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