Polytope of Type {40,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6,3}*1440
if this polytope has a name.
Group : SmallGroup(1440,1992)
Rank : 4
Schlafli Type : {40,6,3}
Number of vertices, edges, etc : 40, 120, 9, 3
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {20,6,3}*720
3-fold quotients : {40,2,3}*480
4-fold quotients : {10,6,3}*360
5-fold quotients : {8,6,3}*288
6-fold quotients : {20,2,3}*240
10-fold quotients : {4,6,3}*144
12-fold quotients : {10,2,3}*120
15-fold quotients : {8,2,3}*96
20-fold quotients : {2,6,3}*72
24-fold quotients : {5,2,3}*60
30-fold quotients : {4,2,3}*48
60-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 91,136)( 92,140)( 93,139)( 94,138)
( 95,137)( 96,141)( 97,145)( 98,144)( 99,143)(100,142)(101,146)(102,150)
(103,149)(104,148)(105,147)(106,151)(107,155)(108,154)(109,153)(110,152)
(111,156)(112,160)(113,159)(114,158)(115,157)(116,161)(117,165)(118,164)
(119,163)(120,162)(121,166)(122,170)(123,169)(124,168)(125,167)(126,171)
(127,175)(128,174)(129,173)(130,172)(131,176)(132,180)(133,179)(134,178)
(135,177)(181,316)(182,320)(183,319)(184,318)(185,317)(186,321)(187,325)
(188,324)(189,323)(190,322)(191,326)(192,330)(193,329)(194,328)(195,327)
(196,331)(197,335)(198,334)(199,333)(200,332)(201,336)(202,340)(203,339)
(204,338)(205,337)(206,341)(207,345)(208,344)(209,343)(210,342)(211,346)
(212,350)(213,349)(214,348)(215,347)(216,351)(217,355)(218,354)(219,353)
(220,352)(221,356)(222,360)(223,359)(224,358)(225,357)(226,271)(227,275)
(228,274)(229,273)(230,272)(231,276)(232,280)(233,279)(234,278)(235,277)
(236,281)(237,285)(238,284)(239,283)(240,282)(241,286)(242,290)(243,289)
(244,288)(245,287)(246,291)(247,295)(248,294)(249,293)(250,292)(251,296)
(252,300)(253,299)(254,298)(255,297)(256,301)(257,305)(258,304)(259,303)
(260,302)(261,306)(262,310)(263,309)(264,308)(265,307)(266,311)(267,315)
(268,314)(269,313)(270,312)(361,451)(362,455)(363,454)(364,453)(365,452)
(366,456)(367,460)(368,459)(369,458)(370,457)(371,461)(372,465)(373,464)
(374,463)(375,462)(376,466)(377,470)(378,469)(379,468)(380,467)(381,471)
(382,475)(383,474)(384,473)(385,472)(386,476)(387,480)(388,479)(389,478)
(390,477)(391,481)(392,485)(393,484)(394,483)(395,482)(396,486)(397,490)
(398,489)(399,488)(400,487)(401,491)(402,495)(403,494)(404,493)(405,492)
(406,496)(407,500)(408,499)(409,498)(410,497)(411,501)(412,505)(413,504)
(414,503)(415,502)(416,506)(417,510)(418,509)(419,508)(420,507)(421,511)
(422,515)(423,514)(424,513)(425,512)(426,516)(427,520)(428,519)(429,518)
(430,517)(431,521)(432,525)(433,524)(434,523)(435,522)(436,526)(437,530)
(438,529)(439,528)(440,527)(441,531)(442,535)(443,534)(444,533)(445,532)
(446,536)(447,540)(448,539)(449,538)(450,537)(542,545)(543,544)(547,550)
(548,549)(552,555)(553,554)(557,560)(558,559)(562,565)(563,564)(567,570)
(568,569)(572,575)(573,574)(577,580)(578,579)(582,585)(583,584)(587,590)
(588,589)(592,595)(593,594)(597,600)(598,599)(602,605)(603,604)(607,610)
(608,609)(612,615)(613,614)(617,620)(618,619)(622,625)(623,624)(627,630)
(628,629)(631,676)(632,680)(633,679)(634,678)(635,677)(636,681)(637,685)
(638,684)(639,683)(640,682)(641,686)(642,690)(643,689)(644,688)(645,687)
(646,691)(647,695)(648,694)(649,693)(650,692)(651,696)(652,700)(653,699)
(654,698)(655,697)(656,701)(657,705)(658,704)(659,703)(660,702)(661,706)
(662,710)(663,709)(664,708)(665,707)(666,711)(667,715)(668,714)(669,713)
(670,712)(671,716)(672,720)(673,719)(674,718)(675,717);;
s1 := ( 1,362)( 2,361)( 3,365)( 4,364)( 5,363)( 6,367)( 7,366)( 8,370)
( 9,369)( 10,368)( 11,372)( 12,371)( 13,375)( 14,374)( 15,373)( 16,392)
( 17,391)( 18,395)( 19,394)( 20,393)( 21,397)( 22,396)( 23,400)( 24,399)
( 25,398)( 26,402)( 27,401)( 28,405)( 29,404)( 30,403)( 31,377)( 32,376)
( 33,380)( 34,379)( 35,378)( 36,382)( 37,381)( 38,385)( 39,384)( 40,383)
( 41,387)( 42,386)( 43,390)( 44,389)( 45,388)( 46,407)( 47,406)( 48,410)
( 49,409)( 50,408)( 51,412)( 52,411)( 53,415)( 54,414)( 55,413)( 56,417)
( 57,416)( 58,420)( 59,419)( 60,418)( 61,437)( 62,436)( 63,440)( 64,439)
( 65,438)( 66,442)( 67,441)( 68,445)( 69,444)( 70,443)( 71,447)( 72,446)
( 73,450)( 74,449)( 75,448)( 76,422)( 77,421)( 78,425)( 79,424)( 80,423)
( 81,427)( 82,426)( 83,430)( 84,429)( 85,428)( 86,432)( 87,431)( 88,435)
( 89,434)( 90,433)( 91,497)( 92,496)( 93,500)( 94,499)( 95,498)( 96,502)
( 97,501)( 98,505)( 99,504)(100,503)(101,507)(102,506)(103,510)(104,509)
(105,508)(106,527)(107,526)(108,530)(109,529)(110,528)(111,532)(112,531)
(113,535)(114,534)(115,533)(116,537)(117,536)(118,540)(119,539)(120,538)
(121,512)(122,511)(123,515)(124,514)(125,513)(126,517)(127,516)(128,520)
(129,519)(130,518)(131,522)(132,521)(133,525)(134,524)(135,523)(136,452)
(137,451)(138,455)(139,454)(140,453)(141,457)(142,456)(143,460)(144,459)
(145,458)(146,462)(147,461)(148,465)(149,464)(150,463)(151,482)(152,481)
(153,485)(154,484)(155,483)(156,487)(157,486)(158,490)(159,489)(160,488)
(161,492)(162,491)(163,495)(164,494)(165,493)(166,467)(167,466)(168,470)
(169,469)(170,468)(171,472)(172,471)(173,475)(174,474)(175,473)(176,477)
(177,476)(178,480)(179,479)(180,478)(181,677)(182,676)(183,680)(184,679)
(185,678)(186,682)(187,681)(188,685)(189,684)(190,683)(191,687)(192,686)
(193,690)(194,689)(195,688)(196,707)(197,706)(198,710)(199,709)(200,708)
(201,712)(202,711)(203,715)(204,714)(205,713)(206,717)(207,716)(208,720)
(209,719)(210,718)(211,692)(212,691)(213,695)(214,694)(215,693)(216,697)
(217,696)(218,700)(219,699)(220,698)(221,702)(222,701)(223,705)(224,704)
(225,703)(226,632)(227,631)(228,635)(229,634)(230,633)(231,637)(232,636)
(233,640)(234,639)(235,638)(236,642)(237,641)(238,645)(239,644)(240,643)
(241,662)(242,661)(243,665)(244,664)(245,663)(246,667)(247,666)(248,670)
(249,669)(250,668)(251,672)(252,671)(253,675)(254,674)(255,673)(256,647)
(257,646)(258,650)(259,649)(260,648)(261,652)(262,651)(263,655)(264,654)
(265,653)(266,657)(267,656)(268,660)(269,659)(270,658)(271,587)(272,586)
(273,590)(274,589)(275,588)(276,592)(277,591)(278,595)(279,594)(280,593)
(281,597)(282,596)(283,600)(284,599)(285,598)(286,617)(287,616)(288,620)
(289,619)(290,618)(291,622)(292,621)(293,625)(294,624)(295,623)(296,627)
(297,626)(298,630)(299,629)(300,628)(301,602)(302,601)(303,605)(304,604)
(305,603)(306,607)(307,606)(308,610)(309,609)(310,608)(311,612)(312,611)
(313,615)(314,614)(315,613)(316,542)(317,541)(318,545)(319,544)(320,543)
(321,547)(322,546)(323,550)(324,549)(325,548)(326,552)(327,551)(328,555)
(329,554)(330,553)(331,572)(332,571)(333,575)(334,574)(335,573)(336,577)
(337,576)(338,580)(339,579)(340,578)(341,582)(342,581)(343,585)(344,584)
(345,583)(346,557)(347,556)(348,560)(349,559)(350,558)(351,562)(352,561)
(353,565)(354,564)(355,563)(356,567)(357,566)(358,570)(359,569)(360,568);;
s2 := ( 1,556)( 2,557)( 3,558)( 4,559)( 5,560)( 6,566)( 7,567)( 8,568)
( 9,569)( 10,570)( 11,561)( 12,562)( 13,563)( 14,564)( 15,565)( 16,541)
( 17,542)( 18,543)( 19,544)( 20,545)( 21,551)( 22,552)( 23,553)( 24,554)
( 25,555)( 26,546)( 27,547)( 28,548)( 29,549)( 30,550)( 31,571)( 32,572)
( 33,573)( 34,574)( 35,575)( 36,581)( 37,582)( 38,583)( 39,584)( 40,585)
( 41,576)( 42,577)( 43,578)( 44,579)( 45,580)( 46,601)( 47,602)( 48,603)
( 49,604)( 50,605)( 51,611)( 52,612)( 53,613)( 54,614)( 55,615)( 56,606)
( 57,607)( 58,608)( 59,609)( 60,610)( 61,586)( 62,587)( 63,588)( 64,589)
( 65,590)( 66,596)( 67,597)( 68,598)( 69,599)( 70,600)( 71,591)( 72,592)
( 73,593)( 74,594)( 75,595)( 76,616)( 77,617)( 78,618)( 79,619)( 80,620)
( 81,626)( 82,627)( 83,628)( 84,629)( 85,630)( 86,621)( 87,622)( 88,623)
( 89,624)( 90,625)( 91,646)( 92,647)( 93,648)( 94,649)( 95,650)( 96,656)
( 97,657)( 98,658)( 99,659)(100,660)(101,651)(102,652)(103,653)(104,654)
(105,655)(106,631)(107,632)(108,633)(109,634)(110,635)(111,641)(112,642)
(113,643)(114,644)(115,645)(116,636)(117,637)(118,638)(119,639)(120,640)
(121,661)(122,662)(123,663)(124,664)(125,665)(126,671)(127,672)(128,673)
(129,674)(130,675)(131,666)(132,667)(133,668)(134,669)(135,670)(136,691)
(137,692)(138,693)(139,694)(140,695)(141,701)(142,702)(143,703)(144,704)
(145,705)(146,696)(147,697)(148,698)(149,699)(150,700)(151,676)(152,677)
(153,678)(154,679)(155,680)(156,686)(157,687)(158,688)(159,689)(160,690)
(161,681)(162,682)(163,683)(164,684)(165,685)(166,706)(167,707)(168,708)
(169,709)(170,710)(171,716)(172,717)(173,718)(174,719)(175,720)(176,711)
(177,712)(178,713)(179,714)(180,715)(181,466)(182,467)(183,468)(184,469)
(185,470)(186,476)(187,477)(188,478)(189,479)(190,480)(191,471)(192,472)
(193,473)(194,474)(195,475)(196,451)(197,452)(198,453)(199,454)(200,455)
(201,461)(202,462)(203,463)(204,464)(205,465)(206,456)(207,457)(208,458)
(209,459)(210,460)(211,481)(212,482)(213,483)(214,484)(215,485)(216,491)
(217,492)(218,493)(219,494)(220,495)(221,486)(222,487)(223,488)(224,489)
(225,490)(226,511)(227,512)(228,513)(229,514)(230,515)(231,521)(232,522)
(233,523)(234,524)(235,525)(236,516)(237,517)(238,518)(239,519)(240,520)
(241,496)(242,497)(243,498)(244,499)(245,500)(246,506)(247,507)(248,508)
(249,509)(250,510)(251,501)(252,502)(253,503)(254,504)(255,505)(256,526)
(257,527)(258,528)(259,529)(260,530)(261,536)(262,537)(263,538)(264,539)
(265,540)(266,531)(267,532)(268,533)(269,534)(270,535)(271,421)(272,422)
(273,423)(274,424)(275,425)(276,431)(277,432)(278,433)(279,434)(280,435)
(281,426)(282,427)(283,428)(284,429)(285,430)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)(296,411)
(297,412)(298,413)(299,414)(300,415)(301,436)(302,437)(303,438)(304,439)
(305,440)(306,446)(307,447)(308,448)(309,449)(310,450)(311,441)(312,442)
(313,443)(314,444)(315,445)(316,376)(317,377)(318,378)(319,379)(320,380)
(321,386)(322,387)(323,388)(324,389)(325,390)(326,381)(327,382)(328,383)
(329,384)(330,385)(331,361)(332,362)(333,363)(334,364)(335,365)(336,371)
(337,372)(338,373)(339,374)(340,375)(341,366)(342,367)(343,368)(344,369)
(345,370)(346,391)(347,392)(348,393)(349,394)(350,395)(351,401)(352,402)
(353,403)(354,404)(355,405)(356,396)(357,397)(358,398)(359,399)(360,400);;
s3 := ( 1,546)( 2,547)( 3,548)( 4,549)( 5,550)( 6,541)( 7,542)( 8,543)
( 9,544)( 10,545)( 11,551)( 12,552)( 13,553)( 14,554)( 15,555)( 16,576)
( 17,577)( 18,578)( 19,579)( 20,580)( 21,571)( 22,572)( 23,573)( 24,574)
( 25,575)( 26,581)( 27,582)( 28,583)( 29,584)( 30,585)( 31,561)( 32,562)
( 33,563)( 34,564)( 35,565)( 36,556)( 37,557)( 38,558)( 39,559)( 40,560)
( 41,566)( 42,567)( 43,568)( 44,569)( 45,570)( 46,591)( 47,592)( 48,593)
( 49,594)( 50,595)( 51,586)( 52,587)( 53,588)( 54,589)( 55,590)( 56,596)
( 57,597)( 58,598)( 59,599)( 60,600)( 61,621)( 62,622)( 63,623)( 64,624)
( 65,625)( 66,616)( 67,617)( 68,618)( 69,619)( 70,620)( 71,626)( 72,627)
( 73,628)( 74,629)( 75,630)( 76,606)( 77,607)( 78,608)( 79,609)( 80,610)
( 81,601)( 82,602)( 83,603)( 84,604)( 85,605)( 86,611)( 87,612)( 88,613)
( 89,614)( 90,615)( 91,636)( 92,637)( 93,638)( 94,639)( 95,640)( 96,631)
( 97,632)( 98,633)( 99,634)(100,635)(101,641)(102,642)(103,643)(104,644)
(105,645)(106,666)(107,667)(108,668)(109,669)(110,670)(111,661)(112,662)
(113,663)(114,664)(115,665)(116,671)(117,672)(118,673)(119,674)(120,675)
(121,651)(122,652)(123,653)(124,654)(125,655)(126,646)(127,647)(128,648)
(129,649)(130,650)(131,656)(132,657)(133,658)(134,659)(135,660)(136,681)
(137,682)(138,683)(139,684)(140,685)(141,676)(142,677)(143,678)(144,679)
(145,680)(146,686)(147,687)(148,688)(149,689)(150,690)(151,711)(152,712)
(153,713)(154,714)(155,715)(156,706)(157,707)(158,708)(159,709)(160,710)
(161,716)(162,717)(163,718)(164,719)(165,720)(166,696)(167,697)(168,698)
(169,699)(170,700)(171,691)(172,692)(173,693)(174,694)(175,695)(176,701)
(177,702)(178,703)(179,704)(180,705)(181,456)(182,457)(183,458)(184,459)
(185,460)(186,451)(187,452)(188,453)(189,454)(190,455)(191,461)(192,462)
(193,463)(194,464)(195,465)(196,486)(197,487)(198,488)(199,489)(200,490)
(201,481)(202,482)(203,483)(204,484)(205,485)(206,491)(207,492)(208,493)
(209,494)(210,495)(211,471)(212,472)(213,473)(214,474)(215,475)(216,466)
(217,467)(218,468)(219,469)(220,470)(221,476)(222,477)(223,478)(224,479)
(225,480)(226,501)(227,502)(228,503)(229,504)(230,505)(231,496)(232,497)
(233,498)(234,499)(235,500)(236,506)(237,507)(238,508)(239,509)(240,510)
(241,531)(242,532)(243,533)(244,534)(245,535)(246,526)(247,527)(248,528)
(249,529)(250,530)(251,536)(252,537)(253,538)(254,539)(255,540)(256,516)
(257,517)(258,518)(259,519)(260,520)(261,511)(262,512)(263,513)(264,514)
(265,515)(266,521)(267,522)(268,523)(269,524)(270,525)(271,411)(272,412)
(273,413)(274,414)(275,415)(276,406)(277,407)(278,408)(279,409)(280,410)
(281,416)(282,417)(283,418)(284,419)(285,420)(286,441)(287,442)(288,443)
(289,444)(290,445)(291,436)(292,437)(293,438)(294,439)(295,440)(296,446)
(297,447)(298,448)(299,449)(300,450)(301,426)(302,427)(303,428)(304,429)
(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)(312,432)
(313,433)(314,434)(315,435)(316,366)(317,367)(318,368)(319,369)(320,370)
(321,361)(322,362)(323,363)(324,364)(325,365)(326,371)(327,372)(328,373)
(329,374)(330,375)(331,396)(332,397)(333,398)(334,399)(335,400)(336,391)
(337,392)(338,393)(339,394)(340,395)(341,401)(342,402)(343,403)(344,404)
(345,405)(346,381)(347,382)(348,383)(349,384)(350,385)(351,376)(352,377)
(353,378)(354,379)(355,380)(356,386)(357,387)(358,388)(359,389)(360,390);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(720)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 91,136)( 92,140)( 93,139)
( 94,138)( 95,137)( 96,141)( 97,145)( 98,144)( 99,143)(100,142)(101,146)
(102,150)(103,149)(104,148)(105,147)(106,151)(107,155)(108,154)(109,153)
(110,152)(111,156)(112,160)(113,159)(114,158)(115,157)(116,161)(117,165)
(118,164)(119,163)(120,162)(121,166)(122,170)(123,169)(124,168)(125,167)
(126,171)(127,175)(128,174)(129,173)(130,172)(131,176)(132,180)(133,179)
(134,178)(135,177)(181,316)(182,320)(183,319)(184,318)(185,317)(186,321)
(187,325)(188,324)(189,323)(190,322)(191,326)(192,330)(193,329)(194,328)
(195,327)(196,331)(197,335)(198,334)(199,333)(200,332)(201,336)(202,340)
(203,339)(204,338)(205,337)(206,341)(207,345)(208,344)(209,343)(210,342)
(211,346)(212,350)(213,349)(214,348)(215,347)(216,351)(217,355)(218,354)
(219,353)(220,352)(221,356)(222,360)(223,359)(224,358)(225,357)(226,271)
(227,275)(228,274)(229,273)(230,272)(231,276)(232,280)(233,279)(234,278)
(235,277)(236,281)(237,285)(238,284)(239,283)(240,282)(241,286)(242,290)
(243,289)(244,288)(245,287)(246,291)(247,295)(248,294)(249,293)(250,292)
(251,296)(252,300)(253,299)(254,298)(255,297)(256,301)(257,305)(258,304)
(259,303)(260,302)(261,306)(262,310)(263,309)(264,308)(265,307)(266,311)
(267,315)(268,314)(269,313)(270,312)(361,451)(362,455)(363,454)(364,453)
(365,452)(366,456)(367,460)(368,459)(369,458)(370,457)(371,461)(372,465)
(373,464)(374,463)(375,462)(376,466)(377,470)(378,469)(379,468)(380,467)
(381,471)(382,475)(383,474)(384,473)(385,472)(386,476)(387,480)(388,479)
(389,478)(390,477)(391,481)(392,485)(393,484)(394,483)(395,482)(396,486)
(397,490)(398,489)(399,488)(400,487)(401,491)(402,495)(403,494)(404,493)
(405,492)(406,496)(407,500)(408,499)(409,498)(410,497)(411,501)(412,505)
(413,504)(414,503)(415,502)(416,506)(417,510)(418,509)(419,508)(420,507)
(421,511)(422,515)(423,514)(424,513)(425,512)(426,516)(427,520)(428,519)
(429,518)(430,517)(431,521)(432,525)(433,524)(434,523)(435,522)(436,526)
(437,530)(438,529)(439,528)(440,527)(441,531)(442,535)(443,534)(444,533)
(445,532)(446,536)(447,540)(448,539)(449,538)(450,537)(542,545)(543,544)
(547,550)(548,549)(552,555)(553,554)(557,560)(558,559)(562,565)(563,564)
(567,570)(568,569)(572,575)(573,574)(577,580)(578,579)(582,585)(583,584)
(587,590)(588,589)(592,595)(593,594)(597,600)(598,599)(602,605)(603,604)
(607,610)(608,609)(612,615)(613,614)(617,620)(618,619)(622,625)(623,624)
(627,630)(628,629)(631,676)(632,680)(633,679)(634,678)(635,677)(636,681)
(637,685)(638,684)(639,683)(640,682)(641,686)(642,690)(643,689)(644,688)
(645,687)(646,691)(647,695)(648,694)(649,693)(650,692)(651,696)(652,700)
(653,699)(654,698)(655,697)(656,701)(657,705)(658,704)(659,703)(660,702)
(661,706)(662,710)(663,709)(664,708)(665,707)(666,711)(667,715)(668,714)
(669,713)(670,712)(671,716)(672,720)(673,719)(674,718)(675,717);
s1 := Sym(720)!( 1,362)( 2,361)( 3,365)( 4,364)( 5,363)( 6,367)( 7,366)
( 8,370)( 9,369)( 10,368)( 11,372)( 12,371)( 13,375)( 14,374)( 15,373)
( 16,392)( 17,391)( 18,395)( 19,394)( 20,393)( 21,397)( 22,396)( 23,400)
( 24,399)( 25,398)( 26,402)( 27,401)( 28,405)( 29,404)( 30,403)( 31,377)
( 32,376)( 33,380)( 34,379)( 35,378)( 36,382)( 37,381)( 38,385)( 39,384)
( 40,383)( 41,387)( 42,386)( 43,390)( 44,389)( 45,388)( 46,407)( 47,406)
( 48,410)( 49,409)( 50,408)( 51,412)( 52,411)( 53,415)( 54,414)( 55,413)
( 56,417)( 57,416)( 58,420)( 59,419)( 60,418)( 61,437)( 62,436)( 63,440)
( 64,439)( 65,438)( 66,442)( 67,441)( 68,445)( 69,444)( 70,443)( 71,447)
( 72,446)( 73,450)( 74,449)( 75,448)( 76,422)( 77,421)( 78,425)( 79,424)
( 80,423)( 81,427)( 82,426)( 83,430)( 84,429)( 85,428)( 86,432)( 87,431)
( 88,435)( 89,434)( 90,433)( 91,497)( 92,496)( 93,500)( 94,499)( 95,498)
( 96,502)( 97,501)( 98,505)( 99,504)(100,503)(101,507)(102,506)(103,510)
(104,509)(105,508)(106,527)(107,526)(108,530)(109,529)(110,528)(111,532)
(112,531)(113,535)(114,534)(115,533)(116,537)(117,536)(118,540)(119,539)
(120,538)(121,512)(122,511)(123,515)(124,514)(125,513)(126,517)(127,516)
(128,520)(129,519)(130,518)(131,522)(132,521)(133,525)(134,524)(135,523)
(136,452)(137,451)(138,455)(139,454)(140,453)(141,457)(142,456)(143,460)
(144,459)(145,458)(146,462)(147,461)(148,465)(149,464)(150,463)(151,482)
(152,481)(153,485)(154,484)(155,483)(156,487)(157,486)(158,490)(159,489)
(160,488)(161,492)(162,491)(163,495)(164,494)(165,493)(166,467)(167,466)
(168,470)(169,469)(170,468)(171,472)(172,471)(173,475)(174,474)(175,473)
(176,477)(177,476)(178,480)(179,479)(180,478)(181,677)(182,676)(183,680)
(184,679)(185,678)(186,682)(187,681)(188,685)(189,684)(190,683)(191,687)
(192,686)(193,690)(194,689)(195,688)(196,707)(197,706)(198,710)(199,709)
(200,708)(201,712)(202,711)(203,715)(204,714)(205,713)(206,717)(207,716)
(208,720)(209,719)(210,718)(211,692)(212,691)(213,695)(214,694)(215,693)
(216,697)(217,696)(218,700)(219,699)(220,698)(221,702)(222,701)(223,705)
(224,704)(225,703)(226,632)(227,631)(228,635)(229,634)(230,633)(231,637)
(232,636)(233,640)(234,639)(235,638)(236,642)(237,641)(238,645)(239,644)
(240,643)(241,662)(242,661)(243,665)(244,664)(245,663)(246,667)(247,666)
(248,670)(249,669)(250,668)(251,672)(252,671)(253,675)(254,674)(255,673)
(256,647)(257,646)(258,650)(259,649)(260,648)(261,652)(262,651)(263,655)
(264,654)(265,653)(266,657)(267,656)(268,660)(269,659)(270,658)(271,587)
(272,586)(273,590)(274,589)(275,588)(276,592)(277,591)(278,595)(279,594)
(280,593)(281,597)(282,596)(283,600)(284,599)(285,598)(286,617)(287,616)
(288,620)(289,619)(290,618)(291,622)(292,621)(293,625)(294,624)(295,623)
(296,627)(297,626)(298,630)(299,629)(300,628)(301,602)(302,601)(303,605)
(304,604)(305,603)(306,607)(307,606)(308,610)(309,609)(310,608)(311,612)
(312,611)(313,615)(314,614)(315,613)(316,542)(317,541)(318,545)(319,544)
(320,543)(321,547)(322,546)(323,550)(324,549)(325,548)(326,552)(327,551)
(328,555)(329,554)(330,553)(331,572)(332,571)(333,575)(334,574)(335,573)
(336,577)(337,576)(338,580)(339,579)(340,578)(341,582)(342,581)(343,585)
(344,584)(345,583)(346,557)(347,556)(348,560)(349,559)(350,558)(351,562)
(352,561)(353,565)(354,564)(355,563)(356,567)(357,566)(358,570)(359,569)
(360,568);
s2 := Sym(720)!( 1,556)( 2,557)( 3,558)( 4,559)( 5,560)( 6,566)( 7,567)
( 8,568)( 9,569)( 10,570)( 11,561)( 12,562)( 13,563)( 14,564)( 15,565)
( 16,541)( 17,542)( 18,543)( 19,544)( 20,545)( 21,551)( 22,552)( 23,553)
( 24,554)( 25,555)( 26,546)( 27,547)( 28,548)( 29,549)( 30,550)( 31,571)
( 32,572)( 33,573)( 34,574)( 35,575)( 36,581)( 37,582)( 38,583)( 39,584)
( 40,585)( 41,576)( 42,577)( 43,578)( 44,579)( 45,580)( 46,601)( 47,602)
( 48,603)( 49,604)( 50,605)( 51,611)( 52,612)( 53,613)( 54,614)( 55,615)
( 56,606)( 57,607)( 58,608)( 59,609)( 60,610)( 61,586)( 62,587)( 63,588)
( 64,589)( 65,590)( 66,596)( 67,597)( 68,598)( 69,599)( 70,600)( 71,591)
( 72,592)( 73,593)( 74,594)( 75,595)( 76,616)( 77,617)( 78,618)( 79,619)
( 80,620)( 81,626)( 82,627)( 83,628)( 84,629)( 85,630)( 86,621)( 87,622)
( 88,623)( 89,624)( 90,625)( 91,646)( 92,647)( 93,648)( 94,649)( 95,650)
( 96,656)( 97,657)( 98,658)( 99,659)(100,660)(101,651)(102,652)(103,653)
(104,654)(105,655)(106,631)(107,632)(108,633)(109,634)(110,635)(111,641)
(112,642)(113,643)(114,644)(115,645)(116,636)(117,637)(118,638)(119,639)
(120,640)(121,661)(122,662)(123,663)(124,664)(125,665)(126,671)(127,672)
(128,673)(129,674)(130,675)(131,666)(132,667)(133,668)(134,669)(135,670)
(136,691)(137,692)(138,693)(139,694)(140,695)(141,701)(142,702)(143,703)
(144,704)(145,705)(146,696)(147,697)(148,698)(149,699)(150,700)(151,676)
(152,677)(153,678)(154,679)(155,680)(156,686)(157,687)(158,688)(159,689)
(160,690)(161,681)(162,682)(163,683)(164,684)(165,685)(166,706)(167,707)
(168,708)(169,709)(170,710)(171,716)(172,717)(173,718)(174,719)(175,720)
(176,711)(177,712)(178,713)(179,714)(180,715)(181,466)(182,467)(183,468)
(184,469)(185,470)(186,476)(187,477)(188,478)(189,479)(190,480)(191,471)
(192,472)(193,473)(194,474)(195,475)(196,451)(197,452)(198,453)(199,454)
(200,455)(201,461)(202,462)(203,463)(204,464)(205,465)(206,456)(207,457)
(208,458)(209,459)(210,460)(211,481)(212,482)(213,483)(214,484)(215,485)
(216,491)(217,492)(218,493)(219,494)(220,495)(221,486)(222,487)(223,488)
(224,489)(225,490)(226,511)(227,512)(228,513)(229,514)(230,515)(231,521)
(232,522)(233,523)(234,524)(235,525)(236,516)(237,517)(238,518)(239,519)
(240,520)(241,496)(242,497)(243,498)(244,499)(245,500)(246,506)(247,507)
(248,508)(249,509)(250,510)(251,501)(252,502)(253,503)(254,504)(255,505)
(256,526)(257,527)(258,528)(259,529)(260,530)(261,536)(262,537)(263,538)
(264,539)(265,540)(266,531)(267,532)(268,533)(269,534)(270,535)(271,421)
(272,422)(273,423)(274,424)(275,425)(276,431)(277,432)(278,433)(279,434)
(280,435)(281,426)(282,427)(283,428)(284,429)(285,430)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)
(296,411)(297,412)(298,413)(299,414)(300,415)(301,436)(302,437)(303,438)
(304,439)(305,440)(306,446)(307,447)(308,448)(309,449)(310,450)(311,441)
(312,442)(313,443)(314,444)(315,445)(316,376)(317,377)(318,378)(319,379)
(320,380)(321,386)(322,387)(323,388)(324,389)(325,390)(326,381)(327,382)
(328,383)(329,384)(330,385)(331,361)(332,362)(333,363)(334,364)(335,365)
(336,371)(337,372)(338,373)(339,374)(340,375)(341,366)(342,367)(343,368)
(344,369)(345,370)(346,391)(347,392)(348,393)(349,394)(350,395)(351,401)
(352,402)(353,403)(354,404)(355,405)(356,396)(357,397)(358,398)(359,399)
(360,400);
s3 := Sym(720)!( 1,546)( 2,547)( 3,548)( 4,549)( 5,550)( 6,541)( 7,542)
( 8,543)( 9,544)( 10,545)( 11,551)( 12,552)( 13,553)( 14,554)( 15,555)
( 16,576)( 17,577)( 18,578)( 19,579)( 20,580)( 21,571)( 22,572)( 23,573)
( 24,574)( 25,575)( 26,581)( 27,582)( 28,583)( 29,584)( 30,585)( 31,561)
( 32,562)( 33,563)( 34,564)( 35,565)( 36,556)( 37,557)( 38,558)( 39,559)
( 40,560)( 41,566)( 42,567)( 43,568)( 44,569)( 45,570)( 46,591)( 47,592)
( 48,593)( 49,594)( 50,595)( 51,586)( 52,587)( 53,588)( 54,589)( 55,590)
( 56,596)( 57,597)( 58,598)( 59,599)( 60,600)( 61,621)( 62,622)( 63,623)
( 64,624)( 65,625)( 66,616)( 67,617)( 68,618)( 69,619)( 70,620)( 71,626)
( 72,627)( 73,628)( 74,629)( 75,630)( 76,606)( 77,607)( 78,608)( 79,609)
( 80,610)( 81,601)( 82,602)( 83,603)( 84,604)( 85,605)( 86,611)( 87,612)
( 88,613)( 89,614)( 90,615)( 91,636)( 92,637)( 93,638)( 94,639)( 95,640)
( 96,631)( 97,632)( 98,633)( 99,634)(100,635)(101,641)(102,642)(103,643)
(104,644)(105,645)(106,666)(107,667)(108,668)(109,669)(110,670)(111,661)
(112,662)(113,663)(114,664)(115,665)(116,671)(117,672)(118,673)(119,674)
(120,675)(121,651)(122,652)(123,653)(124,654)(125,655)(126,646)(127,647)
(128,648)(129,649)(130,650)(131,656)(132,657)(133,658)(134,659)(135,660)
(136,681)(137,682)(138,683)(139,684)(140,685)(141,676)(142,677)(143,678)
(144,679)(145,680)(146,686)(147,687)(148,688)(149,689)(150,690)(151,711)
(152,712)(153,713)(154,714)(155,715)(156,706)(157,707)(158,708)(159,709)
(160,710)(161,716)(162,717)(163,718)(164,719)(165,720)(166,696)(167,697)
(168,698)(169,699)(170,700)(171,691)(172,692)(173,693)(174,694)(175,695)
(176,701)(177,702)(178,703)(179,704)(180,705)(181,456)(182,457)(183,458)
(184,459)(185,460)(186,451)(187,452)(188,453)(189,454)(190,455)(191,461)
(192,462)(193,463)(194,464)(195,465)(196,486)(197,487)(198,488)(199,489)
(200,490)(201,481)(202,482)(203,483)(204,484)(205,485)(206,491)(207,492)
(208,493)(209,494)(210,495)(211,471)(212,472)(213,473)(214,474)(215,475)
(216,466)(217,467)(218,468)(219,469)(220,470)(221,476)(222,477)(223,478)
(224,479)(225,480)(226,501)(227,502)(228,503)(229,504)(230,505)(231,496)
(232,497)(233,498)(234,499)(235,500)(236,506)(237,507)(238,508)(239,509)
(240,510)(241,531)(242,532)(243,533)(244,534)(245,535)(246,526)(247,527)
(248,528)(249,529)(250,530)(251,536)(252,537)(253,538)(254,539)(255,540)
(256,516)(257,517)(258,518)(259,519)(260,520)(261,511)(262,512)(263,513)
(264,514)(265,515)(266,521)(267,522)(268,523)(269,524)(270,525)(271,411)
(272,412)(273,413)(274,414)(275,415)(276,406)(277,407)(278,408)(279,409)
(280,410)(281,416)(282,417)(283,418)(284,419)(285,420)(286,441)(287,442)
(288,443)(289,444)(290,445)(291,436)(292,437)(293,438)(294,439)(295,440)
(296,446)(297,447)(298,448)(299,449)(300,450)(301,426)(302,427)(303,428)
(304,429)(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)
(312,432)(313,433)(314,434)(315,435)(316,366)(317,367)(318,368)(319,369)
(320,370)(321,361)(322,362)(323,363)(324,364)(325,365)(326,371)(327,372)
(328,373)(329,374)(330,375)(331,396)(332,397)(333,398)(334,399)(335,400)
(336,391)(337,392)(338,393)(339,394)(340,395)(341,401)(342,402)(343,403)
(344,404)(345,405)(346,381)(347,382)(348,383)(349,384)(350,385)(351,376)
(352,377)(353,378)(354,379)(355,380)(356,386)(357,387)(358,388)(359,389)
(360,390);
poly := sub<Sym(720)|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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*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*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 >;
References : None.
to this polytope