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Polytope of Type {40,6}

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