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