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# Polytope of Type {6,120}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,120}*1440a
if this polytope has a name.
Group : SmallGroup(1440,1992)
Rank : 3
Schlafli Type : {6,120}
Number of vertices, edges, etc : 6, 360, 120
Order of s0s1s2 : 120
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,60}*720a
3-fold quotients : {6,40}*480
4-fold quotients : {6,30}*360a
5-fold quotients : {6,24}*288c
6-fold quotients : {6,20}*240a
9-fold quotients : {2,40}*160
10-fold quotients : {6,12}*144c
12-fold quotients : {6,10}*120
15-fold quotients : {6,8}*96
18-fold quotients : {2,20}*80
20-fold quotients : {6,6}*72c
30-fold quotients : {6,4}*48a
36-fold quotients : {2,10}*40
40-fold quotients : {3,6}*36
45-fold quotients : {2,8}*32
60-fold quotients : {6,2}*24
72-fold quotients : {2,5}*20
90-fold quotients : {2,4}*16
120-fold quotients : {3,2}*12
180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,541)(  2,542)(  3,543)(  4,544)(  5,545)(  6,551)(  7,552)(  8,553)
(  9,554)( 10,555)( 11,546)( 12,547)( 13,548)( 14,549)( 15,550)( 16,571)
( 17,572)( 18,573)( 19,574)( 20,575)( 21,581)( 22,582)( 23,583)( 24,584)
( 25,585)( 26,576)( 27,577)( 28,578)( 29,579)( 30,580)( 31,556)( 32,557)
( 33,558)( 34,559)( 35,560)( 36,566)( 37,567)( 38,568)( 39,569)( 40,570)
( 41,561)( 42,562)( 43,563)( 44,564)( 45,565)( 46,586)( 47,587)( 48,588)
( 49,589)( 50,590)( 51,596)( 52,597)( 53,598)( 54,599)( 55,600)( 56,591)
( 57,592)( 58,593)( 59,594)( 60,595)( 61,616)( 62,617)( 63,618)( 64,619)
( 65,620)( 66,626)( 67,627)( 68,628)( 69,629)( 70,630)( 71,621)( 72,622)
( 73,623)( 74,624)( 75,625)( 76,601)( 77,602)( 78,603)( 79,604)( 80,605)
( 81,611)( 82,612)( 83,613)( 84,614)( 85,615)( 86,606)( 87,607)( 88,608)
( 89,609)( 90,610)( 91,631)( 92,632)( 93,633)( 94,634)( 95,635)( 96,641)
( 97,642)( 98,643)( 99,644)(100,645)(101,636)(102,637)(103,638)(104,639)
(105,640)(106,661)(107,662)(108,663)(109,664)(110,665)(111,671)(112,672)
(113,673)(114,674)(115,675)(116,666)(117,667)(118,668)(119,669)(120,670)
(121,646)(122,647)(123,648)(124,649)(125,650)(126,656)(127,657)(128,658)
(129,659)(130,660)(131,651)(132,652)(133,653)(134,654)(135,655)(136,676)
(137,677)(138,678)(139,679)(140,680)(141,686)(142,687)(143,688)(144,689)
(145,690)(146,681)(147,682)(148,683)(149,684)(150,685)(151,706)(152,707)
(153,708)(154,709)(155,710)(156,716)(157,717)(158,718)(159,719)(160,720)
(161,711)(162,712)(163,713)(164,714)(165,715)(166,691)(167,692)(168,693)
(169,694)(170,695)(171,701)(172,702)(173,703)(174,704)(175,705)(176,696)
(177,697)(178,698)(179,699)(180,700)(181,451)(182,452)(183,453)(184,454)
(185,455)(186,461)(187,462)(188,463)(189,464)(190,465)(191,456)(192,457)
(193,458)(194,459)(195,460)(196,481)(197,482)(198,483)(199,484)(200,485)
(201,491)(202,492)(203,493)(204,494)(205,495)(206,486)(207,487)(208,488)
(209,489)(210,490)(211,466)(212,467)(213,468)(214,469)(215,470)(216,476)
(217,477)(218,478)(219,479)(220,480)(221,471)(222,472)(223,473)(224,474)
(225,475)(226,496)(227,497)(228,498)(229,499)(230,500)(231,506)(232,507)
(233,508)(234,509)(235,510)(236,501)(237,502)(238,503)(239,504)(240,505)
(241,526)(242,527)(243,528)(244,529)(245,530)(246,536)(247,537)(248,538)
(249,539)(250,540)(251,531)(252,532)(253,533)(254,534)(255,535)(256,511)
(257,512)(258,513)(259,514)(260,515)(261,521)(262,522)(263,523)(264,524)
(265,525)(266,516)(267,517)(268,518)(269,519)(270,520)(271,406)(272,407)
(273,408)(274,409)(275,410)(276,416)(277,417)(278,418)(279,419)(280,420)
(281,411)(282,412)(283,413)(284,414)(285,415)(286,436)(287,437)(288,438)
(289,439)(290,440)(291,446)(292,447)(293,448)(294,449)(295,450)(296,441)
(297,442)(298,443)(299,444)(300,445)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)(312,427)
(313,428)(314,429)(315,430)(316,361)(317,362)(318,363)(319,364)(320,365)
(321,371)(322,372)(323,373)(324,374)(325,375)(326,366)(327,367)(328,368)
(329,369)(330,370)(331,391)(332,392)(333,393)(334,394)(335,395)(336,401)
(337,402)(338,403)(339,404)(340,405)(341,396)(342,397)(343,398)(344,399)
(345,400)(346,376)(347,377)(348,378)(349,379)(350,380)(351,386)(352,387)
(353,388)(354,389)(355,390)(356,381)(357,382)(358,383)(359,384)(360,385);;
s1 := (  1,561)(  2,565)(  3,564)(  4,563)(  5,562)(  6,556)(  7,560)(  8,559)
(  9,558)( 10,557)( 11,566)( 12,570)( 13,569)( 14,568)( 15,567)( 16,546)
( 17,550)( 18,549)( 19,548)( 20,547)( 21,541)( 22,545)( 23,544)( 24,543)
( 25,542)( 26,551)( 27,555)( 28,554)( 29,553)( 30,552)( 31,576)( 32,580)
( 33,579)( 34,578)( 35,577)( 36,571)( 37,575)( 38,574)( 39,573)( 40,572)
( 41,581)( 42,585)( 43,584)( 44,583)( 45,582)( 46,606)( 47,610)( 48,609)
( 49,608)( 50,607)( 51,601)( 52,605)( 53,604)( 54,603)( 55,602)( 56,611)
( 57,615)( 58,614)( 59,613)( 60,612)( 61,591)( 62,595)( 63,594)( 64,593)
( 65,592)( 66,586)( 67,590)( 68,589)( 69,588)( 70,587)( 71,596)( 72,600)
( 73,599)( 74,598)( 75,597)( 76,621)( 77,625)( 78,624)( 79,623)( 80,622)
( 81,616)( 82,620)( 83,619)( 84,618)( 85,617)( 86,626)( 87,630)( 88,629)
( 89,628)( 90,627)( 91,696)( 92,700)( 93,699)( 94,698)( 95,697)( 96,691)
( 97,695)( 98,694)( 99,693)(100,692)(101,701)(102,705)(103,704)(104,703)
(105,702)(106,681)(107,685)(108,684)(109,683)(110,682)(111,676)(112,680)
(113,679)(114,678)(115,677)(116,686)(117,690)(118,689)(119,688)(120,687)
(121,711)(122,715)(123,714)(124,713)(125,712)(126,706)(127,710)(128,709)
(129,708)(130,707)(131,716)(132,720)(133,719)(134,718)(135,717)(136,651)
(137,655)(138,654)(139,653)(140,652)(141,646)(142,650)(143,649)(144,648)
(145,647)(146,656)(147,660)(148,659)(149,658)(150,657)(151,636)(152,640)
(153,639)(154,638)(155,637)(156,631)(157,635)(158,634)(159,633)(160,632)
(161,641)(162,645)(163,644)(164,643)(165,642)(166,666)(167,670)(168,669)
(169,668)(170,667)(171,661)(172,665)(173,664)(174,663)(175,662)(176,671)
(177,675)(178,674)(179,673)(180,672)(181,381)(182,385)(183,384)(184,383)
(185,382)(186,376)(187,380)(188,379)(189,378)(190,377)(191,386)(192,390)
(193,389)(194,388)(195,387)(196,366)(197,370)(198,369)(199,368)(200,367)
(201,361)(202,365)(203,364)(204,363)(205,362)(206,371)(207,375)(208,374)
(209,373)(210,372)(211,396)(212,400)(213,399)(214,398)(215,397)(216,391)
(217,395)(218,394)(219,393)(220,392)(221,401)(222,405)(223,404)(224,403)
(225,402)(226,426)(227,430)(228,429)(229,428)(230,427)(231,421)(232,425)
(233,424)(234,423)(235,422)(236,431)(237,435)(238,434)(239,433)(240,432)
(241,411)(242,415)(243,414)(244,413)(245,412)(246,406)(247,410)(248,409)
(249,408)(250,407)(251,416)(252,420)(253,419)(254,418)(255,417)(256,441)
(257,445)(258,444)(259,443)(260,442)(261,436)(262,440)(263,439)(264,438)
(265,437)(266,446)(267,450)(268,449)(269,448)(270,447)(271,516)(272,520)
(273,519)(274,518)(275,517)(276,511)(277,515)(278,514)(279,513)(280,512)
(281,521)(282,525)(283,524)(284,523)(285,522)(286,501)(287,505)(288,504)
(289,503)(290,502)(291,496)(292,500)(293,499)(294,498)(295,497)(296,506)
(297,510)(298,509)(299,508)(300,507)(301,531)(302,535)(303,534)(304,533)
(305,532)(306,526)(307,530)(308,529)(309,528)(310,527)(311,536)(312,540)
(313,539)(314,538)(315,537)(316,471)(317,475)(318,474)(319,473)(320,472)
(321,466)(322,470)(323,469)(324,468)(325,467)(326,476)(327,480)(328,479)
(329,478)(330,477)(331,456)(332,460)(333,459)(334,458)(335,457)(336,451)
(337,455)(338,454)(339,453)(340,452)(341,461)(342,465)(343,464)(344,463)
(345,462)(346,486)(347,490)(348,489)(349,488)(350,487)(351,481)(352,485)
(353,484)(354,483)(355,482)(356,491)(357,495)(358,494)(359,493)(360,492);;
s2 := (  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);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope