Polytope of Type {4,45,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,45,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,4577)
Rank : 4
Schlafli Type : {4,45,4}
Number of vertices, edges, etc : 4, 90, 90, 4
Order of s0s1s2s3 : 45
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,15,4}*480
5-fold quotients : {4,9,4}*288
15-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)
(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)
(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)
(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)
(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480)
(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)(488,496)
(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)(504,512)
(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)(520,528)
(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)(536,544)
(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)(552,560)
(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)(568,576)
(577,585)(578,586)(579,587)(580,588)(581,589)(582,590)(583,591)(584,592)
(593,601)(594,602)(595,603)(596,604)(597,605)(598,606)(599,607)(600,608)
(609,617)(610,618)(611,619)(612,620)(613,621)(614,622)(615,623)(616,624)
(625,633)(626,634)(627,635)(628,636)(629,637)(630,638)(631,639)(632,640)
(641,649)(642,650)(643,651)(644,652)(645,653)(646,654)(647,655)(648,656)
(657,665)(658,666)(659,667)(660,668)(661,669)(662,670)(663,671)(664,672)
(673,681)(674,682)(675,683)(676,684)(677,685)(678,686)(679,687)(680,688)
(689,697)(690,698)(691,699)(692,700)(693,701)(694,702)(695,703)(696,704)
(705,713)(706,714)(707,715)(708,716)(709,717)(710,718)(711,719)(712,720);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,193)( 50,194)
( 51,196)( 52,195)( 53,197)( 54,198)( 55,200)( 56,199)( 57,205)( 58,206)
( 59,208)( 60,207)( 61,201)( 62,202)( 63,204)( 64,203)( 65,225)( 66,226)
( 67,228)( 68,227)( 69,229)( 70,230)( 71,232)( 72,231)( 73,237)( 74,238)
( 75,240)( 76,239)( 77,233)( 78,234)( 79,236)( 80,235)( 81,209)( 82,210)
( 83,212)( 84,211)( 85,213)( 86,214)( 87,216)( 88,215)( 89,221)( 90,222)
( 91,224)( 92,223)( 93,217)( 94,218)( 95,220)( 96,219)( 97,145)( 98,146)
( 99,148)(100,147)(101,149)(102,150)(103,152)(104,151)(105,157)(106,158)
(107,160)(108,159)(109,153)(110,154)(111,156)(112,155)(113,177)(114,178)
(115,180)(116,179)(117,181)(118,182)(119,184)(120,183)(121,189)(122,190)
(123,192)(124,191)(125,185)(126,186)(127,188)(128,187)(129,161)(130,162)
(131,164)(132,163)(133,165)(134,166)(135,168)(136,167)(137,173)(138,174)
(139,176)(140,175)(141,169)(142,170)(143,172)(144,171)(241,513)(242,514)
(243,516)(244,515)(245,517)(246,518)(247,520)(248,519)(249,525)(250,526)
(251,528)(252,527)(253,521)(254,522)(255,524)(256,523)(257,497)(258,498)
(259,500)(260,499)(261,501)(262,502)(263,504)(264,503)(265,509)(266,510)
(267,512)(268,511)(269,505)(270,506)(271,508)(272,507)(273,481)(274,482)
(275,484)(276,483)(277,485)(278,486)(279,488)(280,487)(281,493)(282,494)
(283,496)(284,495)(285,489)(286,490)(287,492)(288,491)(289,705)(290,706)
(291,708)(292,707)(293,709)(294,710)(295,712)(296,711)(297,717)(298,718)
(299,720)(300,719)(301,713)(302,714)(303,716)(304,715)(305,689)(306,690)
(307,692)(308,691)(309,693)(310,694)(311,696)(312,695)(313,701)(314,702)
(315,704)(316,703)(317,697)(318,698)(319,700)(320,699)(321,673)(322,674)
(323,676)(324,675)(325,677)(326,678)(327,680)(328,679)(329,685)(330,686)
(331,688)(332,687)(333,681)(334,682)(335,684)(336,683)(337,657)(338,658)
(339,660)(340,659)(341,661)(342,662)(343,664)(344,663)(345,669)(346,670)
(347,672)(348,671)(349,665)(350,666)(351,668)(352,667)(353,641)(354,642)
(355,644)(356,643)(357,645)(358,646)(359,648)(360,647)(361,653)(362,654)
(363,656)(364,655)(365,649)(366,650)(367,652)(368,651)(369,625)(370,626)
(371,628)(372,627)(373,629)(374,630)(375,632)(376,631)(377,637)(378,638)
(379,640)(380,639)(381,633)(382,634)(383,636)(384,635)(385,609)(386,610)
(387,612)(388,611)(389,613)(390,614)(391,616)(392,615)(393,621)(394,622)
(395,624)(396,623)(397,617)(398,618)(399,620)(400,619)(401,593)(402,594)
(403,596)(404,595)(405,597)(406,598)(407,600)(408,599)(409,605)(410,606)
(411,608)(412,607)(413,601)(414,602)(415,604)(416,603)(417,577)(418,578)
(419,580)(420,579)(421,581)(422,582)(423,584)(424,583)(425,589)(426,590)
(427,592)(428,591)(429,585)(430,586)(431,588)(432,587)(433,561)(434,562)
(435,564)(436,563)(437,565)(438,566)(439,568)(440,567)(441,573)(442,574)
(443,576)(444,575)(445,569)(446,570)(447,572)(448,571)(449,545)(450,546)
(451,548)(452,547)(453,549)(454,550)(455,552)(456,551)(457,557)(458,558)
(459,560)(460,559)(461,553)(462,554)(463,556)(464,555)(465,529)(466,530)
(467,532)(468,531)(469,533)(470,534)(471,536)(472,535)(473,541)(474,542)
(475,544)(476,543)(477,537)(478,538)(479,540)(480,539);;
s2 := ( 1,289)( 2,292)( 3,291)( 4,290)( 5,301)( 6,304)( 7,303)( 8,302)
( 9,297)( 10,300)( 11,299)( 12,298)( 13,293)( 14,296)( 15,295)( 16,294)
( 17,321)( 18,324)( 19,323)( 20,322)( 21,333)( 22,336)( 23,335)( 24,334)
( 25,329)( 26,332)( 27,331)( 28,330)( 29,325)( 30,328)( 31,327)( 32,326)
( 33,305)( 34,308)( 35,307)( 36,306)( 37,317)( 38,320)( 39,319)( 40,318)
( 41,313)( 42,316)( 43,315)( 44,314)( 45,309)( 46,312)( 47,311)( 48,310)
( 49,241)( 50,244)( 51,243)( 52,242)( 53,253)( 54,256)( 55,255)( 56,254)
( 57,249)( 58,252)( 59,251)( 60,250)( 61,245)( 62,248)( 63,247)( 64,246)
( 65,273)( 66,276)( 67,275)( 68,274)( 69,285)( 70,288)( 71,287)( 72,286)
( 73,281)( 74,284)( 75,283)( 76,282)( 77,277)( 78,280)( 79,279)( 80,278)
( 81,257)( 82,260)( 83,259)( 84,258)( 85,269)( 86,272)( 87,271)( 88,270)
( 89,265)( 90,268)( 91,267)( 92,266)( 93,261)( 94,264)( 95,263)( 96,262)
( 97,433)( 98,436)( 99,435)(100,434)(101,445)(102,448)(103,447)(104,446)
(105,441)(106,444)(107,443)(108,442)(109,437)(110,440)(111,439)(112,438)
(113,465)(114,468)(115,467)(116,466)(117,477)(118,480)(119,479)(120,478)
(121,473)(122,476)(123,475)(124,474)(125,469)(126,472)(127,471)(128,470)
(129,449)(130,452)(131,451)(132,450)(133,461)(134,464)(135,463)(136,462)
(137,457)(138,460)(139,459)(140,458)(141,453)(142,456)(143,455)(144,454)
(145,385)(146,388)(147,387)(148,386)(149,397)(150,400)(151,399)(152,398)
(153,393)(154,396)(155,395)(156,394)(157,389)(158,392)(159,391)(160,390)
(161,417)(162,420)(163,419)(164,418)(165,429)(166,432)(167,431)(168,430)
(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)(176,422)
(177,401)(178,404)(179,403)(180,402)(181,413)(182,416)(183,415)(184,414)
(185,409)(186,412)(187,411)(188,410)(189,405)(190,408)(191,407)(192,406)
(193,337)(194,340)(195,339)(196,338)(197,349)(198,352)(199,351)(200,350)
(201,345)(202,348)(203,347)(204,346)(205,341)(206,344)(207,343)(208,342)
(209,369)(210,372)(211,371)(212,370)(213,381)(214,384)(215,383)(216,382)
(217,377)(218,380)(219,379)(220,378)(221,373)(222,376)(223,375)(224,374)
(225,353)(226,356)(227,355)(228,354)(229,365)(230,368)(231,367)(232,366)
(233,361)(234,364)(235,363)(236,362)(237,357)(238,360)(239,359)(240,358)
(481,561)(482,564)(483,563)(484,562)(485,573)(486,576)(487,575)(488,574)
(489,569)(490,572)(491,571)(492,570)(493,565)(494,568)(495,567)(496,566)
(497,545)(498,548)(499,547)(500,546)(501,557)(502,560)(503,559)(504,558)
(505,553)(506,556)(507,555)(508,554)(509,549)(510,552)(511,551)(512,550)
(513,529)(514,532)(515,531)(516,530)(517,541)(518,544)(519,543)(520,542)
(521,537)(522,540)(523,539)(524,538)(525,533)(526,536)(527,535)(528,534)
(577,705)(578,708)(579,707)(580,706)(581,717)(582,720)(583,719)(584,718)
(585,713)(586,716)(587,715)(588,714)(589,709)(590,712)(591,711)(592,710)
(593,689)(594,692)(595,691)(596,690)(597,701)(598,704)(599,703)(600,702)
(601,697)(602,700)(603,699)(604,698)(605,693)(606,696)(607,695)(608,694)
(609,673)(610,676)(611,675)(612,674)(613,685)(614,688)(615,687)(616,686)
(617,681)(618,684)(619,683)(620,682)(621,677)(622,680)(623,679)(624,678)
(625,657)(626,660)(627,659)(628,658)(629,669)(630,672)(631,671)(632,670)
(633,665)(634,668)(635,667)(636,666)(637,661)(638,664)(639,663)(640,662)
(642,644)(645,653)(646,656)(647,655)(648,654)(650,652);;
s3 := ( 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,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s2*s1*s3*s2*s3*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, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)
(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)
(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)
(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)
(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)
(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)
(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)
(472,480)(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)
(488,496)(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)
(504,512)(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)
(520,528)(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)
(536,544)(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)
(552,560)(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)
(568,576)(577,585)(578,586)(579,587)(580,588)(581,589)(582,590)(583,591)
(584,592)(593,601)(594,602)(595,603)(596,604)(597,605)(598,606)(599,607)
(600,608)(609,617)(610,618)(611,619)(612,620)(613,621)(614,622)(615,623)
(616,624)(625,633)(626,634)(627,635)(628,636)(629,637)(630,638)(631,639)
(632,640)(641,649)(642,650)(643,651)(644,652)(645,653)(646,654)(647,655)
(648,656)(657,665)(658,666)(659,667)(660,668)(661,669)(662,670)(663,671)
(664,672)(673,681)(674,682)(675,683)(676,684)(677,685)(678,686)(679,687)
(680,688)(689,697)(690,698)(691,699)(692,700)(693,701)(694,702)(695,703)
(696,704)(705,713)(706,714)(707,715)(708,716)(709,717)(710,718)(711,719)
(712,720);
s1 := Sym(720)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,193)
( 50,194)( 51,196)( 52,195)( 53,197)( 54,198)( 55,200)( 56,199)( 57,205)
( 58,206)( 59,208)( 60,207)( 61,201)( 62,202)( 63,204)( 64,203)( 65,225)
( 66,226)( 67,228)( 68,227)( 69,229)( 70,230)( 71,232)( 72,231)( 73,237)
( 74,238)( 75,240)( 76,239)( 77,233)( 78,234)( 79,236)( 80,235)( 81,209)
( 82,210)( 83,212)( 84,211)( 85,213)( 86,214)( 87,216)( 88,215)( 89,221)
( 90,222)( 91,224)( 92,223)( 93,217)( 94,218)( 95,220)( 96,219)( 97,145)
( 98,146)( 99,148)(100,147)(101,149)(102,150)(103,152)(104,151)(105,157)
(106,158)(107,160)(108,159)(109,153)(110,154)(111,156)(112,155)(113,177)
(114,178)(115,180)(116,179)(117,181)(118,182)(119,184)(120,183)(121,189)
(122,190)(123,192)(124,191)(125,185)(126,186)(127,188)(128,187)(129,161)
(130,162)(131,164)(132,163)(133,165)(134,166)(135,168)(136,167)(137,173)
(138,174)(139,176)(140,175)(141,169)(142,170)(143,172)(144,171)(241,513)
(242,514)(243,516)(244,515)(245,517)(246,518)(247,520)(248,519)(249,525)
(250,526)(251,528)(252,527)(253,521)(254,522)(255,524)(256,523)(257,497)
(258,498)(259,500)(260,499)(261,501)(262,502)(263,504)(264,503)(265,509)
(266,510)(267,512)(268,511)(269,505)(270,506)(271,508)(272,507)(273,481)
(274,482)(275,484)(276,483)(277,485)(278,486)(279,488)(280,487)(281,493)
(282,494)(283,496)(284,495)(285,489)(286,490)(287,492)(288,491)(289,705)
(290,706)(291,708)(292,707)(293,709)(294,710)(295,712)(296,711)(297,717)
(298,718)(299,720)(300,719)(301,713)(302,714)(303,716)(304,715)(305,689)
(306,690)(307,692)(308,691)(309,693)(310,694)(311,696)(312,695)(313,701)
(314,702)(315,704)(316,703)(317,697)(318,698)(319,700)(320,699)(321,673)
(322,674)(323,676)(324,675)(325,677)(326,678)(327,680)(328,679)(329,685)
(330,686)(331,688)(332,687)(333,681)(334,682)(335,684)(336,683)(337,657)
(338,658)(339,660)(340,659)(341,661)(342,662)(343,664)(344,663)(345,669)
(346,670)(347,672)(348,671)(349,665)(350,666)(351,668)(352,667)(353,641)
(354,642)(355,644)(356,643)(357,645)(358,646)(359,648)(360,647)(361,653)
(362,654)(363,656)(364,655)(365,649)(366,650)(367,652)(368,651)(369,625)
(370,626)(371,628)(372,627)(373,629)(374,630)(375,632)(376,631)(377,637)
(378,638)(379,640)(380,639)(381,633)(382,634)(383,636)(384,635)(385,609)
(386,610)(387,612)(388,611)(389,613)(390,614)(391,616)(392,615)(393,621)
(394,622)(395,624)(396,623)(397,617)(398,618)(399,620)(400,619)(401,593)
(402,594)(403,596)(404,595)(405,597)(406,598)(407,600)(408,599)(409,605)
(410,606)(411,608)(412,607)(413,601)(414,602)(415,604)(416,603)(417,577)
(418,578)(419,580)(420,579)(421,581)(422,582)(423,584)(424,583)(425,589)
(426,590)(427,592)(428,591)(429,585)(430,586)(431,588)(432,587)(433,561)
(434,562)(435,564)(436,563)(437,565)(438,566)(439,568)(440,567)(441,573)
(442,574)(443,576)(444,575)(445,569)(446,570)(447,572)(448,571)(449,545)
(450,546)(451,548)(452,547)(453,549)(454,550)(455,552)(456,551)(457,557)
(458,558)(459,560)(460,559)(461,553)(462,554)(463,556)(464,555)(465,529)
(466,530)(467,532)(468,531)(469,533)(470,534)(471,536)(472,535)(473,541)
(474,542)(475,544)(476,543)(477,537)(478,538)(479,540)(480,539);
s2 := Sym(720)!( 1,289)( 2,292)( 3,291)( 4,290)( 5,301)( 6,304)( 7,303)
( 8,302)( 9,297)( 10,300)( 11,299)( 12,298)( 13,293)( 14,296)( 15,295)
( 16,294)( 17,321)( 18,324)( 19,323)( 20,322)( 21,333)( 22,336)( 23,335)
( 24,334)( 25,329)( 26,332)( 27,331)( 28,330)( 29,325)( 30,328)( 31,327)
( 32,326)( 33,305)( 34,308)( 35,307)( 36,306)( 37,317)( 38,320)( 39,319)
( 40,318)( 41,313)( 42,316)( 43,315)( 44,314)( 45,309)( 46,312)( 47,311)
( 48,310)( 49,241)( 50,244)( 51,243)( 52,242)( 53,253)( 54,256)( 55,255)
( 56,254)( 57,249)( 58,252)( 59,251)( 60,250)( 61,245)( 62,248)( 63,247)
( 64,246)( 65,273)( 66,276)( 67,275)( 68,274)( 69,285)( 70,288)( 71,287)
( 72,286)( 73,281)( 74,284)( 75,283)( 76,282)( 77,277)( 78,280)( 79,279)
( 80,278)( 81,257)( 82,260)( 83,259)( 84,258)( 85,269)( 86,272)( 87,271)
( 88,270)( 89,265)( 90,268)( 91,267)( 92,266)( 93,261)( 94,264)( 95,263)
( 96,262)( 97,433)( 98,436)( 99,435)(100,434)(101,445)(102,448)(103,447)
(104,446)(105,441)(106,444)(107,443)(108,442)(109,437)(110,440)(111,439)
(112,438)(113,465)(114,468)(115,467)(116,466)(117,477)(118,480)(119,479)
(120,478)(121,473)(122,476)(123,475)(124,474)(125,469)(126,472)(127,471)
(128,470)(129,449)(130,452)(131,451)(132,450)(133,461)(134,464)(135,463)
(136,462)(137,457)(138,460)(139,459)(140,458)(141,453)(142,456)(143,455)
(144,454)(145,385)(146,388)(147,387)(148,386)(149,397)(150,400)(151,399)
(152,398)(153,393)(154,396)(155,395)(156,394)(157,389)(158,392)(159,391)
(160,390)(161,417)(162,420)(163,419)(164,418)(165,429)(166,432)(167,431)
(168,430)(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)
(176,422)(177,401)(178,404)(179,403)(180,402)(181,413)(182,416)(183,415)
(184,414)(185,409)(186,412)(187,411)(188,410)(189,405)(190,408)(191,407)
(192,406)(193,337)(194,340)(195,339)(196,338)(197,349)(198,352)(199,351)
(200,350)(201,345)(202,348)(203,347)(204,346)(205,341)(206,344)(207,343)
(208,342)(209,369)(210,372)(211,371)(212,370)(213,381)(214,384)(215,383)
(216,382)(217,377)(218,380)(219,379)(220,378)(221,373)(222,376)(223,375)
(224,374)(225,353)(226,356)(227,355)(228,354)(229,365)(230,368)(231,367)
(232,366)(233,361)(234,364)(235,363)(236,362)(237,357)(238,360)(239,359)
(240,358)(481,561)(482,564)(483,563)(484,562)(485,573)(486,576)(487,575)
(488,574)(489,569)(490,572)(491,571)(492,570)(493,565)(494,568)(495,567)
(496,566)(497,545)(498,548)(499,547)(500,546)(501,557)(502,560)(503,559)
(504,558)(505,553)(506,556)(507,555)(508,554)(509,549)(510,552)(511,551)
(512,550)(513,529)(514,532)(515,531)(516,530)(517,541)(518,544)(519,543)
(520,542)(521,537)(522,540)(523,539)(524,538)(525,533)(526,536)(527,535)
(528,534)(577,705)(578,708)(579,707)(580,706)(581,717)(582,720)(583,719)
(584,718)(585,713)(586,716)(587,715)(588,714)(589,709)(590,712)(591,711)
(592,710)(593,689)(594,692)(595,691)(596,690)(597,701)(598,704)(599,703)
(600,702)(601,697)(602,700)(603,699)(604,698)(605,693)(606,696)(607,695)
(608,694)(609,673)(610,676)(611,675)(612,674)(613,685)(614,688)(615,687)
(616,686)(617,681)(618,684)(619,683)(620,682)(621,677)(622,680)(623,679)
(624,678)(625,657)(626,660)(627,659)(628,658)(629,669)(630,672)(631,671)
(632,670)(633,665)(634,668)(635,667)(636,666)(637,661)(638,664)(639,663)
(640,662)(642,644)(645,653)(646,656)(647,655)(648,654)(650,652);
s3 := 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,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s2*s1*s3*s2*s3*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