Polytope of Type {4,42,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,42,4}*1344g
if this polytope has a name.
Group : SmallGroup(1344,11703)
Rank : 4
Schlafli Type : {4,42,4}
Number of vertices, edges, etc : 4, 84, 84, 4
Order of s0s1s2s3 : 42
Order of s0s1s2s3s2s1 : 2
Special Properties :
Non-Orientable
Flat
Self-Dual
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 : {4,21,4}*672
7-fold quotients : {4,6,4}*192g
14-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,345)( 2,346)( 3,347)( 4,348)( 5,349)( 6,350)( 7,351)( 8,352)
( 9,337)( 10,338)( 11,339)( 12,340)( 13,341)( 14,342)( 15,343)( 16,344)
( 17,361)( 18,362)( 19,363)( 20,364)( 21,365)( 22,366)( 23,367)( 24,368)
( 25,353)( 26,354)( 27,355)( 28,356)( 29,357)( 30,358)( 31,359)( 32,360)
( 33,377)( 34,378)( 35,379)( 36,380)( 37,381)( 38,382)( 39,383)( 40,384)
( 41,369)( 42,370)( 43,371)( 44,372)( 45,373)( 46,374)( 47,375)( 48,376)
( 49,393)( 50,394)( 51,395)( 52,396)( 53,397)( 54,398)( 55,399)( 56,400)
( 57,385)( 58,386)( 59,387)( 60,388)( 61,389)( 62,390)( 63,391)( 64,392)
( 65,409)( 66,410)( 67,411)( 68,412)( 69,413)( 70,414)( 71,415)( 72,416)
( 73,401)( 74,402)( 75,403)( 76,404)( 77,405)( 78,406)( 79,407)( 80,408)
( 81,425)( 82,426)( 83,427)( 84,428)( 85,429)( 86,430)( 87,431)( 88,432)
( 89,417)( 90,418)( 91,419)( 92,420)( 93,421)( 94,422)( 95,423)( 96,424)
( 97,441)( 98,442)( 99,443)(100,444)(101,445)(102,446)(103,447)(104,448)
(105,433)(106,434)(107,435)(108,436)(109,437)(110,438)(111,439)(112,440)
(113,457)(114,458)(115,459)(116,460)(117,461)(118,462)(119,463)(120,464)
(121,449)(122,450)(123,451)(124,452)(125,453)(126,454)(127,455)(128,456)
(129,473)(130,474)(131,475)(132,476)(133,477)(134,478)(135,479)(136,480)
(137,465)(138,466)(139,467)(140,468)(141,469)(142,470)(143,471)(144,472)
(145,489)(146,490)(147,491)(148,492)(149,493)(150,494)(151,495)(152,496)
(153,481)(154,482)(155,483)(156,484)(157,485)(158,486)(159,487)(160,488)
(161,505)(162,506)(163,507)(164,508)(165,509)(166,510)(167,511)(168,512)
(169,497)(170,498)(171,499)(172,500)(173,501)(174,502)(175,503)(176,504)
(177,521)(178,522)(179,523)(180,524)(181,525)(182,526)(183,527)(184,528)
(185,513)(186,514)(187,515)(188,516)(189,517)(190,518)(191,519)(192,520)
(193,537)(194,538)(195,539)(196,540)(197,541)(198,542)(199,543)(200,544)
(201,529)(202,530)(203,531)(204,532)(205,533)(206,534)(207,535)(208,536)
(209,553)(210,554)(211,555)(212,556)(213,557)(214,558)(215,559)(216,560)
(217,545)(218,546)(219,547)(220,548)(221,549)(222,550)(223,551)(224,552)
(225,569)(226,570)(227,571)(228,572)(229,573)(230,574)(231,575)(232,576)
(233,561)(234,562)(235,563)(236,564)(237,565)(238,566)(239,567)(240,568)
(241,585)(242,586)(243,587)(244,588)(245,589)(246,590)(247,591)(248,592)
(249,577)(250,578)(251,579)(252,580)(253,581)(254,582)(255,583)(256,584)
(257,601)(258,602)(259,603)(260,604)(261,605)(262,606)(263,607)(264,608)
(265,593)(266,594)(267,595)(268,596)(269,597)(270,598)(271,599)(272,600)
(273,617)(274,618)(275,619)(276,620)(277,621)(278,622)(279,623)(280,624)
(281,609)(282,610)(283,611)(284,612)(285,613)(286,614)(287,615)(288,616)
(289,633)(290,634)(291,635)(292,636)(293,637)(294,638)(295,639)(296,640)
(297,625)(298,626)(299,627)(300,628)(301,629)(302,630)(303,631)(304,632)
(305,649)(306,650)(307,651)(308,652)(309,653)(310,654)(311,655)(312,656)
(313,641)(314,642)(315,643)(316,644)(317,645)(318,646)(319,647)(320,648)
(321,665)(322,666)(323,667)(324,668)(325,669)(326,670)(327,671)(328,672)
(329,657)(330,658)(331,659)(332,660)(333,661)(334,662)(335,663)(336,664);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 97)( 18, 98)
( 19,100)( 20, 99)( 21,101)( 22,102)( 23,104)( 24,103)( 25,109)( 26,110)
( 27,112)( 28,111)( 29,105)( 30,106)( 31,108)( 32,107)( 33, 81)( 34, 82)
( 35, 84)( 36, 83)( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 93)( 42, 94)
( 43, 96)( 44, 95)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 65)( 50, 66)
( 51, 68)( 52, 67)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 77)( 58, 78)
( 59, 80)( 60, 79)( 61, 73)( 62, 74)( 63, 76)( 64, 75)(113,225)(114,226)
(115,228)(116,227)(117,229)(118,230)(119,232)(120,231)(121,237)(122,238)
(123,240)(124,239)(125,233)(126,234)(127,236)(128,235)(129,321)(130,322)
(131,324)(132,323)(133,325)(134,326)(135,328)(136,327)(137,333)(138,334)
(139,336)(140,335)(141,329)(142,330)(143,332)(144,331)(145,305)(146,306)
(147,308)(148,307)(149,309)(150,310)(151,312)(152,311)(153,317)(154,318)
(155,320)(156,319)(157,313)(158,314)(159,316)(160,315)(161,289)(162,290)
(163,292)(164,291)(165,293)(166,294)(167,296)(168,295)(169,301)(170,302)
(171,304)(172,303)(173,297)(174,298)(175,300)(176,299)(177,273)(178,274)
(179,276)(180,275)(181,277)(182,278)(183,280)(184,279)(185,285)(186,286)
(187,288)(188,287)(189,281)(190,282)(191,284)(192,283)(193,257)(194,258)
(195,260)(196,259)(197,261)(198,262)(199,264)(200,263)(201,269)(202,270)
(203,272)(204,271)(205,265)(206,266)(207,268)(208,267)(209,241)(210,242)
(211,244)(212,243)(213,245)(214,246)(215,248)(216,247)(217,253)(218,254)
(219,256)(220,255)(221,249)(222,250)(223,252)(224,251)(339,340)(343,344)
(345,349)(346,350)(347,352)(348,351)(353,433)(354,434)(355,436)(356,435)
(357,437)(358,438)(359,440)(360,439)(361,445)(362,446)(363,448)(364,447)
(365,441)(366,442)(367,444)(368,443)(369,417)(370,418)(371,420)(372,419)
(373,421)(374,422)(375,424)(376,423)(377,429)(378,430)(379,432)(380,431)
(381,425)(382,426)(383,428)(384,427)(385,401)(386,402)(387,404)(388,403)
(389,405)(390,406)(391,408)(392,407)(393,413)(394,414)(395,416)(396,415)
(397,409)(398,410)(399,412)(400,411)(449,561)(450,562)(451,564)(452,563)
(453,565)(454,566)(455,568)(456,567)(457,573)(458,574)(459,576)(460,575)
(461,569)(462,570)(463,572)(464,571)(465,657)(466,658)(467,660)(468,659)
(469,661)(470,662)(471,664)(472,663)(473,669)(474,670)(475,672)(476,671)
(477,665)(478,666)(479,668)(480,667)(481,641)(482,642)(483,644)(484,643)
(485,645)(486,646)(487,648)(488,647)(489,653)(490,654)(491,656)(492,655)
(493,649)(494,650)(495,652)(496,651)(497,625)(498,626)(499,628)(500,627)
(501,629)(502,630)(503,632)(504,631)(505,637)(506,638)(507,640)(508,639)
(509,633)(510,634)(511,636)(512,635)(513,609)(514,610)(515,612)(516,611)
(517,613)(518,614)(519,616)(520,615)(521,621)(522,622)(523,624)(524,623)
(525,617)(526,618)(527,620)(528,619)(529,593)(530,594)(531,596)(532,595)
(533,597)(534,598)(535,600)(536,599)(537,605)(538,606)(539,608)(540,607)
(541,601)(542,602)(543,604)(544,603)(545,577)(546,578)(547,580)(548,579)
(549,581)(550,582)(551,584)(552,583)(553,589)(554,590)(555,592)(556,591)
(557,585)(558,586)(559,588)(560,587);;
s2 := ( 1,465)( 2,468)( 3,467)( 4,466)( 5,477)( 6,480)( 7,479)( 8,478)
( 9,473)( 10,476)( 11,475)( 12,474)( 13,469)( 14,472)( 15,471)( 16,470)
( 17,449)( 18,452)( 19,451)( 20,450)( 21,461)( 22,464)( 23,463)( 24,462)
( 25,457)( 26,460)( 27,459)( 28,458)( 29,453)( 30,456)( 31,455)( 32,454)
( 33,545)( 34,548)( 35,547)( 36,546)( 37,557)( 38,560)( 39,559)( 40,558)
( 41,553)( 42,556)( 43,555)( 44,554)( 45,549)( 46,552)( 47,551)( 48,550)
( 49,529)( 50,532)( 51,531)( 52,530)( 53,541)( 54,544)( 55,543)( 56,542)
( 57,537)( 58,540)( 59,539)( 60,538)( 61,533)( 62,536)( 63,535)( 64,534)
( 65,513)( 66,516)( 67,515)( 68,514)( 69,525)( 70,528)( 71,527)( 72,526)
( 73,521)( 74,524)( 75,523)( 76,522)( 77,517)( 78,520)( 79,519)( 80,518)
( 81,497)( 82,500)( 83,499)( 84,498)( 85,509)( 86,512)( 87,511)( 88,510)
( 89,505)( 90,508)( 91,507)( 92,506)( 93,501)( 94,504)( 95,503)( 96,502)
( 97,481)( 98,484)( 99,483)(100,482)(101,493)(102,496)(103,495)(104,494)
(105,489)(106,492)(107,491)(108,490)(109,485)(110,488)(111,487)(112,486)
(113,353)(114,356)(115,355)(116,354)(117,365)(118,368)(119,367)(120,366)
(121,361)(122,364)(123,363)(124,362)(125,357)(126,360)(127,359)(128,358)
(129,337)(130,340)(131,339)(132,338)(133,349)(134,352)(135,351)(136,350)
(137,345)(138,348)(139,347)(140,346)(141,341)(142,344)(143,343)(144,342)
(145,433)(146,436)(147,435)(148,434)(149,445)(150,448)(151,447)(152,446)
(153,441)(154,444)(155,443)(156,442)(157,437)(158,440)(159,439)(160,438)
(161,417)(162,420)(163,419)(164,418)(165,429)(166,432)(167,431)(168,430)
(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)(176,422)
(177,401)(178,404)(179,403)(180,402)(181,413)(182,416)(183,415)(184,414)
(185,409)(186,412)(187,411)(188,410)(189,405)(190,408)(191,407)(192,406)
(193,385)(194,388)(195,387)(196,386)(197,397)(198,400)(199,399)(200,398)
(201,393)(202,396)(203,395)(204,394)(205,389)(206,392)(207,391)(208,390)
(209,369)(210,372)(211,371)(212,370)(213,381)(214,384)(215,383)(216,382)
(217,377)(218,380)(219,379)(220,378)(221,373)(222,376)(223,375)(224,374)
(225,577)(226,580)(227,579)(228,578)(229,589)(230,592)(231,591)(232,590)
(233,585)(234,588)(235,587)(236,586)(237,581)(238,584)(239,583)(240,582)
(241,561)(242,564)(243,563)(244,562)(245,573)(246,576)(247,575)(248,574)
(249,569)(250,572)(251,571)(252,570)(253,565)(254,568)(255,567)(256,566)
(257,657)(258,660)(259,659)(260,658)(261,669)(262,672)(263,671)(264,670)
(265,665)(266,668)(267,667)(268,666)(269,661)(270,664)(271,663)(272,662)
(273,641)(274,644)(275,643)(276,642)(277,653)(278,656)(279,655)(280,654)
(281,649)(282,652)(283,651)(284,650)(285,645)(286,648)(287,647)(288,646)
(289,625)(290,628)(291,627)(292,626)(293,637)(294,640)(295,639)(296,638)
(297,633)(298,636)(299,635)(300,634)(301,629)(302,632)(303,631)(304,630)
(305,609)(306,612)(307,611)(308,610)(309,621)(310,624)(311,623)(312,622)
(313,617)(314,620)(315,619)(316,618)(317,613)(318,616)(319,615)(320,614)
(321,593)(322,596)(323,595)(324,594)(325,605)(326,608)(327,607)(328,606)
(329,601)(330,604)(331,603)(332,602)(333,597)(334,600)(335,599)(336,598);;
s3 := ( 1,338)( 2,337)( 3,340)( 4,339)( 5,342)( 6,341)( 7,344)( 8,343)
( 9,346)( 10,345)( 11,348)( 12,347)( 13,350)( 14,349)( 15,352)( 16,351)
( 17,354)( 18,353)( 19,356)( 20,355)( 21,358)( 22,357)( 23,360)( 24,359)
( 25,362)( 26,361)( 27,364)( 28,363)( 29,366)( 30,365)( 31,368)( 32,367)
( 33,370)( 34,369)( 35,372)( 36,371)( 37,374)( 38,373)( 39,376)( 40,375)
( 41,378)( 42,377)( 43,380)( 44,379)( 45,382)( 46,381)( 47,384)( 48,383)
( 49,386)( 50,385)( 51,388)( 52,387)( 53,390)( 54,389)( 55,392)( 56,391)
( 57,394)( 58,393)( 59,396)( 60,395)( 61,398)( 62,397)( 63,400)( 64,399)
( 65,402)( 66,401)( 67,404)( 68,403)( 69,406)( 70,405)( 71,408)( 72,407)
( 73,410)( 74,409)( 75,412)( 76,411)( 77,414)( 78,413)( 79,416)( 80,415)
( 81,418)( 82,417)( 83,420)( 84,419)( 85,422)( 86,421)( 87,424)( 88,423)
( 89,426)( 90,425)( 91,428)( 92,427)( 93,430)( 94,429)( 95,432)( 96,431)
( 97,434)( 98,433)( 99,436)(100,435)(101,438)(102,437)(103,440)(104,439)
(105,442)(106,441)(107,444)(108,443)(109,446)(110,445)(111,448)(112,447)
(113,450)(114,449)(115,452)(116,451)(117,454)(118,453)(119,456)(120,455)
(121,458)(122,457)(123,460)(124,459)(125,462)(126,461)(127,464)(128,463)
(129,466)(130,465)(131,468)(132,467)(133,470)(134,469)(135,472)(136,471)
(137,474)(138,473)(139,476)(140,475)(141,478)(142,477)(143,480)(144,479)
(145,482)(146,481)(147,484)(148,483)(149,486)(150,485)(151,488)(152,487)
(153,490)(154,489)(155,492)(156,491)(157,494)(158,493)(159,496)(160,495)
(161,498)(162,497)(163,500)(164,499)(165,502)(166,501)(167,504)(168,503)
(169,506)(170,505)(171,508)(172,507)(173,510)(174,509)(175,512)(176,511)
(177,514)(178,513)(179,516)(180,515)(181,518)(182,517)(183,520)(184,519)
(185,522)(186,521)(187,524)(188,523)(189,526)(190,525)(191,528)(192,527)
(193,530)(194,529)(195,532)(196,531)(197,534)(198,533)(199,536)(200,535)
(201,538)(202,537)(203,540)(204,539)(205,542)(206,541)(207,544)(208,543)
(209,546)(210,545)(211,548)(212,547)(213,550)(214,549)(215,552)(216,551)
(217,554)(218,553)(219,556)(220,555)(221,558)(222,557)(223,560)(224,559)
(225,562)(226,561)(227,564)(228,563)(229,566)(230,565)(231,568)(232,567)
(233,570)(234,569)(235,572)(236,571)(237,574)(238,573)(239,576)(240,575)
(241,578)(242,577)(243,580)(244,579)(245,582)(246,581)(247,584)(248,583)
(249,586)(250,585)(251,588)(252,587)(253,590)(254,589)(255,592)(256,591)
(257,594)(258,593)(259,596)(260,595)(261,598)(262,597)(263,600)(264,599)
(265,602)(266,601)(267,604)(268,603)(269,606)(270,605)(271,608)(272,607)
(273,610)(274,609)(275,612)(276,611)(277,614)(278,613)(279,616)(280,615)
(281,618)(282,617)(283,620)(284,619)(285,622)(286,621)(287,624)(288,623)
(289,626)(290,625)(291,628)(292,627)(293,630)(294,629)(295,632)(296,631)
(297,634)(298,633)(299,636)(300,635)(301,638)(302,637)(303,640)(304,639)
(305,642)(306,641)(307,644)(308,643)(309,646)(310,645)(311,648)(312,647)
(313,650)(314,649)(315,652)(316,651)(317,654)(318,653)(319,656)(320,655)
(321,658)(322,657)(323,660)(324,659)(325,662)(326,661)(327,664)(328,663)
(329,666)(330,665)(331,668)(332,667)(333,670)(334,669)(335,672)(336,671);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s1*s3*s2*s1*s3*s0*s1*s2*s0*s1*s0,
s1*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*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(672)!( 1,345)( 2,346)( 3,347)( 4,348)( 5,349)( 6,350)( 7,351)
( 8,352)( 9,337)( 10,338)( 11,339)( 12,340)( 13,341)( 14,342)( 15,343)
( 16,344)( 17,361)( 18,362)( 19,363)( 20,364)( 21,365)( 22,366)( 23,367)
( 24,368)( 25,353)( 26,354)( 27,355)( 28,356)( 29,357)( 30,358)( 31,359)
( 32,360)( 33,377)( 34,378)( 35,379)( 36,380)( 37,381)( 38,382)( 39,383)
( 40,384)( 41,369)( 42,370)( 43,371)( 44,372)( 45,373)( 46,374)( 47,375)
( 48,376)( 49,393)( 50,394)( 51,395)( 52,396)( 53,397)( 54,398)( 55,399)
( 56,400)( 57,385)( 58,386)( 59,387)( 60,388)( 61,389)( 62,390)( 63,391)
( 64,392)( 65,409)( 66,410)( 67,411)( 68,412)( 69,413)( 70,414)( 71,415)
( 72,416)( 73,401)( 74,402)( 75,403)( 76,404)( 77,405)( 78,406)( 79,407)
( 80,408)( 81,425)( 82,426)( 83,427)( 84,428)( 85,429)( 86,430)( 87,431)
( 88,432)( 89,417)( 90,418)( 91,419)( 92,420)( 93,421)( 94,422)( 95,423)
( 96,424)( 97,441)( 98,442)( 99,443)(100,444)(101,445)(102,446)(103,447)
(104,448)(105,433)(106,434)(107,435)(108,436)(109,437)(110,438)(111,439)
(112,440)(113,457)(114,458)(115,459)(116,460)(117,461)(118,462)(119,463)
(120,464)(121,449)(122,450)(123,451)(124,452)(125,453)(126,454)(127,455)
(128,456)(129,473)(130,474)(131,475)(132,476)(133,477)(134,478)(135,479)
(136,480)(137,465)(138,466)(139,467)(140,468)(141,469)(142,470)(143,471)
(144,472)(145,489)(146,490)(147,491)(148,492)(149,493)(150,494)(151,495)
(152,496)(153,481)(154,482)(155,483)(156,484)(157,485)(158,486)(159,487)
(160,488)(161,505)(162,506)(163,507)(164,508)(165,509)(166,510)(167,511)
(168,512)(169,497)(170,498)(171,499)(172,500)(173,501)(174,502)(175,503)
(176,504)(177,521)(178,522)(179,523)(180,524)(181,525)(182,526)(183,527)
(184,528)(185,513)(186,514)(187,515)(188,516)(189,517)(190,518)(191,519)
(192,520)(193,537)(194,538)(195,539)(196,540)(197,541)(198,542)(199,543)
(200,544)(201,529)(202,530)(203,531)(204,532)(205,533)(206,534)(207,535)
(208,536)(209,553)(210,554)(211,555)(212,556)(213,557)(214,558)(215,559)
(216,560)(217,545)(218,546)(219,547)(220,548)(221,549)(222,550)(223,551)
(224,552)(225,569)(226,570)(227,571)(228,572)(229,573)(230,574)(231,575)
(232,576)(233,561)(234,562)(235,563)(236,564)(237,565)(238,566)(239,567)
(240,568)(241,585)(242,586)(243,587)(244,588)(245,589)(246,590)(247,591)
(248,592)(249,577)(250,578)(251,579)(252,580)(253,581)(254,582)(255,583)
(256,584)(257,601)(258,602)(259,603)(260,604)(261,605)(262,606)(263,607)
(264,608)(265,593)(266,594)(267,595)(268,596)(269,597)(270,598)(271,599)
(272,600)(273,617)(274,618)(275,619)(276,620)(277,621)(278,622)(279,623)
(280,624)(281,609)(282,610)(283,611)(284,612)(285,613)(286,614)(287,615)
(288,616)(289,633)(290,634)(291,635)(292,636)(293,637)(294,638)(295,639)
(296,640)(297,625)(298,626)(299,627)(300,628)(301,629)(302,630)(303,631)
(304,632)(305,649)(306,650)(307,651)(308,652)(309,653)(310,654)(311,655)
(312,656)(313,641)(314,642)(315,643)(316,644)(317,645)(318,646)(319,647)
(320,648)(321,665)(322,666)(323,667)(324,668)(325,669)(326,670)(327,671)
(328,672)(329,657)(330,658)(331,659)(332,660)(333,661)(334,662)(335,663)
(336,664);
s1 := Sym(672)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 97)
( 18, 98)( 19,100)( 20, 99)( 21,101)( 22,102)( 23,104)( 24,103)( 25,109)
( 26,110)( 27,112)( 28,111)( 29,105)( 30,106)( 31,108)( 32,107)( 33, 81)
( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 93)
( 42, 94)( 43, 96)( 44, 95)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 65)
( 50, 66)( 51, 68)( 52, 67)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 77)
( 58, 78)( 59, 80)( 60, 79)( 61, 73)( 62, 74)( 63, 76)( 64, 75)(113,225)
(114,226)(115,228)(116,227)(117,229)(118,230)(119,232)(120,231)(121,237)
(122,238)(123,240)(124,239)(125,233)(126,234)(127,236)(128,235)(129,321)
(130,322)(131,324)(132,323)(133,325)(134,326)(135,328)(136,327)(137,333)
(138,334)(139,336)(140,335)(141,329)(142,330)(143,332)(144,331)(145,305)
(146,306)(147,308)(148,307)(149,309)(150,310)(151,312)(152,311)(153,317)
(154,318)(155,320)(156,319)(157,313)(158,314)(159,316)(160,315)(161,289)
(162,290)(163,292)(164,291)(165,293)(166,294)(167,296)(168,295)(169,301)
(170,302)(171,304)(172,303)(173,297)(174,298)(175,300)(176,299)(177,273)
(178,274)(179,276)(180,275)(181,277)(182,278)(183,280)(184,279)(185,285)
(186,286)(187,288)(188,287)(189,281)(190,282)(191,284)(192,283)(193,257)
(194,258)(195,260)(196,259)(197,261)(198,262)(199,264)(200,263)(201,269)
(202,270)(203,272)(204,271)(205,265)(206,266)(207,268)(208,267)(209,241)
(210,242)(211,244)(212,243)(213,245)(214,246)(215,248)(216,247)(217,253)
(218,254)(219,256)(220,255)(221,249)(222,250)(223,252)(224,251)(339,340)
(343,344)(345,349)(346,350)(347,352)(348,351)(353,433)(354,434)(355,436)
(356,435)(357,437)(358,438)(359,440)(360,439)(361,445)(362,446)(363,448)
(364,447)(365,441)(366,442)(367,444)(368,443)(369,417)(370,418)(371,420)
(372,419)(373,421)(374,422)(375,424)(376,423)(377,429)(378,430)(379,432)
(380,431)(381,425)(382,426)(383,428)(384,427)(385,401)(386,402)(387,404)
(388,403)(389,405)(390,406)(391,408)(392,407)(393,413)(394,414)(395,416)
(396,415)(397,409)(398,410)(399,412)(400,411)(449,561)(450,562)(451,564)
(452,563)(453,565)(454,566)(455,568)(456,567)(457,573)(458,574)(459,576)
(460,575)(461,569)(462,570)(463,572)(464,571)(465,657)(466,658)(467,660)
(468,659)(469,661)(470,662)(471,664)(472,663)(473,669)(474,670)(475,672)
(476,671)(477,665)(478,666)(479,668)(480,667)(481,641)(482,642)(483,644)
(484,643)(485,645)(486,646)(487,648)(488,647)(489,653)(490,654)(491,656)
(492,655)(493,649)(494,650)(495,652)(496,651)(497,625)(498,626)(499,628)
(500,627)(501,629)(502,630)(503,632)(504,631)(505,637)(506,638)(507,640)
(508,639)(509,633)(510,634)(511,636)(512,635)(513,609)(514,610)(515,612)
(516,611)(517,613)(518,614)(519,616)(520,615)(521,621)(522,622)(523,624)
(524,623)(525,617)(526,618)(527,620)(528,619)(529,593)(530,594)(531,596)
(532,595)(533,597)(534,598)(535,600)(536,599)(537,605)(538,606)(539,608)
(540,607)(541,601)(542,602)(543,604)(544,603)(545,577)(546,578)(547,580)
(548,579)(549,581)(550,582)(551,584)(552,583)(553,589)(554,590)(555,592)
(556,591)(557,585)(558,586)(559,588)(560,587);
s2 := Sym(672)!( 1,465)( 2,468)( 3,467)( 4,466)( 5,477)( 6,480)( 7,479)
( 8,478)( 9,473)( 10,476)( 11,475)( 12,474)( 13,469)( 14,472)( 15,471)
( 16,470)( 17,449)( 18,452)( 19,451)( 20,450)( 21,461)( 22,464)( 23,463)
( 24,462)( 25,457)( 26,460)( 27,459)( 28,458)( 29,453)( 30,456)( 31,455)
( 32,454)( 33,545)( 34,548)( 35,547)( 36,546)( 37,557)( 38,560)( 39,559)
( 40,558)( 41,553)( 42,556)( 43,555)( 44,554)( 45,549)( 46,552)( 47,551)
( 48,550)( 49,529)( 50,532)( 51,531)( 52,530)( 53,541)( 54,544)( 55,543)
( 56,542)( 57,537)( 58,540)( 59,539)( 60,538)( 61,533)( 62,536)( 63,535)
( 64,534)( 65,513)( 66,516)( 67,515)( 68,514)( 69,525)( 70,528)( 71,527)
( 72,526)( 73,521)( 74,524)( 75,523)( 76,522)( 77,517)( 78,520)( 79,519)
( 80,518)( 81,497)( 82,500)( 83,499)( 84,498)( 85,509)( 86,512)( 87,511)
( 88,510)( 89,505)( 90,508)( 91,507)( 92,506)( 93,501)( 94,504)( 95,503)
( 96,502)( 97,481)( 98,484)( 99,483)(100,482)(101,493)(102,496)(103,495)
(104,494)(105,489)(106,492)(107,491)(108,490)(109,485)(110,488)(111,487)
(112,486)(113,353)(114,356)(115,355)(116,354)(117,365)(118,368)(119,367)
(120,366)(121,361)(122,364)(123,363)(124,362)(125,357)(126,360)(127,359)
(128,358)(129,337)(130,340)(131,339)(132,338)(133,349)(134,352)(135,351)
(136,350)(137,345)(138,348)(139,347)(140,346)(141,341)(142,344)(143,343)
(144,342)(145,433)(146,436)(147,435)(148,434)(149,445)(150,448)(151,447)
(152,446)(153,441)(154,444)(155,443)(156,442)(157,437)(158,440)(159,439)
(160,438)(161,417)(162,420)(163,419)(164,418)(165,429)(166,432)(167,431)
(168,430)(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)
(176,422)(177,401)(178,404)(179,403)(180,402)(181,413)(182,416)(183,415)
(184,414)(185,409)(186,412)(187,411)(188,410)(189,405)(190,408)(191,407)
(192,406)(193,385)(194,388)(195,387)(196,386)(197,397)(198,400)(199,399)
(200,398)(201,393)(202,396)(203,395)(204,394)(205,389)(206,392)(207,391)
(208,390)(209,369)(210,372)(211,371)(212,370)(213,381)(214,384)(215,383)
(216,382)(217,377)(218,380)(219,379)(220,378)(221,373)(222,376)(223,375)
(224,374)(225,577)(226,580)(227,579)(228,578)(229,589)(230,592)(231,591)
(232,590)(233,585)(234,588)(235,587)(236,586)(237,581)(238,584)(239,583)
(240,582)(241,561)(242,564)(243,563)(244,562)(245,573)(246,576)(247,575)
(248,574)(249,569)(250,572)(251,571)(252,570)(253,565)(254,568)(255,567)
(256,566)(257,657)(258,660)(259,659)(260,658)(261,669)(262,672)(263,671)
(264,670)(265,665)(266,668)(267,667)(268,666)(269,661)(270,664)(271,663)
(272,662)(273,641)(274,644)(275,643)(276,642)(277,653)(278,656)(279,655)
(280,654)(281,649)(282,652)(283,651)(284,650)(285,645)(286,648)(287,647)
(288,646)(289,625)(290,628)(291,627)(292,626)(293,637)(294,640)(295,639)
(296,638)(297,633)(298,636)(299,635)(300,634)(301,629)(302,632)(303,631)
(304,630)(305,609)(306,612)(307,611)(308,610)(309,621)(310,624)(311,623)
(312,622)(313,617)(314,620)(315,619)(316,618)(317,613)(318,616)(319,615)
(320,614)(321,593)(322,596)(323,595)(324,594)(325,605)(326,608)(327,607)
(328,606)(329,601)(330,604)(331,603)(332,602)(333,597)(334,600)(335,599)
(336,598);
s3 := Sym(672)!( 1,338)( 2,337)( 3,340)( 4,339)( 5,342)( 6,341)( 7,344)
( 8,343)( 9,346)( 10,345)( 11,348)( 12,347)( 13,350)( 14,349)( 15,352)
( 16,351)( 17,354)( 18,353)( 19,356)( 20,355)( 21,358)( 22,357)( 23,360)
( 24,359)( 25,362)( 26,361)( 27,364)( 28,363)( 29,366)( 30,365)( 31,368)
( 32,367)( 33,370)( 34,369)( 35,372)( 36,371)( 37,374)( 38,373)( 39,376)
( 40,375)( 41,378)( 42,377)( 43,380)( 44,379)( 45,382)( 46,381)( 47,384)
( 48,383)( 49,386)( 50,385)( 51,388)( 52,387)( 53,390)( 54,389)( 55,392)
( 56,391)( 57,394)( 58,393)( 59,396)( 60,395)( 61,398)( 62,397)( 63,400)
( 64,399)( 65,402)( 66,401)( 67,404)( 68,403)( 69,406)( 70,405)( 71,408)
( 72,407)( 73,410)( 74,409)( 75,412)( 76,411)( 77,414)( 78,413)( 79,416)
( 80,415)( 81,418)( 82,417)( 83,420)( 84,419)( 85,422)( 86,421)( 87,424)
( 88,423)( 89,426)( 90,425)( 91,428)( 92,427)( 93,430)( 94,429)( 95,432)
( 96,431)( 97,434)( 98,433)( 99,436)(100,435)(101,438)(102,437)(103,440)
(104,439)(105,442)(106,441)(107,444)(108,443)(109,446)(110,445)(111,448)
(112,447)(113,450)(114,449)(115,452)(116,451)(117,454)(118,453)(119,456)
(120,455)(121,458)(122,457)(123,460)(124,459)(125,462)(126,461)(127,464)
(128,463)(129,466)(130,465)(131,468)(132,467)(133,470)(134,469)(135,472)
(136,471)(137,474)(138,473)(139,476)(140,475)(141,478)(142,477)(143,480)
(144,479)(145,482)(146,481)(147,484)(148,483)(149,486)(150,485)(151,488)
(152,487)(153,490)(154,489)(155,492)(156,491)(157,494)(158,493)(159,496)
(160,495)(161,498)(162,497)(163,500)(164,499)(165,502)(166,501)(167,504)
(168,503)(169,506)(170,505)(171,508)(172,507)(173,510)(174,509)(175,512)
(176,511)(177,514)(178,513)(179,516)(180,515)(181,518)(182,517)(183,520)
(184,519)(185,522)(186,521)(187,524)(188,523)(189,526)(190,525)(191,528)
(192,527)(193,530)(194,529)(195,532)(196,531)(197,534)(198,533)(199,536)
(200,535)(201,538)(202,537)(203,540)(204,539)(205,542)(206,541)(207,544)
(208,543)(209,546)(210,545)(211,548)(212,547)(213,550)(214,549)(215,552)
(216,551)(217,554)(218,553)(219,556)(220,555)(221,558)(222,557)(223,560)
(224,559)(225,562)(226,561)(227,564)(228,563)(229,566)(230,565)(231,568)
(232,567)(233,570)(234,569)(235,572)(236,571)(237,574)(238,573)(239,576)
(240,575)(241,578)(242,577)(243,580)(244,579)(245,582)(246,581)(247,584)
(248,583)(249,586)(250,585)(251,588)(252,587)(253,590)(254,589)(255,592)
(256,591)(257,594)(258,593)(259,596)(260,595)(261,598)(262,597)(263,600)
(264,599)(265,602)(266,601)(267,604)(268,603)(269,606)(270,605)(271,608)
(272,607)(273,610)(274,609)(275,612)(276,611)(277,614)(278,613)(279,616)
(280,615)(281,618)(282,617)(283,620)(284,619)(285,622)(286,621)(287,624)
(288,623)(289,626)(290,625)(291,628)(292,627)(293,630)(294,629)(295,632)
(296,631)(297,634)(298,633)(299,636)(300,635)(301,638)(302,637)(303,640)
(304,639)(305,642)(306,641)(307,644)(308,643)(309,646)(310,645)(311,648)
(312,647)(313,650)(314,649)(315,652)(316,651)(317,654)(318,653)(319,656)
(320,655)(321,658)(322,657)(323,660)(324,659)(325,662)(326,661)(327,664)
(328,663)(329,666)(330,665)(331,668)(332,667)(333,670)(334,669)(335,672)
(336,671);
poly := sub<Sym(672)|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,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s1*s3*s2*s1*s3*s0*s1*s2*s0*s1*s0,
s1*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*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope