Polytope of Type {45,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {45,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,4571)
Rank : 3
Schlafli Type : {45,4}
Number of vertices, edges, etc : 180, 360, 16
Order of s0s1s2 : 45
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {15,4}*480
9-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 48)( 26, 47)
( 27, 45)( 28, 46)( 29, 43)( 30, 44)( 31, 42)( 32, 41)( 49,193)( 50,194)
( 51,196)( 52,195)( 53,198)( 54,197)( 55,199)( 56,200)( 57,208)( 58,207)
( 59,205)( 60,206)( 61,203)( 62,204)( 63,202)( 64,201)( 65,225)( 66,226)
( 67,228)( 68,227)( 69,230)( 70,229)( 71,231)( 72,232)( 73,240)( 74,239)
( 75,237)( 76,238)( 77,235)( 78,236)( 79,234)( 80,233)( 81,209)( 82,210)
( 83,212)( 84,211)( 85,214)( 86,213)( 87,215)( 88,216)( 89,224)( 90,223)
( 91,221)( 92,222)( 93,219)( 94,220)( 95,218)( 96,217)( 97,145)( 98,146)
( 99,148)(100,147)(101,150)(102,149)(103,151)(104,152)(105,160)(106,159)
(107,157)(108,158)(109,155)(110,156)(111,154)(112,153)(113,177)(114,178)
(115,180)(116,179)(117,182)(118,181)(119,183)(120,184)(121,192)(122,191)
(123,189)(124,190)(125,187)(126,188)(127,186)(128,185)(129,161)(130,162)
(131,164)(132,163)(133,166)(134,165)(135,167)(136,168)(137,176)(138,175)
(139,173)(140,174)(141,171)(142,172)(143,170)(144,169)(241,513)(242,514)
(243,516)(244,515)(245,518)(246,517)(247,519)(248,520)(249,528)(250,527)
(251,525)(252,526)(253,523)(254,524)(255,522)(256,521)(257,497)(258,498)
(259,500)(260,499)(261,502)(262,501)(263,503)(264,504)(265,512)(266,511)
(267,509)(268,510)(269,507)(270,508)(271,506)(272,505)(273,481)(274,482)
(275,484)(276,483)(277,486)(278,485)(279,487)(280,488)(281,496)(282,495)
(283,493)(284,494)(285,491)(286,492)(287,490)(288,489)(289,705)(290,706)
(291,708)(292,707)(293,710)(294,709)(295,711)(296,712)(297,720)(298,719)
(299,717)(300,718)(301,715)(302,716)(303,714)(304,713)(305,689)(306,690)
(307,692)(308,691)(309,694)(310,693)(311,695)(312,696)(313,704)(314,703)
(315,701)(316,702)(317,699)(318,700)(319,698)(320,697)(321,673)(322,674)
(323,676)(324,675)(325,678)(326,677)(327,679)(328,680)(329,688)(330,687)
(331,685)(332,686)(333,683)(334,684)(335,682)(336,681)(337,657)(338,658)
(339,660)(340,659)(341,662)(342,661)(343,663)(344,664)(345,672)(346,671)
(347,669)(348,670)(349,667)(350,668)(351,666)(352,665)(353,641)(354,642)
(355,644)(356,643)(357,646)(358,645)(359,647)(360,648)(361,656)(362,655)
(363,653)(364,654)(365,651)(366,652)(367,650)(368,649)(369,625)(370,626)
(371,628)(372,627)(373,630)(374,629)(375,631)(376,632)(377,640)(378,639)
(379,637)(380,638)(381,635)(382,636)(383,634)(384,633)(385,609)(386,610)
(387,612)(388,611)(389,614)(390,613)(391,615)(392,616)(393,624)(394,623)
(395,621)(396,622)(397,619)(398,620)(399,618)(400,617)(401,593)(402,594)
(403,596)(404,595)(405,598)(406,597)(407,599)(408,600)(409,608)(410,607)
(411,605)(412,606)(413,603)(414,604)(415,602)(416,601)(417,577)(418,578)
(419,580)(420,579)(421,582)(422,581)(423,583)(424,584)(425,592)(426,591)
(427,589)(428,590)(429,587)(430,588)(431,586)(432,585)(433,561)(434,562)
(435,564)(436,563)(437,566)(438,565)(439,567)(440,568)(441,576)(442,575)
(443,573)(444,574)(445,571)(446,572)(447,570)(448,569)(449,545)(450,546)
(451,548)(452,547)(453,550)(454,549)(455,551)(456,552)(457,560)(458,559)
(459,557)(460,558)(461,555)(462,556)(463,554)(464,553)(465,529)(466,530)
(467,532)(468,531)(469,534)(470,533)(471,535)(472,536)(473,544)(474,543)
(475,541)(476,542)(477,539)(478,540)(479,538)(480,537);;
s1 := ( 1,289)( 2,298)( 3,299)( 4,292)( 5,304)( 6,295)( 7,294)( 8,301)
( 9,297)( 10,290)( 11,291)( 12,300)( 13,296)( 14,303)( 15,302)( 16,293)
( 17,321)( 18,330)( 19,331)( 20,324)( 21,336)( 22,327)( 23,326)( 24,333)
( 25,329)( 26,322)( 27,323)( 28,332)( 29,328)( 30,335)( 31,334)( 32,325)
( 33,305)( 34,314)( 35,315)( 36,308)( 37,320)( 38,311)( 39,310)( 40,317)
( 41,313)( 42,306)( 43,307)( 44,316)( 45,312)( 46,319)( 47,318)( 48,309)
( 49,241)( 50,250)( 51,251)( 52,244)( 53,256)( 54,247)( 55,246)( 56,253)
( 57,249)( 58,242)( 59,243)( 60,252)( 61,248)( 62,255)( 63,254)( 64,245)
( 65,273)( 66,282)( 67,283)( 68,276)( 69,288)( 70,279)( 71,278)( 72,285)
( 73,281)( 74,274)( 75,275)( 76,284)( 77,280)( 78,287)( 79,286)( 80,277)
( 81,257)( 82,266)( 83,267)( 84,260)( 85,272)( 86,263)( 87,262)( 88,269)
( 89,265)( 90,258)( 91,259)( 92,268)( 93,264)( 94,271)( 95,270)( 96,261)
( 97,433)( 98,442)( 99,443)(100,436)(101,448)(102,439)(103,438)(104,445)
(105,441)(106,434)(107,435)(108,444)(109,440)(110,447)(111,446)(112,437)
(113,465)(114,474)(115,475)(116,468)(117,480)(118,471)(119,470)(120,477)
(121,473)(122,466)(123,467)(124,476)(125,472)(126,479)(127,478)(128,469)
(129,449)(130,458)(131,459)(132,452)(133,464)(134,455)(135,454)(136,461)
(137,457)(138,450)(139,451)(140,460)(141,456)(142,463)(143,462)(144,453)
(145,385)(146,394)(147,395)(148,388)(149,400)(150,391)(151,390)(152,397)
(153,393)(154,386)(155,387)(156,396)(157,392)(158,399)(159,398)(160,389)
(161,417)(162,426)(163,427)(164,420)(165,432)(166,423)(167,422)(168,429)
(169,425)(170,418)(171,419)(172,428)(173,424)(174,431)(175,430)(176,421)
(177,401)(178,410)(179,411)(180,404)(181,416)(182,407)(183,406)(184,413)
(185,409)(186,402)(187,403)(188,412)(189,408)(190,415)(191,414)(192,405)
(193,337)(194,346)(195,347)(196,340)(197,352)(198,343)(199,342)(200,349)
(201,345)(202,338)(203,339)(204,348)(205,344)(206,351)(207,350)(208,341)
(209,369)(210,378)(211,379)(212,372)(213,384)(214,375)(215,374)(216,381)
(217,377)(218,370)(219,371)(220,380)(221,376)(222,383)(223,382)(224,373)
(225,353)(226,362)(227,363)(228,356)(229,368)(230,359)(231,358)(232,365)
(233,361)(234,354)(235,355)(236,364)(237,360)(238,367)(239,366)(240,357)
(481,561)(482,570)(483,571)(484,564)(485,576)(486,567)(487,566)(488,573)
(489,569)(490,562)(491,563)(492,572)(493,568)(494,575)(495,574)(496,565)
(497,545)(498,554)(499,555)(500,548)(501,560)(502,551)(503,550)(504,557)
(505,553)(506,546)(507,547)(508,556)(509,552)(510,559)(511,558)(512,549)
(513,529)(514,538)(515,539)(516,532)(517,544)(518,535)(519,534)(520,541)
(521,537)(522,530)(523,531)(524,540)(525,536)(526,543)(527,542)(528,533)
(577,705)(578,714)(579,715)(580,708)(581,720)(582,711)(583,710)(584,717)
(585,713)(586,706)(587,707)(588,716)(589,712)(590,719)(591,718)(592,709)
(593,689)(594,698)(595,699)(596,692)(597,704)(598,695)(599,694)(600,701)
(601,697)(602,690)(603,691)(604,700)(605,696)(606,703)(607,702)(608,693)
(609,673)(610,682)(611,683)(612,676)(613,688)(614,679)(615,678)(616,685)
(617,681)(618,674)(619,675)(620,684)(621,680)(622,687)(623,686)(624,677)
(625,657)(626,666)(627,667)(628,660)(629,672)(630,663)(631,662)(632,669)
(633,665)(634,658)(635,659)(636,668)(637,664)(638,671)(639,670)(640,661)
(642,650)(643,651)(645,656)(646,647)(648,653)(654,655);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)
(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)
(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)
(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)
(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)
(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)
(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)
(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)
(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)
(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)
(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)
(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)
(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)
(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)
(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)
(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720);;
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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(720)!( 3, 4)( 5, 6)( 9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 48)
( 26, 47)( 27, 45)( 28, 46)( 29, 43)( 30, 44)( 31, 42)( 32, 41)( 49,193)
( 50,194)( 51,196)( 52,195)( 53,198)( 54,197)( 55,199)( 56,200)( 57,208)
( 58,207)( 59,205)( 60,206)( 61,203)( 62,204)( 63,202)( 64,201)( 65,225)
( 66,226)( 67,228)( 68,227)( 69,230)( 70,229)( 71,231)( 72,232)( 73,240)
( 74,239)( 75,237)( 76,238)( 77,235)( 78,236)( 79,234)( 80,233)( 81,209)
( 82,210)( 83,212)( 84,211)( 85,214)( 86,213)( 87,215)( 88,216)( 89,224)
( 90,223)( 91,221)( 92,222)( 93,219)( 94,220)( 95,218)( 96,217)( 97,145)
( 98,146)( 99,148)(100,147)(101,150)(102,149)(103,151)(104,152)(105,160)
(106,159)(107,157)(108,158)(109,155)(110,156)(111,154)(112,153)(113,177)
(114,178)(115,180)(116,179)(117,182)(118,181)(119,183)(120,184)(121,192)
(122,191)(123,189)(124,190)(125,187)(126,188)(127,186)(128,185)(129,161)
(130,162)(131,164)(132,163)(133,166)(134,165)(135,167)(136,168)(137,176)
(138,175)(139,173)(140,174)(141,171)(142,172)(143,170)(144,169)(241,513)
(242,514)(243,516)(244,515)(245,518)(246,517)(247,519)(248,520)(249,528)
(250,527)(251,525)(252,526)(253,523)(254,524)(255,522)(256,521)(257,497)
(258,498)(259,500)(260,499)(261,502)(262,501)(263,503)(264,504)(265,512)
(266,511)(267,509)(268,510)(269,507)(270,508)(271,506)(272,505)(273,481)
(274,482)(275,484)(276,483)(277,486)(278,485)(279,487)(280,488)(281,496)
(282,495)(283,493)(284,494)(285,491)(286,492)(287,490)(288,489)(289,705)
(290,706)(291,708)(292,707)(293,710)(294,709)(295,711)(296,712)(297,720)
(298,719)(299,717)(300,718)(301,715)(302,716)(303,714)(304,713)(305,689)
(306,690)(307,692)(308,691)(309,694)(310,693)(311,695)(312,696)(313,704)
(314,703)(315,701)(316,702)(317,699)(318,700)(319,698)(320,697)(321,673)
(322,674)(323,676)(324,675)(325,678)(326,677)(327,679)(328,680)(329,688)
(330,687)(331,685)(332,686)(333,683)(334,684)(335,682)(336,681)(337,657)
(338,658)(339,660)(340,659)(341,662)(342,661)(343,663)(344,664)(345,672)
(346,671)(347,669)(348,670)(349,667)(350,668)(351,666)(352,665)(353,641)
(354,642)(355,644)(356,643)(357,646)(358,645)(359,647)(360,648)(361,656)
(362,655)(363,653)(364,654)(365,651)(366,652)(367,650)(368,649)(369,625)
(370,626)(371,628)(372,627)(373,630)(374,629)(375,631)(376,632)(377,640)
(378,639)(379,637)(380,638)(381,635)(382,636)(383,634)(384,633)(385,609)
(386,610)(387,612)(388,611)(389,614)(390,613)(391,615)(392,616)(393,624)
(394,623)(395,621)(396,622)(397,619)(398,620)(399,618)(400,617)(401,593)
(402,594)(403,596)(404,595)(405,598)(406,597)(407,599)(408,600)(409,608)
(410,607)(411,605)(412,606)(413,603)(414,604)(415,602)(416,601)(417,577)
(418,578)(419,580)(420,579)(421,582)(422,581)(423,583)(424,584)(425,592)
(426,591)(427,589)(428,590)(429,587)(430,588)(431,586)(432,585)(433,561)
(434,562)(435,564)(436,563)(437,566)(438,565)(439,567)(440,568)(441,576)
(442,575)(443,573)(444,574)(445,571)(446,572)(447,570)(448,569)(449,545)
(450,546)(451,548)(452,547)(453,550)(454,549)(455,551)(456,552)(457,560)
(458,559)(459,557)(460,558)(461,555)(462,556)(463,554)(464,553)(465,529)
(466,530)(467,532)(468,531)(469,534)(470,533)(471,535)(472,536)(473,544)
(474,543)(475,541)(476,542)(477,539)(478,540)(479,538)(480,537);
s1 := Sym(720)!( 1,289)( 2,298)( 3,299)( 4,292)( 5,304)( 6,295)( 7,294)
( 8,301)( 9,297)( 10,290)( 11,291)( 12,300)( 13,296)( 14,303)( 15,302)
( 16,293)( 17,321)( 18,330)( 19,331)( 20,324)( 21,336)( 22,327)( 23,326)
( 24,333)( 25,329)( 26,322)( 27,323)( 28,332)( 29,328)( 30,335)( 31,334)
( 32,325)( 33,305)( 34,314)( 35,315)( 36,308)( 37,320)( 38,311)( 39,310)
( 40,317)( 41,313)( 42,306)( 43,307)( 44,316)( 45,312)( 46,319)( 47,318)
( 48,309)( 49,241)( 50,250)( 51,251)( 52,244)( 53,256)( 54,247)( 55,246)
( 56,253)( 57,249)( 58,242)( 59,243)( 60,252)( 61,248)( 62,255)( 63,254)
( 64,245)( 65,273)( 66,282)( 67,283)( 68,276)( 69,288)( 70,279)( 71,278)
( 72,285)( 73,281)( 74,274)( 75,275)( 76,284)( 77,280)( 78,287)( 79,286)
( 80,277)( 81,257)( 82,266)( 83,267)( 84,260)( 85,272)( 86,263)( 87,262)
( 88,269)( 89,265)( 90,258)( 91,259)( 92,268)( 93,264)( 94,271)( 95,270)
( 96,261)( 97,433)( 98,442)( 99,443)(100,436)(101,448)(102,439)(103,438)
(104,445)(105,441)(106,434)(107,435)(108,444)(109,440)(110,447)(111,446)
(112,437)(113,465)(114,474)(115,475)(116,468)(117,480)(118,471)(119,470)
(120,477)(121,473)(122,466)(123,467)(124,476)(125,472)(126,479)(127,478)
(128,469)(129,449)(130,458)(131,459)(132,452)(133,464)(134,455)(135,454)
(136,461)(137,457)(138,450)(139,451)(140,460)(141,456)(142,463)(143,462)
(144,453)(145,385)(146,394)(147,395)(148,388)(149,400)(150,391)(151,390)
(152,397)(153,393)(154,386)(155,387)(156,396)(157,392)(158,399)(159,398)
(160,389)(161,417)(162,426)(163,427)(164,420)(165,432)(166,423)(167,422)
(168,429)(169,425)(170,418)(171,419)(172,428)(173,424)(174,431)(175,430)
(176,421)(177,401)(178,410)(179,411)(180,404)(181,416)(182,407)(183,406)
(184,413)(185,409)(186,402)(187,403)(188,412)(189,408)(190,415)(191,414)
(192,405)(193,337)(194,346)(195,347)(196,340)(197,352)(198,343)(199,342)
(200,349)(201,345)(202,338)(203,339)(204,348)(205,344)(206,351)(207,350)
(208,341)(209,369)(210,378)(211,379)(212,372)(213,384)(214,375)(215,374)
(216,381)(217,377)(218,370)(219,371)(220,380)(221,376)(222,383)(223,382)
(224,373)(225,353)(226,362)(227,363)(228,356)(229,368)(230,359)(231,358)
(232,365)(233,361)(234,354)(235,355)(236,364)(237,360)(238,367)(239,366)
(240,357)(481,561)(482,570)(483,571)(484,564)(485,576)(486,567)(487,566)
(488,573)(489,569)(490,562)(491,563)(492,572)(493,568)(494,575)(495,574)
(496,565)(497,545)(498,554)(499,555)(500,548)(501,560)(502,551)(503,550)
(504,557)(505,553)(506,546)(507,547)(508,556)(509,552)(510,559)(511,558)
(512,549)(513,529)(514,538)(515,539)(516,532)(517,544)(518,535)(519,534)
(520,541)(521,537)(522,530)(523,531)(524,540)(525,536)(526,543)(527,542)
(528,533)(577,705)(578,714)(579,715)(580,708)(581,720)(582,711)(583,710)
(584,717)(585,713)(586,706)(587,707)(588,716)(589,712)(590,719)(591,718)
(592,709)(593,689)(594,698)(595,699)(596,692)(597,704)(598,695)(599,694)
(600,701)(601,697)(602,690)(603,691)(604,700)(605,696)(606,703)(607,702)
(608,693)(609,673)(610,682)(611,683)(612,676)(613,688)(614,679)(615,678)
(616,685)(617,681)(618,674)(619,675)(620,684)(621,680)(622,687)(623,686)
(624,677)(625,657)(626,666)(627,667)(628,660)(629,672)(630,663)(631,662)
(632,669)(633,665)(634,658)(635,659)(636,668)(637,664)(638,671)(639,670)
(640,661)(642,650)(643,651)(645,656)(646,647)(648,653)(654,655);
s2 := Sym(720)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)
(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)
(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)
(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)
(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)
(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)
(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)
(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)
(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)
(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)
(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)
(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)
(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)
(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)
(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)
(719,720);
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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope