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