Polytope of Type {21,12,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {21,12,2}*1344
if this polytope has a name.
Group : SmallGroup(1344,11334)
Rank : 4
Schlafli Type : {21,12,2}
Number of vertices, edges, etc : 28, 168, 16, 2
Order of s0s1s2s3 : 56
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 : {21,6,2}*672
7-fold quotients : {3,12,2}*192
14-fold quotients : {3,6,2}*96
24-fold quotients : {7,2,2}*56
28-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,505)( 2,506)( 3,510)( 4,509)( 5,508)( 6,507)( 7,512)( 8,511)
( 9,553)( 10,554)( 11,558)( 12,557)( 13,556)( 14,555)( 15,560)( 16,559)
( 17,545)( 18,546)( 19,550)( 20,549)( 21,548)( 22,547)( 23,552)( 24,551)
( 25,537)( 26,538)( 27,542)( 28,541)( 29,540)( 30,539)( 31,544)( 32,543)
( 33,529)( 34,530)( 35,534)( 36,533)( 37,532)( 38,531)( 39,536)( 40,535)
( 41,521)( 42,522)( 43,526)( 44,525)( 45,524)( 46,523)( 47,528)( 48,527)
( 49,513)( 50,514)( 51,518)( 52,517)( 53,516)( 54,515)( 55,520)( 56,519)
( 57,617)( 58,618)( 59,622)( 60,621)( 61,620)( 62,619)( 63,624)( 64,623)
( 65,665)( 66,666)( 67,670)( 68,669)( 69,668)( 70,667)( 71,672)( 72,671)
( 73,657)( 74,658)( 75,662)( 76,661)( 77,660)( 78,659)( 79,664)( 80,663)
( 81,649)( 82,650)( 83,654)( 84,653)( 85,652)( 86,651)( 87,656)( 88,655)
( 89,641)( 90,642)( 91,646)( 92,645)( 93,644)( 94,643)( 95,648)( 96,647)
( 97,633)( 98,634)( 99,638)(100,637)(101,636)(102,635)(103,640)(104,639)
(105,625)(106,626)(107,630)(108,629)(109,628)(110,627)(111,632)(112,631)
(113,561)(114,562)(115,566)(116,565)(117,564)(118,563)(119,568)(120,567)
(121,609)(122,610)(123,614)(124,613)(125,612)(126,611)(127,616)(128,615)
(129,601)(130,602)(131,606)(132,605)(133,604)(134,603)(135,608)(136,607)
(137,593)(138,594)(139,598)(140,597)(141,596)(142,595)(143,600)(144,599)
(145,585)(146,586)(147,590)(148,589)(149,588)(150,587)(151,592)(152,591)
(153,577)(154,578)(155,582)(156,581)(157,580)(158,579)(159,584)(160,583)
(161,569)(162,570)(163,574)(164,573)(165,572)(166,571)(167,576)(168,575)
(169,338)(170,337)(171,341)(172,342)(173,339)(174,340)(175,343)(176,344)
(177,386)(178,385)(179,389)(180,390)(181,387)(182,388)(183,391)(184,392)
(185,378)(186,377)(187,381)(188,382)(189,379)(190,380)(191,383)(192,384)
(193,370)(194,369)(195,373)(196,374)(197,371)(198,372)(199,375)(200,376)
(201,362)(202,361)(203,365)(204,366)(205,363)(206,364)(207,367)(208,368)
(209,354)(210,353)(211,357)(212,358)(213,355)(214,356)(215,359)(216,360)
(217,346)(218,345)(219,349)(220,350)(221,347)(222,348)(223,351)(224,352)
(225,450)(226,449)(227,453)(228,454)(229,451)(230,452)(231,455)(232,456)
(233,498)(234,497)(235,501)(236,502)(237,499)(238,500)(239,503)(240,504)
(241,490)(242,489)(243,493)(244,494)(245,491)(246,492)(247,495)(248,496)
(249,482)(250,481)(251,485)(252,486)(253,483)(254,484)(255,487)(256,488)
(257,474)(258,473)(259,477)(260,478)(261,475)(262,476)(263,479)(264,480)
(265,466)(266,465)(267,469)(268,470)(269,467)(270,468)(271,471)(272,472)
(273,458)(274,457)(275,461)(276,462)(277,459)(278,460)(279,463)(280,464)
(281,394)(282,393)(283,397)(284,398)(285,395)(286,396)(287,399)(288,400)
(289,442)(290,441)(291,445)(292,446)(293,443)(294,444)(295,447)(296,448)
(297,434)(298,433)(299,437)(300,438)(301,435)(302,436)(303,439)(304,440)
(305,426)(306,425)(307,429)(308,430)(309,427)(310,428)(311,431)(312,432)
(313,418)(314,417)(315,421)(316,422)(317,419)(318,420)(319,423)(320,424)
(321,410)(322,409)(323,413)(324,414)(325,411)(326,412)(327,415)(328,416)
(329,402)(330,401)(331,405)(332,406)(333,403)(334,404)(335,407)(336,408);;
s1 := ( 1,569)( 2,570)( 3,572)( 4,571)( 5,575)( 6,576)( 7,573)( 8,574)
( 9,561)( 10,562)( 11,564)( 12,563)( 13,567)( 14,568)( 15,565)( 16,566)
( 17,609)( 18,610)( 19,612)( 20,611)( 21,615)( 22,616)( 23,613)( 24,614)
( 25,601)( 26,602)( 27,604)( 28,603)( 29,607)( 30,608)( 31,605)( 32,606)
( 33,593)( 34,594)( 35,596)( 36,595)( 37,599)( 38,600)( 39,597)( 40,598)
( 41,585)( 42,586)( 43,588)( 44,587)( 45,591)( 46,592)( 47,589)( 48,590)
( 49,577)( 50,578)( 51,580)( 52,579)( 53,583)( 54,584)( 55,581)( 56,582)
( 57,513)( 58,514)( 59,516)( 60,515)( 61,519)( 62,520)( 63,517)( 64,518)
( 65,505)( 66,506)( 67,508)( 68,507)( 69,511)( 70,512)( 71,509)( 72,510)
( 73,553)( 74,554)( 75,556)( 76,555)( 77,559)( 78,560)( 79,557)( 80,558)
( 81,545)( 82,546)( 83,548)( 84,547)( 85,551)( 86,552)( 87,549)( 88,550)
( 89,537)( 90,538)( 91,540)( 92,539)( 93,543)( 94,544)( 95,541)( 96,542)
( 97,529)( 98,530)( 99,532)(100,531)(101,535)(102,536)(103,533)(104,534)
(105,521)(106,522)(107,524)(108,523)(109,527)(110,528)(111,525)(112,526)
(113,625)(114,626)(115,628)(116,627)(117,631)(118,632)(119,629)(120,630)
(121,617)(122,618)(123,620)(124,619)(125,623)(126,624)(127,621)(128,622)
(129,665)(130,666)(131,668)(132,667)(133,671)(134,672)(135,669)(136,670)
(137,657)(138,658)(139,660)(140,659)(141,663)(142,664)(143,661)(144,662)
(145,649)(146,650)(147,652)(148,651)(149,655)(150,656)(151,653)(152,654)
(153,641)(154,642)(155,644)(156,643)(157,647)(158,648)(159,645)(160,646)
(161,633)(162,634)(163,636)(164,635)(165,639)(166,640)(167,637)(168,638)
(169,402)(170,401)(171,403)(172,404)(173,408)(174,407)(175,406)(176,405)
(177,394)(178,393)(179,395)(180,396)(181,400)(182,399)(183,398)(184,397)
(185,442)(186,441)(187,443)(188,444)(189,448)(190,447)(191,446)(192,445)
(193,434)(194,433)(195,435)(196,436)(197,440)(198,439)(199,438)(200,437)
(201,426)(202,425)(203,427)(204,428)(205,432)(206,431)(207,430)(208,429)
(209,418)(210,417)(211,419)(212,420)(213,424)(214,423)(215,422)(216,421)
(217,410)(218,409)(219,411)(220,412)(221,416)(222,415)(223,414)(224,413)
(225,346)(226,345)(227,347)(228,348)(229,352)(230,351)(231,350)(232,349)
(233,338)(234,337)(235,339)(236,340)(237,344)(238,343)(239,342)(240,341)
(241,386)(242,385)(243,387)(244,388)(245,392)(246,391)(247,390)(248,389)
(249,378)(250,377)(251,379)(252,380)(253,384)(254,383)(255,382)(256,381)
(257,370)(258,369)(259,371)(260,372)(261,376)(262,375)(263,374)(264,373)
(265,362)(266,361)(267,363)(268,364)(269,368)(270,367)(271,366)(272,365)
(273,354)(274,353)(275,355)(276,356)(277,360)(278,359)(279,358)(280,357)
(281,458)(282,457)(283,459)(284,460)(285,464)(286,463)(287,462)(288,461)
(289,450)(290,449)(291,451)(292,452)(293,456)(294,455)(295,454)(296,453)
(297,498)(298,497)(299,499)(300,500)(301,504)(302,503)(303,502)(304,501)
(305,490)(306,489)(307,491)(308,492)(309,496)(310,495)(311,494)(312,493)
(313,482)(314,481)(315,483)(316,484)(317,488)(318,487)(319,486)(320,485)
(321,474)(322,473)(323,475)(324,476)(325,480)(326,479)(327,478)(328,477)
(329,466)(330,465)(331,467)(332,468)(333,472)(334,471)(335,470)(336,469);;
s2 := ( 1,175)( 2,176)( 3,171)( 4,172)( 5,174)( 6,173)( 7,169)( 8,170)
( 9,183)( 10,184)( 11,179)( 12,180)( 13,182)( 14,181)( 15,177)( 16,178)
( 17,191)( 18,192)( 19,187)( 20,188)( 21,190)( 22,189)( 23,185)( 24,186)
( 25,199)( 26,200)( 27,195)( 28,196)( 29,198)( 30,197)( 31,193)( 32,194)
( 33,207)( 34,208)( 35,203)( 36,204)( 37,206)( 38,205)( 39,201)( 40,202)
( 41,215)( 42,216)( 43,211)( 44,212)( 45,214)( 46,213)( 47,209)( 48,210)
( 49,223)( 50,224)( 51,219)( 52,220)( 53,222)( 54,221)( 55,217)( 56,218)
( 57,287)( 58,288)( 59,283)( 60,284)( 61,286)( 62,285)( 63,281)( 64,282)
( 65,295)( 66,296)( 67,291)( 68,292)( 69,294)( 70,293)( 71,289)( 72,290)
( 73,303)( 74,304)( 75,299)( 76,300)( 77,302)( 78,301)( 79,297)( 80,298)
( 81,311)( 82,312)( 83,307)( 84,308)( 85,310)( 86,309)( 87,305)( 88,306)
( 89,319)( 90,320)( 91,315)( 92,316)( 93,318)( 94,317)( 95,313)( 96,314)
( 97,327)( 98,328)( 99,323)(100,324)(101,326)(102,325)(103,321)(104,322)
(105,335)(106,336)(107,331)(108,332)(109,334)(110,333)(111,329)(112,330)
(113,231)(114,232)(115,227)(116,228)(117,230)(118,229)(119,225)(120,226)
(121,239)(122,240)(123,235)(124,236)(125,238)(126,237)(127,233)(128,234)
(129,247)(130,248)(131,243)(132,244)(133,246)(134,245)(135,241)(136,242)
(137,255)(138,256)(139,251)(140,252)(141,254)(142,253)(143,249)(144,250)
(145,263)(146,264)(147,259)(148,260)(149,262)(150,261)(151,257)(152,258)
(153,271)(154,272)(155,267)(156,268)(157,270)(158,269)(159,265)(160,266)
(161,279)(162,280)(163,275)(164,276)(165,278)(166,277)(167,273)(168,274)
(337,511)(338,512)(339,507)(340,508)(341,510)(342,509)(343,505)(344,506)
(345,519)(346,520)(347,515)(348,516)(349,518)(350,517)(351,513)(352,514)
(353,527)(354,528)(355,523)(356,524)(357,526)(358,525)(359,521)(360,522)
(361,535)(362,536)(363,531)(364,532)(365,534)(366,533)(367,529)(368,530)
(369,543)(370,544)(371,539)(372,540)(373,542)(374,541)(375,537)(376,538)
(377,551)(378,552)(379,547)(380,548)(381,550)(382,549)(383,545)(384,546)
(385,559)(386,560)(387,555)(388,556)(389,558)(390,557)(391,553)(392,554)
(393,623)(394,624)(395,619)(396,620)(397,622)(398,621)(399,617)(400,618)
(401,631)(402,632)(403,627)(404,628)(405,630)(406,629)(407,625)(408,626)
(409,639)(410,640)(411,635)(412,636)(413,638)(414,637)(415,633)(416,634)
(417,647)(418,648)(419,643)(420,644)(421,646)(422,645)(423,641)(424,642)
(425,655)(426,656)(427,651)(428,652)(429,654)(430,653)(431,649)(432,650)
(433,663)(434,664)(435,659)(436,660)(437,662)(438,661)(439,657)(440,658)
(441,671)(442,672)(443,667)(444,668)(445,670)(446,669)(447,665)(448,666)
(449,567)(450,568)(451,563)(452,564)(453,566)(454,565)(455,561)(456,562)
(457,575)(458,576)(459,571)(460,572)(461,574)(462,573)(463,569)(464,570)
(465,583)(466,584)(467,579)(468,580)(469,582)(470,581)(471,577)(472,578)
(473,591)(474,592)(475,587)(476,588)(477,590)(478,589)(479,585)(480,586)
(481,599)(482,600)(483,595)(484,596)(485,598)(486,597)(487,593)(488,594)
(489,607)(490,608)(491,603)(492,604)(493,606)(494,605)(495,601)(496,602)
(497,615)(498,616)(499,611)(500,612)(501,614)(502,613)(503,609)(504,610);;
s3 := (673,674);;
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,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(674)!( 1,505)( 2,506)( 3,510)( 4,509)( 5,508)( 6,507)( 7,512)
( 8,511)( 9,553)( 10,554)( 11,558)( 12,557)( 13,556)( 14,555)( 15,560)
( 16,559)( 17,545)( 18,546)( 19,550)( 20,549)( 21,548)( 22,547)( 23,552)
( 24,551)( 25,537)( 26,538)( 27,542)( 28,541)( 29,540)( 30,539)( 31,544)
( 32,543)( 33,529)( 34,530)( 35,534)( 36,533)( 37,532)( 38,531)( 39,536)
( 40,535)( 41,521)( 42,522)( 43,526)( 44,525)( 45,524)( 46,523)( 47,528)
( 48,527)( 49,513)( 50,514)( 51,518)( 52,517)( 53,516)( 54,515)( 55,520)
( 56,519)( 57,617)( 58,618)( 59,622)( 60,621)( 61,620)( 62,619)( 63,624)
( 64,623)( 65,665)( 66,666)( 67,670)( 68,669)( 69,668)( 70,667)( 71,672)
( 72,671)( 73,657)( 74,658)( 75,662)( 76,661)( 77,660)( 78,659)( 79,664)
( 80,663)( 81,649)( 82,650)( 83,654)( 84,653)( 85,652)( 86,651)( 87,656)
( 88,655)( 89,641)( 90,642)( 91,646)( 92,645)( 93,644)( 94,643)( 95,648)
( 96,647)( 97,633)( 98,634)( 99,638)(100,637)(101,636)(102,635)(103,640)
(104,639)(105,625)(106,626)(107,630)(108,629)(109,628)(110,627)(111,632)
(112,631)(113,561)(114,562)(115,566)(116,565)(117,564)(118,563)(119,568)
(120,567)(121,609)(122,610)(123,614)(124,613)(125,612)(126,611)(127,616)
(128,615)(129,601)(130,602)(131,606)(132,605)(133,604)(134,603)(135,608)
(136,607)(137,593)(138,594)(139,598)(140,597)(141,596)(142,595)(143,600)
(144,599)(145,585)(146,586)(147,590)(148,589)(149,588)(150,587)(151,592)
(152,591)(153,577)(154,578)(155,582)(156,581)(157,580)(158,579)(159,584)
(160,583)(161,569)(162,570)(163,574)(164,573)(165,572)(166,571)(167,576)
(168,575)(169,338)(170,337)(171,341)(172,342)(173,339)(174,340)(175,343)
(176,344)(177,386)(178,385)(179,389)(180,390)(181,387)(182,388)(183,391)
(184,392)(185,378)(186,377)(187,381)(188,382)(189,379)(190,380)(191,383)
(192,384)(193,370)(194,369)(195,373)(196,374)(197,371)(198,372)(199,375)
(200,376)(201,362)(202,361)(203,365)(204,366)(205,363)(206,364)(207,367)
(208,368)(209,354)(210,353)(211,357)(212,358)(213,355)(214,356)(215,359)
(216,360)(217,346)(218,345)(219,349)(220,350)(221,347)(222,348)(223,351)
(224,352)(225,450)(226,449)(227,453)(228,454)(229,451)(230,452)(231,455)
(232,456)(233,498)(234,497)(235,501)(236,502)(237,499)(238,500)(239,503)
(240,504)(241,490)(242,489)(243,493)(244,494)(245,491)(246,492)(247,495)
(248,496)(249,482)(250,481)(251,485)(252,486)(253,483)(254,484)(255,487)
(256,488)(257,474)(258,473)(259,477)(260,478)(261,475)(262,476)(263,479)
(264,480)(265,466)(266,465)(267,469)(268,470)(269,467)(270,468)(271,471)
(272,472)(273,458)(274,457)(275,461)(276,462)(277,459)(278,460)(279,463)
(280,464)(281,394)(282,393)(283,397)(284,398)(285,395)(286,396)(287,399)
(288,400)(289,442)(290,441)(291,445)(292,446)(293,443)(294,444)(295,447)
(296,448)(297,434)(298,433)(299,437)(300,438)(301,435)(302,436)(303,439)
(304,440)(305,426)(306,425)(307,429)(308,430)(309,427)(310,428)(311,431)
(312,432)(313,418)(314,417)(315,421)(316,422)(317,419)(318,420)(319,423)
(320,424)(321,410)(322,409)(323,413)(324,414)(325,411)(326,412)(327,415)
(328,416)(329,402)(330,401)(331,405)(332,406)(333,403)(334,404)(335,407)
(336,408);
s1 := Sym(674)!( 1,569)( 2,570)( 3,572)( 4,571)( 5,575)( 6,576)( 7,573)
( 8,574)( 9,561)( 10,562)( 11,564)( 12,563)( 13,567)( 14,568)( 15,565)
( 16,566)( 17,609)( 18,610)( 19,612)( 20,611)( 21,615)( 22,616)( 23,613)
( 24,614)( 25,601)( 26,602)( 27,604)( 28,603)( 29,607)( 30,608)( 31,605)
( 32,606)( 33,593)( 34,594)( 35,596)( 36,595)( 37,599)( 38,600)( 39,597)
( 40,598)( 41,585)( 42,586)( 43,588)( 44,587)( 45,591)( 46,592)( 47,589)
( 48,590)( 49,577)( 50,578)( 51,580)( 52,579)( 53,583)( 54,584)( 55,581)
( 56,582)( 57,513)( 58,514)( 59,516)( 60,515)( 61,519)( 62,520)( 63,517)
( 64,518)( 65,505)( 66,506)( 67,508)( 68,507)( 69,511)( 70,512)( 71,509)
( 72,510)( 73,553)( 74,554)( 75,556)( 76,555)( 77,559)( 78,560)( 79,557)
( 80,558)( 81,545)( 82,546)( 83,548)( 84,547)( 85,551)( 86,552)( 87,549)
( 88,550)( 89,537)( 90,538)( 91,540)( 92,539)( 93,543)( 94,544)( 95,541)
( 96,542)( 97,529)( 98,530)( 99,532)(100,531)(101,535)(102,536)(103,533)
(104,534)(105,521)(106,522)(107,524)(108,523)(109,527)(110,528)(111,525)
(112,526)(113,625)(114,626)(115,628)(116,627)(117,631)(118,632)(119,629)
(120,630)(121,617)(122,618)(123,620)(124,619)(125,623)(126,624)(127,621)
(128,622)(129,665)(130,666)(131,668)(132,667)(133,671)(134,672)(135,669)
(136,670)(137,657)(138,658)(139,660)(140,659)(141,663)(142,664)(143,661)
(144,662)(145,649)(146,650)(147,652)(148,651)(149,655)(150,656)(151,653)
(152,654)(153,641)(154,642)(155,644)(156,643)(157,647)(158,648)(159,645)
(160,646)(161,633)(162,634)(163,636)(164,635)(165,639)(166,640)(167,637)
(168,638)(169,402)(170,401)(171,403)(172,404)(173,408)(174,407)(175,406)
(176,405)(177,394)(178,393)(179,395)(180,396)(181,400)(182,399)(183,398)
(184,397)(185,442)(186,441)(187,443)(188,444)(189,448)(190,447)(191,446)
(192,445)(193,434)(194,433)(195,435)(196,436)(197,440)(198,439)(199,438)
(200,437)(201,426)(202,425)(203,427)(204,428)(205,432)(206,431)(207,430)
(208,429)(209,418)(210,417)(211,419)(212,420)(213,424)(214,423)(215,422)
(216,421)(217,410)(218,409)(219,411)(220,412)(221,416)(222,415)(223,414)
(224,413)(225,346)(226,345)(227,347)(228,348)(229,352)(230,351)(231,350)
(232,349)(233,338)(234,337)(235,339)(236,340)(237,344)(238,343)(239,342)
(240,341)(241,386)(242,385)(243,387)(244,388)(245,392)(246,391)(247,390)
(248,389)(249,378)(250,377)(251,379)(252,380)(253,384)(254,383)(255,382)
(256,381)(257,370)(258,369)(259,371)(260,372)(261,376)(262,375)(263,374)
(264,373)(265,362)(266,361)(267,363)(268,364)(269,368)(270,367)(271,366)
(272,365)(273,354)(274,353)(275,355)(276,356)(277,360)(278,359)(279,358)
(280,357)(281,458)(282,457)(283,459)(284,460)(285,464)(286,463)(287,462)
(288,461)(289,450)(290,449)(291,451)(292,452)(293,456)(294,455)(295,454)
(296,453)(297,498)(298,497)(299,499)(300,500)(301,504)(302,503)(303,502)
(304,501)(305,490)(306,489)(307,491)(308,492)(309,496)(310,495)(311,494)
(312,493)(313,482)(314,481)(315,483)(316,484)(317,488)(318,487)(319,486)
(320,485)(321,474)(322,473)(323,475)(324,476)(325,480)(326,479)(327,478)
(328,477)(329,466)(330,465)(331,467)(332,468)(333,472)(334,471)(335,470)
(336,469);
s2 := Sym(674)!( 1,175)( 2,176)( 3,171)( 4,172)( 5,174)( 6,173)( 7,169)
( 8,170)( 9,183)( 10,184)( 11,179)( 12,180)( 13,182)( 14,181)( 15,177)
( 16,178)( 17,191)( 18,192)( 19,187)( 20,188)( 21,190)( 22,189)( 23,185)
( 24,186)( 25,199)( 26,200)( 27,195)( 28,196)( 29,198)( 30,197)( 31,193)
( 32,194)( 33,207)( 34,208)( 35,203)( 36,204)( 37,206)( 38,205)( 39,201)
( 40,202)( 41,215)( 42,216)( 43,211)( 44,212)( 45,214)( 46,213)( 47,209)
( 48,210)( 49,223)( 50,224)( 51,219)( 52,220)( 53,222)( 54,221)( 55,217)
( 56,218)( 57,287)( 58,288)( 59,283)( 60,284)( 61,286)( 62,285)( 63,281)
( 64,282)( 65,295)( 66,296)( 67,291)( 68,292)( 69,294)( 70,293)( 71,289)
( 72,290)( 73,303)( 74,304)( 75,299)( 76,300)( 77,302)( 78,301)( 79,297)
( 80,298)( 81,311)( 82,312)( 83,307)( 84,308)( 85,310)( 86,309)( 87,305)
( 88,306)( 89,319)( 90,320)( 91,315)( 92,316)( 93,318)( 94,317)( 95,313)
( 96,314)( 97,327)( 98,328)( 99,323)(100,324)(101,326)(102,325)(103,321)
(104,322)(105,335)(106,336)(107,331)(108,332)(109,334)(110,333)(111,329)
(112,330)(113,231)(114,232)(115,227)(116,228)(117,230)(118,229)(119,225)
(120,226)(121,239)(122,240)(123,235)(124,236)(125,238)(126,237)(127,233)
(128,234)(129,247)(130,248)(131,243)(132,244)(133,246)(134,245)(135,241)
(136,242)(137,255)(138,256)(139,251)(140,252)(141,254)(142,253)(143,249)
(144,250)(145,263)(146,264)(147,259)(148,260)(149,262)(150,261)(151,257)
(152,258)(153,271)(154,272)(155,267)(156,268)(157,270)(158,269)(159,265)
(160,266)(161,279)(162,280)(163,275)(164,276)(165,278)(166,277)(167,273)
(168,274)(337,511)(338,512)(339,507)(340,508)(341,510)(342,509)(343,505)
(344,506)(345,519)(346,520)(347,515)(348,516)(349,518)(350,517)(351,513)
(352,514)(353,527)(354,528)(355,523)(356,524)(357,526)(358,525)(359,521)
(360,522)(361,535)(362,536)(363,531)(364,532)(365,534)(366,533)(367,529)
(368,530)(369,543)(370,544)(371,539)(372,540)(373,542)(374,541)(375,537)
(376,538)(377,551)(378,552)(379,547)(380,548)(381,550)(382,549)(383,545)
(384,546)(385,559)(386,560)(387,555)(388,556)(389,558)(390,557)(391,553)
(392,554)(393,623)(394,624)(395,619)(396,620)(397,622)(398,621)(399,617)
(400,618)(401,631)(402,632)(403,627)(404,628)(405,630)(406,629)(407,625)
(408,626)(409,639)(410,640)(411,635)(412,636)(413,638)(414,637)(415,633)
(416,634)(417,647)(418,648)(419,643)(420,644)(421,646)(422,645)(423,641)
(424,642)(425,655)(426,656)(427,651)(428,652)(429,654)(430,653)(431,649)
(432,650)(433,663)(434,664)(435,659)(436,660)(437,662)(438,661)(439,657)
(440,658)(441,671)(442,672)(443,667)(444,668)(445,670)(446,669)(447,665)
(448,666)(449,567)(450,568)(451,563)(452,564)(453,566)(454,565)(455,561)
(456,562)(457,575)(458,576)(459,571)(460,572)(461,574)(462,573)(463,569)
(464,570)(465,583)(466,584)(467,579)(468,580)(469,582)(470,581)(471,577)
(472,578)(473,591)(474,592)(475,587)(476,588)(477,590)(478,589)(479,585)
(480,586)(481,599)(482,600)(483,595)(484,596)(485,598)(486,597)(487,593)
(488,594)(489,607)(490,608)(491,603)(492,604)(493,606)(494,605)(495,601)
(496,602)(497,615)(498,616)(499,611)(500,612)(501,614)(502,613)(503,609)
(504,610);
s3 := Sym(674)!(673,674);
poly := sub<Sym(674)|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, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >;
to this polytope