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