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Polytope of Type {30,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,12,2}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5328)
Rank : 4
Schlafli Type : {30,12,2}
Number of vertices, edges, etc : 30, 180, 12, 2
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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 : {30,6,2}*720a
   3-fold quotients : {10,12,2}*480
   5-fold quotients : {6,12,2}*288b
   6-fold quotients : {10,6,2}*240
   9-fold quotients : {10,4,2}*160
   10-fold quotients : {6,6,2}*144b
   15-fold quotients : {2,12,2}*96
   18-fold quotients : {10,2,2}*80
   20-fold quotients : {6,3,2}*72
   30-fold quotients : {2,6,2}*48
   36-fold quotients : {5,2,2}*40
   45-fold quotients : {2,4,2}*32
   60-fold quotients : {2,3,2}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,541)(  2,545)(  3,544)(  4,543)(  5,542)(  6,551)(  7,555)(  8,554)
(  9,553)( 10,552)( 11,546)( 12,550)( 13,549)( 14,548)( 15,547)( 16,556)
( 17,560)( 18,559)( 19,558)( 20,557)( 21,566)( 22,570)( 23,569)( 24,568)
( 25,567)( 26,561)( 27,565)( 28,564)( 29,563)( 30,562)( 31,571)( 32,575)
( 33,574)( 34,573)( 35,572)( 36,581)( 37,585)( 38,584)( 39,583)( 40,582)
( 41,576)( 42,580)( 43,579)( 44,578)( 45,577)( 46,586)( 47,590)( 48,589)
( 49,588)( 50,587)( 51,596)( 52,600)( 53,599)( 54,598)( 55,597)( 56,591)
( 57,595)( 58,594)( 59,593)( 60,592)( 61,601)( 62,605)( 63,604)( 64,603)
( 65,602)( 66,611)( 67,615)( 68,614)( 69,613)( 70,612)( 71,606)( 72,610)
( 73,609)( 74,608)( 75,607)( 76,616)( 77,620)( 78,619)( 79,618)( 80,617)
( 81,626)( 82,630)( 83,629)( 84,628)( 85,627)( 86,621)( 87,625)( 88,624)
( 89,623)( 90,622)( 91,631)( 92,635)( 93,634)( 94,633)( 95,632)( 96,641)
( 97,645)( 98,644)( 99,643)(100,642)(101,636)(102,640)(103,639)(104,638)
(105,637)(106,646)(107,650)(108,649)(109,648)(110,647)(111,656)(112,660)
(113,659)(114,658)(115,657)(116,651)(117,655)(118,654)(119,653)(120,652)
(121,661)(122,665)(123,664)(124,663)(125,662)(126,671)(127,675)(128,674)
(129,673)(130,672)(131,666)(132,670)(133,669)(134,668)(135,667)(136,676)
(137,680)(138,679)(139,678)(140,677)(141,686)(142,690)(143,689)(144,688)
(145,687)(146,681)(147,685)(148,684)(149,683)(150,682)(151,691)(152,695)
(153,694)(154,693)(155,692)(156,701)(157,705)(158,704)(159,703)(160,702)
(161,696)(162,700)(163,699)(164,698)(165,697)(166,706)(167,710)(168,709)
(169,708)(170,707)(171,716)(172,720)(173,719)(174,718)(175,717)(176,711)
(177,715)(178,714)(179,713)(180,712)(181,406)(182,410)(183,409)(184,408)
(185,407)(186,416)(187,420)(188,419)(189,418)(190,417)(191,411)(192,415)
(193,414)(194,413)(195,412)(196,421)(197,425)(198,424)(199,423)(200,422)
(201,431)(202,435)(203,434)(204,433)(205,432)(206,426)(207,430)(208,429)
(209,428)(210,427)(211,436)(212,440)(213,439)(214,438)(215,437)(216,446)
(217,450)(218,449)(219,448)(220,447)(221,441)(222,445)(223,444)(224,443)
(225,442)(226,361)(227,365)(228,364)(229,363)(230,362)(231,371)(232,375)
(233,374)(234,373)(235,372)(236,366)(237,370)(238,369)(239,368)(240,367)
(241,376)(242,380)(243,379)(244,378)(245,377)(246,386)(247,390)(248,389)
(249,388)(250,387)(251,381)(252,385)(253,384)(254,383)(255,382)(256,391)
(257,395)(258,394)(259,393)(260,392)(261,401)(262,405)(263,404)(264,403)
(265,402)(266,396)(267,400)(268,399)(269,398)(270,397)(271,496)(272,500)
(273,499)(274,498)(275,497)(276,506)(277,510)(278,509)(279,508)(280,507)
(281,501)(282,505)(283,504)(284,503)(285,502)(286,511)(287,515)(288,514)
(289,513)(290,512)(291,521)(292,525)(293,524)(294,523)(295,522)(296,516)
(297,520)(298,519)(299,518)(300,517)(301,526)(302,530)(303,529)(304,528)
(305,527)(306,536)(307,540)(308,539)(309,538)(310,537)(311,531)(312,535)
(313,534)(314,533)(315,532)(316,451)(317,455)(318,454)(319,453)(320,452)
(321,461)(322,465)(323,464)(324,463)(325,462)(326,456)(327,460)(328,459)
(329,458)(330,457)(331,466)(332,470)(333,469)(334,468)(335,467)(336,476)
(337,480)(338,479)(339,478)(340,477)(341,471)(342,475)(343,474)(344,473)
(345,472)(346,481)(347,485)(348,484)(349,483)(350,482)(351,491)(352,495)
(353,494)(354,493)(355,492)(356,486)(357,490)(358,489)(359,488)(360,487);;
s1 := (  1,637)(  2,636)(  3,640)(  4,639)(  5,638)(  6,632)(  7,631)(  8,635)
(  9,634)( 10,633)( 11,642)( 12,641)( 13,645)( 14,644)( 15,643)( 16,667)
( 17,666)( 18,670)( 19,669)( 20,668)( 21,662)( 22,661)( 23,665)( 24,664)
( 25,663)( 26,672)( 27,671)( 28,675)( 29,674)( 30,673)( 31,652)( 32,651)
( 33,655)( 34,654)( 35,653)( 36,647)( 37,646)( 38,650)( 39,649)( 40,648)
( 41,657)( 42,656)( 43,660)( 44,659)( 45,658)( 46,682)( 47,681)( 48,685)
( 49,684)( 50,683)( 51,677)( 52,676)( 53,680)( 54,679)( 55,678)( 56,687)
( 57,686)( 58,690)( 59,689)( 60,688)( 61,712)( 62,711)( 63,715)( 64,714)
( 65,713)( 66,707)( 67,706)( 68,710)( 69,709)( 70,708)( 71,717)( 72,716)
( 73,720)( 74,719)( 75,718)( 76,697)( 77,696)( 78,700)( 79,699)( 80,698)
( 81,692)( 82,691)( 83,695)( 84,694)( 85,693)( 86,702)( 87,701)( 88,705)
( 89,704)( 90,703)( 91,547)( 92,546)( 93,550)( 94,549)( 95,548)( 96,542)
( 97,541)( 98,545)( 99,544)(100,543)(101,552)(102,551)(103,555)(104,554)
(105,553)(106,577)(107,576)(108,580)(109,579)(110,578)(111,572)(112,571)
(113,575)(114,574)(115,573)(116,582)(117,581)(118,585)(119,584)(120,583)
(121,562)(122,561)(123,565)(124,564)(125,563)(126,557)(127,556)(128,560)
(129,559)(130,558)(131,567)(132,566)(133,570)(134,569)(135,568)(136,592)
(137,591)(138,595)(139,594)(140,593)(141,587)(142,586)(143,590)(144,589)
(145,588)(146,597)(147,596)(148,600)(149,599)(150,598)(151,622)(152,621)
(153,625)(154,624)(155,623)(156,617)(157,616)(158,620)(159,619)(160,618)
(161,627)(162,626)(163,630)(164,629)(165,628)(166,607)(167,606)(168,610)
(169,609)(170,608)(171,602)(172,601)(173,605)(174,604)(175,603)(176,612)
(177,611)(178,615)(179,614)(180,613)(181,502)(182,501)(183,505)(184,504)
(185,503)(186,497)(187,496)(188,500)(189,499)(190,498)(191,507)(192,506)
(193,510)(194,509)(195,508)(196,532)(197,531)(198,535)(199,534)(200,533)
(201,527)(202,526)(203,530)(204,529)(205,528)(206,537)(207,536)(208,540)
(209,539)(210,538)(211,517)(212,516)(213,520)(214,519)(215,518)(216,512)
(217,511)(218,515)(219,514)(220,513)(221,522)(222,521)(223,525)(224,524)
(225,523)(226,457)(227,456)(228,460)(229,459)(230,458)(231,452)(232,451)
(233,455)(234,454)(235,453)(236,462)(237,461)(238,465)(239,464)(240,463)
(241,487)(242,486)(243,490)(244,489)(245,488)(246,482)(247,481)(248,485)
(249,484)(250,483)(251,492)(252,491)(253,495)(254,494)(255,493)(256,472)
(257,471)(258,475)(259,474)(260,473)(261,467)(262,466)(263,470)(264,469)
(265,468)(266,477)(267,476)(268,480)(269,479)(270,478)(271,412)(272,411)
(273,415)(274,414)(275,413)(276,407)(277,406)(278,410)(279,409)(280,408)
(281,417)(282,416)(283,420)(284,419)(285,418)(286,442)(287,441)(288,445)
(289,444)(290,443)(291,437)(292,436)(293,440)(294,439)(295,438)(296,447)
(297,446)(298,450)(299,449)(300,448)(301,427)(302,426)(303,430)(304,429)
(305,428)(306,422)(307,421)(308,425)(309,424)(310,423)(311,432)(312,431)
(313,435)(314,434)(315,433)(316,367)(317,366)(318,370)(319,369)(320,368)
(321,362)(322,361)(323,365)(324,364)(325,363)(326,372)(327,371)(328,375)
(329,374)(330,373)(331,397)(332,396)(333,400)(334,399)(335,398)(336,392)
(337,391)(338,395)(339,394)(340,393)(341,402)(342,401)(343,405)(344,404)
(345,403)(346,382)(347,381)(348,385)(349,384)(350,383)(351,377)(352,376)
(353,380)(354,379)(355,378)(356,387)(357,386)(358,390)(359,389)(360,388);;
s2 := (  1,286)(  2,287)(  3,288)(  4,289)(  5,290)(  6,296)(  7,297)(  8,298)
(  9,299)( 10,300)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,271)
( 17,272)( 18,273)( 19,274)( 20,275)( 21,281)( 22,282)( 23,283)( 24,284)
( 25,285)( 26,276)( 27,277)( 28,278)( 29,279)( 30,280)( 31,301)( 32,302)
( 33,303)( 34,304)( 35,305)( 36,311)( 37,312)( 38,313)( 39,314)( 40,315)
( 41,306)( 42,307)( 43,308)( 44,309)( 45,310)( 46,331)( 47,332)( 48,333)
( 49,334)( 50,335)( 51,341)( 52,342)( 53,343)( 54,344)( 55,345)( 56,336)
( 57,337)( 58,338)( 59,339)( 60,340)( 61,316)( 62,317)( 63,318)( 64,319)
( 65,320)( 66,326)( 67,327)( 68,328)( 69,329)( 70,330)( 71,321)( 72,322)
( 73,323)( 74,324)( 75,325)( 76,346)( 77,347)( 78,348)( 79,349)( 80,350)
( 81,356)( 82,357)( 83,358)( 84,359)( 85,360)( 86,351)( 87,352)( 88,353)
( 89,354)( 90,355)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,251)
( 97,252)( 98,253)( 99,254)(100,255)(101,246)(102,247)(103,248)(104,249)
(105,250)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)(112,237)
(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)(120,235)
(121,256)(122,257)(123,258)(124,259)(125,260)(126,266)(127,267)(128,268)
(129,269)(130,270)(131,261)(132,262)(133,263)(134,264)(135,265)(136,196)
(137,197)(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)(144,209)
(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,181)(152,182)
(153,183)(154,184)(155,185)(156,191)(157,192)(158,193)(159,194)(160,195)
(161,186)(162,187)(163,188)(164,189)(165,190)(166,211)(167,212)(168,213)
(169,214)(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)(176,216)
(177,217)(178,218)(179,219)(180,220)(361,646)(362,647)(363,648)(364,649)
(365,650)(366,656)(367,657)(368,658)(369,659)(370,660)(371,651)(372,652)
(373,653)(374,654)(375,655)(376,631)(377,632)(378,633)(379,634)(380,635)
(381,641)(382,642)(383,643)(384,644)(385,645)(386,636)(387,637)(388,638)
(389,639)(390,640)(391,661)(392,662)(393,663)(394,664)(395,665)(396,671)
(397,672)(398,673)(399,674)(400,675)(401,666)(402,667)(403,668)(404,669)
(405,670)(406,691)(407,692)(408,693)(409,694)(410,695)(411,701)(412,702)
(413,703)(414,704)(415,705)(416,696)(417,697)(418,698)(419,699)(420,700)
(421,676)(422,677)(423,678)(424,679)(425,680)(426,686)(427,687)(428,688)
(429,689)(430,690)(431,681)(432,682)(433,683)(434,684)(435,685)(436,706)
(437,707)(438,708)(439,709)(440,710)(441,716)(442,717)(443,718)(444,719)
(445,720)(446,711)(447,712)(448,713)(449,714)(450,715)(451,601)(452,602)
(453,603)(454,604)(455,605)(456,611)(457,612)(458,613)(459,614)(460,615)
(461,606)(462,607)(463,608)(464,609)(465,610)(466,586)(467,587)(468,588)
(469,589)(470,590)(471,596)(472,597)(473,598)(474,599)(475,600)(476,591)
(477,592)(478,593)(479,594)(480,595)(481,616)(482,617)(483,618)(484,619)
(485,620)(486,626)(487,627)(488,628)(489,629)(490,630)(491,621)(492,622)
(493,623)(494,624)(495,625)(496,556)(497,557)(498,558)(499,559)(500,560)
(501,566)(502,567)(503,568)(504,569)(505,570)(506,561)(507,562)(508,563)
(509,564)(510,565)(511,541)(512,542)(513,543)(514,544)(515,545)(516,551)
(517,552)(518,553)(519,554)(520,555)(521,546)(522,547)(523,548)(524,549)
(525,550)(526,571)(527,572)(528,573)(529,574)(530,575)(531,581)(532,582)
(533,583)(534,584)(535,585)(536,576)(537,577)(538,578)(539,579)(540,580);;
s3 := (721,722);;
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, s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(722)!(  1,541)(  2,545)(  3,544)(  4,543)(  5,542)(  6,551)(  7,555)
(  8,554)(  9,553)( 10,552)( 11,546)( 12,550)( 13,549)( 14,548)( 15,547)
( 16,556)( 17,560)( 18,559)( 19,558)( 20,557)( 21,566)( 22,570)( 23,569)
( 24,568)( 25,567)( 26,561)( 27,565)( 28,564)( 29,563)( 30,562)( 31,571)
( 32,575)( 33,574)( 34,573)( 35,572)( 36,581)( 37,585)( 38,584)( 39,583)
( 40,582)( 41,576)( 42,580)( 43,579)( 44,578)( 45,577)( 46,586)( 47,590)
( 48,589)( 49,588)( 50,587)( 51,596)( 52,600)( 53,599)( 54,598)( 55,597)
( 56,591)( 57,595)( 58,594)( 59,593)( 60,592)( 61,601)( 62,605)( 63,604)
( 64,603)( 65,602)( 66,611)( 67,615)( 68,614)( 69,613)( 70,612)( 71,606)
( 72,610)( 73,609)( 74,608)( 75,607)( 76,616)( 77,620)( 78,619)( 79,618)
( 80,617)( 81,626)( 82,630)( 83,629)( 84,628)( 85,627)( 86,621)( 87,625)
( 88,624)( 89,623)( 90,622)( 91,631)( 92,635)( 93,634)( 94,633)( 95,632)
( 96,641)( 97,645)( 98,644)( 99,643)(100,642)(101,636)(102,640)(103,639)
(104,638)(105,637)(106,646)(107,650)(108,649)(109,648)(110,647)(111,656)
(112,660)(113,659)(114,658)(115,657)(116,651)(117,655)(118,654)(119,653)
(120,652)(121,661)(122,665)(123,664)(124,663)(125,662)(126,671)(127,675)
(128,674)(129,673)(130,672)(131,666)(132,670)(133,669)(134,668)(135,667)
(136,676)(137,680)(138,679)(139,678)(140,677)(141,686)(142,690)(143,689)
(144,688)(145,687)(146,681)(147,685)(148,684)(149,683)(150,682)(151,691)
(152,695)(153,694)(154,693)(155,692)(156,701)(157,705)(158,704)(159,703)
(160,702)(161,696)(162,700)(163,699)(164,698)(165,697)(166,706)(167,710)
(168,709)(169,708)(170,707)(171,716)(172,720)(173,719)(174,718)(175,717)
(176,711)(177,715)(178,714)(179,713)(180,712)(181,406)(182,410)(183,409)
(184,408)(185,407)(186,416)(187,420)(188,419)(189,418)(190,417)(191,411)
(192,415)(193,414)(194,413)(195,412)(196,421)(197,425)(198,424)(199,423)
(200,422)(201,431)(202,435)(203,434)(204,433)(205,432)(206,426)(207,430)
(208,429)(209,428)(210,427)(211,436)(212,440)(213,439)(214,438)(215,437)
(216,446)(217,450)(218,449)(219,448)(220,447)(221,441)(222,445)(223,444)
(224,443)(225,442)(226,361)(227,365)(228,364)(229,363)(230,362)(231,371)
(232,375)(233,374)(234,373)(235,372)(236,366)(237,370)(238,369)(239,368)
(240,367)(241,376)(242,380)(243,379)(244,378)(245,377)(246,386)(247,390)
(248,389)(249,388)(250,387)(251,381)(252,385)(253,384)(254,383)(255,382)
(256,391)(257,395)(258,394)(259,393)(260,392)(261,401)(262,405)(263,404)
(264,403)(265,402)(266,396)(267,400)(268,399)(269,398)(270,397)(271,496)
(272,500)(273,499)(274,498)(275,497)(276,506)(277,510)(278,509)(279,508)
(280,507)(281,501)(282,505)(283,504)(284,503)(285,502)(286,511)(287,515)
(288,514)(289,513)(290,512)(291,521)(292,525)(293,524)(294,523)(295,522)
(296,516)(297,520)(298,519)(299,518)(300,517)(301,526)(302,530)(303,529)
(304,528)(305,527)(306,536)(307,540)(308,539)(309,538)(310,537)(311,531)
(312,535)(313,534)(314,533)(315,532)(316,451)(317,455)(318,454)(319,453)
(320,452)(321,461)(322,465)(323,464)(324,463)(325,462)(326,456)(327,460)
(328,459)(329,458)(330,457)(331,466)(332,470)(333,469)(334,468)(335,467)
(336,476)(337,480)(338,479)(339,478)(340,477)(341,471)(342,475)(343,474)
(344,473)(345,472)(346,481)(347,485)(348,484)(349,483)(350,482)(351,491)
(352,495)(353,494)(354,493)(355,492)(356,486)(357,490)(358,489)(359,488)
(360,487);
s1 := Sym(722)!(  1,637)(  2,636)(  3,640)(  4,639)(  5,638)(  6,632)(  7,631)
(  8,635)(  9,634)( 10,633)( 11,642)( 12,641)( 13,645)( 14,644)( 15,643)
( 16,667)( 17,666)( 18,670)( 19,669)( 20,668)( 21,662)( 22,661)( 23,665)
( 24,664)( 25,663)( 26,672)( 27,671)( 28,675)( 29,674)( 30,673)( 31,652)
( 32,651)( 33,655)( 34,654)( 35,653)( 36,647)( 37,646)( 38,650)( 39,649)
( 40,648)( 41,657)( 42,656)( 43,660)( 44,659)( 45,658)( 46,682)( 47,681)
( 48,685)( 49,684)( 50,683)( 51,677)( 52,676)( 53,680)( 54,679)( 55,678)
( 56,687)( 57,686)( 58,690)( 59,689)( 60,688)( 61,712)( 62,711)( 63,715)
( 64,714)( 65,713)( 66,707)( 67,706)( 68,710)( 69,709)( 70,708)( 71,717)
( 72,716)( 73,720)( 74,719)( 75,718)( 76,697)( 77,696)( 78,700)( 79,699)
( 80,698)( 81,692)( 82,691)( 83,695)( 84,694)( 85,693)( 86,702)( 87,701)
( 88,705)( 89,704)( 90,703)( 91,547)( 92,546)( 93,550)( 94,549)( 95,548)
( 96,542)( 97,541)( 98,545)( 99,544)(100,543)(101,552)(102,551)(103,555)
(104,554)(105,553)(106,577)(107,576)(108,580)(109,579)(110,578)(111,572)
(112,571)(113,575)(114,574)(115,573)(116,582)(117,581)(118,585)(119,584)
(120,583)(121,562)(122,561)(123,565)(124,564)(125,563)(126,557)(127,556)
(128,560)(129,559)(130,558)(131,567)(132,566)(133,570)(134,569)(135,568)
(136,592)(137,591)(138,595)(139,594)(140,593)(141,587)(142,586)(143,590)
(144,589)(145,588)(146,597)(147,596)(148,600)(149,599)(150,598)(151,622)
(152,621)(153,625)(154,624)(155,623)(156,617)(157,616)(158,620)(159,619)
(160,618)(161,627)(162,626)(163,630)(164,629)(165,628)(166,607)(167,606)
(168,610)(169,609)(170,608)(171,602)(172,601)(173,605)(174,604)(175,603)
(176,612)(177,611)(178,615)(179,614)(180,613)(181,502)(182,501)(183,505)
(184,504)(185,503)(186,497)(187,496)(188,500)(189,499)(190,498)(191,507)
(192,506)(193,510)(194,509)(195,508)(196,532)(197,531)(198,535)(199,534)
(200,533)(201,527)(202,526)(203,530)(204,529)(205,528)(206,537)(207,536)
(208,540)(209,539)(210,538)(211,517)(212,516)(213,520)(214,519)(215,518)
(216,512)(217,511)(218,515)(219,514)(220,513)(221,522)(222,521)(223,525)
(224,524)(225,523)(226,457)(227,456)(228,460)(229,459)(230,458)(231,452)
(232,451)(233,455)(234,454)(235,453)(236,462)(237,461)(238,465)(239,464)
(240,463)(241,487)(242,486)(243,490)(244,489)(245,488)(246,482)(247,481)
(248,485)(249,484)(250,483)(251,492)(252,491)(253,495)(254,494)(255,493)
(256,472)(257,471)(258,475)(259,474)(260,473)(261,467)(262,466)(263,470)
(264,469)(265,468)(266,477)(267,476)(268,480)(269,479)(270,478)(271,412)
(272,411)(273,415)(274,414)(275,413)(276,407)(277,406)(278,410)(279,409)
(280,408)(281,417)(282,416)(283,420)(284,419)(285,418)(286,442)(287,441)
(288,445)(289,444)(290,443)(291,437)(292,436)(293,440)(294,439)(295,438)
(296,447)(297,446)(298,450)(299,449)(300,448)(301,427)(302,426)(303,430)
(304,429)(305,428)(306,422)(307,421)(308,425)(309,424)(310,423)(311,432)
(312,431)(313,435)(314,434)(315,433)(316,367)(317,366)(318,370)(319,369)
(320,368)(321,362)(322,361)(323,365)(324,364)(325,363)(326,372)(327,371)
(328,375)(329,374)(330,373)(331,397)(332,396)(333,400)(334,399)(335,398)
(336,392)(337,391)(338,395)(339,394)(340,393)(341,402)(342,401)(343,405)
(344,404)(345,403)(346,382)(347,381)(348,385)(349,384)(350,383)(351,377)
(352,376)(353,380)(354,379)(355,378)(356,387)(357,386)(358,390)(359,389)
(360,388);
s2 := Sym(722)!(  1,286)(  2,287)(  3,288)(  4,289)(  5,290)(  6,296)(  7,297)
(  8,298)(  9,299)( 10,300)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)
( 16,271)( 17,272)( 18,273)( 19,274)( 20,275)( 21,281)( 22,282)( 23,283)
( 24,284)( 25,285)( 26,276)( 27,277)( 28,278)( 29,279)( 30,280)( 31,301)
( 32,302)( 33,303)( 34,304)( 35,305)( 36,311)( 37,312)( 38,313)( 39,314)
( 40,315)( 41,306)( 42,307)( 43,308)( 44,309)( 45,310)( 46,331)( 47,332)
( 48,333)( 49,334)( 50,335)( 51,341)( 52,342)( 53,343)( 54,344)( 55,345)
( 56,336)( 57,337)( 58,338)( 59,339)( 60,340)( 61,316)( 62,317)( 63,318)
( 64,319)( 65,320)( 66,326)( 67,327)( 68,328)( 69,329)( 70,330)( 71,321)
( 72,322)( 73,323)( 74,324)( 75,325)( 76,346)( 77,347)( 78,348)( 79,349)
( 80,350)( 81,356)( 82,357)( 83,358)( 84,359)( 85,360)( 86,351)( 87,352)
( 88,353)( 89,354)( 90,355)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,251)( 97,252)( 98,253)( 99,254)(100,255)(101,246)(102,247)(103,248)
(104,249)(105,250)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)
(112,237)(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)
(120,235)(121,256)(122,257)(123,258)(124,259)(125,260)(126,266)(127,267)
(128,268)(129,269)(130,270)(131,261)(132,262)(133,263)(134,264)(135,265)
(136,196)(137,197)(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)
(144,209)(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,181)
(152,182)(153,183)(154,184)(155,185)(156,191)(157,192)(158,193)(159,194)
(160,195)(161,186)(162,187)(163,188)(164,189)(165,190)(166,211)(167,212)
(168,213)(169,214)(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)
(176,216)(177,217)(178,218)(179,219)(180,220)(361,646)(362,647)(363,648)
(364,649)(365,650)(366,656)(367,657)(368,658)(369,659)(370,660)(371,651)
(372,652)(373,653)(374,654)(375,655)(376,631)(377,632)(378,633)(379,634)
(380,635)(381,641)(382,642)(383,643)(384,644)(385,645)(386,636)(387,637)
(388,638)(389,639)(390,640)(391,661)(392,662)(393,663)(394,664)(395,665)
(396,671)(397,672)(398,673)(399,674)(400,675)(401,666)(402,667)(403,668)
(404,669)(405,670)(406,691)(407,692)(408,693)(409,694)(410,695)(411,701)
(412,702)(413,703)(414,704)(415,705)(416,696)(417,697)(418,698)(419,699)
(420,700)(421,676)(422,677)(423,678)(424,679)(425,680)(426,686)(427,687)
(428,688)(429,689)(430,690)(431,681)(432,682)(433,683)(434,684)(435,685)
(436,706)(437,707)(438,708)(439,709)(440,710)(441,716)(442,717)(443,718)
(444,719)(445,720)(446,711)(447,712)(448,713)(449,714)(450,715)(451,601)
(452,602)(453,603)(454,604)(455,605)(456,611)(457,612)(458,613)(459,614)
(460,615)(461,606)(462,607)(463,608)(464,609)(465,610)(466,586)(467,587)
(468,588)(469,589)(470,590)(471,596)(472,597)(473,598)(474,599)(475,600)
(476,591)(477,592)(478,593)(479,594)(480,595)(481,616)(482,617)(483,618)
(484,619)(485,620)(486,626)(487,627)(488,628)(489,629)(490,630)(491,621)
(492,622)(493,623)(494,624)(495,625)(496,556)(497,557)(498,558)(499,559)
(500,560)(501,566)(502,567)(503,568)(504,569)(505,570)(506,561)(507,562)
(508,563)(509,564)(510,565)(511,541)(512,542)(513,543)(514,544)(515,545)
(516,551)(517,552)(518,553)(519,554)(520,555)(521,546)(522,547)(523,548)
(524,549)(525,550)(526,571)(527,572)(528,573)(529,574)(530,575)(531,581)
(532,582)(533,583)(534,584)(535,585)(536,576)(537,577)(538,578)(539,579)
(540,580);
s3 := Sym(722)!(721,722);
poly := sub<Sym(722)|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, 
s2*s3*s2*s3, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >; 
 

to this polytope