Questions?
See the FAQ
or other info.

Polytope of Type {6,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,40}*1440
if this polytope has a name.
Group : SmallGroup(1440,5181)
Rank : 3
Schlafli Type : {6,40}
Number of vertices, edges, etc : 18, 360, 120
Order of s0s1s2 : 40
Order of s0s1s2s1 : 6
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 : {6,20}*720
   4-fold quotients : {6,20}*360
   5-fold quotients : {6,8}*288
   9-fold quotients : {2,40}*160
   10-fold quotients : {6,4}*144
   18-fold quotients : {2,20}*80
   20-fold quotients : {6,4}*72
   36-fold quotients : {2,10}*40
   45-fold quotients : {2,8}*32
   72-fold quotients : {2,5}*20
   90-fold quotients : {2,4}*16
   180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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, 16)(  2, 20)(  3, 19)(  4, 18)(  5, 17)(  6, 21)(  7, 25)(  8, 24)
(  9, 23)( 10, 22)( 11, 26)( 12, 30)( 13, 29)( 14, 28)( 15, 27)( 32, 35)
( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 46, 61)( 47, 65)( 48, 64)
( 49, 63)( 50, 62)( 51, 66)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 71)
( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 77, 80)( 78, 79)( 82, 85)( 83, 84)
( 87, 90)( 88, 89)( 91,151)( 92,155)( 93,154)( 94,153)( 95,152)( 96,156)
( 97,160)( 98,159)( 99,158)(100,157)(101,161)(102,165)(103,164)(104,163)
(105,162)(106,136)(107,140)(108,139)(109,138)(110,137)(111,141)(112,145)
(113,144)(114,143)(115,142)(116,146)(117,150)(118,149)(119,148)(120,147)
(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)(181,241)
(182,245)(183,244)(184,243)(185,242)(186,246)(187,250)(188,249)(189,248)
(190,247)(191,251)(192,255)(193,254)(194,253)(195,252)(196,226)(197,230)
(198,229)(199,228)(200,227)(201,231)(202,235)(203,234)(204,233)(205,232)
(206,236)(207,240)(208,239)(209,238)(210,237)(211,256)(212,260)(213,259)
(214,258)(215,257)(216,261)(217,265)(218,264)(219,263)(220,262)(221,266)
(222,270)(223,269)(224,268)(225,267)(271,286)(272,290)(273,289)(274,288)
(275,287)(276,291)(277,295)(278,294)(279,293)(280,292)(281,296)(282,300)
(283,299)(284,298)(285,297)(302,305)(303,304)(307,310)(308,309)(312,315)
(313,314)(316,331)(317,335)(318,334)(319,333)(320,332)(321,336)(322,340)
(323,339)(324,338)(325,337)(326,341)(327,345)(328,344)(329,343)(330,342)
(347,350)(348,349)(352,355)(353,354)(357,360)(358,359)(361,466)(362,470)
(363,469)(364,468)(365,467)(366,471)(367,475)(368,474)(369,473)(370,472)
(371,476)(372,480)(373,479)(374,478)(375,477)(376,451)(377,455)(378,454)
(379,453)(380,452)(381,456)(382,460)(383,459)(384,458)(385,457)(386,461)
(387,465)(388,464)(389,463)(390,462)(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)(406,511)(407,515)(408,514)(409,513)(410,512)
(411,516)(412,520)(413,519)(414,518)(415,517)(416,521)(417,525)(418,524)
(419,523)(420,522)(421,496)(422,500)(423,499)(424,498)(425,497)(426,501)
(427,505)(428,504)(429,503)(430,502)(431,506)(432,510)(433,509)(434,508)
(435,507)(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)
(541,691)(542,695)(543,694)(544,693)(545,692)(546,696)(547,700)(548,699)
(549,698)(550,697)(551,701)(552,705)(553,704)(554,703)(555,702)(556,676)
(557,680)(558,679)(559,678)(560,677)(561,681)(562,685)(563,684)(564,683)
(565,682)(566,686)(567,690)(568,689)(569,688)(570,687)(571,706)(572,710)
(573,709)(574,708)(575,707)(576,711)(577,715)(578,714)(579,713)(580,712)
(581,716)(582,720)(583,719)(584,718)(585,717)(586,646)(587,650)(588,649)
(589,648)(590,647)(591,651)(592,655)(593,654)(594,653)(595,652)(596,656)
(597,660)(598,659)(599,658)(600,657)(601,631)(602,635)(603,634)(604,633)
(605,632)(606,636)(607,640)(608,639)(609,638)(610,637)(611,641)(612,645)
(613,644)(614,643)(615,642)(616,661)(617,665)(618,664)(619,663)(620,662)
(621,666)(622,670)(623,669)(624,668)(625,667)(626,671)(627,675)(628,674)
(629,673)(630,672);;
s2 := (  1,362)(  2,361)(  3,365)(  4,364)(  5,363)(  6,392)(  7,391)(  8,395)
(  9,394)( 10,393)( 11,377)( 12,376)( 13,380)( 14,379)( 15,378)( 16,372)
( 17,371)( 18,375)( 19,374)( 20,373)( 21,402)( 22,401)( 23,405)( 24,404)
( 25,403)( 26,387)( 27,386)( 28,390)( 29,389)( 30,388)( 31,367)( 32,366)
( 33,370)( 34,369)( 35,368)( 36,397)( 37,396)( 38,400)( 39,399)( 40,398)
( 41,382)( 42,381)( 43,385)( 44,384)( 45,383)( 46,407)( 47,406)( 48,410)
( 49,409)( 50,408)( 51,437)( 52,436)( 53,440)( 54,439)( 55,438)( 56,422)
( 57,421)( 58,425)( 59,424)( 60,423)( 61,417)( 62,416)( 63,420)( 64,419)
( 65,418)( 66,447)( 67,446)( 68,450)( 69,449)( 70,448)( 71,432)( 72,431)
( 73,435)( 74,434)( 75,433)( 76,412)( 77,411)( 78,415)( 79,414)( 80,413)
( 81,442)( 82,441)( 83,445)( 84,444)( 85,443)( 86,427)( 87,426)( 88,430)
( 89,429)( 90,428)( 91,497)( 92,496)( 93,500)( 94,499)( 95,498)( 96,527)
( 97,526)( 98,530)( 99,529)(100,528)(101,512)(102,511)(103,515)(104,514)
(105,513)(106,507)(107,506)(108,510)(109,509)(110,508)(111,537)(112,536)
(113,540)(114,539)(115,538)(116,522)(117,521)(118,525)(119,524)(120,523)
(121,502)(122,501)(123,505)(124,504)(125,503)(126,532)(127,531)(128,535)
(129,534)(130,533)(131,517)(132,516)(133,520)(134,519)(135,518)(136,452)
(137,451)(138,455)(139,454)(140,453)(141,482)(142,481)(143,485)(144,484)
(145,483)(146,467)(147,466)(148,470)(149,469)(150,468)(151,462)(152,461)
(153,465)(154,464)(155,463)(156,492)(157,491)(158,495)(159,494)(160,493)
(161,477)(162,476)(163,480)(164,479)(165,478)(166,457)(167,456)(168,460)
(169,459)(170,458)(171,487)(172,486)(173,490)(174,489)(175,488)(176,472)
(177,471)(178,475)(179,474)(180,473)(181,587)(182,586)(183,590)(184,589)
(185,588)(186,617)(187,616)(188,620)(189,619)(190,618)(191,602)(192,601)
(193,605)(194,604)(195,603)(196,597)(197,596)(198,600)(199,599)(200,598)
(201,627)(202,626)(203,630)(204,629)(205,628)(206,612)(207,611)(208,615)
(209,614)(210,613)(211,592)(212,591)(213,595)(214,594)(215,593)(216,622)
(217,621)(218,625)(219,624)(220,623)(221,607)(222,606)(223,610)(224,609)
(225,608)(226,542)(227,541)(228,545)(229,544)(230,543)(231,572)(232,571)
(233,575)(234,574)(235,573)(236,557)(237,556)(238,560)(239,559)(240,558)
(241,552)(242,551)(243,555)(244,554)(245,553)(246,582)(247,581)(248,585)
(249,584)(250,583)(251,567)(252,566)(253,570)(254,569)(255,568)(256,547)
(257,546)(258,550)(259,549)(260,548)(261,577)(262,576)(263,580)(264,579)
(265,578)(266,562)(267,561)(268,565)(269,564)(270,563)(271,632)(272,631)
(273,635)(274,634)(275,633)(276,662)(277,661)(278,665)(279,664)(280,663)
(281,647)(282,646)(283,650)(284,649)(285,648)(286,642)(287,641)(288,645)
(289,644)(290,643)(291,672)(292,671)(293,675)(294,674)(295,673)(296,657)
(297,656)(298,660)(299,659)(300,658)(301,637)(302,636)(303,640)(304,639)
(305,638)(306,667)(307,666)(308,670)(309,669)(310,668)(311,652)(312,651)
(313,655)(314,654)(315,653)(316,677)(317,676)(318,680)(319,679)(320,678)
(321,707)(322,706)(323,710)(324,709)(325,708)(326,692)(327,691)(328,695)
(329,694)(330,693)(331,687)(332,686)(333,690)(334,689)(335,688)(336,717)
(337,716)(338,720)(339,719)(340,718)(341,702)(342,701)(343,705)(344,704)
(345,703)(346,682)(347,681)(348,685)(349,684)(350,683)(351,712)(352,711)
(353,715)(354,714)(355,713)(356,697)(357,696)(358,700)(359,699)(360,698);;
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*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
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*s1*s2*s1*s2 ];;
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, 16)(  2, 20)(  3, 19)(  4, 18)(  5, 17)(  6, 21)(  7, 25)
(  8, 24)(  9, 23)( 10, 22)( 11, 26)( 12, 30)( 13, 29)( 14, 28)( 15, 27)
( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 46, 61)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 66)( 52, 70)( 53, 69)( 54, 68)( 55, 67)
( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 77, 80)( 78, 79)( 82, 85)
( 83, 84)( 87, 90)( 88, 89)( 91,151)( 92,155)( 93,154)( 94,153)( 95,152)
( 96,156)( 97,160)( 98,159)( 99,158)(100,157)(101,161)(102,165)(103,164)
(104,163)(105,162)(106,136)(107,140)(108,139)(109,138)(110,137)(111,141)
(112,145)(113,144)(114,143)(115,142)(116,146)(117,150)(118,149)(119,148)
(120,147)(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)
(181,241)(182,245)(183,244)(184,243)(185,242)(186,246)(187,250)(188,249)
(189,248)(190,247)(191,251)(192,255)(193,254)(194,253)(195,252)(196,226)
(197,230)(198,229)(199,228)(200,227)(201,231)(202,235)(203,234)(204,233)
(205,232)(206,236)(207,240)(208,239)(209,238)(210,237)(211,256)(212,260)
(213,259)(214,258)(215,257)(216,261)(217,265)(218,264)(219,263)(220,262)
(221,266)(222,270)(223,269)(224,268)(225,267)(271,286)(272,290)(273,289)
(274,288)(275,287)(276,291)(277,295)(278,294)(279,293)(280,292)(281,296)
(282,300)(283,299)(284,298)(285,297)(302,305)(303,304)(307,310)(308,309)
(312,315)(313,314)(316,331)(317,335)(318,334)(319,333)(320,332)(321,336)
(322,340)(323,339)(324,338)(325,337)(326,341)(327,345)(328,344)(329,343)
(330,342)(347,350)(348,349)(352,355)(353,354)(357,360)(358,359)(361,466)
(362,470)(363,469)(364,468)(365,467)(366,471)(367,475)(368,474)(369,473)
(370,472)(371,476)(372,480)(373,479)(374,478)(375,477)(376,451)(377,455)
(378,454)(379,453)(380,452)(381,456)(382,460)(383,459)(384,458)(385,457)
(386,461)(387,465)(388,464)(389,463)(390,462)(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)(406,511)(407,515)(408,514)(409,513)
(410,512)(411,516)(412,520)(413,519)(414,518)(415,517)(416,521)(417,525)
(418,524)(419,523)(420,522)(421,496)(422,500)(423,499)(424,498)(425,497)
(426,501)(427,505)(428,504)(429,503)(430,502)(431,506)(432,510)(433,509)
(434,508)(435,507)(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)(541,691)(542,695)(543,694)(544,693)(545,692)(546,696)(547,700)
(548,699)(549,698)(550,697)(551,701)(552,705)(553,704)(554,703)(555,702)
(556,676)(557,680)(558,679)(559,678)(560,677)(561,681)(562,685)(563,684)
(564,683)(565,682)(566,686)(567,690)(568,689)(569,688)(570,687)(571,706)
(572,710)(573,709)(574,708)(575,707)(576,711)(577,715)(578,714)(579,713)
(580,712)(581,716)(582,720)(583,719)(584,718)(585,717)(586,646)(587,650)
(588,649)(589,648)(590,647)(591,651)(592,655)(593,654)(594,653)(595,652)
(596,656)(597,660)(598,659)(599,658)(600,657)(601,631)(602,635)(603,634)
(604,633)(605,632)(606,636)(607,640)(608,639)(609,638)(610,637)(611,641)
(612,645)(613,644)(614,643)(615,642)(616,661)(617,665)(618,664)(619,663)
(620,662)(621,666)(622,670)(623,669)(624,668)(625,667)(626,671)(627,675)
(628,674)(629,673)(630,672);
s2 := Sym(720)!(  1,362)(  2,361)(  3,365)(  4,364)(  5,363)(  6,392)(  7,391)
(  8,395)(  9,394)( 10,393)( 11,377)( 12,376)( 13,380)( 14,379)( 15,378)
( 16,372)( 17,371)( 18,375)( 19,374)( 20,373)( 21,402)( 22,401)( 23,405)
( 24,404)( 25,403)( 26,387)( 27,386)( 28,390)( 29,389)( 30,388)( 31,367)
( 32,366)( 33,370)( 34,369)( 35,368)( 36,397)( 37,396)( 38,400)( 39,399)
( 40,398)( 41,382)( 42,381)( 43,385)( 44,384)( 45,383)( 46,407)( 47,406)
( 48,410)( 49,409)( 50,408)( 51,437)( 52,436)( 53,440)( 54,439)( 55,438)
( 56,422)( 57,421)( 58,425)( 59,424)( 60,423)( 61,417)( 62,416)( 63,420)
( 64,419)( 65,418)( 66,447)( 67,446)( 68,450)( 69,449)( 70,448)( 71,432)
( 72,431)( 73,435)( 74,434)( 75,433)( 76,412)( 77,411)( 78,415)( 79,414)
( 80,413)( 81,442)( 82,441)( 83,445)( 84,444)( 85,443)( 86,427)( 87,426)
( 88,430)( 89,429)( 90,428)( 91,497)( 92,496)( 93,500)( 94,499)( 95,498)
( 96,527)( 97,526)( 98,530)( 99,529)(100,528)(101,512)(102,511)(103,515)
(104,514)(105,513)(106,507)(107,506)(108,510)(109,509)(110,508)(111,537)
(112,536)(113,540)(114,539)(115,538)(116,522)(117,521)(118,525)(119,524)
(120,523)(121,502)(122,501)(123,505)(124,504)(125,503)(126,532)(127,531)
(128,535)(129,534)(130,533)(131,517)(132,516)(133,520)(134,519)(135,518)
(136,452)(137,451)(138,455)(139,454)(140,453)(141,482)(142,481)(143,485)
(144,484)(145,483)(146,467)(147,466)(148,470)(149,469)(150,468)(151,462)
(152,461)(153,465)(154,464)(155,463)(156,492)(157,491)(158,495)(159,494)
(160,493)(161,477)(162,476)(163,480)(164,479)(165,478)(166,457)(167,456)
(168,460)(169,459)(170,458)(171,487)(172,486)(173,490)(174,489)(175,488)
(176,472)(177,471)(178,475)(179,474)(180,473)(181,587)(182,586)(183,590)
(184,589)(185,588)(186,617)(187,616)(188,620)(189,619)(190,618)(191,602)
(192,601)(193,605)(194,604)(195,603)(196,597)(197,596)(198,600)(199,599)
(200,598)(201,627)(202,626)(203,630)(204,629)(205,628)(206,612)(207,611)
(208,615)(209,614)(210,613)(211,592)(212,591)(213,595)(214,594)(215,593)
(216,622)(217,621)(218,625)(219,624)(220,623)(221,607)(222,606)(223,610)
(224,609)(225,608)(226,542)(227,541)(228,545)(229,544)(230,543)(231,572)
(232,571)(233,575)(234,574)(235,573)(236,557)(237,556)(238,560)(239,559)
(240,558)(241,552)(242,551)(243,555)(244,554)(245,553)(246,582)(247,581)
(248,585)(249,584)(250,583)(251,567)(252,566)(253,570)(254,569)(255,568)
(256,547)(257,546)(258,550)(259,549)(260,548)(261,577)(262,576)(263,580)
(264,579)(265,578)(266,562)(267,561)(268,565)(269,564)(270,563)(271,632)
(272,631)(273,635)(274,634)(275,633)(276,662)(277,661)(278,665)(279,664)
(280,663)(281,647)(282,646)(283,650)(284,649)(285,648)(286,642)(287,641)
(288,645)(289,644)(290,643)(291,672)(292,671)(293,675)(294,674)(295,673)
(296,657)(297,656)(298,660)(299,659)(300,658)(301,637)(302,636)(303,640)
(304,639)(305,638)(306,667)(307,666)(308,670)(309,669)(310,668)(311,652)
(312,651)(313,655)(314,654)(315,653)(316,677)(317,676)(318,680)(319,679)
(320,678)(321,707)(322,706)(323,710)(324,709)(325,708)(326,692)(327,691)
(328,695)(329,694)(330,693)(331,687)(332,686)(333,690)(334,689)(335,688)
(336,717)(337,716)(338,720)(339,719)(340,718)(341,702)(342,701)(343,705)
(344,704)(345,703)(346,682)(347,681)(348,685)(349,684)(350,683)(351,712)
(352,711)(353,715)(354,714)(355,713)(356,697)(357,696)(358,700)(359,699)
(360,698);
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*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
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*s1*s2*s1*s2 >; 
 
References : None.
to this polytope