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Polytope of Type {28,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,6,4}*1344a
Also Known As : {{28,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1344,7535)
Rank : 4
Schlafli Type : {28,6,4}
Number of vertices, edges, etc : 28, 84, 12, 4
Order of s0s1s2s3 : 84
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {28,6,2}*672a, {14,6,4}*672a
   3-fold quotients : {28,2,4}*448
   4-fold quotients : {14,6,2}*336
   6-fold quotients : {28,2,2}*224, {14,2,4}*224
   7-fold quotients : {4,6,4}*192a
   12-fold quotients : {7,2,4}*112, {14,2,2}*112
   14-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   21-fold quotients : {4,2,4}*64
   24-fold quotients : {7,2,2}*56
   28-fold quotients : {2,6,2}*48
   42-fold quotients : {2,2,4}*32, {4,2,2}*32
   56-fold quotients : {2,3,2}*24
   84-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)
( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 85,106)( 86,112)( 87,111)( 88,110)
( 89,109)( 90,108)( 91,107)( 92,113)( 93,119)( 94,118)( 95,117)( 96,116)
( 97,115)( 98,114)( 99,120)(100,126)(101,125)(102,124)(103,123)(104,122)
(105,121)(127,148)(128,154)(129,153)(130,152)(131,151)(132,150)(133,149)
(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)(141,162)
(142,168)(143,167)(144,166)(145,165)(146,164)(147,163)(170,175)(171,174)
(172,173)(177,182)(178,181)(179,180)(184,189)(185,188)(186,187)(191,196)
(192,195)(193,194)(198,203)(199,202)(200,201)(205,210)(206,209)(207,208)
(212,217)(213,216)(214,215)(219,224)(220,223)(221,222)(226,231)(227,230)
(228,229)(233,238)(234,237)(235,236)(240,245)(241,244)(242,243)(247,252)
(248,251)(249,250)(253,274)(254,280)(255,279)(256,278)(257,277)(258,276)
(259,275)(260,281)(261,287)(262,286)(263,285)(264,284)(265,283)(266,282)
(267,288)(268,294)(269,293)(270,292)(271,291)(272,290)(273,289)(295,316)
(296,322)(297,321)(298,320)(299,319)(300,318)(301,317)(302,323)(303,329)
(304,328)(305,327)(306,326)(307,325)(308,324)(309,330)(310,336)(311,335)
(312,334)(313,333)(314,332)(315,331)(337,358)(338,364)(339,363)(340,362)
(341,361)(342,360)(343,359)(344,365)(345,371)(346,370)(347,369)(348,368)
(349,367)(350,366)(351,372)(352,378)(353,377)(354,376)(355,375)(356,374)
(357,373)(379,400)(380,406)(381,405)(382,404)(383,403)(384,402)(385,401)
(386,407)(387,413)(388,412)(389,411)(390,410)(391,409)(392,408)(393,414)
(394,420)(395,419)(396,418)(397,417)(398,416)(399,415)(422,427)(423,426)
(424,425)(429,434)(430,433)(431,432)(436,441)(437,440)(438,439)(443,448)
(444,447)(445,446)(450,455)(451,454)(452,453)(457,462)(458,461)(459,460)
(464,469)(465,468)(466,467)(471,476)(472,475)(473,474)(478,483)(479,482)
(480,481)(485,490)(486,489)(487,488)(492,497)(493,496)(494,495)(499,504)
(500,503)(501,502)(505,526)(506,532)(507,531)(508,530)(509,529)(510,528)
(511,527)(512,533)(513,539)(514,538)(515,537)(516,536)(517,535)(518,534)
(519,540)(520,546)(521,545)(522,544)(523,543)(524,542)(525,541)(547,568)
(548,574)(549,573)(550,572)(551,571)(552,570)(553,569)(554,575)(555,581)
(556,580)(557,579)(558,578)(559,577)(560,576)(561,582)(562,588)(563,587)
(564,586)(565,585)(566,584)(567,583)(590,595)(591,594)(592,593)(597,602)
(598,601)(599,600)(604,609)(605,608)(606,607)(611,616)(612,615)(613,614)
(618,623)(619,622)(620,621)(625,630)(626,629)(627,628)(632,637)(633,636)
(634,635)(639,644)(640,643)(641,642)(646,651)(647,650)(648,649)(653,658)
(654,657)(655,656)(660,665)(661,664)(662,663)(667,672)(668,671)(669,670);;
s1 := (  1,338)(  2,337)(  3,343)(  4,342)(  5,341)(  6,340)(  7,339)(  8,352)
(  9,351)( 10,357)( 11,356)( 12,355)( 13,354)( 14,353)( 15,345)( 16,344)
( 17,350)( 18,349)( 19,348)( 20,347)( 21,346)( 22,359)( 23,358)( 24,364)
( 25,363)( 26,362)( 27,361)( 28,360)( 29,373)( 30,372)( 31,378)( 32,377)
( 33,376)( 34,375)( 35,374)( 36,366)( 37,365)( 38,371)( 39,370)( 40,369)
( 41,368)( 42,367)( 43,380)( 44,379)( 45,385)( 46,384)( 47,383)( 48,382)
( 49,381)( 50,394)( 51,393)( 52,399)( 53,398)( 54,397)( 55,396)( 56,395)
( 57,387)( 58,386)( 59,392)( 60,391)( 61,390)( 62,389)( 63,388)( 64,401)
( 65,400)( 66,406)( 67,405)( 68,404)( 69,403)( 70,402)( 71,415)( 72,414)
( 73,420)( 74,419)( 75,418)( 76,417)( 77,416)( 78,408)( 79,407)( 80,413)
( 81,412)( 82,411)( 83,410)( 84,409)( 85,443)( 86,442)( 87,448)( 88,447)
( 89,446)( 90,445)( 91,444)( 92,457)( 93,456)( 94,462)( 95,461)( 96,460)
( 97,459)( 98,458)( 99,450)(100,449)(101,455)(102,454)(103,453)(104,452)
(105,451)(106,422)(107,421)(108,427)(109,426)(110,425)(111,424)(112,423)
(113,436)(114,435)(115,441)(116,440)(117,439)(118,438)(119,437)(120,429)
(121,428)(122,434)(123,433)(124,432)(125,431)(126,430)(127,485)(128,484)
(129,490)(130,489)(131,488)(132,487)(133,486)(134,499)(135,498)(136,504)
(137,503)(138,502)(139,501)(140,500)(141,492)(142,491)(143,497)(144,496)
(145,495)(146,494)(147,493)(148,464)(149,463)(150,469)(151,468)(152,467)
(153,466)(154,465)(155,478)(156,477)(157,483)(158,482)(159,481)(160,480)
(161,479)(162,471)(163,470)(164,476)(165,475)(166,474)(167,473)(168,472)
(169,506)(170,505)(171,511)(172,510)(173,509)(174,508)(175,507)(176,520)
(177,519)(178,525)(179,524)(180,523)(181,522)(182,521)(183,513)(184,512)
(185,518)(186,517)(187,516)(188,515)(189,514)(190,527)(191,526)(192,532)
(193,531)(194,530)(195,529)(196,528)(197,541)(198,540)(199,546)(200,545)
(201,544)(202,543)(203,542)(204,534)(205,533)(206,539)(207,538)(208,537)
(209,536)(210,535)(211,548)(212,547)(213,553)(214,552)(215,551)(216,550)
(217,549)(218,562)(219,561)(220,567)(221,566)(222,565)(223,564)(224,563)
(225,555)(226,554)(227,560)(228,559)(229,558)(230,557)(231,556)(232,569)
(233,568)(234,574)(235,573)(236,572)(237,571)(238,570)(239,583)(240,582)
(241,588)(242,587)(243,586)(244,585)(245,584)(246,576)(247,575)(248,581)
(249,580)(250,579)(251,578)(252,577)(253,611)(254,610)(255,616)(256,615)
(257,614)(258,613)(259,612)(260,625)(261,624)(262,630)(263,629)(264,628)
(265,627)(266,626)(267,618)(268,617)(269,623)(270,622)(271,621)(272,620)
(273,619)(274,590)(275,589)(276,595)(277,594)(278,593)(279,592)(280,591)
(281,604)(282,603)(283,609)(284,608)(285,607)(286,606)(287,605)(288,597)
(289,596)(290,602)(291,601)(292,600)(293,599)(294,598)(295,653)(296,652)
(297,658)(298,657)(299,656)(300,655)(301,654)(302,667)(303,666)(304,672)
(305,671)(306,670)(307,669)(308,668)(309,660)(310,659)(311,665)(312,664)
(313,663)(314,662)(315,661)(316,632)(317,631)(318,637)(319,636)(320,635)
(321,634)(322,633)(323,646)(324,645)(325,651)(326,650)(327,649)(328,648)
(329,647)(330,639)(331,638)(332,644)(333,643)(334,642)(335,641)(336,640);;
s2 := (  1,428)(  2,429)(  3,430)(  4,431)(  5,432)(  6,433)(  7,434)(  8,421)
(  9,422)( 10,423)( 11,424)( 12,425)( 13,426)( 14,427)( 15,435)( 16,436)
( 17,437)( 18,438)( 19,439)( 20,440)( 21,441)( 22,449)( 23,450)( 24,451)
( 25,452)( 26,453)( 27,454)( 28,455)( 29,442)( 30,443)( 31,444)( 32,445)
( 33,446)( 34,447)( 35,448)( 36,456)( 37,457)( 38,458)( 39,459)( 40,460)
( 41,461)( 42,462)( 43,470)( 44,471)( 45,472)( 46,473)( 47,474)( 48,475)
( 49,476)( 50,463)( 51,464)( 52,465)( 53,466)( 54,467)( 55,468)( 56,469)
( 57,477)( 58,478)( 59,479)( 60,480)( 61,481)( 62,482)( 63,483)( 64,491)
( 65,492)( 66,493)( 67,494)( 68,495)( 69,496)( 70,497)( 71,484)( 72,485)
( 73,486)( 74,487)( 75,488)( 76,489)( 77,490)( 78,498)( 79,499)( 80,500)
( 81,501)( 82,502)( 83,503)( 84,504)( 85,365)( 86,366)( 87,367)( 88,368)
( 89,369)( 90,370)( 91,371)( 92,358)( 93,359)( 94,360)( 95,361)( 96,362)
( 97,363)( 98,364)( 99,372)(100,373)(101,374)(102,375)(103,376)(104,377)
(105,378)(106,344)(107,345)(108,346)(109,347)(110,348)(111,349)(112,350)
(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,351)
(121,352)(122,353)(123,354)(124,355)(125,356)(126,357)(127,407)(128,408)
(129,409)(130,410)(131,411)(132,412)(133,413)(134,400)(135,401)(136,402)
(137,403)(138,404)(139,405)(140,406)(141,414)(142,415)(143,416)(144,417)
(145,418)(146,419)(147,420)(148,386)(149,387)(150,388)(151,389)(152,390)
(153,391)(154,392)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)
(161,385)(162,393)(163,394)(164,395)(165,396)(166,397)(167,398)(168,399)
(169,596)(170,597)(171,598)(172,599)(173,600)(174,601)(175,602)(176,589)
(177,590)(178,591)(179,592)(180,593)(181,594)(182,595)(183,603)(184,604)
(185,605)(186,606)(187,607)(188,608)(189,609)(190,617)(191,618)(192,619)
(193,620)(194,621)(195,622)(196,623)(197,610)(198,611)(199,612)(200,613)
(201,614)(202,615)(203,616)(204,624)(205,625)(206,626)(207,627)(208,628)
(209,629)(210,630)(211,638)(212,639)(213,640)(214,641)(215,642)(216,643)
(217,644)(218,631)(219,632)(220,633)(221,634)(222,635)(223,636)(224,637)
(225,645)(226,646)(227,647)(228,648)(229,649)(230,650)(231,651)(232,659)
(233,660)(234,661)(235,662)(236,663)(237,664)(238,665)(239,652)(240,653)
(241,654)(242,655)(243,656)(244,657)(245,658)(246,666)(247,667)(248,668)
(249,669)(250,670)(251,671)(252,672)(253,533)(254,534)(255,535)(256,536)
(257,537)(258,538)(259,539)(260,526)(261,527)(262,528)(263,529)(264,530)
(265,531)(266,532)(267,540)(268,541)(269,542)(270,543)(271,544)(272,545)
(273,546)(274,512)(275,513)(276,514)(277,515)(278,516)(279,517)(280,518)
(281,505)(282,506)(283,507)(284,508)(285,509)(286,510)(287,511)(288,519)
(289,520)(290,521)(291,522)(292,523)(293,524)(294,525)(295,575)(296,576)
(297,577)(298,578)(299,579)(300,580)(301,581)(302,568)(303,569)(304,570)
(305,571)(306,572)(307,573)(308,574)(309,582)(310,583)(311,584)(312,585)
(313,586)(314,587)(315,588)(316,554)(317,555)(318,556)(319,557)(320,558)
(321,559)(322,560)(323,547)(324,548)(325,549)(326,550)(327,551)(328,552)
(329,553)(330,561)(331,562)(332,563)(333,564)(334,565)(335,566)(336,567);;
s3 := (  1,169)(  2,170)(  3,171)(  4,172)(  5,173)(  6,174)(  7,175)(  8,176)
(  9,177)( 10,178)( 11,179)( 12,180)( 13,181)( 14,182)( 15,183)( 16,184)
( 17,185)( 18,186)( 19,187)( 20,188)( 21,189)( 22,190)( 23,191)( 24,192)
( 25,193)( 26,194)( 27,195)( 28,196)( 29,197)( 30,198)( 31,199)( 32,200)
( 33,201)( 34,202)( 35,203)( 36,204)( 37,205)( 38,206)( 39,207)( 40,208)
( 41,209)( 42,210)( 43,211)( 44,212)( 45,213)( 46,214)( 47,215)( 48,216)
( 49,217)( 50,218)( 51,219)( 52,220)( 53,221)( 54,222)( 55,223)( 56,224)
( 57,225)( 58,226)( 59,227)( 60,228)( 61,229)( 62,230)( 63,231)( 64,232)
( 65,233)( 66,234)( 67,235)( 68,236)( 69,237)( 70,238)( 71,239)( 72,240)
( 73,241)( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,247)( 80,248)
( 81,249)( 82,250)( 83,251)( 84,252)( 85,295)( 86,296)( 87,297)( 88,298)
( 89,299)( 90,300)( 91,301)( 92,302)( 93,303)( 94,304)( 95,305)( 96,306)
( 97,307)( 98,308)( 99,309)(100,310)(101,311)(102,312)(103,313)(104,314)
(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)
(113,323)(114,324)(115,325)(116,326)(117,327)(118,328)(119,329)(120,330)
(121,331)(122,332)(123,333)(124,334)(125,335)(126,336)(127,253)(128,254)
(129,255)(130,256)(131,257)(132,258)(133,259)(134,260)(135,261)(136,262)
(137,263)(138,264)(139,265)(140,266)(141,267)(142,268)(143,269)(144,270)
(145,271)(146,272)(147,273)(148,274)(149,275)(150,276)(151,277)(152,278)
(153,279)(154,280)(155,281)(156,282)(157,283)(158,284)(159,285)(160,286)
(161,287)(162,288)(163,289)(164,290)(165,291)(166,292)(167,293)(168,294)
(337,505)(338,506)(339,507)(340,508)(341,509)(342,510)(343,511)(344,512)
(345,513)(346,514)(347,515)(348,516)(349,517)(350,518)(351,519)(352,520)
(353,521)(354,522)(355,523)(356,524)(357,525)(358,526)(359,527)(360,528)
(361,529)(362,530)(363,531)(364,532)(365,533)(366,534)(367,535)(368,536)
(369,537)(370,538)(371,539)(372,540)(373,541)(374,542)(375,543)(376,544)
(377,545)(378,546)(379,547)(380,548)(381,549)(382,550)(383,551)(384,552)
(385,553)(386,554)(387,555)(388,556)(389,557)(390,558)(391,559)(392,560)
(393,561)(394,562)(395,563)(396,564)(397,565)(398,566)(399,567)(400,568)
(401,569)(402,570)(403,571)(404,572)(405,573)(406,574)(407,575)(408,576)
(409,577)(410,578)(411,579)(412,580)(413,581)(414,582)(415,583)(416,584)
(417,585)(418,586)(419,587)(420,588)(421,631)(422,632)(423,633)(424,634)
(425,635)(426,636)(427,637)(428,638)(429,639)(430,640)(431,641)(432,642)
(433,643)(434,644)(435,645)(436,646)(437,647)(438,648)(439,649)(440,650)
(441,651)(442,652)(443,653)(444,654)(445,655)(446,656)(447,657)(448,658)
(449,659)(450,660)(451,661)(452,662)(453,663)(454,664)(455,665)(456,666)
(457,667)(458,668)(459,669)(460,670)(461,671)(462,672)(463,589)(464,590)
(465,591)(466,592)(467,593)(468,594)(469,595)(470,596)(471,597)(472,598)
(473,599)(474,600)(475,601)(476,602)(477,603)(478,604)(479,605)(480,606)
(481,607)(482,608)(483,609)(484,610)(485,611)(486,612)(487,613)(488,614)
(489,615)(490,616)(491,617)(492,618)(493,619)(494,620)(495,621)(496,622)
(497,623)(498,624)(499,625)(500,626)(501,627)(502,628)(503,629)(504,630);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(672)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)
( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 85,106)( 86,112)( 87,111)
( 88,110)( 89,109)( 90,108)( 91,107)( 92,113)( 93,119)( 94,118)( 95,117)
( 96,116)( 97,115)( 98,114)( 99,120)(100,126)(101,125)(102,124)(103,123)
(104,122)(105,121)(127,148)(128,154)(129,153)(130,152)(131,151)(132,150)
(133,149)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)
(141,162)(142,168)(143,167)(144,166)(145,165)(146,164)(147,163)(170,175)
(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)(185,188)(186,187)
(191,196)(192,195)(193,194)(198,203)(199,202)(200,201)(205,210)(206,209)
(207,208)(212,217)(213,216)(214,215)(219,224)(220,223)(221,222)(226,231)
(227,230)(228,229)(233,238)(234,237)(235,236)(240,245)(241,244)(242,243)
(247,252)(248,251)(249,250)(253,274)(254,280)(255,279)(256,278)(257,277)
(258,276)(259,275)(260,281)(261,287)(262,286)(263,285)(264,284)(265,283)
(266,282)(267,288)(268,294)(269,293)(270,292)(271,291)(272,290)(273,289)
(295,316)(296,322)(297,321)(298,320)(299,319)(300,318)(301,317)(302,323)
(303,329)(304,328)(305,327)(306,326)(307,325)(308,324)(309,330)(310,336)
(311,335)(312,334)(313,333)(314,332)(315,331)(337,358)(338,364)(339,363)
(340,362)(341,361)(342,360)(343,359)(344,365)(345,371)(346,370)(347,369)
(348,368)(349,367)(350,366)(351,372)(352,378)(353,377)(354,376)(355,375)
(356,374)(357,373)(379,400)(380,406)(381,405)(382,404)(383,403)(384,402)
(385,401)(386,407)(387,413)(388,412)(389,411)(390,410)(391,409)(392,408)
(393,414)(394,420)(395,419)(396,418)(397,417)(398,416)(399,415)(422,427)
(423,426)(424,425)(429,434)(430,433)(431,432)(436,441)(437,440)(438,439)
(443,448)(444,447)(445,446)(450,455)(451,454)(452,453)(457,462)(458,461)
(459,460)(464,469)(465,468)(466,467)(471,476)(472,475)(473,474)(478,483)
(479,482)(480,481)(485,490)(486,489)(487,488)(492,497)(493,496)(494,495)
(499,504)(500,503)(501,502)(505,526)(506,532)(507,531)(508,530)(509,529)
(510,528)(511,527)(512,533)(513,539)(514,538)(515,537)(516,536)(517,535)
(518,534)(519,540)(520,546)(521,545)(522,544)(523,543)(524,542)(525,541)
(547,568)(548,574)(549,573)(550,572)(551,571)(552,570)(553,569)(554,575)
(555,581)(556,580)(557,579)(558,578)(559,577)(560,576)(561,582)(562,588)
(563,587)(564,586)(565,585)(566,584)(567,583)(590,595)(591,594)(592,593)
(597,602)(598,601)(599,600)(604,609)(605,608)(606,607)(611,616)(612,615)
(613,614)(618,623)(619,622)(620,621)(625,630)(626,629)(627,628)(632,637)
(633,636)(634,635)(639,644)(640,643)(641,642)(646,651)(647,650)(648,649)
(653,658)(654,657)(655,656)(660,665)(661,664)(662,663)(667,672)(668,671)
(669,670);
s1 := Sym(672)!(  1,338)(  2,337)(  3,343)(  4,342)(  5,341)(  6,340)(  7,339)
(  8,352)(  9,351)( 10,357)( 11,356)( 12,355)( 13,354)( 14,353)( 15,345)
( 16,344)( 17,350)( 18,349)( 19,348)( 20,347)( 21,346)( 22,359)( 23,358)
( 24,364)( 25,363)( 26,362)( 27,361)( 28,360)( 29,373)( 30,372)( 31,378)
( 32,377)( 33,376)( 34,375)( 35,374)( 36,366)( 37,365)( 38,371)( 39,370)
( 40,369)( 41,368)( 42,367)( 43,380)( 44,379)( 45,385)( 46,384)( 47,383)
( 48,382)( 49,381)( 50,394)( 51,393)( 52,399)( 53,398)( 54,397)( 55,396)
( 56,395)( 57,387)( 58,386)( 59,392)( 60,391)( 61,390)( 62,389)( 63,388)
( 64,401)( 65,400)( 66,406)( 67,405)( 68,404)( 69,403)( 70,402)( 71,415)
( 72,414)( 73,420)( 74,419)( 75,418)( 76,417)( 77,416)( 78,408)( 79,407)
( 80,413)( 81,412)( 82,411)( 83,410)( 84,409)( 85,443)( 86,442)( 87,448)
( 88,447)( 89,446)( 90,445)( 91,444)( 92,457)( 93,456)( 94,462)( 95,461)
( 96,460)( 97,459)( 98,458)( 99,450)(100,449)(101,455)(102,454)(103,453)
(104,452)(105,451)(106,422)(107,421)(108,427)(109,426)(110,425)(111,424)
(112,423)(113,436)(114,435)(115,441)(116,440)(117,439)(118,438)(119,437)
(120,429)(121,428)(122,434)(123,433)(124,432)(125,431)(126,430)(127,485)
(128,484)(129,490)(130,489)(131,488)(132,487)(133,486)(134,499)(135,498)
(136,504)(137,503)(138,502)(139,501)(140,500)(141,492)(142,491)(143,497)
(144,496)(145,495)(146,494)(147,493)(148,464)(149,463)(150,469)(151,468)
(152,467)(153,466)(154,465)(155,478)(156,477)(157,483)(158,482)(159,481)
(160,480)(161,479)(162,471)(163,470)(164,476)(165,475)(166,474)(167,473)
(168,472)(169,506)(170,505)(171,511)(172,510)(173,509)(174,508)(175,507)
(176,520)(177,519)(178,525)(179,524)(180,523)(181,522)(182,521)(183,513)
(184,512)(185,518)(186,517)(187,516)(188,515)(189,514)(190,527)(191,526)
(192,532)(193,531)(194,530)(195,529)(196,528)(197,541)(198,540)(199,546)
(200,545)(201,544)(202,543)(203,542)(204,534)(205,533)(206,539)(207,538)
(208,537)(209,536)(210,535)(211,548)(212,547)(213,553)(214,552)(215,551)
(216,550)(217,549)(218,562)(219,561)(220,567)(221,566)(222,565)(223,564)
(224,563)(225,555)(226,554)(227,560)(228,559)(229,558)(230,557)(231,556)
(232,569)(233,568)(234,574)(235,573)(236,572)(237,571)(238,570)(239,583)
(240,582)(241,588)(242,587)(243,586)(244,585)(245,584)(246,576)(247,575)
(248,581)(249,580)(250,579)(251,578)(252,577)(253,611)(254,610)(255,616)
(256,615)(257,614)(258,613)(259,612)(260,625)(261,624)(262,630)(263,629)
(264,628)(265,627)(266,626)(267,618)(268,617)(269,623)(270,622)(271,621)
(272,620)(273,619)(274,590)(275,589)(276,595)(277,594)(278,593)(279,592)
(280,591)(281,604)(282,603)(283,609)(284,608)(285,607)(286,606)(287,605)
(288,597)(289,596)(290,602)(291,601)(292,600)(293,599)(294,598)(295,653)
(296,652)(297,658)(298,657)(299,656)(300,655)(301,654)(302,667)(303,666)
(304,672)(305,671)(306,670)(307,669)(308,668)(309,660)(310,659)(311,665)
(312,664)(313,663)(314,662)(315,661)(316,632)(317,631)(318,637)(319,636)
(320,635)(321,634)(322,633)(323,646)(324,645)(325,651)(326,650)(327,649)
(328,648)(329,647)(330,639)(331,638)(332,644)(333,643)(334,642)(335,641)
(336,640);
s2 := Sym(672)!(  1,428)(  2,429)(  3,430)(  4,431)(  5,432)(  6,433)(  7,434)
(  8,421)(  9,422)( 10,423)( 11,424)( 12,425)( 13,426)( 14,427)( 15,435)
( 16,436)( 17,437)( 18,438)( 19,439)( 20,440)( 21,441)( 22,449)( 23,450)
( 24,451)( 25,452)( 26,453)( 27,454)( 28,455)( 29,442)( 30,443)( 31,444)
( 32,445)( 33,446)( 34,447)( 35,448)( 36,456)( 37,457)( 38,458)( 39,459)
( 40,460)( 41,461)( 42,462)( 43,470)( 44,471)( 45,472)( 46,473)( 47,474)
( 48,475)( 49,476)( 50,463)( 51,464)( 52,465)( 53,466)( 54,467)( 55,468)
( 56,469)( 57,477)( 58,478)( 59,479)( 60,480)( 61,481)( 62,482)( 63,483)
( 64,491)( 65,492)( 66,493)( 67,494)( 68,495)( 69,496)( 70,497)( 71,484)
( 72,485)( 73,486)( 74,487)( 75,488)( 76,489)( 77,490)( 78,498)( 79,499)
( 80,500)( 81,501)( 82,502)( 83,503)( 84,504)( 85,365)( 86,366)( 87,367)
( 88,368)( 89,369)( 90,370)( 91,371)( 92,358)( 93,359)( 94,360)( 95,361)
( 96,362)( 97,363)( 98,364)( 99,372)(100,373)(101,374)(102,375)(103,376)
(104,377)(105,378)(106,344)(107,345)(108,346)(109,347)(110,348)(111,349)
(112,350)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)
(120,351)(121,352)(122,353)(123,354)(124,355)(125,356)(126,357)(127,407)
(128,408)(129,409)(130,410)(131,411)(132,412)(133,413)(134,400)(135,401)
(136,402)(137,403)(138,404)(139,405)(140,406)(141,414)(142,415)(143,416)
(144,417)(145,418)(146,419)(147,420)(148,386)(149,387)(150,388)(151,389)
(152,390)(153,391)(154,392)(155,379)(156,380)(157,381)(158,382)(159,383)
(160,384)(161,385)(162,393)(163,394)(164,395)(165,396)(166,397)(167,398)
(168,399)(169,596)(170,597)(171,598)(172,599)(173,600)(174,601)(175,602)
(176,589)(177,590)(178,591)(179,592)(180,593)(181,594)(182,595)(183,603)
(184,604)(185,605)(186,606)(187,607)(188,608)(189,609)(190,617)(191,618)
(192,619)(193,620)(194,621)(195,622)(196,623)(197,610)(198,611)(199,612)
(200,613)(201,614)(202,615)(203,616)(204,624)(205,625)(206,626)(207,627)
(208,628)(209,629)(210,630)(211,638)(212,639)(213,640)(214,641)(215,642)
(216,643)(217,644)(218,631)(219,632)(220,633)(221,634)(222,635)(223,636)
(224,637)(225,645)(226,646)(227,647)(228,648)(229,649)(230,650)(231,651)
(232,659)(233,660)(234,661)(235,662)(236,663)(237,664)(238,665)(239,652)
(240,653)(241,654)(242,655)(243,656)(244,657)(245,658)(246,666)(247,667)
(248,668)(249,669)(250,670)(251,671)(252,672)(253,533)(254,534)(255,535)
(256,536)(257,537)(258,538)(259,539)(260,526)(261,527)(262,528)(263,529)
(264,530)(265,531)(266,532)(267,540)(268,541)(269,542)(270,543)(271,544)
(272,545)(273,546)(274,512)(275,513)(276,514)(277,515)(278,516)(279,517)
(280,518)(281,505)(282,506)(283,507)(284,508)(285,509)(286,510)(287,511)
(288,519)(289,520)(290,521)(291,522)(292,523)(293,524)(294,525)(295,575)
(296,576)(297,577)(298,578)(299,579)(300,580)(301,581)(302,568)(303,569)
(304,570)(305,571)(306,572)(307,573)(308,574)(309,582)(310,583)(311,584)
(312,585)(313,586)(314,587)(315,588)(316,554)(317,555)(318,556)(319,557)
(320,558)(321,559)(322,560)(323,547)(324,548)(325,549)(326,550)(327,551)
(328,552)(329,553)(330,561)(331,562)(332,563)(333,564)(334,565)(335,566)
(336,567);
s3 := Sym(672)!(  1,169)(  2,170)(  3,171)(  4,172)(  5,173)(  6,174)(  7,175)
(  8,176)(  9,177)( 10,178)( 11,179)( 12,180)( 13,181)( 14,182)( 15,183)
( 16,184)( 17,185)( 18,186)( 19,187)( 20,188)( 21,189)( 22,190)( 23,191)
( 24,192)( 25,193)( 26,194)( 27,195)( 28,196)( 29,197)( 30,198)( 31,199)
( 32,200)( 33,201)( 34,202)( 35,203)( 36,204)( 37,205)( 38,206)( 39,207)
( 40,208)( 41,209)( 42,210)( 43,211)( 44,212)( 45,213)( 46,214)( 47,215)
( 48,216)( 49,217)( 50,218)( 51,219)( 52,220)( 53,221)( 54,222)( 55,223)
( 56,224)( 57,225)( 58,226)( 59,227)( 60,228)( 61,229)( 62,230)( 63,231)
( 64,232)( 65,233)( 66,234)( 67,235)( 68,236)( 69,237)( 70,238)( 71,239)
( 72,240)( 73,241)( 74,242)( 75,243)( 76,244)( 77,245)( 78,246)( 79,247)
( 80,248)( 81,249)( 82,250)( 83,251)( 84,252)( 85,295)( 86,296)( 87,297)
( 88,298)( 89,299)( 90,300)( 91,301)( 92,302)( 93,303)( 94,304)( 95,305)
( 96,306)( 97,307)( 98,308)( 99,309)(100,310)(101,311)(102,312)(103,313)
(104,314)(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)
(112,322)(113,323)(114,324)(115,325)(116,326)(117,327)(118,328)(119,329)
(120,330)(121,331)(122,332)(123,333)(124,334)(125,335)(126,336)(127,253)
(128,254)(129,255)(130,256)(131,257)(132,258)(133,259)(134,260)(135,261)
(136,262)(137,263)(138,264)(139,265)(140,266)(141,267)(142,268)(143,269)
(144,270)(145,271)(146,272)(147,273)(148,274)(149,275)(150,276)(151,277)
(152,278)(153,279)(154,280)(155,281)(156,282)(157,283)(158,284)(159,285)
(160,286)(161,287)(162,288)(163,289)(164,290)(165,291)(166,292)(167,293)
(168,294)(337,505)(338,506)(339,507)(340,508)(341,509)(342,510)(343,511)
(344,512)(345,513)(346,514)(347,515)(348,516)(349,517)(350,518)(351,519)
(352,520)(353,521)(354,522)(355,523)(356,524)(357,525)(358,526)(359,527)
(360,528)(361,529)(362,530)(363,531)(364,532)(365,533)(366,534)(367,535)
(368,536)(369,537)(370,538)(371,539)(372,540)(373,541)(374,542)(375,543)
(376,544)(377,545)(378,546)(379,547)(380,548)(381,549)(382,550)(383,551)
(384,552)(385,553)(386,554)(387,555)(388,556)(389,557)(390,558)(391,559)
(392,560)(393,561)(394,562)(395,563)(396,564)(397,565)(398,566)(399,567)
(400,568)(401,569)(402,570)(403,571)(404,572)(405,573)(406,574)(407,575)
(408,576)(409,577)(410,578)(411,579)(412,580)(413,581)(414,582)(415,583)
(416,584)(417,585)(418,586)(419,587)(420,588)(421,631)(422,632)(423,633)
(424,634)(425,635)(426,636)(427,637)(428,638)(429,639)(430,640)(431,641)
(432,642)(433,643)(434,644)(435,645)(436,646)(437,647)(438,648)(439,649)
(440,650)(441,651)(442,652)(443,653)(444,654)(445,655)(446,656)(447,657)
(448,658)(449,659)(450,660)(451,661)(452,662)(453,663)(454,664)(455,665)
(456,666)(457,667)(458,668)(459,669)(460,670)(461,671)(462,672)(463,589)
(464,590)(465,591)(466,592)(467,593)(468,594)(469,595)(470,596)(471,597)
(472,598)(473,599)(474,600)(475,601)(476,602)(477,603)(478,604)(479,605)
(480,606)(481,607)(482,608)(483,609)(484,610)(485,611)(486,612)(487,613)
(488,614)(489,615)(490,616)(491,617)(492,618)(493,619)(494,620)(495,621)
(496,622)(497,623)(498,624)(499,625)(500,626)(501,627)(502,628)(503,629)
(504,630);
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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope