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# Polytope of Type {12,30}

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

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

```
References : None.
to this polytope