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