Polytope of Type {4,36,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,36,4}*1152i
if this polytope has a name.
Group : SmallGroup(1152,155431)
Rank : 4
Schlafli Type : {4,36,4}
Number of vertices, edges, etc : 4, 72, 72, 4
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
Non-Orientable
Flat
Self-Dual
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 : {4,18,4}*576d
3-fold quotients : {4,12,4}*384i
4-fold quotients : {4,9,4}*288
6-fold quotients : {4,6,4}*192d
12-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)( 8,160)
( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)
( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)( 24,176)
( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)
( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)( 56,208)
( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)
( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)( 72,224)
( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)( 80,216)
( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)(104,256)
(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)(112,248)
(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)(120,272)
(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)(128,264)
(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)
(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)(144,280)
(289,441)(290,442)(291,443)(292,444)(293,445)(294,446)(295,447)(296,448)
(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)(304,440)
(305,457)(306,458)(307,459)(308,460)(309,461)(310,462)(311,463)(312,464)
(313,449)(314,450)(315,451)(316,452)(317,453)(318,454)(319,455)(320,456)
(321,473)(322,474)(323,475)(324,476)(325,477)(326,478)(327,479)(328,480)
(329,465)(330,466)(331,467)(332,468)(333,469)(334,470)(335,471)(336,472)
(337,489)(338,490)(339,491)(340,492)(341,493)(342,494)(343,495)(344,496)
(345,481)(346,482)(347,483)(348,484)(349,485)(350,486)(351,487)(352,488)
(353,505)(354,506)(355,507)(356,508)(357,509)(358,510)(359,511)(360,512)
(361,497)(362,498)(363,499)(364,500)(365,501)(366,502)(367,503)(368,504)
(369,521)(370,522)(371,523)(372,524)(373,525)(374,526)(375,527)(376,528)
(377,513)(378,514)(379,515)(380,516)(381,517)(382,518)(383,519)(384,520)
(385,537)(386,538)(387,539)(388,540)(389,541)(390,542)(391,543)(392,544)
(393,529)(394,530)(395,531)(396,532)(397,533)(398,534)(399,535)(400,536)
(401,553)(402,554)(403,555)(404,556)(405,557)(406,558)(407,559)(408,560)
(409,545)(410,546)(411,547)(412,548)(413,549)(414,550)(415,551)(416,552)
(417,569)(418,570)(419,571)(420,572)(421,573)(422,574)(423,575)(424,576)
(425,561)(426,562)(427,563)(428,564)(429,565)(430,566)(431,567)(432,568);;
s1 := ( 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)(289,433)(290,434)(291,436)(292,435)
(293,437)(294,438)(295,440)(296,439)(297,445)(298,446)(299,448)(300,447)
(301,441)(302,442)(303,444)(304,443)(305,465)(306,466)(307,468)(308,467)
(309,469)(310,470)(311,472)(312,471)(313,477)(314,478)(315,480)(316,479)
(317,473)(318,474)(319,476)(320,475)(321,449)(322,450)(323,452)(324,451)
(325,453)(326,454)(327,456)(328,455)(329,461)(330,462)(331,464)(332,463)
(333,457)(334,458)(335,460)(336,459)(337,561)(338,562)(339,564)(340,563)
(341,565)(342,566)(343,568)(344,567)(345,573)(346,574)(347,576)(348,575)
(349,569)(350,570)(351,572)(352,571)(353,545)(354,546)(355,548)(356,547)
(357,549)(358,550)(359,552)(360,551)(361,557)(362,558)(363,560)(364,559)
(365,553)(366,554)(367,556)(368,555)(369,529)(370,530)(371,532)(372,531)
(373,533)(374,534)(375,536)(376,535)(377,541)(378,542)(379,544)(380,543)
(381,537)(382,538)(383,540)(384,539)(385,513)(386,514)(387,516)(388,515)
(389,517)(390,518)(391,520)(392,519)(393,525)(394,526)(395,528)(396,527)
(397,521)(398,522)(399,524)(400,523)(401,497)(402,498)(403,500)(404,499)
(405,501)(406,502)(407,504)(408,503)(409,509)(410,510)(411,512)(412,511)
(413,505)(414,506)(415,508)(416,507)(417,481)(418,482)(419,484)(420,483)
(421,485)(422,486)(423,488)(424,487)(425,493)(426,494)(427,496)(428,495)
(429,489)(430,490)(431,492)(432,491);;
s2 := ( 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);;
s3 := ( 1,146)( 2,145)( 3,148)( 4,147)( 5,150)( 6,149)( 7,152)( 8,151)
( 9,154)( 10,153)( 11,156)( 12,155)( 13,158)( 14,157)( 15,160)( 16,159)
( 17,162)( 18,161)( 19,164)( 20,163)( 21,166)( 22,165)( 23,168)( 24,167)
( 25,170)( 26,169)( 27,172)( 28,171)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,178)( 34,177)( 35,180)( 36,179)( 37,182)( 38,181)( 39,184)( 40,183)
( 41,186)( 42,185)( 43,188)( 44,187)( 45,190)( 46,189)( 47,192)( 48,191)
( 49,194)( 50,193)( 51,196)( 52,195)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,202)( 58,201)( 59,204)( 60,203)( 61,206)( 62,205)( 63,208)( 64,207)
( 65,210)( 66,209)( 67,212)( 68,211)( 69,214)( 70,213)( 71,216)( 72,215)
( 73,218)( 74,217)( 75,220)( 76,219)( 77,222)( 78,221)( 79,224)( 80,223)
( 81,226)( 82,225)( 83,228)( 84,227)( 85,230)( 86,229)( 87,232)( 88,231)
( 89,234)( 90,233)( 91,236)( 92,235)( 93,238)( 94,237)( 95,240)( 96,239)
( 97,242)( 98,241)( 99,244)(100,243)(101,246)(102,245)(103,248)(104,247)
(105,250)(106,249)(107,252)(108,251)(109,254)(110,253)(111,256)(112,255)
(113,258)(114,257)(115,260)(116,259)(117,262)(118,261)(119,264)(120,263)
(121,266)(122,265)(123,268)(124,267)(125,270)(126,269)(127,272)(128,271)
(129,274)(130,273)(131,276)(132,275)(133,278)(134,277)(135,280)(136,279)
(137,282)(138,281)(139,284)(140,283)(141,286)(142,285)(143,288)(144,287)
(289,434)(290,433)(291,436)(292,435)(293,438)(294,437)(295,440)(296,439)
(297,442)(298,441)(299,444)(300,443)(301,446)(302,445)(303,448)(304,447)
(305,450)(306,449)(307,452)(308,451)(309,454)(310,453)(311,456)(312,455)
(313,458)(314,457)(315,460)(316,459)(317,462)(318,461)(319,464)(320,463)
(321,466)(322,465)(323,468)(324,467)(325,470)(326,469)(327,472)(328,471)
(329,474)(330,473)(331,476)(332,475)(333,478)(334,477)(335,480)(336,479)
(337,482)(338,481)(339,484)(340,483)(341,486)(342,485)(343,488)(344,487)
(345,490)(346,489)(347,492)(348,491)(349,494)(350,493)(351,496)(352,495)
(353,498)(354,497)(355,500)(356,499)(357,502)(358,501)(359,504)(360,503)
(361,506)(362,505)(363,508)(364,507)(365,510)(366,509)(367,512)(368,511)
(369,514)(370,513)(371,516)(372,515)(373,518)(374,517)(375,520)(376,519)
(377,522)(378,521)(379,524)(380,523)(381,526)(382,525)(383,528)(384,527)
(385,530)(386,529)(387,532)(388,531)(389,534)(390,533)(391,536)(392,535)
(393,538)(394,537)(395,540)(396,539)(397,542)(398,541)(399,544)(400,543)
(401,546)(402,545)(403,548)(404,547)(405,550)(406,549)(407,552)(408,551)
(409,554)(410,553)(411,556)(412,555)(413,558)(414,557)(415,560)(416,559)
(417,562)(418,561)(419,564)(420,563)(421,566)(422,565)(423,568)(424,567)
(425,570)(426,569)(427,572)(428,571)(429,574)(430,573)(431,576)(432,575);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s1*s3*s2*s1*s3*s0*s1*s2*s0*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)
( 8,160)( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)
( 16,152)( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)
( 24,176)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)
( 32,168)( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)
( 56,208)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)
( 64,200)( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)
( 72,224)( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)
( 80,216)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)
(104,256)(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)
(112,248)(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)
(120,272)(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)
(128,264)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)
(136,288)(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)
(144,280)(289,441)(290,442)(291,443)(292,444)(293,445)(294,446)(295,447)
(296,448)(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)
(304,440)(305,457)(306,458)(307,459)(308,460)(309,461)(310,462)(311,463)
(312,464)(313,449)(314,450)(315,451)(316,452)(317,453)(318,454)(319,455)
(320,456)(321,473)(322,474)(323,475)(324,476)(325,477)(326,478)(327,479)
(328,480)(329,465)(330,466)(331,467)(332,468)(333,469)(334,470)(335,471)
(336,472)(337,489)(338,490)(339,491)(340,492)(341,493)(342,494)(343,495)
(344,496)(345,481)(346,482)(347,483)(348,484)(349,485)(350,486)(351,487)
(352,488)(353,505)(354,506)(355,507)(356,508)(357,509)(358,510)(359,511)
(360,512)(361,497)(362,498)(363,499)(364,500)(365,501)(366,502)(367,503)
(368,504)(369,521)(370,522)(371,523)(372,524)(373,525)(374,526)(375,527)
(376,528)(377,513)(378,514)(379,515)(380,516)(381,517)(382,518)(383,519)
(384,520)(385,537)(386,538)(387,539)(388,540)(389,541)(390,542)(391,543)
(392,544)(393,529)(394,530)(395,531)(396,532)(397,533)(398,534)(399,535)
(400,536)(401,553)(402,554)(403,555)(404,556)(405,557)(406,558)(407,559)
(408,560)(409,545)(410,546)(411,547)(412,548)(413,549)(414,550)(415,551)
(416,552)(417,569)(418,570)(419,571)(420,572)(421,573)(422,574)(423,575)
(424,576)(425,561)(426,562)(427,563)(428,564)(429,565)(430,566)(431,567)
(432,568);
s1 := 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)(289,433)(290,434)(291,436)
(292,435)(293,437)(294,438)(295,440)(296,439)(297,445)(298,446)(299,448)
(300,447)(301,441)(302,442)(303,444)(304,443)(305,465)(306,466)(307,468)
(308,467)(309,469)(310,470)(311,472)(312,471)(313,477)(314,478)(315,480)
(316,479)(317,473)(318,474)(319,476)(320,475)(321,449)(322,450)(323,452)
(324,451)(325,453)(326,454)(327,456)(328,455)(329,461)(330,462)(331,464)
(332,463)(333,457)(334,458)(335,460)(336,459)(337,561)(338,562)(339,564)
(340,563)(341,565)(342,566)(343,568)(344,567)(345,573)(346,574)(347,576)
(348,575)(349,569)(350,570)(351,572)(352,571)(353,545)(354,546)(355,548)
(356,547)(357,549)(358,550)(359,552)(360,551)(361,557)(362,558)(363,560)
(364,559)(365,553)(366,554)(367,556)(368,555)(369,529)(370,530)(371,532)
(372,531)(373,533)(374,534)(375,536)(376,535)(377,541)(378,542)(379,544)
(380,543)(381,537)(382,538)(383,540)(384,539)(385,513)(386,514)(387,516)
(388,515)(389,517)(390,518)(391,520)(392,519)(393,525)(394,526)(395,528)
(396,527)(397,521)(398,522)(399,524)(400,523)(401,497)(402,498)(403,500)
(404,499)(405,501)(406,502)(407,504)(408,503)(409,509)(410,510)(411,512)
(412,511)(413,505)(414,506)(415,508)(416,507)(417,481)(418,482)(419,484)
(420,483)(421,485)(422,486)(423,488)(424,487)(425,493)(426,494)(427,496)
(428,495)(429,489)(430,490)(431,492)(432,491);
s2 := 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);
s3 := Sym(576)!( 1,146)( 2,145)( 3,148)( 4,147)( 5,150)( 6,149)( 7,152)
( 8,151)( 9,154)( 10,153)( 11,156)( 12,155)( 13,158)( 14,157)( 15,160)
( 16,159)( 17,162)( 18,161)( 19,164)( 20,163)( 21,166)( 22,165)( 23,168)
( 24,167)( 25,170)( 26,169)( 27,172)( 28,171)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,178)( 34,177)( 35,180)( 36,179)( 37,182)( 38,181)( 39,184)
( 40,183)( 41,186)( 42,185)( 43,188)( 44,187)( 45,190)( 46,189)( 47,192)
( 48,191)( 49,194)( 50,193)( 51,196)( 52,195)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,202)( 58,201)( 59,204)( 60,203)( 61,206)( 62,205)( 63,208)
( 64,207)( 65,210)( 66,209)( 67,212)( 68,211)( 69,214)( 70,213)( 71,216)
( 72,215)( 73,218)( 74,217)( 75,220)( 76,219)( 77,222)( 78,221)( 79,224)
( 80,223)( 81,226)( 82,225)( 83,228)( 84,227)( 85,230)( 86,229)( 87,232)
( 88,231)( 89,234)( 90,233)( 91,236)( 92,235)( 93,238)( 94,237)( 95,240)
( 96,239)( 97,242)( 98,241)( 99,244)(100,243)(101,246)(102,245)(103,248)
(104,247)(105,250)(106,249)(107,252)(108,251)(109,254)(110,253)(111,256)
(112,255)(113,258)(114,257)(115,260)(116,259)(117,262)(118,261)(119,264)
(120,263)(121,266)(122,265)(123,268)(124,267)(125,270)(126,269)(127,272)
(128,271)(129,274)(130,273)(131,276)(132,275)(133,278)(134,277)(135,280)
(136,279)(137,282)(138,281)(139,284)(140,283)(141,286)(142,285)(143,288)
(144,287)(289,434)(290,433)(291,436)(292,435)(293,438)(294,437)(295,440)
(296,439)(297,442)(298,441)(299,444)(300,443)(301,446)(302,445)(303,448)
(304,447)(305,450)(306,449)(307,452)(308,451)(309,454)(310,453)(311,456)
(312,455)(313,458)(314,457)(315,460)(316,459)(317,462)(318,461)(319,464)
(320,463)(321,466)(322,465)(323,468)(324,467)(325,470)(326,469)(327,472)
(328,471)(329,474)(330,473)(331,476)(332,475)(333,478)(334,477)(335,480)
(336,479)(337,482)(338,481)(339,484)(340,483)(341,486)(342,485)(343,488)
(344,487)(345,490)(346,489)(347,492)(348,491)(349,494)(350,493)(351,496)
(352,495)(353,498)(354,497)(355,500)(356,499)(357,502)(358,501)(359,504)
(360,503)(361,506)(362,505)(363,508)(364,507)(365,510)(366,509)(367,512)
(368,511)(369,514)(370,513)(371,516)(372,515)(373,518)(374,517)(375,520)
(376,519)(377,522)(378,521)(379,524)(380,523)(381,526)(382,525)(383,528)
(384,527)(385,530)(386,529)(387,532)(388,531)(389,534)(390,533)(391,536)
(392,535)(393,538)(394,537)(395,540)(396,539)(397,542)(398,541)(399,544)
(400,543)(401,546)(402,545)(403,548)(404,547)(405,550)(406,549)(407,552)
(408,551)(409,554)(410,553)(411,556)(412,555)(413,558)(414,557)(415,560)
(416,559)(417,562)(418,561)(419,564)(420,563)(421,566)(422,565)(423,568)
(424,567)(425,570)(426,569)(427,572)(428,571)(429,574)(430,573)(431,576)
(432,575);
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, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s1*s3*s2*s1*s3*s0*s1*s2*s0*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;
References : None.
to this polytope