Polytope of Type {120,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,6}*1440a
if this polytope has a name.
Group : SmallGroup(1440,1992)
Rank : 3
Schlafli Type : {120,6}
Number of vertices, edges, etc : 120, 360, 6
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,6}*720a
   3-fold quotients : {40,6}*480
   4-fold quotients : {30,6}*360a
   5-fold quotients : {24,6}*288c
   6-fold quotients : {20,6}*240a
   9-fold quotients : {40,2}*160
   10-fold quotients : {12,6}*144c
   12-fold quotients : {10,6}*120
   15-fold quotients : {8,6}*96
   18-fold quotients : {20,2}*80
   20-fold quotients : {6,6}*72b
   30-fold quotients : {4,6}*48a
   36-fold quotients : {10,2}*40
   40-fold quotients : {6,3}*36
   45-fold quotients : {8,2}*32
   60-fold quotients : {2,6}*24
   72-fold quotients : {5,2}*20
   90-fold quotients : {4,2}*16
   120-fold quotients : {2,3}*12
   180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,361)(  2,365)(  3,364)(  4,363)(  5,362)(  6,366)(  7,370)(  8,369)
(  9,368)( 10,367)( 11,371)( 12,375)( 13,374)( 14,373)( 15,372)( 16,391)
( 17,395)( 18,394)( 19,393)( 20,392)( 21,396)( 22,400)( 23,399)( 24,398)
( 25,397)( 26,401)( 27,405)( 28,404)( 29,403)( 30,402)( 31,376)( 32,380)
( 33,379)( 34,378)( 35,377)( 36,381)( 37,385)( 38,384)( 39,383)( 40,382)
( 41,386)( 42,390)( 43,389)( 44,388)( 45,387)( 46,406)( 47,410)( 48,409)
( 49,408)( 50,407)( 51,411)( 52,415)( 53,414)( 54,413)( 55,412)( 56,416)
( 57,420)( 58,419)( 59,418)( 60,417)( 61,436)( 62,440)( 63,439)( 64,438)
( 65,437)( 66,441)( 67,445)( 68,444)( 69,443)( 70,442)( 71,446)( 72,450)
( 73,449)( 74,448)( 75,447)( 76,421)( 77,425)( 78,424)( 79,423)( 80,422)
( 81,426)( 82,430)( 83,429)( 84,428)( 85,427)( 86,431)( 87,435)( 88,434)
( 89,433)( 90,432)( 91,496)( 92,500)( 93,499)( 94,498)( 95,497)( 96,501)
( 97,505)( 98,504)( 99,503)(100,502)(101,506)(102,510)(103,509)(104,508)
(105,507)(106,526)(107,530)(108,529)(109,528)(110,527)(111,531)(112,535)
(113,534)(114,533)(115,532)(116,536)(117,540)(118,539)(119,538)(120,537)
(121,511)(122,515)(123,514)(124,513)(125,512)(126,516)(127,520)(128,519)
(129,518)(130,517)(131,521)(132,525)(133,524)(134,523)(135,522)(136,451)
(137,455)(138,454)(139,453)(140,452)(141,456)(142,460)(143,459)(144,458)
(145,457)(146,461)(147,465)(148,464)(149,463)(150,462)(151,481)(152,485)
(153,484)(154,483)(155,482)(156,486)(157,490)(158,489)(159,488)(160,487)
(161,491)(162,495)(163,494)(164,493)(165,492)(166,466)(167,470)(168,469)
(169,468)(170,467)(171,471)(172,475)(173,474)(174,473)(175,472)(176,476)
(177,480)(178,479)(179,478)(180,477)(181,676)(182,680)(183,679)(184,678)
(185,677)(186,681)(187,685)(188,684)(189,683)(190,682)(191,686)(192,690)
(193,689)(194,688)(195,687)(196,706)(197,710)(198,709)(199,708)(200,707)
(201,711)(202,715)(203,714)(204,713)(205,712)(206,716)(207,720)(208,719)
(209,718)(210,717)(211,691)(212,695)(213,694)(214,693)(215,692)(216,696)
(217,700)(218,699)(219,698)(220,697)(221,701)(222,705)(223,704)(224,703)
(225,702)(226,631)(227,635)(228,634)(229,633)(230,632)(231,636)(232,640)
(233,639)(234,638)(235,637)(236,641)(237,645)(238,644)(239,643)(240,642)
(241,661)(242,665)(243,664)(244,663)(245,662)(246,666)(247,670)(248,669)
(249,668)(250,667)(251,671)(252,675)(253,674)(254,673)(255,672)(256,646)
(257,650)(258,649)(259,648)(260,647)(261,651)(262,655)(263,654)(264,653)
(265,652)(266,656)(267,660)(268,659)(269,658)(270,657)(271,586)(272,590)
(273,589)(274,588)(275,587)(276,591)(277,595)(278,594)(279,593)(280,592)
(281,596)(282,600)(283,599)(284,598)(285,597)(286,616)(287,620)(288,619)
(289,618)(290,617)(291,621)(292,625)(293,624)(294,623)(295,622)(296,626)
(297,630)(298,629)(299,628)(300,627)(301,601)(302,605)(303,604)(304,603)
(305,602)(306,606)(307,610)(308,609)(309,608)(310,607)(311,611)(312,615)
(313,614)(314,613)(315,612)(316,541)(317,545)(318,544)(319,543)(320,542)
(321,546)(322,550)(323,549)(324,548)(325,547)(326,551)(327,555)(328,554)
(329,553)(330,552)(331,571)(332,575)(333,574)(334,573)(335,572)(336,576)
(337,580)(338,579)(339,578)(340,577)(341,581)(342,585)(343,584)(344,583)
(345,582)(346,556)(347,560)(348,559)(349,558)(350,557)(351,561)(352,565)
(353,564)(354,563)(355,562)(356,566)(357,570)(358,569)(359,568)(360,567);;
s1 := (  1,557)(  2,556)(  3,560)(  4,559)(  5,558)(  6,567)(  7,566)(  8,570)
(  9,569)( 10,568)( 11,562)( 12,561)( 13,565)( 14,564)( 15,563)( 16,542)
( 17,541)( 18,545)( 19,544)( 20,543)( 21,552)( 22,551)( 23,555)( 24,554)
( 25,553)( 26,547)( 27,546)( 28,550)( 29,549)( 30,548)( 31,572)( 32,571)
( 33,575)( 34,574)( 35,573)( 36,582)( 37,581)( 38,585)( 39,584)( 40,583)
( 41,577)( 42,576)( 43,580)( 44,579)( 45,578)( 46,602)( 47,601)( 48,605)
( 49,604)( 50,603)( 51,612)( 52,611)( 53,615)( 54,614)( 55,613)( 56,607)
( 57,606)( 58,610)( 59,609)( 60,608)( 61,587)( 62,586)( 63,590)( 64,589)
( 65,588)( 66,597)( 67,596)( 68,600)( 69,599)( 70,598)( 71,592)( 72,591)
( 73,595)( 74,594)( 75,593)( 76,617)( 77,616)( 78,620)( 79,619)( 80,618)
( 81,627)( 82,626)( 83,630)( 84,629)( 85,628)( 86,622)( 87,621)( 88,625)
( 89,624)( 90,623)( 91,692)( 92,691)( 93,695)( 94,694)( 95,693)( 96,702)
( 97,701)( 98,705)( 99,704)(100,703)(101,697)(102,696)(103,700)(104,699)
(105,698)(106,677)(107,676)(108,680)(109,679)(110,678)(111,687)(112,686)
(113,690)(114,689)(115,688)(116,682)(117,681)(118,685)(119,684)(120,683)
(121,707)(122,706)(123,710)(124,709)(125,708)(126,717)(127,716)(128,720)
(129,719)(130,718)(131,712)(132,711)(133,715)(134,714)(135,713)(136,647)
(137,646)(138,650)(139,649)(140,648)(141,657)(142,656)(143,660)(144,659)
(145,658)(146,652)(147,651)(148,655)(149,654)(150,653)(151,632)(152,631)
(153,635)(154,634)(155,633)(156,642)(157,641)(158,645)(159,644)(160,643)
(161,637)(162,636)(163,640)(164,639)(165,638)(166,662)(167,661)(168,665)
(169,664)(170,663)(171,672)(172,671)(173,675)(174,674)(175,673)(176,667)
(177,666)(178,670)(179,669)(180,668)(181,377)(182,376)(183,380)(184,379)
(185,378)(186,387)(187,386)(188,390)(189,389)(190,388)(191,382)(192,381)
(193,385)(194,384)(195,383)(196,362)(197,361)(198,365)(199,364)(200,363)
(201,372)(202,371)(203,375)(204,374)(205,373)(206,367)(207,366)(208,370)
(209,369)(210,368)(211,392)(212,391)(213,395)(214,394)(215,393)(216,402)
(217,401)(218,405)(219,404)(220,403)(221,397)(222,396)(223,400)(224,399)
(225,398)(226,422)(227,421)(228,425)(229,424)(230,423)(231,432)(232,431)
(233,435)(234,434)(235,433)(236,427)(237,426)(238,430)(239,429)(240,428)
(241,407)(242,406)(243,410)(244,409)(245,408)(246,417)(247,416)(248,420)
(249,419)(250,418)(251,412)(252,411)(253,415)(254,414)(255,413)(256,437)
(257,436)(258,440)(259,439)(260,438)(261,447)(262,446)(263,450)(264,449)
(265,448)(266,442)(267,441)(268,445)(269,444)(270,443)(271,512)(272,511)
(273,515)(274,514)(275,513)(276,522)(277,521)(278,525)(279,524)(280,523)
(281,517)(282,516)(283,520)(284,519)(285,518)(286,497)(287,496)(288,500)
(289,499)(290,498)(291,507)(292,506)(293,510)(294,509)(295,508)(296,502)
(297,501)(298,505)(299,504)(300,503)(301,527)(302,526)(303,530)(304,529)
(305,528)(306,537)(307,536)(308,540)(309,539)(310,538)(311,532)(312,531)
(313,535)(314,534)(315,533)(316,467)(317,466)(318,470)(319,469)(320,468)
(321,477)(322,476)(323,480)(324,479)(325,478)(326,472)(327,471)(328,475)
(329,474)(330,473)(331,452)(332,451)(333,455)(334,454)(335,453)(336,462)
(337,461)(338,465)(339,464)(340,463)(341,457)(342,456)(343,460)(344,459)
(345,458)(346,482)(347,481)(348,485)(349,484)(350,483)(351,492)(352,491)
(353,495)(354,494)(355,493)(356,487)(357,486)(358,490)(359,489)(360,488);;
s2 := (  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]);;

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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*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*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(720)!(  1,361)(  2,365)(  3,364)(  4,363)(  5,362)(  6,366)(  7,370)
(  8,369)(  9,368)( 10,367)( 11,371)( 12,375)( 13,374)( 14,373)( 15,372)
( 16,391)( 17,395)( 18,394)( 19,393)( 20,392)( 21,396)( 22,400)( 23,399)
( 24,398)( 25,397)( 26,401)( 27,405)( 28,404)( 29,403)( 30,402)( 31,376)
( 32,380)( 33,379)( 34,378)( 35,377)( 36,381)( 37,385)( 38,384)( 39,383)
( 40,382)( 41,386)( 42,390)( 43,389)( 44,388)( 45,387)( 46,406)( 47,410)
( 48,409)( 49,408)( 50,407)( 51,411)( 52,415)( 53,414)( 54,413)( 55,412)
( 56,416)( 57,420)( 58,419)( 59,418)( 60,417)( 61,436)( 62,440)( 63,439)
( 64,438)( 65,437)( 66,441)( 67,445)( 68,444)( 69,443)( 70,442)( 71,446)
( 72,450)( 73,449)( 74,448)( 75,447)( 76,421)( 77,425)( 78,424)( 79,423)
( 80,422)( 81,426)( 82,430)( 83,429)( 84,428)( 85,427)( 86,431)( 87,435)
( 88,434)( 89,433)( 90,432)( 91,496)( 92,500)( 93,499)( 94,498)( 95,497)
( 96,501)( 97,505)( 98,504)( 99,503)(100,502)(101,506)(102,510)(103,509)
(104,508)(105,507)(106,526)(107,530)(108,529)(109,528)(110,527)(111,531)
(112,535)(113,534)(114,533)(115,532)(116,536)(117,540)(118,539)(119,538)
(120,537)(121,511)(122,515)(123,514)(124,513)(125,512)(126,516)(127,520)
(128,519)(129,518)(130,517)(131,521)(132,525)(133,524)(134,523)(135,522)
(136,451)(137,455)(138,454)(139,453)(140,452)(141,456)(142,460)(143,459)
(144,458)(145,457)(146,461)(147,465)(148,464)(149,463)(150,462)(151,481)
(152,485)(153,484)(154,483)(155,482)(156,486)(157,490)(158,489)(159,488)
(160,487)(161,491)(162,495)(163,494)(164,493)(165,492)(166,466)(167,470)
(168,469)(169,468)(170,467)(171,471)(172,475)(173,474)(174,473)(175,472)
(176,476)(177,480)(178,479)(179,478)(180,477)(181,676)(182,680)(183,679)
(184,678)(185,677)(186,681)(187,685)(188,684)(189,683)(190,682)(191,686)
(192,690)(193,689)(194,688)(195,687)(196,706)(197,710)(198,709)(199,708)
(200,707)(201,711)(202,715)(203,714)(204,713)(205,712)(206,716)(207,720)
(208,719)(209,718)(210,717)(211,691)(212,695)(213,694)(214,693)(215,692)
(216,696)(217,700)(218,699)(219,698)(220,697)(221,701)(222,705)(223,704)
(224,703)(225,702)(226,631)(227,635)(228,634)(229,633)(230,632)(231,636)
(232,640)(233,639)(234,638)(235,637)(236,641)(237,645)(238,644)(239,643)
(240,642)(241,661)(242,665)(243,664)(244,663)(245,662)(246,666)(247,670)
(248,669)(249,668)(250,667)(251,671)(252,675)(253,674)(254,673)(255,672)
(256,646)(257,650)(258,649)(259,648)(260,647)(261,651)(262,655)(263,654)
(264,653)(265,652)(266,656)(267,660)(268,659)(269,658)(270,657)(271,586)
(272,590)(273,589)(274,588)(275,587)(276,591)(277,595)(278,594)(279,593)
(280,592)(281,596)(282,600)(283,599)(284,598)(285,597)(286,616)(287,620)
(288,619)(289,618)(290,617)(291,621)(292,625)(293,624)(294,623)(295,622)
(296,626)(297,630)(298,629)(299,628)(300,627)(301,601)(302,605)(303,604)
(304,603)(305,602)(306,606)(307,610)(308,609)(309,608)(310,607)(311,611)
(312,615)(313,614)(314,613)(315,612)(316,541)(317,545)(318,544)(319,543)
(320,542)(321,546)(322,550)(323,549)(324,548)(325,547)(326,551)(327,555)
(328,554)(329,553)(330,552)(331,571)(332,575)(333,574)(334,573)(335,572)
(336,576)(337,580)(338,579)(339,578)(340,577)(341,581)(342,585)(343,584)
(344,583)(345,582)(346,556)(347,560)(348,559)(349,558)(350,557)(351,561)
(352,565)(353,564)(354,563)(355,562)(356,566)(357,570)(358,569)(359,568)
(360,567);
s1 := Sym(720)!(  1,557)(  2,556)(  3,560)(  4,559)(  5,558)(  6,567)(  7,566)
(  8,570)(  9,569)( 10,568)( 11,562)( 12,561)( 13,565)( 14,564)( 15,563)
( 16,542)( 17,541)( 18,545)( 19,544)( 20,543)( 21,552)( 22,551)( 23,555)
( 24,554)( 25,553)( 26,547)( 27,546)( 28,550)( 29,549)( 30,548)( 31,572)
( 32,571)( 33,575)( 34,574)( 35,573)( 36,582)( 37,581)( 38,585)( 39,584)
( 40,583)( 41,577)( 42,576)( 43,580)( 44,579)( 45,578)( 46,602)( 47,601)
( 48,605)( 49,604)( 50,603)( 51,612)( 52,611)( 53,615)( 54,614)( 55,613)
( 56,607)( 57,606)( 58,610)( 59,609)( 60,608)( 61,587)( 62,586)( 63,590)
( 64,589)( 65,588)( 66,597)( 67,596)( 68,600)( 69,599)( 70,598)( 71,592)
( 72,591)( 73,595)( 74,594)( 75,593)( 76,617)( 77,616)( 78,620)( 79,619)
( 80,618)( 81,627)( 82,626)( 83,630)( 84,629)( 85,628)( 86,622)( 87,621)
( 88,625)( 89,624)( 90,623)( 91,692)( 92,691)( 93,695)( 94,694)( 95,693)
( 96,702)( 97,701)( 98,705)( 99,704)(100,703)(101,697)(102,696)(103,700)
(104,699)(105,698)(106,677)(107,676)(108,680)(109,679)(110,678)(111,687)
(112,686)(113,690)(114,689)(115,688)(116,682)(117,681)(118,685)(119,684)
(120,683)(121,707)(122,706)(123,710)(124,709)(125,708)(126,717)(127,716)
(128,720)(129,719)(130,718)(131,712)(132,711)(133,715)(134,714)(135,713)
(136,647)(137,646)(138,650)(139,649)(140,648)(141,657)(142,656)(143,660)
(144,659)(145,658)(146,652)(147,651)(148,655)(149,654)(150,653)(151,632)
(152,631)(153,635)(154,634)(155,633)(156,642)(157,641)(158,645)(159,644)
(160,643)(161,637)(162,636)(163,640)(164,639)(165,638)(166,662)(167,661)
(168,665)(169,664)(170,663)(171,672)(172,671)(173,675)(174,674)(175,673)
(176,667)(177,666)(178,670)(179,669)(180,668)(181,377)(182,376)(183,380)
(184,379)(185,378)(186,387)(187,386)(188,390)(189,389)(190,388)(191,382)
(192,381)(193,385)(194,384)(195,383)(196,362)(197,361)(198,365)(199,364)
(200,363)(201,372)(202,371)(203,375)(204,374)(205,373)(206,367)(207,366)
(208,370)(209,369)(210,368)(211,392)(212,391)(213,395)(214,394)(215,393)
(216,402)(217,401)(218,405)(219,404)(220,403)(221,397)(222,396)(223,400)
(224,399)(225,398)(226,422)(227,421)(228,425)(229,424)(230,423)(231,432)
(232,431)(233,435)(234,434)(235,433)(236,427)(237,426)(238,430)(239,429)
(240,428)(241,407)(242,406)(243,410)(244,409)(245,408)(246,417)(247,416)
(248,420)(249,419)(250,418)(251,412)(252,411)(253,415)(254,414)(255,413)
(256,437)(257,436)(258,440)(259,439)(260,438)(261,447)(262,446)(263,450)
(264,449)(265,448)(266,442)(267,441)(268,445)(269,444)(270,443)(271,512)
(272,511)(273,515)(274,514)(275,513)(276,522)(277,521)(278,525)(279,524)
(280,523)(281,517)(282,516)(283,520)(284,519)(285,518)(286,497)(287,496)
(288,500)(289,499)(290,498)(291,507)(292,506)(293,510)(294,509)(295,508)
(296,502)(297,501)(298,505)(299,504)(300,503)(301,527)(302,526)(303,530)
(304,529)(305,528)(306,537)(307,536)(308,540)(309,539)(310,538)(311,532)
(312,531)(313,535)(314,534)(315,533)(316,467)(317,466)(318,470)(319,469)
(320,468)(321,477)(322,476)(323,480)(324,479)(325,478)(326,472)(327,471)
(328,475)(329,474)(330,473)(331,452)(332,451)(333,455)(334,454)(335,453)
(336,462)(337,461)(338,465)(339,464)(340,463)(341,457)(342,456)(343,460)
(344,459)(345,458)(346,482)(347,481)(348,485)(349,484)(350,483)(351,492)
(352,491)(353,495)(354,494)(355,493)(356,487)(357,486)(358,490)(359,489)
(360,488);
s2 := 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>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*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*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*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 >;

References : None.
to this polytope