Polytope of Type {6,4,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,16}*1152
if this polytope has a name.
Group : SmallGroup(1152,32083)
Rank : 4
Schlafli Type : {6,4,16}
Number of vertices, edges, etc : 9, 18, 48, 16
Order of s0s1s2s3 : 16
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 : {6,4,8}*576
4-fold quotients : {6,4,4}*288
8-fold quotients : {6,4,2}*144
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 37)( 2, 39)( 3, 38)( 4, 43)( 5, 45)( 6, 44)( 7, 40)( 8, 42)
( 9, 41)( 10, 46)( 11, 48)( 12, 47)( 13, 52)( 14, 54)( 15, 53)( 16, 49)
( 17, 51)( 18, 50)( 19, 55)( 20, 57)( 21, 56)( 22, 61)( 23, 63)( 24, 62)
( 25, 58)( 26, 60)( 27, 59)( 28, 64)( 29, 66)( 30, 65)( 31, 70)( 32, 72)
( 33, 71)( 34, 67)( 35, 69)( 36, 68)( 73,109)( 74,111)( 75,110)( 76,115)
( 77,117)( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)( 84,119)
( 85,124)( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,127)( 92,129)
( 93,128)( 94,133)( 95,135)( 96,134)( 97,130)( 98,132)( 99,131)(100,136)
(101,138)(102,137)(103,142)(104,144)(105,143)(106,139)(107,141)(108,140)
(145,181)(146,183)(147,182)(148,187)(149,189)(150,188)(151,184)(152,186)
(153,185)(154,190)(155,192)(156,191)(157,196)(158,198)(159,197)(160,193)
(161,195)(162,194)(163,199)(164,201)(165,200)(166,205)(167,207)(168,206)
(169,202)(170,204)(171,203)(172,208)(173,210)(174,209)(175,214)(176,216)
(177,215)(178,211)(179,213)(180,212)(217,253)(218,255)(219,254)(220,259)
(221,261)(222,260)(223,256)(224,258)(225,257)(226,262)(227,264)(228,263)
(229,268)(230,270)(231,269)(232,265)(233,267)(234,266)(235,271)(236,273)
(237,272)(238,277)(239,279)(240,278)(241,274)(242,276)(243,275)(244,280)
(245,282)(246,281)(247,286)(248,288)(249,287)(250,283)(251,285)(252,284)
(289,325)(290,327)(291,326)(292,331)(293,333)(294,332)(295,328)(296,330)
(297,329)(298,334)(299,336)(300,335)(301,340)(302,342)(303,341)(304,337)
(305,339)(306,338)(307,343)(308,345)(309,344)(310,349)(311,351)(312,350)
(313,346)(314,348)(315,347)(316,352)(317,354)(318,353)(319,358)(320,360)
(321,359)(322,355)(323,357)(324,356)(361,397)(362,399)(363,398)(364,403)
(365,405)(366,404)(367,400)(368,402)(369,401)(370,406)(371,408)(372,407)
(373,412)(374,414)(375,413)(376,409)(377,411)(378,410)(379,415)(380,417)
(381,416)(382,421)(383,423)(384,422)(385,418)(386,420)(387,419)(388,424)
(389,426)(390,425)(391,430)(392,432)(393,431)(394,427)(395,429)(396,428)
(433,469)(434,471)(435,470)(436,475)(437,477)(438,476)(439,472)(440,474)
(441,473)(442,478)(443,480)(444,479)(445,484)(446,486)(447,485)(448,481)
(449,483)(450,482)(451,487)(452,489)(453,488)(454,493)(455,495)(456,494)
(457,490)(458,492)(459,491)(460,496)(461,498)(462,497)(463,502)(464,504)
(465,503)(466,499)(467,501)(468,500)(505,541)(506,543)(507,542)(508,547)
(509,549)(510,548)(511,544)(512,546)(513,545)(514,550)(515,552)(516,551)
(517,556)(518,558)(519,557)(520,553)(521,555)(522,554)(523,559)(524,561)
(525,560)(526,565)(527,567)(528,566)(529,562)(530,564)(531,563)(532,568)
(533,570)(534,569)(535,574)(536,576)(537,575)(538,571)(539,573)(540,572);;
s1 := ( 1,146)( 2,145)( 3,147)( 4,150)( 5,149)( 6,148)( 7,151)( 8,153)
( 9,152)( 10,155)( 11,154)( 12,156)( 13,159)( 14,158)( 15,157)( 16,160)
( 17,162)( 18,161)( 19,164)( 20,163)( 21,165)( 22,168)( 23,167)( 24,166)
( 25,169)( 26,171)( 27,170)( 28,173)( 29,172)( 30,174)( 31,177)( 32,176)
( 33,175)( 34,178)( 35,180)( 36,179)( 37,182)( 38,181)( 39,183)( 40,186)
( 41,185)( 42,184)( 43,187)( 44,189)( 45,188)( 46,191)( 47,190)( 48,192)
( 49,195)( 50,194)( 51,193)( 52,196)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,207)( 63,206)( 64,209)
( 65,208)( 66,210)( 67,213)( 68,212)( 69,211)( 70,214)( 71,216)( 72,215)
( 73,218)( 74,217)( 75,219)( 76,222)( 77,221)( 78,220)( 79,223)( 80,225)
( 81,224)( 82,227)( 83,226)( 84,228)( 85,231)( 86,230)( 87,229)( 88,232)
( 89,234)( 90,233)( 91,236)( 92,235)( 93,237)( 94,240)( 95,239)( 96,238)
( 97,241)( 98,243)( 99,242)(100,245)(101,244)(102,246)(103,249)(104,248)
(105,247)(106,250)(107,252)(108,251)(109,254)(110,253)(111,255)(112,258)
(113,257)(114,256)(115,259)(116,261)(117,260)(118,263)(119,262)(120,264)
(121,267)(122,266)(123,265)(124,268)(125,270)(126,269)(127,272)(128,271)
(129,273)(130,276)(131,275)(132,274)(133,277)(134,279)(135,278)(136,281)
(137,280)(138,282)(139,285)(140,284)(141,283)(142,286)(143,288)(144,287)
(289,434)(290,433)(291,435)(292,438)(293,437)(294,436)(295,439)(296,441)
(297,440)(298,443)(299,442)(300,444)(301,447)(302,446)(303,445)(304,448)
(305,450)(306,449)(307,452)(308,451)(309,453)(310,456)(311,455)(312,454)
(313,457)(314,459)(315,458)(316,461)(317,460)(318,462)(319,465)(320,464)
(321,463)(322,466)(323,468)(324,467)(325,470)(326,469)(327,471)(328,474)
(329,473)(330,472)(331,475)(332,477)(333,476)(334,479)(335,478)(336,480)
(337,483)(338,482)(339,481)(340,484)(341,486)(342,485)(343,488)(344,487)
(345,489)(346,492)(347,491)(348,490)(349,493)(350,495)(351,494)(352,497)
(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)(360,503)
(361,506)(362,505)(363,507)(364,510)(365,509)(366,508)(367,511)(368,513)
(369,512)(370,515)(371,514)(372,516)(373,519)(374,518)(375,517)(376,520)
(377,522)(378,521)(379,524)(380,523)(381,525)(382,528)(383,527)(384,526)
(385,529)(386,531)(387,530)(388,533)(389,532)(390,534)(391,537)(392,536)
(393,535)(394,538)(395,540)(396,539)(397,542)(398,541)(399,543)(400,546)
(401,545)(402,544)(403,547)(404,549)(405,548)(406,551)(407,550)(408,552)
(409,555)(410,554)(411,553)(412,556)(413,558)(414,557)(415,560)(416,559)
(417,561)(418,564)(419,563)(420,562)(421,565)(422,567)(423,566)(424,569)
(425,568)(426,570)(427,573)(428,572)(429,571)(430,574)(431,576)(432,575);;
s2 := ( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)
( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)
( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)
( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 91)( 74, 96)
( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)( 81, 95)( 82,100)
( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)( 89,102)( 90,104)
(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)(115,133)(116,129)
(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)(123,137)(124,142)
(125,138)(126,140)(145,181)(146,186)(147,188)(148,184)(149,189)(150,182)
(151,187)(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)(158,198)
(159,191)(160,196)(161,192)(162,194)(163,208)(164,213)(165,215)(166,211)
(167,216)(168,209)(169,214)(170,210)(171,212)(172,199)(173,204)(174,206)
(175,202)(176,207)(177,200)(178,205)(179,201)(180,203)(217,271)(218,276)
(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)(225,275)(226,280)
(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)(233,282)(234,284)
(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)(241,259)(242,255)
(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)(249,263)(250,268)
(251,264)(252,266)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)
(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)
(303,371)(304,376)(305,372)(306,374)(307,388)(308,393)(309,395)(310,391)
(311,396)(312,389)(313,394)(314,390)(315,392)(316,379)(317,384)(318,386)
(319,382)(320,387)(321,380)(322,385)(323,381)(324,383)(325,397)(326,402)
(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)
(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)
(343,424)(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)(350,426)
(351,428)(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)(358,421)
(359,417)(360,419)(433,541)(434,546)(435,548)(436,544)(437,549)(438,542)
(439,547)(440,543)(441,545)(442,550)(443,555)(444,557)(445,553)(446,558)
(447,551)(448,556)(449,552)(450,554)(451,568)(452,573)(453,575)(454,571)
(455,576)(456,569)(457,574)(458,570)(459,572)(460,559)(461,564)(462,566)
(463,562)(464,567)(465,560)(466,565)(467,561)(468,563)(469,505)(470,510)
(471,512)(472,508)(473,513)(474,506)(475,511)(476,507)(477,509)(478,514)
(479,519)(480,521)(481,517)(482,522)(483,515)(484,520)(485,516)(486,518)
(487,532)(488,537)(489,539)(490,535)(491,540)(492,533)(493,538)(494,534)
(495,536)(496,523)(497,528)(498,530)(499,526)(500,531)(501,524)(502,529)
(503,525)(504,527);;
s3 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)
( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)
( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)
( 33,312)( 34,313)( 35,314)( 36,315)( 37,325)( 38,326)( 39,327)( 40,328)
( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)( 48,336)
( 49,337)( 50,338)( 51,339)( 52,340)( 53,341)( 54,342)( 55,352)( 56,353)
( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)
( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)
( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)( 80,386)
( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)( 88,394)
( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)( 96,366)
( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)(104,374)
(105,375)(106,376)(107,377)(108,378)(109,415)(110,416)(111,417)(112,418)
(113,419)(114,420)(115,421)(116,422)(117,423)(118,424)(119,425)(120,426)
(121,427)(122,428)(123,429)(124,430)(125,431)(126,432)(127,397)(128,398)
(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)
(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)(144,414)
(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)
(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)
(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)
(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)
(177,456)(178,457)(179,458)(180,459)(181,469)(182,470)(183,471)(184,472)
(185,473)(186,474)(187,475)(188,476)(189,477)(190,478)(191,479)(192,480)
(193,481)(194,482)(195,483)(196,484)(197,485)(198,486)(199,496)(200,497)
(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)
(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)
(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)(224,530)
(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)(232,538)
(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)(240,510)
(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)(248,518)
(249,519)(250,520)(251,521)(252,522)(253,559)(254,560)(255,561)(256,562)
(257,563)(258,564)(259,565)(260,566)(261,567)(262,568)(263,569)(264,570)
(265,571)(266,572)(267,573)(268,574)(269,575)(270,576)(271,541)(272,542)
(273,543)(274,544)(275,545)(276,546)(277,547)(278,548)(279,549)(280,550)
(281,551)(282,552)(283,553)(284,554)(285,555)(286,556)(287,557)(288,558);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*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*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1, 37)( 2, 39)( 3, 38)( 4, 43)( 5, 45)( 6, 44)( 7, 40)
( 8, 42)( 9, 41)( 10, 46)( 11, 48)( 12, 47)( 13, 52)( 14, 54)( 15, 53)
( 16, 49)( 17, 51)( 18, 50)( 19, 55)( 20, 57)( 21, 56)( 22, 61)( 23, 63)
( 24, 62)( 25, 58)( 26, 60)( 27, 59)( 28, 64)( 29, 66)( 30, 65)( 31, 70)
( 32, 72)( 33, 71)( 34, 67)( 35, 69)( 36, 68)( 73,109)( 74,111)( 75,110)
( 76,115)( 77,117)( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)
( 84,119)( 85,124)( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,127)
( 92,129)( 93,128)( 94,133)( 95,135)( 96,134)( 97,130)( 98,132)( 99,131)
(100,136)(101,138)(102,137)(103,142)(104,144)(105,143)(106,139)(107,141)
(108,140)(145,181)(146,183)(147,182)(148,187)(149,189)(150,188)(151,184)
(152,186)(153,185)(154,190)(155,192)(156,191)(157,196)(158,198)(159,197)
(160,193)(161,195)(162,194)(163,199)(164,201)(165,200)(166,205)(167,207)
(168,206)(169,202)(170,204)(171,203)(172,208)(173,210)(174,209)(175,214)
(176,216)(177,215)(178,211)(179,213)(180,212)(217,253)(218,255)(219,254)
(220,259)(221,261)(222,260)(223,256)(224,258)(225,257)(226,262)(227,264)
(228,263)(229,268)(230,270)(231,269)(232,265)(233,267)(234,266)(235,271)
(236,273)(237,272)(238,277)(239,279)(240,278)(241,274)(242,276)(243,275)
(244,280)(245,282)(246,281)(247,286)(248,288)(249,287)(250,283)(251,285)
(252,284)(289,325)(290,327)(291,326)(292,331)(293,333)(294,332)(295,328)
(296,330)(297,329)(298,334)(299,336)(300,335)(301,340)(302,342)(303,341)
(304,337)(305,339)(306,338)(307,343)(308,345)(309,344)(310,349)(311,351)
(312,350)(313,346)(314,348)(315,347)(316,352)(317,354)(318,353)(319,358)
(320,360)(321,359)(322,355)(323,357)(324,356)(361,397)(362,399)(363,398)
(364,403)(365,405)(366,404)(367,400)(368,402)(369,401)(370,406)(371,408)
(372,407)(373,412)(374,414)(375,413)(376,409)(377,411)(378,410)(379,415)
(380,417)(381,416)(382,421)(383,423)(384,422)(385,418)(386,420)(387,419)
(388,424)(389,426)(390,425)(391,430)(392,432)(393,431)(394,427)(395,429)
(396,428)(433,469)(434,471)(435,470)(436,475)(437,477)(438,476)(439,472)
(440,474)(441,473)(442,478)(443,480)(444,479)(445,484)(446,486)(447,485)
(448,481)(449,483)(450,482)(451,487)(452,489)(453,488)(454,493)(455,495)
(456,494)(457,490)(458,492)(459,491)(460,496)(461,498)(462,497)(463,502)
(464,504)(465,503)(466,499)(467,501)(468,500)(505,541)(506,543)(507,542)
(508,547)(509,549)(510,548)(511,544)(512,546)(513,545)(514,550)(515,552)
(516,551)(517,556)(518,558)(519,557)(520,553)(521,555)(522,554)(523,559)
(524,561)(525,560)(526,565)(527,567)(528,566)(529,562)(530,564)(531,563)
(532,568)(533,570)(534,569)(535,574)(536,576)(537,575)(538,571)(539,573)
(540,572);
s1 := Sym(576)!( 1,146)( 2,145)( 3,147)( 4,150)( 5,149)( 6,148)( 7,151)
( 8,153)( 9,152)( 10,155)( 11,154)( 12,156)( 13,159)( 14,158)( 15,157)
( 16,160)( 17,162)( 18,161)( 19,164)( 20,163)( 21,165)( 22,168)( 23,167)
( 24,166)( 25,169)( 26,171)( 27,170)( 28,173)( 29,172)( 30,174)( 31,177)
( 32,176)( 33,175)( 34,178)( 35,180)( 36,179)( 37,182)( 38,181)( 39,183)
( 40,186)( 41,185)( 42,184)( 43,187)( 44,189)( 45,188)( 46,191)( 47,190)
( 48,192)( 49,195)( 50,194)( 51,193)( 52,196)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,207)( 63,206)
( 64,209)( 65,208)( 66,210)( 67,213)( 68,212)( 69,211)( 70,214)( 71,216)
( 72,215)( 73,218)( 74,217)( 75,219)( 76,222)( 77,221)( 78,220)( 79,223)
( 80,225)( 81,224)( 82,227)( 83,226)( 84,228)( 85,231)( 86,230)( 87,229)
( 88,232)( 89,234)( 90,233)( 91,236)( 92,235)( 93,237)( 94,240)( 95,239)
( 96,238)( 97,241)( 98,243)( 99,242)(100,245)(101,244)(102,246)(103,249)
(104,248)(105,247)(106,250)(107,252)(108,251)(109,254)(110,253)(111,255)
(112,258)(113,257)(114,256)(115,259)(116,261)(117,260)(118,263)(119,262)
(120,264)(121,267)(122,266)(123,265)(124,268)(125,270)(126,269)(127,272)
(128,271)(129,273)(130,276)(131,275)(132,274)(133,277)(134,279)(135,278)
(136,281)(137,280)(138,282)(139,285)(140,284)(141,283)(142,286)(143,288)
(144,287)(289,434)(290,433)(291,435)(292,438)(293,437)(294,436)(295,439)
(296,441)(297,440)(298,443)(299,442)(300,444)(301,447)(302,446)(303,445)
(304,448)(305,450)(306,449)(307,452)(308,451)(309,453)(310,456)(311,455)
(312,454)(313,457)(314,459)(315,458)(316,461)(317,460)(318,462)(319,465)
(320,464)(321,463)(322,466)(323,468)(324,467)(325,470)(326,469)(327,471)
(328,474)(329,473)(330,472)(331,475)(332,477)(333,476)(334,479)(335,478)
(336,480)(337,483)(338,482)(339,481)(340,484)(341,486)(342,485)(343,488)
(344,487)(345,489)(346,492)(347,491)(348,490)(349,493)(350,495)(351,494)
(352,497)(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)
(360,503)(361,506)(362,505)(363,507)(364,510)(365,509)(366,508)(367,511)
(368,513)(369,512)(370,515)(371,514)(372,516)(373,519)(374,518)(375,517)
(376,520)(377,522)(378,521)(379,524)(380,523)(381,525)(382,528)(383,527)
(384,526)(385,529)(386,531)(387,530)(388,533)(389,532)(390,534)(391,537)
(392,536)(393,535)(394,538)(395,540)(396,539)(397,542)(398,541)(399,543)
(400,546)(401,545)(402,544)(403,547)(404,549)(405,548)(406,551)(407,550)
(408,552)(409,555)(410,554)(411,553)(412,556)(413,558)(414,557)(415,560)
(416,559)(417,561)(418,564)(419,563)(420,562)(421,565)(422,567)(423,566)
(424,569)(425,568)(426,570)(427,573)(428,572)(429,571)(430,574)(431,576)
(432,575);
s2 := Sym(576)!( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)
( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)
( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)
( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 91)
( 74, 96)( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)( 81, 95)
( 82,100)( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)( 89,102)
( 90,104)(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)(115,133)
(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)(123,137)
(124,142)(125,138)(126,140)(145,181)(146,186)(147,188)(148,184)(149,189)
(150,182)(151,187)(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)
(158,198)(159,191)(160,196)(161,192)(162,194)(163,208)(164,213)(165,215)
(166,211)(167,216)(168,209)(169,214)(170,210)(171,212)(172,199)(173,204)
(174,206)(175,202)(176,207)(177,200)(178,205)(179,201)(180,203)(217,271)
(218,276)(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)(225,275)
(226,280)(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)(233,282)
(234,284)(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)(241,259)
(242,255)(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)(249,263)
(250,268)(251,264)(252,266)(289,361)(290,366)(291,368)(292,364)(293,369)
(294,362)(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)
(302,378)(303,371)(304,376)(305,372)(306,374)(307,388)(308,393)(309,395)
(310,391)(311,396)(312,389)(313,394)(314,390)(315,392)(316,379)(317,384)
(318,386)(319,382)(320,387)(321,380)(322,385)(323,381)(324,383)(325,397)
(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)
(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)
(342,410)(343,424)(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)
(350,426)(351,428)(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)
(358,421)(359,417)(360,419)(433,541)(434,546)(435,548)(436,544)(437,549)
(438,542)(439,547)(440,543)(441,545)(442,550)(443,555)(444,557)(445,553)
(446,558)(447,551)(448,556)(449,552)(450,554)(451,568)(452,573)(453,575)
(454,571)(455,576)(456,569)(457,574)(458,570)(459,572)(460,559)(461,564)
(462,566)(463,562)(464,567)(465,560)(466,565)(467,561)(468,563)(469,505)
(470,510)(471,512)(472,508)(473,513)(474,506)(475,511)(476,507)(477,509)
(478,514)(479,519)(480,521)(481,517)(482,522)(483,515)(484,520)(485,516)
(486,518)(487,532)(488,537)(489,539)(490,535)(491,540)(492,533)(493,538)
(494,534)(495,536)(496,523)(497,528)(498,530)(499,526)(500,531)(501,524)
(502,529)(503,525)(504,527);
s3 := Sym(576)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)
( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)
( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)
( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 37,325)( 38,326)( 39,327)
( 40,328)( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)
( 48,336)( 49,337)( 50,338)( 51,339)( 52,340)( 53,341)( 54,342)( 55,352)
( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)
( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)
( 72,351)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)
( 80,386)( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)
( 88,394)( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)
( 96,366)( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)
(104,374)(105,375)(106,376)(107,377)(108,378)(109,415)(110,416)(111,417)
(112,418)(113,419)(114,420)(115,421)(116,422)(117,423)(118,424)(119,425)
(120,426)(121,427)(122,428)(123,429)(124,430)(125,431)(126,432)(127,397)
(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)
(136,406)(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)
(144,414)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)
(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)
(160,448)(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)
(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)
(176,455)(177,456)(178,457)(179,458)(180,459)(181,469)(182,470)(183,471)
(184,472)(185,473)(186,474)(187,475)(188,476)(189,477)(190,478)(191,479)
(192,480)(193,481)(194,482)(195,483)(196,484)(197,485)(198,486)(199,496)
(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)
(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)
(216,495)(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)
(224,530)(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)
(232,538)(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)
(240,510)(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)
(248,518)(249,519)(250,520)(251,521)(252,522)(253,559)(254,560)(255,561)
(256,562)(257,563)(258,564)(259,565)(260,566)(261,567)(262,568)(263,569)
(264,570)(265,571)(266,572)(267,573)(268,574)(269,575)(270,576)(271,541)
(272,542)(273,543)(274,544)(275,545)(276,546)(277,547)(278,548)(279,549)
(280,550)(281,551)(282,552)(283,553)(284,554)(285,555)(286,556)(287,557)
(288,558);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*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*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope