556)(520,555)(521,558)(522,557)(523,560)
(524,559)(525,562)(526,561)(527,564)(528,563)(529,566)(530,565)(531,568)
(532,567)(533,570)(534,569)(535,572)(536,571)(537,574)(538,573)(539,576)
(540,575);
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,
s0*s1*s2*s1*s0*s1*s0*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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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