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