Polytope of Type {4,180}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,180}*1440c
if this polytope has a name.
Group : SmallGroup(1440,1522)
Rank : 3
Schlafli Type : {4,180}
Number of vertices, edges, etc : 4, 360, 180
Order of s0s1s2 : 180
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-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 : {4,90}*720b
3-fold quotients : {4,60}*480c
4-fold quotients : {4,45}*360
5-fold quotients : {4,36}*288c
6-fold quotients : {4,30}*240b
10-fold quotients : {4,18}*144b
12-fold quotients : {4,15}*120
15-fold quotients : {4,12}*96c
20-fold quotients : {4,9}*72
30-fold quotients : {4,6}*48c
60-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,183)( 2,184)( 3,181)( 4,182)( 5,187)( 6,188)( 7,185)( 8,186)
( 9,191)( 10,192)( 11,189)( 12,190)( 13,195)( 14,196)( 15,193)( 16,194)
( 17,199)( 18,200)( 19,197)( 20,198)( 21,203)( 22,204)( 23,201)( 24,202)
( 25,207)( 26,208)( 27,205)( 28,206)( 29,211)( 30,212)( 31,209)( 32,210)
( 33,215)( 34,216)( 35,213)( 36,214)( 37,219)( 38,220)( 39,217)( 40,218)
( 41,223)( 42,224)( 43,221)( 44,222)( 45,227)( 46,228)( 47,225)( 48,226)
( 49,231)( 50,232)( 51,229)( 52,230)( 53,235)( 54,236)( 55,233)( 56,234)
( 57,239)( 58,240)( 59,237)( 60,238)( 61,243)( 62,244)( 63,241)( 64,242)
( 65,247)( 66,248)( 67,245)( 68,246)( 69,251)( 70,252)( 71,249)( 72,250)
( 73,255)( 74,256)( 75,253)( 76,254)( 77,259)( 78,260)( 79,257)( 80,258)
( 81,263)( 82,264)( 83,261)( 84,262)( 85,267)( 86,268)( 87,265)( 88,266)
( 89,271)( 90,272)( 91,269)( 92,270)( 93,275)( 94,276)( 95,273)( 96,274)
( 97,279)( 98,280)( 99,277)(100,278)(101,283)(102,284)(103,281)(104,282)
(105,287)(106,288)(107,285)(108,286)(109,291)(110,292)(111,289)(112,290)
(113,295)(114,296)(115,293)(116,294)(117,299)(118,300)(119,297)(120,298)
(121,303)(122,304)(123,301)(124,302)(125,307)(126,308)(127,305)(128,306)
(129,311)(130,312)(131,309)(132,310)(133,315)(134,316)(135,313)(136,314)
(137,319)(138,320)(139,317)(140,318)(141,323)(142,324)(143,321)(144,322)
(145,327)(146,328)(147,325)(148,326)(149,331)(150,332)(151,329)(152,330)
(153,335)(154,336)(155,333)(156,334)(157,339)(158,340)(159,337)(160,338)
(161,343)(162,344)(163,341)(164,342)(165,347)(166,348)(167,345)(168,346)
(169,351)(170,352)(171,349)(172,350)(173,355)(174,356)(175,353)(176,354)
(177,359)(178,360)(179,357)(180,358)(361,543)(362,544)(363,541)(364,542)
(365,547)(366,548)(367,545)(368,546)(369,551)(370,552)(371,549)(372,550)
(373,555)(374,556)(375,553)(376,554)(377,559)(378,560)(379,557)(380,558)
(381,563)(382,564)(383,561)(384,562)(385,567)(386,568)(387,565)(388,566)
(389,571)(390,572)(391,569)(392,570)(393,575)(394,576)(395,573)(396,574)
(397,579)(398,580)(399,577)(400,578)(401,583)(402,584)(403,581)(404,582)
(405,587)(406,588)(407,585)(408,586)(409,591)(410,592)(411,589)(412,590)
(413,595)(414,596)(415,593)(416,594)(417,599)(418,600)(419,597)(420,598)
(421,603)(422,604)(423,601)(424,602)(425,607)(426,608)(427,605)(428,606)
(429,611)(430,612)(431,609)(432,610)(433,615)(434,616)(435,613)(436,614)
(437,619)(438,620)(439,617)(440,618)(441,623)(442,624)(443,621)(444,622)
(445,627)(446,628)(447,625)(448,626)(449,631)(450,632)(451,629)(452,630)
(453,635)(454,636)(455,633)(456,634)(457,639)(458,640)(459,637)(460,638)
(461,643)(462,644)(463,641)(464,642)(465,647)(466,648)(467,645)(468,646)
(469,651)(470,652)(471,649)(472,650)(473,655)(474,656)(475,653)(476,654)
(477,659)(478,660)(479,657)(480,658)(481,663)(482,664)(483,661)(484,662)
(485,667)(486,668)(487,665)(488,666)(489,671)(490,672)(491,669)(492,670)
(493,675)(494,676)(495,673)(496,674)(497,679)(498,680)(499,677)(500,678)
(501,683)(502,684)(503,681)(504,682)(505,687)(506,688)(507,685)(508,686)
(509,691)(510,692)(511,689)(512,690)(513,695)(514,696)(515,693)(516,694)
(517,699)(518,700)(519,697)(520,698)(521,703)(522,704)(523,701)(524,702)
(525,707)(526,708)(527,705)(528,706)(529,711)(530,712)(531,709)(532,710)
(533,715)(534,716)(535,713)(536,714)(537,719)(538,720)(539,717)(540,718);;
s1 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 49)( 14, 50)( 15, 52)
( 16, 51)( 17, 57)( 18, 58)( 19, 60)( 20, 59)( 21, 53)( 22, 54)( 23, 56)
( 24, 55)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)( 31, 48)
( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 61,129)( 62,130)( 63,132)
( 64,131)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)
( 72,123)( 73,177)( 74,178)( 75,180)( 76,179)( 77,173)( 78,174)( 79,176)
( 80,175)( 81,169)( 82,170)( 83,172)( 84,171)( 85,165)( 86,166)( 87,168)
( 88,167)( 89,161)( 90,162)( 91,164)( 92,163)( 93,157)( 94,158)( 95,160)
( 96,159)( 97,153)( 98,154)( 99,156)(100,155)(101,149)(102,150)(103,152)
(104,151)(105,145)(106,146)(107,148)(108,147)(109,141)(110,142)(111,144)
(112,143)(113,137)(114,138)(115,140)(116,139)(117,133)(118,134)(119,136)
(120,135)(183,184)(185,189)(186,190)(187,192)(188,191)(193,229)(194,230)
(195,232)(196,231)(197,237)(198,238)(199,240)(200,239)(201,233)(202,234)
(203,236)(204,235)(205,217)(206,218)(207,220)(208,219)(209,225)(210,226)
(211,228)(212,227)(213,221)(214,222)(215,224)(216,223)(241,309)(242,310)
(243,312)(244,311)(245,305)(246,306)(247,308)(248,307)(249,301)(250,302)
(251,304)(252,303)(253,357)(254,358)(255,360)(256,359)(257,353)(258,354)
(259,356)(260,355)(261,349)(262,350)(263,352)(264,351)(265,345)(266,346)
(267,348)(268,347)(269,341)(270,342)(271,344)(272,343)(273,337)(274,338)
(275,340)(276,339)(277,333)(278,334)(279,336)(280,335)(281,329)(282,330)
(283,332)(284,331)(285,325)(286,326)(287,328)(288,327)(289,321)(290,322)
(291,324)(292,323)(293,317)(294,318)(295,320)(296,319)(297,313)(298,314)
(299,316)(300,315)(361,541)(362,542)(363,544)(364,543)(365,549)(366,550)
(367,552)(368,551)(369,545)(370,546)(371,548)(372,547)(373,589)(374,590)
(375,592)(376,591)(377,597)(378,598)(379,600)(380,599)(381,593)(382,594)
(383,596)(384,595)(385,577)(386,578)(387,580)(388,579)(389,585)(390,586)
(391,588)(392,587)(393,581)(394,582)(395,584)(396,583)(397,565)(398,566)
(399,568)(400,567)(401,573)(402,574)(403,576)(404,575)(405,569)(406,570)
(407,572)(408,571)(409,553)(410,554)(411,556)(412,555)(413,561)(414,562)
(415,564)(416,563)(417,557)(418,558)(419,560)(420,559)(421,669)(422,670)
(423,672)(424,671)(425,665)(426,666)(427,668)(428,667)(429,661)(430,662)
(431,664)(432,663)(433,717)(434,718)(435,720)(436,719)(437,713)(438,714)
(439,716)(440,715)(441,709)(442,710)(443,712)(444,711)(445,705)(446,706)
(447,708)(448,707)(449,701)(450,702)(451,704)(452,703)(453,697)(454,698)
(455,700)(456,699)(457,693)(458,694)(459,696)(460,695)(461,689)(462,690)
(463,692)(464,691)(465,685)(466,686)(467,688)(468,687)(469,681)(470,682)
(471,684)(472,683)(473,677)(474,678)(475,680)(476,679)(477,673)(478,674)
(479,676)(480,675)(481,609)(482,610)(483,612)(484,611)(485,605)(486,606)
(487,608)(488,607)(489,601)(490,602)(491,604)(492,603)(493,657)(494,658)
(495,660)(496,659)(497,653)(498,654)(499,656)(500,655)(501,649)(502,650)
(503,652)(504,651)(505,645)(506,646)(507,648)(508,647)(509,641)(510,642)
(511,644)(512,643)(513,637)(514,638)(515,640)(516,639)(517,633)(518,634)
(519,636)(520,635)(521,629)(522,630)(523,632)(524,631)(525,625)(526,626)
(527,628)(528,627)(529,621)(530,622)(531,624)(532,623)(533,617)(534,618)
(535,620)(536,619)(537,613)(538,614)(539,616)(540,615);;
s2 := ( 1,433)( 2,436)( 3,435)( 4,434)( 5,441)( 6,444)( 7,443)( 8,442)
( 9,437)( 10,440)( 11,439)( 12,438)( 13,421)( 14,424)( 15,423)( 16,422)
( 17,429)( 18,432)( 19,431)( 20,430)( 21,425)( 22,428)( 23,427)( 24,426)
( 25,469)( 26,472)( 27,471)( 28,470)( 29,477)( 30,480)( 31,479)( 32,478)
( 33,473)( 34,476)( 35,475)( 36,474)( 37,457)( 38,460)( 39,459)( 40,458)
( 41,465)( 42,468)( 43,467)( 44,466)( 45,461)( 46,464)( 47,463)( 48,462)
( 49,445)( 50,448)( 51,447)( 52,446)( 53,453)( 54,456)( 55,455)( 56,454)
( 57,449)( 58,452)( 59,451)( 60,450)( 61,373)( 62,376)( 63,375)( 64,374)
( 65,381)( 66,384)( 67,383)( 68,382)( 69,377)( 70,380)( 71,379)( 72,378)
( 73,361)( 74,364)( 75,363)( 76,362)( 77,369)( 78,372)( 79,371)( 80,370)
( 81,365)( 82,368)( 83,367)( 84,366)( 85,409)( 86,412)( 87,411)( 88,410)
( 89,417)( 90,420)( 91,419)( 92,418)( 93,413)( 94,416)( 95,415)( 96,414)
( 97,397)( 98,400)( 99,399)(100,398)(101,405)(102,408)(103,407)(104,406)
(105,401)(106,404)(107,403)(108,402)(109,385)(110,388)(111,387)(112,386)
(113,393)(114,396)(115,395)(116,394)(117,389)(118,392)(119,391)(120,390)
(121,501)(122,504)(123,503)(124,502)(125,497)(126,500)(127,499)(128,498)
(129,493)(130,496)(131,495)(132,494)(133,489)(134,492)(135,491)(136,490)
(137,485)(138,488)(139,487)(140,486)(141,481)(142,484)(143,483)(144,482)
(145,537)(146,540)(147,539)(148,538)(149,533)(150,536)(151,535)(152,534)
(153,529)(154,532)(155,531)(156,530)(157,525)(158,528)(159,527)(160,526)
(161,521)(162,524)(163,523)(164,522)(165,517)(166,520)(167,519)(168,518)
(169,513)(170,516)(171,515)(172,514)(173,509)(174,512)(175,511)(176,510)
(177,505)(178,508)(179,507)(180,506)(181,613)(182,616)(183,615)(184,614)
(185,621)(186,624)(187,623)(188,622)(189,617)(190,620)(191,619)(192,618)
(193,601)(194,604)(195,603)(196,602)(197,609)(198,612)(199,611)(200,610)
(201,605)(202,608)(203,607)(204,606)(205,649)(206,652)(207,651)(208,650)
(209,657)(210,660)(211,659)(212,658)(213,653)(214,656)(215,655)(216,654)
(217,637)(218,640)(219,639)(220,638)(221,645)(222,648)(223,647)(224,646)
(225,641)(226,644)(227,643)(228,642)(229,625)(230,628)(231,627)(232,626)
(233,633)(234,636)(235,635)(236,634)(237,629)(238,632)(239,631)(240,630)
(241,553)(242,556)(243,555)(244,554)(245,561)(246,564)(247,563)(248,562)
(249,557)(250,560)(251,559)(252,558)(253,541)(254,544)(255,543)(256,542)
(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)(264,546)
(265,589)(266,592)(267,591)(268,590)(269,597)(270,600)(271,599)(272,598)
(273,593)(274,596)(275,595)(276,594)(277,577)(278,580)(279,579)(280,578)
(281,585)(282,588)(283,587)(284,586)(285,581)(286,584)(287,583)(288,582)
(289,565)(290,568)(291,567)(292,566)(293,573)(294,576)(295,575)(296,574)
(297,569)(298,572)(299,571)(300,570)(301,681)(302,684)(303,683)(304,682)
(305,677)(306,680)(307,679)(308,678)(309,673)(310,676)(311,675)(312,674)
(313,669)(314,672)(315,671)(316,670)(317,665)(318,668)(319,667)(320,666)
(321,661)(322,664)(323,663)(324,662)(325,717)(326,720)(327,719)(328,718)
(329,713)(330,716)(331,715)(332,714)(333,709)(334,712)(335,711)(336,710)
(337,705)(338,708)(339,707)(340,706)(341,701)(342,704)(343,703)(344,702)
(345,697)(346,700)(347,699)(348,698)(349,693)(350,696)(351,695)(352,694)
(353,689)(354,692)(355,691)(356,690)(357,685)(358,688)(359,687)(360,686);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*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*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)!( 1,183)( 2,184)( 3,181)( 4,182)( 5,187)( 6,188)( 7,185)
( 8,186)( 9,191)( 10,192)( 11,189)( 12,190)( 13,195)( 14,196)( 15,193)
( 16,194)( 17,199)( 18,200)( 19,197)( 20,198)( 21,203)( 22,204)( 23,201)
( 24,202)( 25,207)( 26,208)( 27,205)( 28,206)( 29,211)( 30,212)( 31,209)
( 32,210)( 33,215)( 34,216)( 35,213)( 36,214)( 37,219)( 38,220)( 39,217)
( 40,218)( 41,223)( 42,224)( 43,221)( 44,222)( 45,227)( 46,228)( 47,225)
( 48,226)( 49,231)( 50,232)( 51,229)( 52,230)( 53,235)( 54,236)( 55,233)
( 56,234)( 57,239)( 58,240)( 59,237)( 60,238)( 61,243)( 62,244)( 63,241)
( 64,242)( 65,247)( 66,248)( 67,245)( 68,246)( 69,251)( 70,252)( 71,249)
( 72,250)( 73,255)( 74,256)( 75,253)( 76,254)( 77,259)( 78,260)( 79,257)
( 80,258)( 81,263)( 82,264)( 83,261)( 84,262)( 85,267)( 86,268)( 87,265)
( 88,266)( 89,271)( 90,272)( 91,269)( 92,270)( 93,275)( 94,276)( 95,273)
( 96,274)( 97,279)( 98,280)( 99,277)(100,278)(101,283)(102,284)(103,281)
(104,282)(105,287)(106,288)(107,285)(108,286)(109,291)(110,292)(111,289)
(112,290)(113,295)(114,296)(115,293)(116,294)(117,299)(118,300)(119,297)
(120,298)(121,303)(122,304)(123,301)(124,302)(125,307)(126,308)(127,305)
(128,306)(129,311)(130,312)(131,309)(132,310)(133,315)(134,316)(135,313)
(136,314)(137,319)(138,320)(139,317)(140,318)(141,323)(142,324)(143,321)
(144,322)(145,327)(146,328)(147,325)(148,326)(149,331)(150,332)(151,329)
(152,330)(153,335)(154,336)(155,333)(156,334)(157,339)(158,340)(159,337)
(160,338)(161,343)(162,344)(163,341)(164,342)(165,347)(166,348)(167,345)
(168,346)(169,351)(170,352)(171,349)(172,350)(173,355)(174,356)(175,353)
(176,354)(177,359)(178,360)(179,357)(180,358)(361,543)(362,544)(363,541)
(364,542)(365,547)(366,548)(367,545)(368,546)(369,551)(370,552)(371,549)
(372,550)(373,555)(374,556)(375,553)(376,554)(377,559)(378,560)(379,557)
(380,558)(381,563)(382,564)(383,561)(384,562)(385,567)(386,568)(387,565)
(388,566)(389,571)(390,572)(391,569)(392,570)(393,575)(394,576)(395,573)
(396,574)(397,579)(398,580)(399,577)(400,578)(401,583)(402,584)(403,581)
(404,582)(405,587)(406,588)(407,585)(408,586)(409,591)(410,592)(411,589)
(412,590)(413,595)(414,596)(415,593)(416,594)(417,599)(418,600)(419,597)
(420,598)(421,603)(422,604)(423,601)(424,602)(425,607)(426,608)(427,605)
(428,606)(429,611)(430,612)(431,609)(432,610)(433,615)(434,616)(435,613)
(436,614)(437,619)(438,620)(439,617)(440,618)(441,623)(442,624)(443,621)
(444,622)(445,627)(446,628)(447,625)(448,626)(449,631)(450,632)(451,629)
(452,630)(453,635)(454,636)(455,633)(456,634)(457,639)(458,640)(459,637)
(460,638)(461,643)(462,644)(463,641)(464,642)(465,647)(466,648)(467,645)
(468,646)(469,651)(470,652)(471,649)(472,650)(473,655)(474,656)(475,653)
(476,654)(477,659)(478,660)(479,657)(480,658)(481,663)(482,664)(483,661)
(484,662)(485,667)(486,668)(487,665)(488,666)(489,671)(490,672)(491,669)
(492,670)(493,675)(494,676)(495,673)(496,674)(497,679)(498,680)(499,677)
(500,678)(501,683)(502,684)(503,681)(504,682)(505,687)(506,688)(507,685)
(508,686)(509,691)(510,692)(511,689)(512,690)(513,695)(514,696)(515,693)
(516,694)(517,699)(518,700)(519,697)(520,698)(521,703)(522,704)(523,701)
(524,702)(525,707)(526,708)(527,705)(528,706)(529,711)(530,712)(531,709)
(532,710)(533,715)(534,716)(535,713)(536,714)(537,719)(538,720)(539,717)
(540,718);
s1 := Sym(720)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 49)( 14, 50)
( 15, 52)( 16, 51)( 17, 57)( 18, 58)( 19, 60)( 20, 59)( 21, 53)( 22, 54)
( 23, 56)( 24, 55)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)
( 31, 48)( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 61,129)( 62,130)
( 63,132)( 64,131)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)
( 71,124)( 72,123)( 73,177)( 74,178)( 75,180)( 76,179)( 77,173)( 78,174)
( 79,176)( 80,175)( 81,169)( 82,170)( 83,172)( 84,171)( 85,165)( 86,166)
( 87,168)( 88,167)( 89,161)( 90,162)( 91,164)( 92,163)( 93,157)( 94,158)
( 95,160)( 96,159)( 97,153)( 98,154)( 99,156)(100,155)(101,149)(102,150)
(103,152)(104,151)(105,145)(106,146)(107,148)(108,147)(109,141)(110,142)
(111,144)(112,143)(113,137)(114,138)(115,140)(116,139)(117,133)(118,134)
(119,136)(120,135)(183,184)(185,189)(186,190)(187,192)(188,191)(193,229)
(194,230)(195,232)(196,231)(197,237)(198,238)(199,240)(200,239)(201,233)
(202,234)(203,236)(204,235)(205,217)(206,218)(207,220)(208,219)(209,225)
(210,226)(211,228)(212,227)(213,221)(214,222)(215,224)(216,223)(241,309)
(242,310)(243,312)(244,311)(245,305)(246,306)(247,308)(248,307)(249,301)
(250,302)(251,304)(252,303)(253,357)(254,358)(255,360)(256,359)(257,353)
(258,354)(259,356)(260,355)(261,349)(262,350)(263,352)(264,351)(265,345)
(266,346)(267,348)(268,347)(269,341)(270,342)(271,344)(272,343)(273,337)
(274,338)(275,340)(276,339)(277,333)(278,334)(279,336)(280,335)(281,329)
(282,330)(283,332)(284,331)(285,325)(286,326)(287,328)(288,327)(289,321)
(290,322)(291,324)(292,323)(293,317)(294,318)(295,320)(296,319)(297,313)
(298,314)(299,316)(300,315)(361,541)(362,542)(363,544)(364,543)(365,549)
(366,550)(367,552)(368,551)(369,545)(370,546)(371,548)(372,547)(373,589)
(374,590)(375,592)(376,591)(377,597)(378,598)(379,600)(380,599)(381,593)
(382,594)(383,596)(384,595)(385,577)(386,578)(387,580)(388,579)(389,585)
(390,586)(391,588)(392,587)(393,581)(394,582)(395,584)(396,583)(397,565)
(398,566)(399,568)(400,567)(401,573)(402,574)(403,576)(404,575)(405,569)
(406,570)(407,572)(408,571)(409,553)(410,554)(411,556)(412,555)(413,561)
(414,562)(415,564)(416,563)(417,557)(418,558)(419,560)(420,559)(421,669)
(422,670)(423,672)(424,671)(425,665)(426,666)(427,668)(428,667)(429,661)
(430,662)(431,664)(432,663)(433,717)(434,718)(435,720)(436,719)(437,713)
(438,714)(439,716)(440,715)(441,709)(442,710)(443,712)(444,711)(445,705)
(446,706)(447,708)(448,707)(449,701)(450,702)(451,704)(452,703)(453,697)
(454,698)(455,700)(456,699)(457,693)(458,694)(459,696)(460,695)(461,689)
(462,690)(463,692)(464,691)(465,685)(466,686)(467,688)(468,687)(469,681)
(470,682)(471,684)(472,683)(473,677)(474,678)(475,680)(476,679)(477,673)
(478,674)(479,676)(480,675)(481,609)(482,610)(483,612)(484,611)(485,605)
(486,606)(487,608)(488,607)(489,601)(490,602)(491,604)(492,603)(493,657)
(494,658)(495,660)(496,659)(497,653)(498,654)(499,656)(500,655)(501,649)
(502,650)(503,652)(504,651)(505,645)(506,646)(507,648)(508,647)(509,641)
(510,642)(511,644)(512,643)(513,637)(514,638)(515,640)(516,639)(517,633)
(518,634)(519,636)(520,635)(521,629)(522,630)(523,632)(524,631)(525,625)
(526,626)(527,628)(528,627)(529,621)(530,622)(531,624)(532,623)(533,617)
(534,618)(535,620)(536,619)(537,613)(538,614)(539,616)(540,615);
s2 := Sym(720)!( 1,433)( 2,436)( 3,435)( 4,434)( 5,441)( 6,444)( 7,443)
( 8,442)( 9,437)( 10,440)( 11,439)( 12,438)( 13,421)( 14,424)( 15,423)
( 16,422)( 17,429)( 18,432)( 19,431)( 20,430)( 21,425)( 22,428)( 23,427)
( 24,426)( 25,469)( 26,472)( 27,471)( 28,470)( 29,477)( 30,480)( 31,479)
( 32,478)( 33,473)( 34,476)( 35,475)( 36,474)( 37,457)( 38,460)( 39,459)
( 40,458)( 41,465)( 42,468)( 43,467)( 44,466)( 45,461)( 46,464)( 47,463)
( 48,462)( 49,445)( 50,448)( 51,447)( 52,446)( 53,453)( 54,456)( 55,455)
( 56,454)( 57,449)( 58,452)( 59,451)( 60,450)( 61,373)( 62,376)( 63,375)
( 64,374)( 65,381)( 66,384)( 67,383)( 68,382)( 69,377)( 70,380)( 71,379)
( 72,378)( 73,361)( 74,364)( 75,363)( 76,362)( 77,369)( 78,372)( 79,371)
( 80,370)( 81,365)( 82,368)( 83,367)( 84,366)( 85,409)( 86,412)( 87,411)
( 88,410)( 89,417)( 90,420)( 91,419)( 92,418)( 93,413)( 94,416)( 95,415)
( 96,414)( 97,397)( 98,400)( 99,399)(100,398)(101,405)(102,408)(103,407)
(104,406)(105,401)(106,404)(107,403)(108,402)(109,385)(110,388)(111,387)
(112,386)(113,393)(114,396)(115,395)(116,394)(117,389)(118,392)(119,391)
(120,390)(121,501)(122,504)(123,503)(124,502)(125,497)(126,500)(127,499)
(128,498)(129,493)(130,496)(131,495)(132,494)(133,489)(134,492)(135,491)
(136,490)(137,485)(138,488)(139,487)(140,486)(141,481)(142,484)(143,483)
(144,482)(145,537)(146,540)(147,539)(148,538)(149,533)(150,536)(151,535)
(152,534)(153,529)(154,532)(155,531)(156,530)(157,525)(158,528)(159,527)
(160,526)(161,521)(162,524)(163,523)(164,522)(165,517)(166,520)(167,519)
(168,518)(169,513)(170,516)(171,515)(172,514)(173,509)(174,512)(175,511)
(176,510)(177,505)(178,508)(179,507)(180,506)(181,613)(182,616)(183,615)
(184,614)(185,621)(186,624)(187,623)(188,622)(189,617)(190,620)(191,619)
(192,618)(193,601)(194,604)(195,603)(196,602)(197,609)(198,612)(199,611)
(200,610)(201,605)(202,608)(203,607)(204,606)(205,649)(206,652)(207,651)
(208,650)(209,657)(210,660)(211,659)(212,658)(213,653)(214,656)(215,655)
(216,654)(217,637)(218,640)(219,639)(220,638)(221,645)(222,648)(223,647)
(224,646)(225,641)(226,644)(227,643)(228,642)(229,625)(230,628)(231,627)
(232,626)(233,633)(234,636)(235,635)(236,634)(237,629)(238,632)(239,631)
(240,630)(241,553)(242,556)(243,555)(244,554)(245,561)(246,564)(247,563)
(248,562)(249,557)(250,560)(251,559)(252,558)(253,541)(254,544)(255,543)
(256,542)(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)
(264,546)(265,589)(266,592)(267,591)(268,590)(269,597)(270,600)(271,599)
(272,598)(273,593)(274,596)(275,595)(276,594)(277,577)(278,580)(279,579)
(280,578)(281,585)(282,588)(283,587)(284,586)(285,581)(286,584)(287,583)
(288,582)(289,565)(290,568)(291,567)(292,566)(293,573)(294,576)(295,575)
(296,574)(297,569)(298,572)(299,571)(300,570)(301,681)(302,684)(303,683)
(304,682)(305,677)(306,680)(307,679)(308,678)(309,673)(310,676)(311,675)
(312,674)(313,669)(314,672)(315,671)(316,670)(317,665)(318,668)(319,667)
(320,666)(321,661)(322,664)(323,663)(324,662)(325,717)(326,720)(327,719)
(328,718)(329,713)(330,716)(331,715)(332,714)(333,709)(334,712)(335,711)
(336,710)(337,705)(338,708)(339,707)(340,706)(341,701)(342,704)(343,703)
(344,702)(345,697)(346,700)(347,699)(348,698)(349,693)(350,696)(351,695)
(352,694)(353,689)(354,692)(355,691)(356,690)(357,685)(358,688)(359,687)
(360,686);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*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*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