Polytope of Type {15,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,24}*1440
if this polytope has a name.
Group : SmallGroup(1440,4851)
Rank : 3
Schlafli Type : {15,24}
Number of vertices, edges, etc : 30, 360, 48
Order of s0s1s2 : 60
Order of s0s1s2s1 : 24
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {15,12}*720
3-fold quotients : {15,8}*480
5-fold quotients : {3,24}*288
6-fold quotients : {15,4}*240
8-fold quotients : {15,6}*180
10-fold quotients : {3,12}*144
12-fold quotients : {15,4}*120
15-fold quotients : {3,8}*96
24-fold quotients : {15,2}*60
30-fold quotients : {3,4}*48
40-fold quotients : {3,6}*36
60-fold quotients : {3,4}*24
72-fold quotients : {5,2}*20
120-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,361)( 2,362)( 3,364)( 4,363)( 5,367)( 6,368)( 7,365)( 8,366)
( 9,393)( 10,394)( 11,396)( 12,395)( 13,399)( 14,400)( 15,397)( 16,398)
( 17,385)( 18,386)( 19,388)( 20,387)( 21,391)( 22,392)( 23,389)( 24,390)
( 25,377)( 26,378)( 27,380)( 28,379)( 29,383)( 30,384)( 31,381)( 32,382)
( 33,369)( 34,370)( 35,372)( 36,371)( 37,375)( 38,376)( 39,373)( 40,374)
( 41,441)( 42,442)( 43,444)( 44,443)( 45,447)( 46,448)( 47,445)( 48,446)
( 49,473)( 50,474)( 51,476)( 52,475)( 53,479)( 54,480)( 55,477)( 56,478)
( 57,465)( 58,466)( 59,468)( 60,467)( 61,471)( 62,472)( 63,469)( 64,470)
( 65,457)( 66,458)( 67,460)( 68,459)( 69,463)( 70,464)( 71,461)( 72,462)
( 73,449)( 74,450)( 75,452)( 76,451)( 77,455)( 78,456)( 79,453)( 80,454)
( 81,401)( 82,402)( 83,404)( 84,403)( 85,407)( 86,408)( 87,405)( 88,406)
( 89,433)( 90,434)( 91,436)( 92,435)( 93,439)( 94,440)( 95,437)( 96,438)
( 97,425)( 98,426)( 99,428)(100,427)(101,431)(102,432)(103,429)(104,430)
(105,417)(106,418)(107,420)(108,419)(109,423)(110,424)(111,421)(112,422)
(113,409)(114,410)(115,412)(116,411)(117,415)(118,416)(119,413)(120,414)
(121,601)(122,602)(123,604)(124,603)(125,607)(126,608)(127,605)(128,606)
(129,633)(130,634)(131,636)(132,635)(133,639)(134,640)(135,637)(136,638)
(137,625)(138,626)(139,628)(140,627)(141,631)(142,632)(143,629)(144,630)
(145,617)(146,618)(147,620)(148,619)(149,623)(150,624)(151,621)(152,622)
(153,609)(154,610)(155,612)(156,611)(157,615)(158,616)(159,613)(160,614)
(161,681)(162,682)(163,684)(164,683)(165,687)(166,688)(167,685)(168,686)
(169,713)(170,714)(171,716)(172,715)(173,719)(174,720)(175,717)(176,718)
(177,705)(178,706)(179,708)(180,707)(181,711)(182,712)(183,709)(184,710)
(185,697)(186,698)(187,700)(188,699)(189,703)(190,704)(191,701)(192,702)
(193,689)(194,690)(195,692)(196,691)(197,695)(198,696)(199,693)(200,694)
(201,641)(202,642)(203,644)(204,643)(205,647)(206,648)(207,645)(208,646)
(209,673)(210,674)(211,676)(212,675)(213,679)(214,680)(215,677)(216,678)
(217,665)(218,666)(219,668)(220,667)(221,671)(222,672)(223,669)(224,670)
(225,657)(226,658)(227,660)(228,659)(229,663)(230,664)(231,661)(232,662)
(233,649)(234,650)(235,652)(236,651)(237,655)(238,656)(239,653)(240,654)
(241,481)(242,482)(243,484)(244,483)(245,487)(246,488)(247,485)(248,486)
(249,513)(250,514)(251,516)(252,515)(253,519)(254,520)(255,517)(256,518)
(257,505)(258,506)(259,508)(260,507)(261,511)(262,512)(263,509)(264,510)
(265,497)(266,498)(267,500)(268,499)(269,503)(270,504)(271,501)(272,502)
(273,489)(274,490)(275,492)(276,491)(277,495)(278,496)(279,493)(280,494)
(281,561)(282,562)(283,564)(284,563)(285,567)(286,568)(287,565)(288,566)
(289,593)(290,594)(291,596)(292,595)(293,599)(294,600)(295,597)(296,598)
(297,585)(298,586)(299,588)(300,587)(301,591)(302,592)(303,589)(304,590)
(305,577)(306,578)(307,580)(308,579)(309,583)(310,584)(311,581)(312,582)
(313,569)(314,570)(315,572)(316,571)(317,575)(318,576)(319,573)(320,574)
(321,521)(322,522)(323,524)(324,523)(325,527)(326,528)(327,525)(328,526)
(329,553)(330,554)(331,556)(332,555)(333,559)(334,560)(335,557)(336,558)
(337,545)(338,546)(339,548)(340,547)(341,551)(342,552)(343,549)(344,550)
(345,537)(346,538)(347,540)(348,539)(349,543)(350,544)(351,541)(352,542)
(353,529)(354,530)(355,532)(356,531)(357,535)(358,536)(359,533)(360,534);;
s1 := ( 1,529)( 2,530)( 3,535)( 4,536)( 5,534)( 6,533)( 7,531)( 8,532)
( 9,521)( 10,522)( 11,527)( 12,528)( 13,526)( 14,525)( 15,523)( 16,524)
( 17,553)( 18,554)( 19,559)( 20,560)( 21,558)( 22,557)( 23,555)( 24,556)
( 25,545)( 26,546)( 27,551)( 28,552)( 29,550)( 30,549)( 31,547)( 32,548)
( 33,537)( 34,538)( 35,543)( 36,544)( 37,542)( 38,541)( 39,539)( 40,540)
( 41,489)( 42,490)( 43,495)( 44,496)( 45,494)( 46,493)( 47,491)( 48,492)
( 49,481)( 50,482)( 51,487)( 52,488)( 53,486)( 54,485)( 55,483)( 56,484)
( 57,513)( 58,514)( 59,519)( 60,520)( 61,518)( 62,517)( 63,515)( 64,516)
( 65,505)( 66,506)( 67,511)( 68,512)( 69,510)( 70,509)( 71,507)( 72,508)
( 73,497)( 74,498)( 75,503)( 76,504)( 77,502)( 78,501)( 79,499)( 80,500)
( 81,569)( 82,570)( 83,575)( 84,576)( 85,574)( 86,573)( 87,571)( 88,572)
( 89,561)( 90,562)( 91,567)( 92,568)( 93,566)( 94,565)( 95,563)( 96,564)
( 97,593)( 98,594)( 99,599)(100,600)(101,598)(102,597)(103,595)(104,596)
(105,585)(106,586)(107,591)(108,592)(109,590)(110,589)(111,587)(112,588)
(113,577)(114,578)(115,583)(116,584)(117,582)(118,581)(119,579)(120,580)
(121,409)(122,410)(123,415)(124,416)(125,414)(126,413)(127,411)(128,412)
(129,401)(130,402)(131,407)(132,408)(133,406)(134,405)(135,403)(136,404)
(137,433)(138,434)(139,439)(140,440)(141,438)(142,437)(143,435)(144,436)
(145,425)(146,426)(147,431)(148,432)(149,430)(150,429)(151,427)(152,428)
(153,417)(154,418)(155,423)(156,424)(157,422)(158,421)(159,419)(160,420)
(161,369)(162,370)(163,375)(164,376)(165,374)(166,373)(167,371)(168,372)
(169,361)(170,362)(171,367)(172,368)(173,366)(174,365)(175,363)(176,364)
(177,393)(178,394)(179,399)(180,400)(181,398)(182,397)(183,395)(184,396)
(185,385)(186,386)(187,391)(188,392)(189,390)(190,389)(191,387)(192,388)
(193,377)(194,378)(195,383)(196,384)(197,382)(198,381)(199,379)(200,380)
(201,449)(202,450)(203,455)(204,456)(205,454)(206,453)(207,451)(208,452)
(209,441)(210,442)(211,447)(212,448)(213,446)(214,445)(215,443)(216,444)
(217,473)(218,474)(219,479)(220,480)(221,478)(222,477)(223,475)(224,476)
(225,465)(226,466)(227,471)(228,472)(229,470)(230,469)(231,467)(232,468)
(233,457)(234,458)(235,463)(236,464)(237,462)(238,461)(239,459)(240,460)
(241,649)(242,650)(243,655)(244,656)(245,654)(246,653)(247,651)(248,652)
(249,641)(250,642)(251,647)(252,648)(253,646)(254,645)(255,643)(256,644)
(257,673)(258,674)(259,679)(260,680)(261,678)(262,677)(263,675)(264,676)
(265,665)(266,666)(267,671)(268,672)(269,670)(270,669)(271,667)(272,668)
(273,657)(274,658)(275,663)(276,664)(277,662)(278,661)(279,659)(280,660)
(281,609)(282,610)(283,615)(284,616)(285,614)(286,613)(287,611)(288,612)
(289,601)(290,602)(291,607)(292,608)(293,606)(294,605)(295,603)(296,604)
(297,633)(298,634)(299,639)(300,640)(301,638)(302,637)(303,635)(304,636)
(305,625)(306,626)(307,631)(308,632)(309,630)(310,629)(311,627)(312,628)
(313,617)(314,618)(315,623)(316,624)(317,622)(318,621)(319,619)(320,620)
(321,689)(322,690)(323,695)(324,696)(325,694)(326,693)(327,691)(328,692)
(329,681)(330,682)(331,687)(332,688)(333,686)(334,685)(335,683)(336,684)
(337,713)(338,714)(339,719)(340,720)(341,718)(342,717)(343,715)(344,716)
(345,705)(346,706)(347,711)(348,712)(349,710)(350,709)(351,707)(352,708)
(353,697)(354,698)(355,703)(356,704)(357,702)(358,701)(359,699)(360,700);;
s2 := ( 1,363)( 2,364)( 3,362)( 4,361)( 5,367)( 6,368)( 7,366)( 8,365)
( 9,371)( 10,372)( 11,370)( 12,369)( 13,375)( 14,376)( 15,374)( 16,373)
( 17,379)( 18,380)( 19,378)( 20,377)( 21,383)( 22,384)( 23,382)( 24,381)
( 25,387)( 26,388)( 27,386)( 28,385)( 29,391)( 30,392)( 31,390)( 32,389)
( 33,395)( 34,396)( 35,394)( 36,393)( 37,399)( 38,400)( 39,398)( 40,397)
( 41,443)( 42,444)( 43,442)( 44,441)( 45,447)( 46,448)( 47,446)( 48,445)
( 49,451)( 50,452)( 51,450)( 52,449)( 53,455)( 54,456)( 55,454)( 56,453)
( 57,459)( 58,460)( 59,458)( 60,457)( 61,463)( 62,464)( 63,462)( 64,461)
( 65,467)( 66,468)( 67,466)( 68,465)( 69,471)( 70,472)( 71,470)( 72,469)
( 73,475)( 74,476)( 75,474)( 76,473)( 77,479)( 78,480)( 79,478)( 80,477)
( 81,403)( 82,404)( 83,402)( 84,401)( 85,407)( 86,408)( 87,406)( 88,405)
( 89,411)( 90,412)( 91,410)( 92,409)( 93,415)( 94,416)( 95,414)( 96,413)
( 97,419)( 98,420)( 99,418)(100,417)(101,423)(102,424)(103,422)(104,421)
(105,427)(106,428)(107,426)(108,425)(109,431)(110,432)(111,430)(112,429)
(113,435)(114,436)(115,434)(116,433)(117,439)(118,440)(119,438)(120,437)
(121,483)(122,484)(123,482)(124,481)(125,487)(126,488)(127,486)(128,485)
(129,491)(130,492)(131,490)(132,489)(133,495)(134,496)(135,494)(136,493)
(137,499)(138,500)(139,498)(140,497)(141,503)(142,504)(143,502)(144,501)
(145,507)(146,508)(147,506)(148,505)(149,511)(150,512)(151,510)(152,509)
(153,515)(154,516)(155,514)(156,513)(157,519)(158,520)(159,518)(160,517)
(161,563)(162,564)(163,562)(164,561)(165,567)(166,568)(167,566)(168,565)
(169,571)(170,572)(171,570)(172,569)(173,575)(174,576)(175,574)(176,573)
(177,579)(178,580)(179,578)(180,577)(181,583)(182,584)(183,582)(184,581)
(185,587)(186,588)(187,586)(188,585)(189,591)(190,592)(191,590)(192,589)
(193,595)(194,596)(195,594)(196,593)(197,599)(198,600)(199,598)(200,597)
(201,523)(202,524)(203,522)(204,521)(205,527)(206,528)(207,526)(208,525)
(209,531)(210,532)(211,530)(212,529)(213,535)(214,536)(215,534)(216,533)
(217,539)(218,540)(219,538)(220,537)(221,543)(222,544)(223,542)(224,541)
(225,547)(226,548)(227,546)(228,545)(229,551)(230,552)(231,550)(232,549)
(233,555)(234,556)(235,554)(236,553)(237,559)(238,560)(239,558)(240,557)
(241,603)(242,604)(243,602)(244,601)(245,607)(246,608)(247,606)(248,605)
(249,611)(250,612)(251,610)(252,609)(253,615)(254,616)(255,614)(256,613)
(257,619)(258,620)(259,618)(260,617)(261,623)(262,624)(263,622)(264,621)
(265,627)(266,628)(267,626)(268,625)(269,631)(270,632)(271,630)(272,629)
(273,635)(274,636)(275,634)(276,633)(277,639)(278,640)(279,638)(280,637)
(281,683)(282,684)(283,682)(284,681)(285,687)(286,688)(287,686)(288,685)
(289,691)(290,692)(291,690)(292,689)(293,695)(294,696)(295,694)(296,693)
(297,699)(298,700)(299,698)(300,697)(301,703)(302,704)(303,702)(304,701)
(305,707)(306,708)(307,706)(308,705)(309,711)(310,712)(311,710)(312,709)
(313,715)(314,716)(315,714)(316,713)(317,719)(318,720)(319,718)(320,717)
(321,643)(322,644)(323,642)(324,641)(325,647)(326,648)(327,646)(328,645)
(329,651)(330,652)(331,650)(332,649)(333,655)(334,656)(335,654)(336,653)
(337,659)(338,660)(339,658)(340,657)(341,663)(342,664)(343,662)(344,661)
(345,667)(346,668)(347,666)(348,665)(349,671)(350,672)(351,670)(352,669)
(353,675)(354,676)(355,674)(356,673)(357,679)(358,680)(359,678)(360,677);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(720)!( 1,361)( 2,362)( 3,364)( 4,363)( 5,367)( 6,368)( 7,365)
( 8,366)( 9,393)( 10,394)( 11,396)( 12,395)( 13,399)( 14,400)( 15,397)
( 16,398)( 17,385)( 18,386)( 19,388)( 20,387)( 21,391)( 22,392)( 23,389)
( 24,390)( 25,377)( 26,378)( 27,380)( 28,379)( 29,383)( 30,384)( 31,381)
( 32,382)( 33,369)( 34,370)( 35,372)( 36,371)( 37,375)( 38,376)( 39,373)
( 40,374)( 41,441)( 42,442)( 43,444)( 44,443)( 45,447)( 46,448)( 47,445)
( 48,446)( 49,473)( 50,474)( 51,476)( 52,475)( 53,479)( 54,480)( 55,477)
( 56,478)( 57,465)( 58,466)( 59,468)( 60,467)( 61,471)( 62,472)( 63,469)
( 64,470)( 65,457)( 66,458)( 67,460)( 68,459)( 69,463)( 70,464)( 71,461)
( 72,462)( 73,449)( 74,450)( 75,452)( 76,451)( 77,455)( 78,456)( 79,453)
( 80,454)( 81,401)( 82,402)( 83,404)( 84,403)( 85,407)( 86,408)( 87,405)
( 88,406)( 89,433)( 90,434)( 91,436)( 92,435)( 93,439)( 94,440)( 95,437)
( 96,438)( 97,425)( 98,426)( 99,428)(100,427)(101,431)(102,432)(103,429)
(104,430)(105,417)(106,418)(107,420)(108,419)(109,423)(110,424)(111,421)
(112,422)(113,409)(114,410)(115,412)(116,411)(117,415)(118,416)(119,413)
(120,414)(121,601)(122,602)(123,604)(124,603)(125,607)(126,608)(127,605)
(128,606)(129,633)(130,634)(131,636)(132,635)(133,639)(134,640)(135,637)
(136,638)(137,625)(138,626)(139,628)(140,627)(141,631)(142,632)(143,629)
(144,630)(145,617)(146,618)(147,620)(148,619)(149,623)(150,624)(151,621)
(152,622)(153,609)(154,610)(155,612)(156,611)(157,615)(158,616)(159,613)
(160,614)(161,681)(162,682)(163,684)(164,683)(165,687)(166,688)(167,685)
(168,686)(169,713)(170,714)(171,716)(172,715)(173,719)(174,720)(175,717)
(176,718)(177,705)(178,706)(179,708)(180,707)(181,711)(182,712)(183,709)
(184,710)(185,697)(186,698)(187,700)(188,699)(189,703)(190,704)(191,701)
(192,702)(193,689)(194,690)(195,692)(196,691)(197,695)(198,696)(199,693)
(200,694)(201,641)(202,642)(203,644)(204,643)(205,647)(206,648)(207,645)
(208,646)(209,673)(210,674)(211,676)(212,675)(213,679)(214,680)(215,677)
(216,678)(217,665)(218,666)(219,668)(220,667)(221,671)(222,672)(223,669)
(224,670)(225,657)(226,658)(227,660)(228,659)(229,663)(230,664)(231,661)
(232,662)(233,649)(234,650)(235,652)(236,651)(237,655)(238,656)(239,653)
(240,654)(241,481)(242,482)(243,484)(244,483)(245,487)(246,488)(247,485)
(248,486)(249,513)(250,514)(251,516)(252,515)(253,519)(254,520)(255,517)
(256,518)(257,505)(258,506)(259,508)(260,507)(261,511)(262,512)(263,509)
(264,510)(265,497)(266,498)(267,500)(268,499)(269,503)(270,504)(271,501)
(272,502)(273,489)(274,490)(275,492)(276,491)(277,495)(278,496)(279,493)
(280,494)(281,561)(282,562)(283,564)(284,563)(285,567)(286,568)(287,565)
(288,566)(289,593)(290,594)(291,596)(292,595)(293,599)(294,600)(295,597)
(296,598)(297,585)(298,586)(299,588)(300,587)(301,591)(302,592)(303,589)
(304,590)(305,577)(306,578)(307,580)(308,579)(309,583)(310,584)(311,581)
(312,582)(313,569)(314,570)(315,572)(316,571)(317,575)(318,576)(319,573)
(320,574)(321,521)(322,522)(323,524)(324,523)(325,527)(326,528)(327,525)
(328,526)(329,553)(330,554)(331,556)(332,555)(333,559)(334,560)(335,557)
(336,558)(337,545)(338,546)(339,548)(340,547)(341,551)(342,552)(343,549)
(344,550)(345,537)(346,538)(347,540)(348,539)(349,543)(350,544)(351,541)
(352,542)(353,529)(354,530)(355,532)(356,531)(357,535)(358,536)(359,533)
(360,534);
s1 := Sym(720)!( 1,529)( 2,530)( 3,535)( 4,536)( 5,534)( 6,533)( 7,531)
( 8,532)( 9,521)( 10,522)( 11,527)( 12,528)( 13,526)( 14,525)( 15,523)
( 16,524)( 17,553)( 18,554)( 19,559)( 20,560)( 21,558)( 22,557)( 23,555)
( 24,556)( 25,545)( 26,546)( 27,551)( 28,552)( 29,550)( 30,549)( 31,547)
( 32,548)( 33,537)( 34,538)( 35,543)( 36,544)( 37,542)( 38,541)( 39,539)
( 40,540)( 41,489)( 42,490)( 43,495)( 44,496)( 45,494)( 46,493)( 47,491)
( 48,492)( 49,481)( 50,482)( 51,487)( 52,488)( 53,486)( 54,485)( 55,483)
( 56,484)( 57,513)( 58,514)( 59,519)( 60,520)( 61,518)( 62,517)( 63,515)
( 64,516)( 65,505)( 66,506)( 67,511)( 68,512)( 69,510)( 70,509)( 71,507)
( 72,508)( 73,497)( 74,498)( 75,503)( 76,504)( 77,502)( 78,501)( 79,499)
( 80,500)( 81,569)( 82,570)( 83,575)( 84,576)( 85,574)( 86,573)( 87,571)
( 88,572)( 89,561)( 90,562)( 91,567)( 92,568)( 93,566)( 94,565)( 95,563)
( 96,564)( 97,593)( 98,594)( 99,599)(100,600)(101,598)(102,597)(103,595)
(104,596)(105,585)(106,586)(107,591)(108,592)(109,590)(110,589)(111,587)
(112,588)(113,577)(114,578)(115,583)(116,584)(117,582)(118,581)(119,579)
(120,580)(121,409)(122,410)(123,415)(124,416)(125,414)(126,413)(127,411)
(128,412)(129,401)(130,402)(131,407)(132,408)(133,406)(134,405)(135,403)
(136,404)(137,433)(138,434)(139,439)(140,440)(141,438)(142,437)(143,435)
(144,436)(145,425)(146,426)(147,431)(148,432)(149,430)(150,429)(151,427)
(152,428)(153,417)(154,418)(155,423)(156,424)(157,422)(158,421)(159,419)
(160,420)(161,369)(162,370)(163,375)(164,376)(165,374)(166,373)(167,371)
(168,372)(169,361)(170,362)(171,367)(172,368)(173,366)(174,365)(175,363)
(176,364)(177,393)(178,394)(179,399)(180,400)(181,398)(182,397)(183,395)
(184,396)(185,385)(186,386)(187,391)(188,392)(189,390)(190,389)(191,387)
(192,388)(193,377)(194,378)(195,383)(196,384)(197,382)(198,381)(199,379)
(200,380)(201,449)(202,450)(203,455)(204,456)(205,454)(206,453)(207,451)
(208,452)(209,441)(210,442)(211,447)(212,448)(213,446)(214,445)(215,443)
(216,444)(217,473)(218,474)(219,479)(220,480)(221,478)(222,477)(223,475)
(224,476)(225,465)(226,466)(227,471)(228,472)(229,470)(230,469)(231,467)
(232,468)(233,457)(234,458)(235,463)(236,464)(237,462)(238,461)(239,459)
(240,460)(241,649)(242,650)(243,655)(244,656)(245,654)(246,653)(247,651)
(248,652)(249,641)(250,642)(251,647)(252,648)(253,646)(254,645)(255,643)
(256,644)(257,673)(258,674)(259,679)(260,680)(261,678)(262,677)(263,675)
(264,676)(265,665)(266,666)(267,671)(268,672)(269,670)(270,669)(271,667)
(272,668)(273,657)(274,658)(275,663)(276,664)(277,662)(278,661)(279,659)
(280,660)(281,609)(282,610)(283,615)(284,616)(285,614)(286,613)(287,611)
(288,612)(289,601)(290,602)(291,607)(292,608)(293,606)(294,605)(295,603)
(296,604)(297,633)(298,634)(299,639)(300,640)(301,638)(302,637)(303,635)
(304,636)(305,625)(306,626)(307,631)(308,632)(309,630)(310,629)(311,627)
(312,628)(313,617)(314,618)(315,623)(316,624)(317,622)(318,621)(319,619)
(320,620)(321,689)(322,690)(323,695)(324,696)(325,694)(326,693)(327,691)
(328,692)(329,681)(330,682)(331,687)(332,688)(333,686)(334,685)(335,683)
(336,684)(337,713)(338,714)(339,719)(340,720)(341,718)(342,717)(343,715)
(344,716)(345,705)(346,706)(347,711)(348,712)(349,710)(350,709)(351,707)
(352,708)(353,697)(354,698)(355,703)(356,704)(357,702)(358,701)(359,699)
(360,700);
s2 := Sym(720)!( 1,363)( 2,364)( 3,362)( 4,361)( 5,367)( 6,368)( 7,366)
( 8,365)( 9,371)( 10,372)( 11,370)( 12,369)( 13,375)( 14,376)( 15,374)
( 16,373)( 17,379)( 18,380)( 19,378)( 20,377)( 21,383)( 22,384)( 23,382)
( 24,381)( 25,387)( 26,388)( 27,386)( 28,385)( 29,391)( 30,392)( 31,390)
( 32,389)( 33,395)( 34,396)( 35,394)( 36,393)( 37,399)( 38,400)( 39,398)
( 40,397)( 41,443)( 42,444)( 43,442)( 44,441)( 45,447)( 46,448)( 47,446)
( 48,445)( 49,451)( 50,452)( 51,450)( 52,449)( 53,455)( 54,456)( 55,454)
( 56,453)( 57,459)( 58,460)( 59,458)( 60,457)( 61,463)( 62,464)( 63,462)
( 64,461)( 65,467)( 66,468)( 67,466)( 68,465)( 69,471)( 70,472)( 71,470)
( 72,469)( 73,475)( 74,476)( 75,474)( 76,473)( 77,479)( 78,480)( 79,478)
( 80,477)( 81,403)( 82,404)( 83,402)( 84,401)( 85,407)( 86,408)( 87,406)
( 88,405)( 89,411)( 90,412)( 91,410)( 92,409)( 93,415)( 94,416)( 95,414)
( 96,413)( 97,419)( 98,420)( 99,418)(100,417)(101,423)(102,424)(103,422)
(104,421)(105,427)(106,428)(107,426)(108,425)(109,431)(110,432)(111,430)
(112,429)(113,435)(114,436)(115,434)(116,433)(117,439)(118,440)(119,438)
(120,437)(121,483)(122,484)(123,482)(124,481)(125,487)(126,488)(127,486)
(128,485)(129,491)(130,492)(131,490)(132,489)(133,495)(134,496)(135,494)
(136,493)(137,499)(138,500)(139,498)(140,497)(141,503)(142,504)(143,502)
(144,501)(145,507)(146,508)(147,506)(148,505)(149,511)(150,512)(151,510)
(152,509)(153,515)(154,516)(155,514)(156,513)(157,519)(158,520)(159,518)
(160,517)(161,563)(162,564)(163,562)(164,561)(165,567)(166,568)(167,566)
(168,565)(169,571)(170,572)(171,570)(172,569)(173,575)(174,576)(175,574)
(176,573)(177,579)(178,580)(179,578)(180,577)(181,583)(182,584)(183,582)
(184,581)(185,587)(186,588)(187,586)(188,585)(189,591)(190,592)(191,590)
(192,589)(193,595)(194,596)(195,594)(196,593)(197,599)(198,600)(199,598)
(200,597)(201,523)(202,524)(203,522)(204,521)(205,527)(206,528)(207,526)
(208,525)(209,531)(210,532)(211,530)(212,529)(213,535)(214,536)(215,534)
(216,533)(217,539)(218,540)(219,538)(220,537)(221,543)(222,544)(223,542)
(224,541)(225,547)(226,548)(227,546)(228,545)(229,551)(230,552)(231,550)
(232,549)(233,555)(234,556)(235,554)(236,553)(237,559)(238,560)(239,558)
(240,557)(241,603)(242,604)(243,602)(244,601)(245,607)(246,608)(247,606)
(248,605)(249,611)(250,612)(251,610)(252,609)(253,615)(254,616)(255,614)
(256,613)(257,619)(258,620)(259,618)(260,617)(261,623)(262,624)(263,622)
(264,621)(265,627)(266,628)(267,626)(268,625)(269,631)(270,632)(271,630)
(272,629)(273,635)(274,636)(275,634)(276,633)(277,639)(278,640)(279,638)
(280,637)(281,683)(282,684)(283,682)(284,681)(285,687)(286,688)(287,686)
(288,685)(289,691)(290,692)(291,690)(292,689)(293,695)(294,696)(295,694)
(296,693)(297,699)(298,700)(299,698)(300,697)(301,703)(302,704)(303,702)
(304,701)(305,707)(306,708)(307,706)(308,705)(309,711)(310,712)(311,710)
(312,709)(313,715)(314,716)(315,714)(316,713)(317,719)(318,720)(319,718)
(320,717)(321,643)(322,644)(323,642)(324,641)(325,647)(326,648)(327,646)
(328,645)(329,651)(330,652)(331,650)(332,649)(333,655)(334,656)(335,654)
(336,653)(337,659)(338,660)(339,658)(340,657)(341,663)(342,664)(343,662)
(344,661)(345,667)(346,668)(347,666)(348,665)(349,671)(350,672)(351,670)
(352,669)(353,675)(354,676)(355,674)(356,673)(357,679)(358,680)(359,678)
(360,677);
poly := sub<Sym(720)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*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 >;
References : None.
to this polytope