Polytope of Type {45,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {45,8}*1440
if this polytope has a name.
Group : SmallGroup(1440,1528)
Rank : 3
Schlafli Type : {45,8}
Number of vertices, edges, etc : 90, 360, 16
Order of s0s1s2 : 180
Order of s0s1s2s1 : 8
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 : {45,4}*720
3-fold quotients : {15,8}*480
4-fold quotients : {45,4}*360
5-fold quotients : {9,8}*288
6-fold quotients : {15,4}*240
8-fold quotients : {45,2}*180
10-fold quotients : {9,4}*144
12-fold quotients : {15,4}*120
15-fold quotients : {3,8}*96
20-fold quotients : {9,4}*72
24-fold quotients : {15,2}*60
30-fold quotients : {3,4}*48
40-fold quotients : {9,2}*36
60-fold quotients : {3,4}*24
72-fold quotients : {5,2}*20
120-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,103)
( 30,104)( 31,101)( 32,102)( 33,113)( 34,114)( 35,116)( 36,115)( 37,119)
( 38,120)( 39,117)( 40,118)( 41,105)( 42,106)( 43,108)( 44,107)( 45,111)
( 46,112)( 47,109)( 48,110)( 49, 73)( 50, 74)( 51, 76)( 52, 75)( 53, 79)
( 54, 80)( 55, 77)( 56, 78)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 95)
( 62, 96)( 63, 93)( 64, 94)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 87)
( 70, 88)( 71, 85)( 72, 86)(121,257)(122,258)(123,260)(124,259)(125,263)
(126,264)(127,261)(128,262)(129,249)(130,250)(131,252)(132,251)(133,255)
(134,256)(135,253)(136,254)(137,241)(138,242)(139,244)(140,243)(141,247)
(142,248)(143,245)(144,246)(145,353)(146,354)(147,356)(148,355)(149,359)
(150,360)(151,357)(152,358)(153,345)(154,346)(155,348)(156,347)(157,351)
(158,352)(159,349)(160,350)(161,337)(162,338)(163,340)(164,339)(165,343)
(166,344)(167,341)(168,342)(169,329)(170,330)(171,332)(172,331)(173,335)
(174,336)(175,333)(176,334)(177,321)(178,322)(179,324)(180,323)(181,327)
(182,328)(183,325)(184,326)(185,313)(186,314)(187,316)(188,315)(189,319)
(190,320)(191,317)(192,318)(193,305)(194,306)(195,308)(196,307)(197,311)
(198,312)(199,309)(200,310)(201,297)(202,298)(203,300)(204,299)(205,303)
(206,304)(207,301)(208,302)(209,289)(210,290)(211,292)(212,291)(213,295)
(214,296)(215,293)(216,294)(217,281)(218,282)(219,284)(220,283)(221,287)
(222,288)(223,285)(224,286)(225,273)(226,274)(227,276)(228,275)(229,279)
(230,280)(231,277)(232,278)(233,265)(234,266)(235,268)(236,267)(237,271)
(238,272)(239,269)(240,270)(361,362)(365,368)(366,367)(369,378)(370,377)
(371,379)(372,380)(373,384)(374,383)(375,382)(376,381)(385,458)(386,457)
(387,459)(388,460)(389,464)(390,463)(391,462)(392,461)(393,474)(394,473)
(395,475)(396,476)(397,480)(398,479)(399,478)(400,477)(401,466)(402,465)
(403,467)(404,468)(405,472)(406,471)(407,470)(408,469)(409,434)(410,433)
(411,435)(412,436)(413,440)(414,439)(415,438)(416,437)(417,450)(418,449)
(419,451)(420,452)(421,456)(422,455)(423,454)(424,453)(425,442)(426,441)
(427,443)(428,444)(429,448)(430,447)(431,446)(432,445)(481,618)(482,617)
(483,619)(484,620)(485,624)(486,623)(487,622)(488,621)(489,610)(490,609)
(491,611)(492,612)(493,616)(494,615)(495,614)(496,613)(497,602)(498,601)
(499,603)(500,604)(501,608)(502,607)(503,606)(504,605)(505,714)(506,713)
(507,715)(508,716)(509,720)(510,719)(511,718)(512,717)(513,706)(514,705)
(515,707)(516,708)(517,712)(518,711)(519,710)(520,709)(521,698)(522,697)
(523,699)(524,700)(525,704)(526,703)(527,702)(528,701)(529,690)(530,689)
(531,691)(532,692)(533,696)(534,695)(535,694)(536,693)(537,682)(538,681)
(539,683)(540,684)(541,688)(542,687)(543,686)(544,685)(545,674)(546,673)
(547,675)(548,676)(549,680)(550,679)(551,678)(552,677)(553,666)(554,665)
(555,667)(556,668)(557,672)(558,671)(559,670)(560,669)(561,658)(562,657)
(563,659)(564,660)(565,664)(566,663)(567,662)(568,661)(569,650)(570,649)
(571,651)(572,652)(573,656)(574,655)(575,654)(576,653)(577,642)(578,641)
(579,643)(580,644)(581,648)(582,647)(583,646)(584,645)(585,634)(586,633)
(587,635)(588,636)(589,640)(590,639)(591,638)(592,637)(593,626)(594,625)
(595,627)(596,628)(597,632)(598,631)(599,630)(600,629);;
s1 := ( 1,145)( 2,146)( 3,151)( 4,152)( 5,150)( 6,149)( 7,147)( 8,148)
( 9,161)( 10,162)( 11,167)( 12,168)( 13,166)( 14,165)( 15,163)( 16,164)
( 17,153)( 18,154)( 19,159)( 20,160)( 21,158)( 22,157)( 23,155)( 24,156)
( 25,121)( 26,122)( 27,127)( 28,128)( 29,126)( 30,125)( 31,123)( 32,124)
( 33,137)( 34,138)( 35,143)( 36,144)( 37,142)( 38,141)( 39,139)( 40,140)
( 41,129)( 42,130)( 43,135)( 44,136)( 45,134)( 46,133)( 47,131)( 48,132)
( 49,217)( 50,218)( 51,223)( 52,224)( 53,222)( 54,221)( 55,219)( 56,220)
( 57,233)( 58,234)( 59,239)( 60,240)( 61,238)( 62,237)( 63,235)( 64,236)
( 65,225)( 66,226)( 67,231)( 68,232)( 69,230)( 70,229)( 71,227)( 72,228)
( 73,193)( 74,194)( 75,199)( 76,200)( 77,198)( 78,197)( 79,195)( 80,196)
( 81,209)( 82,210)( 83,215)( 84,216)( 85,214)( 86,213)( 87,211)( 88,212)
( 89,201)( 90,202)( 91,207)( 92,208)( 93,206)( 94,205)( 95,203)( 96,204)
( 97,169)( 98,170)( 99,175)(100,176)(101,174)(102,173)(103,171)(104,172)
(105,185)(106,186)(107,191)(108,192)(109,190)(110,189)(111,187)(112,188)
(113,177)(114,178)(115,183)(116,184)(117,182)(118,181)(119,179)(120,180)
(241,281)(242,282)(243,287)(244,288)(245,286)(246,285)(247,283)(248,284)
(249,273)(250,274)(251,279)(252,280)(253,278)(254,277)(255,275)(256,276)
(257,265)(258,266)(259,271)(260,272)(261,270)(262,269)(263,267)(264,268)
(289,353)(290,354)(291,359)(292,360)(293,358)(294,357)(295,355)(296,356)
(297,345)(298,346)(299,351)(300,352)(301,350)(302,349)(303,347)(304,348)
(305,337)(306,338)(307,343)(308,344)(309,342)(310,341)(311,339)(312,340)
(313,329)(314,330)(315,335)(316,336)(317,334)(318,333)(319,331)(320,332)
(323,327)(324,328)(325,326)(361,506)(362,505)(363,512)(364,511)(365,509)
(366,510)(367,508)(368,507)(369,522)(370,521)(371,528)(372,527)(373,525)
(374,526)(375,524)(376,523)(377,514)(378,513)(379,520)(380,519)(381,517)
(382,518)(383,516)(384,515)(385,482)(386,481)(387,488)(388,487)(389,485)
(390,486)(391,484)(392,483)(393,498)(394,497)(395,504)(396,503)(397,501)
(398,502)(399,500)(400,499)(401,490)(402,489)(403,496)(404,495)(405,493)
(406,494)(407,492)(408,491)(409,578)(410,577)(411,584)(412,583)(413,581)
(414,582)(415,580)(416,579)(417,594)(418,593)(419,600)(420,599)(421,597)
(422,598)(423,596)(424,595)(425,586)(426,585)(427,592)(428,591)(429,589)
(430,590)(431,588)(432,587)(433,554)(434,553)(435,560)(436,559)(437,557)
(438,558)(439,556)(440,555)(441,570)(442,569)(443,576)(444,575)(445,573)
(446,574)(447,572)(448,571)(449,562)(450,561)(451,568)(452,567)(453,565)
(454,566)(455,564)(456,563)(457,530)(458,529)(459,536)(460,535)(461,533)
(462,534)(463,532)(464,531)(465,546)(466,545)(467,552)(468,551)(469,549)
(470,550)(471,548)(472,547)(473,538)(474,537)(475,544)(476,543)(477,541)
(478,542)(479,540)(480,539)(601,642)(602,641)(603,648)(604,647)(605,645)
(606,646)(607,644)(608,643)(609,634)(610,633)(611,640)(612,639)(613,637)
(614,638)(615,636)(616,635)(617,626)(618,625)(619,632)(620,631)(621,629)
(622,630)(623,628)(624,627)(649,714)(650,713)(651,720)(652,719)(653,717)
(654,718)(655,716)(656,715)(657,706)(658,705)(659,712)(660,711)(661,709)
(662,710)(663,708)(664,707)(665,698)(666,697)(667,704)(668,703)(669,701)
(670,702)(671,700)(672,699)(673,690)(674,689)(675,696)(676,695)(677,693)
(678,694)(679,692)(680,691)(681,682)(683,688)(684,687);;
s2 := ( 1,363)( 2,364)( 3,362)( 4,361)( 5,367)( 6,368)( 7,366)( 8,365)
( 9,371)( 10,372)( 11,370)( 12,369)( 13,375)( 14,376)( 15,374)( 16,373)
( 17,379)( 18,380)( 19,378)( 20,377)( 21,383)( 22,384)( 23,382)( 24,381)
( 25,387)( 26,388)( 27,386)( 28,385)( 29,391)( 30,392)( 31,390)( 32,389)
( 33,395)( 34,396)( 35,394)( 36,393)( 37,399)( 38,400)( 39,398)( 40,397)
( 41,403)( 42,404)( 43,402)( 44,401)( 45,407)( 46,408)( 47,406)( 48,405)
( 49,411)( 50,412)( 51,410)( 52,409)( 53,415)( 54,416)( 55,414)( 56,413)
( 57,419)( 58,420)( 59,418)( 60,417)( 61,423)( 62,424)( 63,422)( 64,421)
( 65,427)( 66,428)( 67,426)( 68,425)( 69,431)( 70,432)( 71,430)( 72,429)
( 73,435)( 74,436)( 75,434)( 76,433)( 77,439)( 78,440)( 79,438)( 80,437)
( 81,443)( 82,444)( 83,442)( 84,441)( 85,447)( 86,448)( 87,446)( 88,445)
( 89,451)( 90,452)( 91,450)( 92,449)( 93,455)( 94,456)( 95,454)( 96,453)
( 97,459)( 98,460)( 99,458)(100,457)(101,463)(102,464)(103,462)(104,461)
(105,467)(106,468)(107,466)(108,465)(109,471)(110,472)(111,470)(112,469)
(113,475)(114,476)(115,474)(116,473)(117,479)(118,480)(119,478)(120,477)
(121,483)(122,484)(123,482)(124,481)(125,487)(126,488)(127,486)(128,485)
(129,491)(130,492)(131,490)(132,489)(133,495)(134,496)(135,494)(136,493)
(137,499)(138,500)(139,498)(140,497)(141,503)(142,504)(143,502)(144,501)
(145,507)(146,508)(147,506)(148,505)(149,511)(150,512)(151,510)(152,509)
(153,515)(154,516)(155,514)(156,513)(157,519)(158,520)(159,518)(160,517)
(161,523)(162,524)(163,522)(164,521)(165,527)(166,528)(167,526)(168,525)
(169,531)(170,532)(171,530)(172,529)(173,535)(174,536)(175,534)(176,533)
(177,539)(178,540)(179,538)(180,537)(181,543)(182,544)(183,542)(184,541)
(185,547)(186,548)(187,546)(188,545)(189,551)(190,552)(191,550)(192,549)
(193,555)(194,556)(195,554)(196,553)(197,559)(198,560)(199,558)(200,557)
(201,563)(202,564)(203,562)(204,561)(205,567)(206,568)(207,566)(208,565)
(209,571)(210,572)(211,570)(212,569)(213,575)(214,576)(215,574)(216,573)
(217,579)(218,580)(219,578)(220,577)(221,583)(222,584)(223,582)(224,581)
(225,587)(226,588)(227,586)(228,585)(229,591)(230,592)(231,590)(232,589)
(233,595)(234,596)(235,594)(236,593)(237,599)(238,600)(239,598)(240,597)
(241,603)(242,604)(243,602)(244,601)(245,607)(246,608)(247,606)(248,605)
(249,611)(250,612)(251,610)(252,609)(253,615)(254,616)(255,614)(256,613)
(257,619)(258,620)(259,618)(260,617)(261,623)(262,624)(263,622)(264,621)
(265,627)(266,628)(267,626)(268,625)(269,631)(270,632)(271,630)(272,629)
(273,635)(274,636)(275,634)(276,633)(277,639)(278,640)(279,638)(280,637)
(281,643)(282,644)(283,642)(284,641)(285,647)(286,648)(287,646)(288,645)
(289,651)(290,652)(291,650)(292,649)(293,655)(294,656)(295,654)(296,653)
(297,659)(298,660)(299,658)(300,657)(301,663)(302,664)(303,662)(304,661)
(305,667)(306,668)(307,666)(308,665)(309,671)(310,672)(311,670)(312,669)
(313,675)(314,676)(315,674)(316,673)(317,679)(318,680)(319,678)(320,677)
(321,683)(322,684)(323,682)(324,681)(325,687)(326,688)(327,686)(328,685)
(329,691)(330,692)(331,690)(332,689)(333,695)(334,696)(335,694)(336,693)
(337,699)(338,700)(339,698)(340,697)(341,703)(342,704)(343,702)(344,701)
(345,707)(346,708)(347,706)(348,705)(349,711)(350,712)(351,710)(352,709)
(353,715)(354,716)(355,714)(356,713)(357,719)(358,720)(359,718)(360,717);;
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*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)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 25, 97)( 26, 98)( 27,100)( 28, 99)
( 29,103)( 30,104)( 31,101)( 32,102)( 33,113)( 34,114)( 35,116)( 36,115)
( 37,119)( 38,120)( 39,117)( 40,118)( 41,105)( 42,106)( 43,108)( 44,107)
( 45,111)( 46,112)( 47,109)( 48,110)( 49, 73)( 50, 74)( 51, 76)( 52, 75)
( 53, 79)( 54, 80)( 55, 77)( 56, 78)( 57, 89)( 58, 90)( 59, 92)( 60, 91)
( 61, 95)( 62, 96)( 63, 93)( 64, 94)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 87)( 70, 88)( 71, 85)( 72, 86)(121,257)(122,258)(123,260)(124,259)
(125,263)(126,264)(127,261)(128,262)(129,249)(130,250)(131,252)(132,251)
(133,255)(134,256)(135,253)(136,254)(137,241)(138,242)(139,244)(140,243)
(141,247)(142,248)(143,245)(144,246)(145,353)(146,354)(147,356)(148,355)
(149,359)(150,360)(151,357)(152,358)(153,345)(154,346)(155,348)(156,347)
(157,351)(158,352)(159,349)(160,350)(161,337)(162,338)(163,340)(164,339)
(165,343)(166,344)(167,341)(168,342)(169,329)(170,330)(171,332)(172,331)
(173,335)(174,336)(175,333)(176,334)(177,321)(178,322)(179,324)(180,323)
(181,327)(182,328)(183,325)(184,326)(185,313)(186,314)(187,316)(188,315)
(189,319)(190,320)(191,317)(192,318)(193,305)(194,306)(195,308)(196,307)
(197,311)(198,312)(199,309)(200,310)(201,297)(202,298)(203,300)(204,299)
(205,303)(206,304)(207,301)(208,302)(209,289)(210,290)(211,292)(212,291)
(213,295)(214,296)(215,293)(216,294)(217,281)(218,282)(219,284)(220,283)
(221,287)(222,288)(223,285)(224,286)(225,273)(226,274)(227,276)(228,275)
(229,279)(230,280)(231,277)(232,278)(233,265)(234,266)(235,268)(236,267)
(237,271)(238,272)(239,269)(240,270)(361,362)(365,368)(366,367)(369,378)
(370,377)(371,379)(372,380)(373,384)(374,383)(375,382)(376,381)(385,458)
(386,457)(387,459)(388,460)(389,464)(390,463)(391,462)(392,461)(393,474)
(394,473)(395,475)(396,476)(397,480)(398,479)(399,478)(400,477)(401,466)
(402,465)(403,467)(404,468)(405,472)(406,471)(407,470)(408,469)(409,434)
(410,433)(411,435)(412,436)(413,440)(414,439)(415,438)(416,437)(417,450)
(418,449)(419,451)(420,452)(421,456)(422,455)(423,454)(424,453)(425,442)
(426,441)(427,443)(428,444)(429,448)(430,447)(431,446)(432,445)(481,618)
(482,617)(483,619)(484,620)(485,624)(486,623)(487,622)(488,621)(489,610)
(490,609)(491,611)(492,612)(493,616)(494,615)(495,614)(496,613)(497,602)
(498,601)(499,603)(500,604)(501,608)(502,607)(503,606)(504,605)(505,714)
(506,713)(507,715)(508,716)(509,720)(510,719)(511,718)(512,717)(513,706)
(514,705)(515,707)(516,708)(517,712)(518,711)(519,710)(520,709)(521,698)
(522,697)(523,699)(524,700)(525,704)(526,703)(527,702)(528,701)(529,690)
(530,689)(531,691)(532,692)(533,696)(534,695)(535,694)(536,693)(537,682)
(538,681)(539,683)(540,684)(541,688)(542,687)(543,686)(544,685)(545,674)
(546,673)(547,675)(548,676)(549,680)(550,679)(551,678)(552,677)(553,666)
(554,665)(555,667)(556,668)(557,672)(558,671)(559,670)(560,669)(561,658)
(562,657)(563,659)(564,660)(565,664)(566,663)(567,662)(568,661)(569,650)
(570,649)(571,651)(572,652)(573,656)(574,655)(575,654)(576,653)(577,642)
(578,641)(579,643)(580,644)(581,648)(582,647)(583,646)(584,645)(585,634)
(586,633)(587,635)(588,636)(589,640)(590,639)(591,638)(592,637)(593,626)
(594,625)(595,627)(596,628)(597,632)(598,631)(599,630)(600,629);
s1 := Sym(720)!( 1,145)( 2,146)( 3,151)( 4,152)( 5,150)( 6,149)( 7,147)
( 8,148)( 9,161)( 10,162)( 11,167)( 12,168)( 13,166)( 14,165)( 15,163)
( 16,164)( 17,153)( 18,154)( 19,159)( 20,160)( 21,158)( 22,157)( 23,155)
( 24,156)( 25,121)( 26,122)( 27,127)( 28,128)( 29,126)( 30,125)( 31,123)
( 32,124)( 33,137)( 34,138)( 35,143)( 36,144)( 37,142)( 38,141)( 39,139)
( 40,140)( 41,129)( 42,130)( 43,135)( 44,136)( 45,134)( 46,133)( 47,131)
( 48,132)( 49,217)( 50,218)( 51,223)( 52,224)( 53,222)( 54,221)( 55,219)
( 56,220)( 57,233)( 58,234)( 59,239)( 60,240)( 61,238)( 62,237)( 63,235)
( 64,236)( 65,225)( 66,226)( 67,231)( 68,232)( 69,230)( 70,229)( 71,227)
( 72,228)( 73,193)( 74,194)( 75,199)( 76,200)( 77,198)( 78,197)( 79,195)
( 80,196)( 81,209)( 82,210)( 83,215)( 84,216)( 85,214)( 86,213)( 87,211)
( 88,212)( 89,201)( 90,202)( 91,207)( 92,208)( 93,206)( 94,205)( 95,203)
( 96,204)( 97,169)( 98,170)( 99,175)(100,176)(101,174)(102,173)(103,171)
(104,172)(105,185)(106,186)(107,191)(108,192)(109,190)(110,189)(111,187)
(112,188)(113,177)(114,178)(115,183)(116,184)(117,182)(118,181)(119,179)
(120,180)(241,281)(242,282)(243,287)(244,288)(245,286)(246,285)(247,283)
(248,284)(249,273)(250,274)(251,279)(252,280)(253,278)(254,277)(255,275)
(256,276)(257,265)(258,266)(259,271)(260,272)(261,270)(262,269)(263,267)
(264,268)(289,353)(290,354)(291,359)(292,360)(293,358)(294,357)(295,355)
(296,356)(297,345)(298,346)(299,351)(300,352)(301,350)(302,349)(303,347)
(304,348)(305,337)(306,338)(307,343)(308,344)(309,342)(310,341)(311,339)
(312,340)(313,329)(314,330)(315,335)(316,336)(317,334)(318,333)(319,331)
(320,332)(323,327)(324,328)(325,326)(361,506)(362,505)(363,512)(364,511)
(365,509)(366,510)(367,508)(368,507)(369,522)(370,521)(371,528)(372,527)
(373,525)(374,526)(375,524)(376,523)(377,514)(378,513)(379,520)(380,519)
(381,517)(382,518)(383,516)(384,515)(385,482)(386,481)(387,488)(388,487)
(389,485)(390,486)(391,484)(392,483)(393,498)(394,497)(395,504)(396,503)
(397,501)(398,502)(399,500)(400,499)(401,490)(402,489)(403,496)(404,495)
(405,493)(406,494)(407,492)(408,491)(409,578)(410,577)(411,584)(412,583)
(413,581)(414,582)(415,580)(416,579)(417,594)(418,593)(419,600)(420,599)
(421,597)(422,598)(423,596)(424,595)(425,586)(426,585)(427,592)(428,591)
(429,589)(430,590)(431,588)(432,587)(433,554)(434,553)(435,560)(436,559)
(437,557)(438,558)(439,556)(440,555)(441,570)(442,569)(443,576)(444,575)
(445,573)(446,574)(447,572)(448,571)(449,562)(450,561)(451,568)(452,567)
(453,565)(454,566)(455,564)(456,563)(457,530)(458,529)(459,536)(460,535)
(461,533)(462,534)(463,532)(464,531)(465,546)(466,545)(467,552)(468,551)
(469,549)(470,550)(471,548)(472,547)(473,538)(474,537)(475,544)(476,543)
(477,541)(478,542)(479,540)(480,539)(601,642)(602,641)(603,648)(604,647)
(605,645)(606,646)(607,644)(608,643)(609,634)(610,633)(611,640)(612,639)
(613,637)(614,638)(615,636)(616,635)(617,626)(618,625)(619,632)(620,631)
(621,629)(622,630)(623,628)(624,627)(649,714)(650,713)(651,720)(652,719)
(653,717)(654,718)(655,716)(656,715)(657,706)(658,705)(659,712)(660,711)
(661,709)(662,710)(663,708)(664,707)(665,698)(666,697)(667,704)(668,703)
(669,701)(670,702)(671,700)(672,699)(673,690)(674,689)(675,696)(676,695)
(677,693)(678,694)(679,692)(680,691)(681,682)(683,688)(684,687);
s2 := Sym(720)!( 1,363)( 2,364)( 3,362)( 4,361)( 5,367)( 6,368)( 7,366)
( 8,365)( 9,371)( 10,372)( 11,370)( 12,369)( 13,375)( 14,376)( 15,374)
( 16,373)( 17,379)( 18,380)( 19,378)( 20,377)( 21,383)( 22,384)( 23,382)
( 24,381)( 25,387)( 26,388)( 27,386)( 28,385)( 29,391)( 30,392)( 31,390)
( 32,389)( 33,395)( 34,396)( 35,394)( 36,393)( 37,399)( 38,400)( 39,398)
( 40,397)( 41,403)( 42,404)( 43,402)( 44,401)( 45,407)( 46,408)( 47,406)
( 48,405)( 49,411)( 50,412)( 51,410)( 52,409)( 53,415)( 54,416)( 55,414)
( 56,413)( 57,419)( 58,420)( 59,418)( 60,417)( 61,423)( 62,424)( 63,422)
( 64,421)( 65,427)( 66,428)( 67,426)( 68,425)( 69,431)( 70,432)( 71,430)
( 72,429)( 73,435)( 74,436)( 75,434)( 76,433)( 77,439)( 78,440)( 79,438)
( 80,437)( 81,443)( 82,444)( 83,442)( 84,441)( 85,447)( 86,448)( 87,446)
( 88,445)( 89,451)( 90,452)( 91,450)( 92,449)( 93,455)( 94,456)( 95,454)
( 96,453)( 97,459)( 98,460)( 99,458)(100,457)(101,463)(102,464)(103,462)
(104,461)(105,467)(106,468)(107,466)(108,465)(109,471)(110,472)(111,470)
(112,469)(113,475)(114,476)(115,474)(116,473)(117,479)(118,480)(119,478)
(120,477)(121,483)(122,484)(123,482)(124,481)(125,487)(126,488)(127,486)
(128,485)(129,491)(130,492)(131,490)(132,489)(133,495)(134,496)(135,494)
(136,493)(137,499)(138,500)(139,498)(140,497)(141,503)(142,504)(143,502)
(144,501)(145,507)(146,508)(147,506)(148,505)(149,511)(150,512)(151,510)
(152,509)(153,515)(154,516)(155,514)(156,513)(157,519)(158,520)(159,518)
(160,517)(161,523)(162,524)(163,522)(164,521)(165,527)(166,528)(167,526)
(168,525)(169,531)(170,532)(171,530)(172,529)(173,535)(174,536)(175,534)
(176,533)(177,539)(178,540)(179,538)(180,537)(181,543)(182,544)(183,542)
(184,541)(185,547)(186,548)(187,546)(188,545)(189,551)(190,552)(191,550)
(192,549)(193,555)(194,556)(195,554)(196,553)(197,559)(198,560)(199,558)
(200,557)(201,563)(202,564)(203,562)(204,561)(205,567)(206,568)(207,566)
(208,565)(209,571)(210,572)(211,570)(212,569)(213,575)(214,576)(215,574)
(216,573)(217,579)(218,580)(219,578)(220,577)(221,583)(222,584)(223,582)
(224,581)(225,587)(226,588)(227,586)(228,585)(229,591)(230,592)(231,590)
(232,589)(233,595)(234,596)(235,594)(236,593)(237,599)(238,600)(239,598)
(240,597)(241,603)(242,604)(243,602)(244,601)(245,607)(246,608)(247,606)
(248,605)(249,611)(250,612)(251,610)(252,609)(253,615)(254,616)(255,614)
(256,613)(257,619)(258,620)(259,618)(260,617)(261,623)(262,624)(263,622)
(264,621)(265,627)(266,628)(267,626)(268,625)(269,631)(270,632)(271,630)
(272,629)(273,635)(274,636)(275,634)(276,633)(277,639)(278,640)(279,638)
(280,637)(281,643)(282,644)(283,642)(284,641)(285,647)(286,648)(287,646)
(288,645)(289,651)(290,652)(291,650)(292,649)(293,655)(294,656)(295,654)
(296,653)(297,659)(298,660)(299,658)(300,657)(301,663)(302,664)(303,662)
(304,661)(305,667)(306,668)(307,666)(308,665)(309,671)(310,672)(311,670)
(312,669)(313,675)(314,676)(315,674)(316,673)(317,679)(318,680)(319,678)
(320,677)(321,683)(322,684)(323,682)(324,681)(325,687)(326,688)(327,686)
(328,685)(329,691)(330,692)(331,690)(332,689)(333,695)(334,696)(335,694)
(336,693)(337,699)(338,700)(339,698)(340,697)(341,703)(342,704)(343,702)
(344,701)(345,707)(346,708)(347,706)(348,705)(349,711)(350,712)(351,710)
(352,709)(353,715)(354,716)(355,714)(356,713)(357,719)(358,720)(359,718)
(360,717);
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*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