Polytope of Type {4,4,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,18}*1152c
if this polytope has a name.
Group : SmallGroup(1152,154282)
Rank : 4
Schlafli Type : {4,4,18}
Number of vertices, edges, etc : 8, 16, 72, 18
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 4
Special Properties :
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 : {4,4,9}*576a
3-fold quotients : {4,4,6}*384c
4-fold quotients : {2,4,18}*288c
6-fold quotients : {4,4,3}*192a
8-fold quotients : {2,4,9}*144
12-fold quotients : {2,4,6}*96b
24-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,145)( 2,146)( 3,147)( 4,148)( 5,150)( 6,149)( 7,152)( 8,151)
( 9,155)( 10,156)( 11,153)( 12,154)( 13,160)( 14,159)( 15,158)( 16,157)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,166)( 22,165)( 23,168)( 24,167)
( 25,171)( 26,172)( 27,169)( 28,170)( 29,176)( 30,175)( 31,174)( 32,173)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,182)( 38,181)( 39,184)( 40,183)
( 41,187)( 42,188)( 43,185)( 44,186)( 45,192)( 46,191)( 47,190)( 48,189)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,203)( 58,204)( 59,201)( 60,202)( 61,208)( 62,207)( 63,206)( 64,205)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,214)( 70,213)( 71,216)( 72,215)
( 73,219)( 74,220)( 75,217)( 76,218)( 77,224)( 78,223)( 79,222)( 80,221)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,230)( 86,229)( 87,232)( 88,231)
( 89,235)( 90,236)( 91,233)( 92,234)( 93,240)( 94,239)( 95,238)( 96,237)
( 97,241)( 98,242)( 99,243)(100,244)(101,246)(102,245)(103,248)(104,247)
(105,251)(106,252)(107,249)(108,250)(109,256)(110,255)(111,254)(112,253)
(113,257)(114,258)(115,259)(116,260)(117,262)(118,261)(119,264)(120,263)
(121,267)(122,268)(123,265)(124,266)(125,272)(126,271)(127,270)(128,269)
(129,273)(130,274)(131,275)(132,276)(133,278)(134,277)(135,280)(136,279)
(137,283)(138,284)(139,281)(140,282)(141,288)(142,287)(143,286)(144,285)
(289,433)(290,434)(291,435)(292,436)(293,438)(294,437)(295,440)(296,439)
(297,443)(298,444)(299,441)(300,442)(301,448)(302,447)(303,446)(304,445)
(305,449)(306,450)(307,451)(308,452)(309,454)(310,453)(311,456)(312,455)
(313,459)(314,460)(315,457)(316,458)(317,464)(318,463)(319,462)(320,461)
(321,465)(322,466)(323,467)(324,468)(325,470)(326,469)(327,472)(328,471)
(329,475)(330,476)(331,473)(332,474)(333,480)(334,479)(335,478)(336,477)
(337,481)(338,482)(339,483)(340,484)(341,486)(342,485)(343,488)(344,487)
(345,491)(346,492)(347,489)(348,490)(349,496)(350,495)(351,494)(352,493)
(353,497)(354,498)(355,499)(356,500)(357,502)(358,501)(359,504)(360,503)
(361,507)(362,508)(363,505)(364,506)(365,512)(366,511)(367,510)(368,509)
(369,513)(370,514)(371,515)(372,516)(373,518)(374,517)(375,520)(376,519)
(377,523)(378,524)(379,521)(380,522)(381,528)(382,527)(383,526)(384,525)
(385,529)(386,530)(387,531)(388,532)(389,534)(390,533)(391,536)(392,535)
(393,539)(394,540)(395,537)(396,538)(397,544)(398,543)(399,542)(400,541)
(401,545)(402,546)(403,547)(404,548)(405,550)(406,549)(407,552)(408,551)
(409,555)(410,556)(411,553)(412,554)(413,560)(414,559)(415,558)(416,557)
(417,561)(418,562)(419,563)(420,564)(421,566)(422,565)(423,568)(424,567)
(425,571)(426,572)(427,569)(428,570)(429,576)(430,575)(431,574)(432,573);;
s1 := ( 1,297)( 2,298)( 3,299)( 4,300)( 5,301)( 6,302)( 7,303)( 8,304)
( 9,289)( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,296)
( 17,313)( 18,314)( 19,315)( 20,316)( 21,317)( 22,318)( 23,319)( 24,320)
( 25,305)( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)
( 33,329)( 34,330)( 35,331)( 36,332)( 37,333)( 38,334)( 39,335)( 40,336)
( 41,321)( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)( 48,328)
( 49,345)( 50,346)( 51,347)( 52,348)( 53,349)( 54,350)( 55,351)( 56,352)
( 57,337)( 58,338)( 59,339)( 60,340)( 61,341)( 62,342)( 63,343)( 64,344)
( 65,361)( 66,362)( 67,363)( 68,364)( 69,365)( 70,366)( 71,367)( 72,368)
( 73,353)( 74,354)( 75,355)( 76,356)( 77,357)( 78,358)( 79,359)( 80,360)
( 81,377)( 82,378)( 83,379)( 84,380)( 85,381)( 86,382)( 87,383)( 88,384)
( 89,369)( 90,370)( 91,371)( 92,372)( 93,373)( 94,374)( 95,375)( 96,376)
( 97,393)( 98,394)( 99,395)(100,396)(101,397)(102,398)(103,399)(104,400)
(105,385)(106,386)(107,387)(108,388)(109,389)(110,390)(111,391)(112,392)
(113,409)(114,410)(115,411)(116,412)(117,413)(118,414)(119,415)(120,416)
(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)(128,408)
(129,425)(130,426)(131,427)(132,428)(133,429)(134,430)(135,431)(136,432)
(137,417)(138,418)(139,419)(140,420)(141,421)(142,422)(143,423)(144,424)
(145,441)(146,442)(147,443)(148,444)(149,445)(150,446)(151,447)(152,448)
(153,433)(154,434)(155,435)(156,436)(157,437)(158,438)(159,439)(160,440)
(161,457)(162,458)(163,459)(164,460)(165,461)(166,462)(167,463)(168,464)
(169,449)(170,450)(171,451)(172,452)(173,453)(174,454)(175,455)(176,456)
(177,473)(178,474)(179,475)(180,476)(181,477)(182,478)(183,479)(184,480)
(185,465)(186,466)(187,467)(188,468)(189,469)(190,470)(191,471)(192,472)
(193,489)(194,490)(195,491)(196,492)(197,493)(198,494)(199,495)(200,496)
(201,481)(202,482)(203,483)(204,484)(205,485)(206,486)(207,487)(208,488)
(209,505)(210,506)(211,507)(212,508)(213,509)(214,510)(215,511)(216,512)
(217,497)(218,498)(219,499)(220,500)(221,501)(222,502)(223,503)(224,504)
(225,521)(226,522)(227,523)(228,524)(229,525)(230,526)(231,527)(232,528)
(233,513)(234,514)(235,515)(236,516)(237,517)(238,518)(239,519)(240,520)
(241,537)(242,538)(243,539)(244,540)(245,541)(246,542)(247,543)(248,544)
(249,529)(250,530)(251,531)(252,532)(253,533)(254,534)(255,535)(256,536)
(257,553)(258,554)(259,555)(260,556)(261,557)(262,558)(263,559)(264,560)
(265,545)(266,546)(267,547)(268,548)(269,549)(270,550)(271,551)(272,552)
(273,569)(274,570)(275,571)(276,572)(277,573)(278,574)(279,575)(280,576)
(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)(288,568);;
s2 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,129)( 50,130)
( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)( 58,142)
( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)( 66,114)
( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)
( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)( 82, 98)
( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)(147,148)(151,152)
(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)
(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)
(173,185)(174,186)(175,188)(176,187)(193,273)(194,274)(195,276)(196,275)
(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)(203,288)(204,287)
(205,281)(206,282)(207,284)(208,283)(209,257)(210,258)(211,260)(212,259)
(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)(220,271)
(221,265)(222,266)(223,268)(224,267)(225,241)(226,242)(227,244)(228,243)
(229,245)(230,246)(231,248)(232,247)(233,253)(234,254)(235,256)(236,255)
(237,249)(238,250)(239,252)(240,251)(291,292)(295,296)(297,301)(298,302)
(299,304)(300,303)(305,321)(306,322)(307,324)(308,323)(309,325)(310,326)
(311,328)(312,327)(313,333)(314,334)(315,336)(316,335)(317,329)(318,330)
(319,332)(320,331)(337,417)(338,418)(339,420)(340,419)(341,421)(342,422)
(343,424)(344,423)(345,429)(346,430)(347,432)(348,431)(349,425)(350,426)
(351,428)(352,427)(353,401)(354,402)(355,404)(356,403)(357,405)(358,406)
(359,408)(360,407)(361,413)(362,414)(363,416)(364,415)(365,409)(366,410)
(367,412)(368,411)(369,385)(370,386)(371,388)(372,387)(373,389)(374,390)
(375,392)(376,391)(377,397)(378,398)(379,400)(380,399)(381,393)(382,394)
(383,396)(384,395)(435,436)(439,440)(441,445)(442,446)(443,448)(444,447)
(449,465)(450,466)(451,468)(452,467)(453,469)(454,470)(455,472)(456,471)
(457,477)(458,478)(459,480)(460,479)(461,473)(462,474)(463,476)(464,475)
(481,561)(482,562)(483,564)(484,563)(485,565)(486,566)(487,568)(488,567)
(489,573)(490,574)(491,576)(492,575)(493,569)(494,570)(495,572)(496,571)
(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)(503,552)(504,551)
(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)(511,556)(512,555)
(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)(519,536)(520,535)
(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)(527,540)(528,539);;
s3 := ( 1,337)( 2,340)( 3,339)( 4,338)( 5,349)( 6,352)( 7,351)( 8,350)
( 9,345)( 10,348)( 11,347)( 12,346)( 13,341)( 14,344)( 15,343)( 16,342)
( 17,369)( 18,372)( 19,371)( 20,370)( 21,381)( 22,384)( 23,383)( 24,382)
( 25,377)( 26,380)( 27,379)( 28,378)( 29,373)( 30,376)( 31,375)( 32,374)
( 33,353)( 34,356)( 35,355)( 36,354)( 37,365)( 38,368)( 39,367)( 40,366)
( 41,361)( 42,364)( 43,363)( 44,362)( 45,357)( 46,360)( 47,359)( 48,358)
( 49,289)( 50,292)( 51,291)( 52,290)( 53,301)( 54,304)( 55,303)( 56,302)
( 57,297)( 58,300)( 59,299)( 60,298)( 61,293)( 62,296)( 63,295)( 64,294)
( 65,321)( 66,324)( 67,323)( 68,322)( 69,333)( 70,336)( 71,335)( 72,334)
( 73,329)( 74,332)( 75,331)( 76,330)( 77,325)( 78,328)( 79,327)( 80,326)
( 81,305)( 82,308)( 83,307)( 84,306)( 85,317)( 86,320)( 87,319)( 88,318)
( 89,313)( 90,316)( 91,315)( 92,314)( 93,309)( 94,312)( 95,311)( 96,310)
( 97,417)( 98,420)( 99,419)(100,418)(101,429)(102,432)(103,431)(104,430)
(105,425)(106,428)(107,427)(108,426)(109,421)(110,424)(111,423)(112,422)
(113,401)(114,404)(115,403)(116,402)(117,413)(118,416)(119,415)(120,414)
(121,409)(122,412)(123,411)(124,410)(125,405)(126,408)(127,407)(128,406)
(129,385)(130,388)(131,387)(132,386)(133,397)(134,400)(135,399)(136,398)
(137,393)(138,396)(139,395)(140,394)(141,389)(142,392)(143,391)(144,390)
(145,481)(146,484)(147,483)(148,482)(149,493)(150,496)(151,495)(152,494)
(153,489)(154,492)(155,491)(156,490)(157,485)(158,488)(159,487)(160,486)
(161,513)(162,516)(163,515)(164,514)(165,525)(166,528)(167,527)(168,526)
(169,521)(170,524)(171,523)(172,522)(173,517)(174,520)(175,519)(176,518)
(177,497)(178,500)(179,499)(180,498)(181,509)(182,512)(183,511)(184,510)
(185,505)(186,508)(187,507)(188,506)(189,501)(190,504)(191,503)(192,502)
(193,433)(194,436)(195,435)(196,434)(197,445)(198,448)(199,447)(200,446)
(201,441)(202,444)(203,443)(204,442)(205,437)(206,440)(207,439)(208,438)
(209,465)(210,468)(211,467)(212,466)(213,477)(214,480)(215,479)(216,478)
(217,473)(218,476)(219,475)(220,474)(221,469)(222,472)(223,471)(224,470)
(225,449)(226,452)(227,451)(228,450)(229,461)(230,464)(231,463)(232,462)
(233,457)(234,460)(235,459)(236,458)(237,453)(238,456)(239,455)(240,454)
(241,561)(242,564)(243,563)(244,562)(245,573)(246,576)(247,575)(248,574)
(249,569)(250,572)(251,571)(252,570)(253,565)(254,568)(255,567)(256,566)
(257,545)(258,548)(259,547)(260,546)(261,557)(262,560)(263,559)(264,558)
(265,553)(266,556)(267,555)(268,554)(269,549)(270,552)(271,551)(272,550)
(273,529)(274,532)(275,531)(276,530)(277,541)(278,544)(279,543)(280,542)
(281,537)(282,540)(283,539)(284,538)(285,533)(286,536)(287,535)(288,534);;
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*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s0*s1*s2*s3*s1*s2*s1*s0*s1*s2*s3*s1*s2*s1,
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,145)( 2,146)( 3,147)( 4,148)( 5,150)( 6,149)( 7,152)
( 8,151)( 9,155)( 10,156)( 11,153)( 12,154)( 13,160)( 14,159)( 15,158)
( 16,157)( 17,161)( 18,162)( 19,163)( 20,164)( 21,166)( 22,165)( 23,168)
( 24,167)( 25,171)( 26,172)( 27,169)( 28,170)( 29,176)( 30,175)( 31,174)
( 32,173)( 33,177)( 34,178)( 35,179)( 36,180)( 37,182)( 38,181)( 39,184)
( 40,183)( 41,187)( 42,188)( 43,185)( 44,186)( 45,192)( 46,191)( 47,190)
( 48,189)( 49,193)( 50,194)( 51,195)( 52,196)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,203)( 58,204)( 59,201)( 60,202)( 61,208)( 62,207)( 63,206)
( 64,205)( 65,209)( 66,210)( 67,211)( 68,212)( 69,214)( 70,213)( 71,216)
( 72,215)( 73,219)( 74,220)( 75,217)( 76,218)( 77,224)( 78,223)( 79,222)
( 80,221)( 81,225)( 82,226)( 83,227)( 84,228)( 85,230)( 86,229)( 87,232)
( 88,231)( 89,235)( 90,236)( 91,233)( 92,234)( 93,240)( 94,239)( 95,238)
( 96,237)( 97,241)( 98,242)( 99,243)(100,244)(101,246)(102,245)(103,248)
(104,247)(105,251)(106,252)(107,249)(108,250)(109,256)(110,255)(111,254)
(112,253)(113,257)(114,258)(115,259)(116,260)(117,262)(118,261)(119,264)
(120,263)(121,267)(122,268)(123,265)(124,266)(125,272)(126,271)(127,270)
(128,269)(129,273)(130,274)(131,275)(132,276)(133,278)(134,277)(135,280)
(136,279)(137,283)(138,284)(139,281)(140,282)(141,288)(142,287)(143,286)
(144,285)(289,433)(290,434)(291,435)(292,436)(293,438)(294,437)(295,440)
(296,439)(297,443)(298,444)(299,441)(300,442)(301,448)(302,447)(303,446)
(304,445)(305,449)(306,450)(307,451)(308,452)(309,454)(310,453)(311,456)
(312,455)(313,459)(314,460)(315,457)(316,458)(317,464)(318,463)(319,462)
(320,461)(321,465)(322,466)(323,467)(324,468)(325,470)(326,469)(327,472)
(328,471)(329,475)(330,476)(331,473)(332,474)(333,480)(334,479)(335,478)
(336,477)(337,481)(338,482)(339,483)(340,484)(341,486)(342,485)(343,488)
(344,487)(345,491)(346,492)(347,489)(348,490)(349,496)(350,495)(351,494)
(352,493)(353,497)(354,498)(355,499)(356,500)(357,502)(358,501)(359,504)
(360,503)(361,507)(362,508)(363,505)(364,506)(365,512)(366,511)(367,510)
(368,509)(369,513)(370,514)(371,515)(372,516)(373,518)(374,517)(375,520)
(376,519)(377,523)(378,524)(379,521)(380,522)(381,528)(382,527)(383,526)
(384,525)(385,529)(386,530)(387,531)(388,532)(389,534)(390,533)(391,536)
(392,535)(393,539)(394,540)(395,537)(396,538)(397,544)(398,543)(399,542)
(400,541)(401,545)(402,546)(403,547)(404,548)(405,550)(406,549)(407,552)
(408,551)(409,555)(410,556)(411,553)(412,554)(413,560)(414,559)(415,558)
(416,557)(417,561)(418,562)(419,563)(420,564)(421,566)(422,565)(423,568)
(424,567)(425,571)(426,572)(427,569)(428,570)(429,576)(430,575)(431,574)
(432,573);
s1 := Sym(576)!( 1,297)( 2,298)( 3,299)( 4,300)( 5,301)( 6,302)( 7,303)
( 8,304)( 9,289)( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)
( 16,296)( 17,313)( 18,314)( 19,315)( 20,316)( 21,317)( 22,318)( 23,319)
( 24,320)( 25,305)( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)
( 32,312)( 33,329)( 34,330)( 35,331)( 36,332)( 37,333)( 38,334)( 39,335)
( 40,336)( 41,321)( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)
( 48,328)( 49,345)( 50,346)( 51,347)( 52,348)( 53,349)( 54,350)( 55,351)
( 56,352)( 57,337)( 58,338)( 59,339)( 60,340)( 61,341)( 62,342)( 63,343)
( 64,344)( 65,361)( 66,362)( 67,363)( 68,364)( 69,365)( 70,366)( 71,367)
( 72,368)( 73,353)( 74,354)( 75,355)( 76,356)( 77,357)( 78,358)( 79,359)
( 80,360)( 81,377)( 82,378)( 83,379)( 84,380)( 85,381)( 86,382)( 87,383)
( 88,384)( 89,369)( 90,370)( 91,371)( 92,372)( 93,373)( 94,374)( 95,375)
( 96,376)( 97,393)( 98,394)( 99,395)(100,396)(101,397)(102,398)(103,399)
(104,400)(105,385)(106,386)(107,387)(108,388)(109,389)(110,390)(111,391)
(112,392)(113,409)(114,410)(115,411)(116,412)(117,413)(118,414)(119,415)
(120,416)(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)
(128,408)(129,425)(130,426)(131,427)(132,428)(133,429)(134,430)(135,431)
(136,432)(137,417)(138,418)(139,419)(140,420)(141,421)(142,422)(143,423)
(144,424)(145,441)(146,442)(147,443)(148,444)(149,445)(150,446)(151,447)
(152,448)(153,433)(154,434)(155,435)(156,436)(157,437)(158,438)(159,439)
(160,440)(161,457)(162,458)(163,459)(164,460)(165,461)(166,462)(167,463)
(168,464)(169,449)(170,450)(171,451)(172,452)(173,453)(174,454)(175,455)
(176,456)(177,473)(178,474)(179,475)(180,476)(181,477)(182,478)(183,479)
(184,480)(185,465)(186,466)(187,467)(188,468)(189,469)(190,470)(191,471)
(192,472)(193,489)(194,490)(195,491)(196,492)(197,493)(198,494)(199,495)
(200,496)(201,481)(202,482)(203,483)(204,484)(205,485)(206,486)(207,487)
(208,488)(209,505)(210,506)(211,507)(212,508)(213,509)(214,510)(215,511)
(216,512)(217,497)(218,498)(219,499)(220,500)(221,501)(222,502)(223,503)
(224,504)(225,521)(226,522)(227,523)(228,524)(229,525)(230,526)(231,527)
(232,528)(233,513)(234,514)(235,515)(236,516)(237,517)(238,518)(239,519)
(240,520)(241,537)(242,538)(243,539)(244,540)(245,541)(246,542)(247,543)
(248,544)(249,529)(250,530)(251,531)(252,532)(253,533)(254,534)(255,535)
(256,536)(257,553)(258,554)(259,555)(260,556)(261,557)(262,558)(263,559)
(264,560)(265,545)(266,546)(267,547)(268,548)(269,549)(270,550)(271,551)
(272,552)(273,569)(274,570)(275,571)(276,572)(277,573)(278,574)(279,575)
(280,576)(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)
(288,568);
s2 := Sym(576)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,129)
( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)
( 58,142)( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)
( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)
( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)
( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)(147,148)
(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)
(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)
(172,191)(173,185)(174,186)(175,188)(176,187)(193,273)(194,274)(195,276)
(196,275)(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)(203,288)
(204,287)(205,281)(206,282)(207,284)(208,283)(209,257)(210,258)(211,260)
(212,259)(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)
(220,271)(221,265)(222,266)(223,268)(224,267)(225,241)(226,242)(227,244)
(228,243)(229,245)(230,246)(231,248)(232,247)(233,253)(234,254)(235,256)
(236,255)(237,249)(238,250)(239,252)(240,251)(291,292)(295,296)(297,301)
(298,302)(299,304)(300,303)(305,321)(306,322)(307,324)(308,323)(309,325)
(310,326)(311,328)(312,327)(313,333)(314,334)(315,336)(316,335)(317,329)
(318,330)(319,332)(320,331)(337,417)(338,418)(339,420)(340,419)(341,421)
(342,422)(343,424)(344,423)(345,429)(346,430)(347,432)(348,431)(349,425)
(350,426)(351,428)(352,427)(353,401)(354,402)(355,404)(356,403)(357,405)
(358,406)(359,408)(360,407)(361,413)(362,414)(363,416)(364,415)(365,409)
(366,410)(367,412)(368,411)(369,385)(370,386)(371,388)(372,387)(373,389)
(374,390)(375,392)(376,391)(377,397)(378,398)(379,400)(380,399)(381,393)
(382,394)(383,396)(384,395)(435,436)(439,440)(441,445)(442,446)(443,448)
(444,447)(449,465)(450,466)(451,468)(452,467)(453,469)(454,470)(455,472)
(456,471)(457,477)(458,478)(459,480)(460,479)(461,473)(462,474)(463,476)
(464,475)(481,561)(482,562)(483,564)(484,563)(485,565)(486,566)(487,568)
(488,567)(489,573)(490,574)(491,576)(492,575)(493,569)(494,570)(495,572)
(496,571)(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)(503,552)
(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)(511,556)
(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)(519,536)
(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)(527,540)
(528,539);
s3 := Sym(576)!( 1,337)( 2,340)( 3,339)( 4,338)( 5,349)( 6,352)( 7,351)
( 8,350)( 9,345)( 10,348)( 11,347)( 12,346)( 13,341)( 14,344)( 15,343)
( 16,342)( 17,369)( 18,372)( 19,371)( 20,370)( 21,381)( 22,384)( 23,383)
( 24,382)( 25,377)( 26,380)( 27,379)( 28,378)( 29,373)( 30,376)( 31,375)
( 32,374)( 33,353)( 34,356)( 35,355)( 36,354)( 37,365)( 38,368)( 39,367)
( 40,366)( 41,361)( 42,364)( 43,363)( 44,362)( 45,357)( 46,360)( 47,359)
( 48,358)( 49,289)( 50,292)( 51,291)( 52,290)( 53,301)( 54,304)( 55,303)
( 56,302)( 57,297)( 58,300)( 59,299)( 60,298)( 61,293)( 62,296)( 63,295)
( 64,294)( 65,321)( 66,324)( 67,323)( 68,322)( 69,333)( 70,336)( 71,335)
( 72,334)( 73,329)( 74,332)( 75,331)( 76,330)( 77,325)( 78,328)( 79,327)
( 80,326)( 81,305)( 82,308)( 83,307)( 84,306)( 85,317)( 86,320)( 87,319)
( 88,318)( 89,313)( 90,316)( 91,315)( 92,314)( 93,309)( 94,312)( 95,311)
( 96,310)( 97,417)( 98,420)( 99,419)(100,418)(101,429)(102,432)(103,431)
(104,430)(105,425)(106,428)(107,427)(108,426)(109,421)(110,424)(111,423)
(112,422)(113,401)(114,404)(115,403)(116,402)(117,413)(118,416)(119,415)
(120,414)(121,409)(122,412)(123,411)(124,410)(125,405)(126,408)(127,407)
(128,406)(129,385)(130,388)(131,387)(132,386)(133,397)(134,400)(135,399)
(136,398)(137,393)(138,396)(139,395)(140,394)(141,389)(142,392)(143,391)
(144,390)(145,481)(146,484)(147,483)(148,482)(149,493)(150,496)(151,495)
(152,494)(153,489)(154,492)(155,491)(156,490)(157,485)(158,488)(159,487)
(160,486)(161,513)(162,516)(163,515)(164,514)(165,525)(166,528)(167,527)
(168,526)(169,521)(170,524)(171,523)(172,522)(173,517)(174,520)(175,519)
(176,518)(177,497)(178,500)(179,499)(180,498)(181,509)(182,512)(183,511)
(184,510)(185,505)(186,508)(187,507)(188,506)(189,501)(190,504)(191,503)
(192,502)(193,433)(194,436)(195,435)(196,434)(197,445)(198,448)(199,447)
(200,446)(201,441)(202,444)(203,443)(204,442)(205,437)(206,440)(207,439)
(208,438)(209,465)(210,468)(211,467)(212,466)(213,477)(214,480)(215,479)
(216,478)(217,473)(218,476)(219,475)(220,474)(221,469)(222,472)(223,471)
(224,470)(225,449)(226,452)(227,451)(228,450)(229,461)(230,464)(231,463)
(232,462)(233,457)(234,460)(235,459)(236,458)(237,453)(238,456)(239,455)
(240,454)(241,561)(242,564)(243,563)(244,562)(245,573)(246,576)(247,575)
(248,574)(249,569)(250,572)(251,571)(252,570)(253,565)(254,568)(255,567)
(256,566)(257,545)(258,548)(259,547)(260,546)(261,557)(262,560)(263,559)
(264,558)(265,553)(266,556)(267,555)(268,554)(269,549)(270,552)(271,551)
(272,550)(273,529)(274,532)(275,531)(276,530)(277,541)(278,544)(279,543)
(280,542)(281,537)(282,540)(283,539)(284,538)(285,533)(286,536)(287,535)
(288,534);
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*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s0*s1*s2*s3*s1*s2*s1*s0*s1*s2*s3*s1*s2*s1,
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s1*s2*s1 >;
References : None.
to this polytope