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Polytope of Type {42,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,8}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11408)
Rank : 3
Schlafli Type : {42,8}
Number of vertices, edges, etc : 84, 336, 16
Order of s0s1s2 : 84
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {21,8}*672, {42,4}*672
   4-fold quotients : {21,4}*336, {42,4}*336b, {42,4}*336c
   7-fold quotients : {6,8}*192b
   8-fold quotients : {21,4}*168, {42,2}*168
   14-fold quotients : {3,8}*96, {6,4}*96
   16-fold quotients : {21,2}*84
   24-fold quotients : {14,2}*56
   28-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {7,2}*28
   56-fold quotients : {3,4}*24, {6,2}*24
   112-fold quotients : {3,2}*12
   168-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5,  7)(  6,  8)(  9, 49)( 10, 50)( 11, 52)( 12, 51)( 13, 55)
( 14, 56)( 15, 53)( 16, 54)( 17, 41)( 18, 42)( 19, 44)( 20, 43)( 21, 47)
( 22, 48)( 23, 45)( 24, 46)( 25, 33)( 26, 34)( 27, 36)( 28, 35)( 29, 39)
( 30, 40)( 31, 37)( 32, 38)( 57,113)( 58,114)( 59,116)( 60,115)( 61,119)
( 62,120)( 63,117)( 64,118)( 65,161)( 66,162)( 67,164)( 68,163)( 69,167)
( 70,168)( 71,165)( 72,166)( 73,153)( 74,154)( 75,156)( 76,155)( 77,159)
( 78,160)( 79,157)( 80,158)( 81,145)( 82,146)( 83,148)( 84,147)( 85,151)
( 86,152)( 87,149)( 88,150)( 89,137)( 90,138)( 91,140)( 92,139)( 93,143)
( 94,144)( 95,141)( 96,142)( 97,129)( 98,130)( 99,132)(100,131)(101,135)
(102,136)(103,133)(104,134)(105,121)(106,122)(107,124)(108,123)(109,127)
(110,128)(111,125)(112,126)(169,170)(173,176)(174,175)(177,218)(178,217)
(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,210)(186,209)
(187,211)(188,212)(189,216)(190,215)(191,214)(192,213)(193,202)(194,201)
(195,203)(196,204)(197,208)(198,207)(199,206)(200,205)(225,282)(226,281)
(227,283)(228,284)(229,288)(230,287)(231,286)(232,285)(233,330)(234,329)
(235,331)(236,332)(237,336)(238,335)(239,334)(240,333)(241,322)(242,321)
(243,323)(244,324)(245,328)(246,327)(247,326)(248,325)(249,314)(250,313)
(251,315)(252,316)(253,320)(254,319)(255,318)(256,317)(257,306)(258,305)
(259,307)(260,308)(261,312)(262,311)(263,310)(264,309)(265,298)(266,297)
(267,299)(268,300)(269,304)(270,303)(271,302)(272,301)(273,290)(274,289)
(275,291)(276,292)(277,296)(278,295)(279,294)(280,293)(339,340)(341,343)
(342,344)(345,385)(346,386)(347,388)(348,387)(349,391)(350,392)(351,389)
(352,390)(353,377)(354,378)(355,380)(356,379)(357,383)(358,384)(359,381)
(360,382)(361,369)(362,370)(363,372)(364,371)(365,375)(366,376)(367,373)
(368,374)(393,449)(394,450)(395,452)(396,451)(397,455)(398,456)(399,453)
(400,454)(401,497)(402,498)(403,500)(404,499)(405,503)(406,504)(407,501)
(408,502)(409,489)(410,490)(411,492)(412,491)(413,495)(414,496)(415,493)
(416,494)(417,481)(418,482)(419,484)(420,483)(421,487)(422,488)(423,485)
(424,486)(425,473)(426,474)(427,476)(428,475)(429,479)(430,480)(431,477)
(432,478)(433,465)(434,466)(435,468)(436,467)(437,471)(438,472)(439,469)
(440,470)(441,457)(442,458)(443,460)(444,459)(445,463)(446,464)(447,461)
(448,462)(505,506)(509,512)(510,511)(513,554)(514,553)(515,555)(516,556)
(517,560)(518,559)(519,558)(520,557)(521,546)(522,545)(523,547)(524,548)
(525,552)(526,551)(527,550)(528,549)(529,538)(530,537)(531,539)(532,540)
(533,544)(534,543)(535,542)(536,541)(561,618)(562,617)(563,619)(564,620)
(565,624)(566,623)(567,622)(568,621)(569,666)(570,665)(571,667)(572,668)
(573,672)(574,671)(575,670)(576,669)(577,658)(578,657)(579,659)(580,660)
(581,664)(582,663)(583,662)(584,661)(585,650)(586,649)(587,651)(588,652)
(589,656)(590,655)(591,654)(592,653)(593,642)(594,641)(595,643)(596,644)
(597,648)(598,647)(599,646)(600,645)(601,634)(602,633)(603,635)(604,636)
(605,640)(606,639)(607,638)(608,637)(609,626)(610,625)(611,627)(612,628)
(613,632)(614,631)(615,630)(616,629);;
s1 := (  1,401)(  2,402)(  3,407)(  4,408)(  5,406)(  6,405)(  7,403)(  8,404)
(  9,393)( 10,394)( 11,399)( 12,400)( 13,398)( 14,397)( 15,395)( 16,396)
( 17,441)( 18,442)( 19,447)( 20,448)( 21,446)( 22,445)( 23,443)( 24,444)
( 25,433)( 26,434)( 27,439)( 28,440)( 29,438)( 30,437)( 31,435)( 32,436)
( 33,425)( 34,426)( 35,431)( 36,432)( 37,430)( 38,429)( 39,427)( 40,428)
( 41,417)( 42,418)( 43,423)( 44,424)( 45,422)( 46,421)( 47,419)( 48,420)
( 49,409)( 50,410)( 51,415)( 52,416)( 53,414)( 54,413)( 55,411)( 56,412)
( 57,345)( 58,346)( 59,351)( 60,352)( 61,350)( 62,349)( 63,347)( 64,348)
( 65,337)( 66,338)( 67,343)( 68,344)( 69,342)( 70,341)( 71,339)( 72,340)
( 73,385)( 74,386)( 75,391)( 76,392)( 77,390)( 78,389)( 79,387)( 80,388)
( 81,377)( 82,378)( 83,383)( 84,384)( 85,382)( 86,381)( 87,379)( 88,380)
( 89,369)( 90,370)( 91,375)( 92,376)( 93,374)( 94,373)( 95,371)( 96,372)
( 97,361)( 98,362)( 99,367)(100,368)(101,366)(102,365)(103,363)(104,364)
(105,353)(106,354)(107,359)(108,360)(109,358)(110,357)(111,355)(112,356)
(113,457)(114,458)(115,463)(116,464)(117,462)(118,461)(119,459)(120,460)
(121,449)(122,450)(123,455)(124,456)(125,454)(126,453)(127,451)(128,452)
(129,497)(130,498)(131,503)(132,504)(133,502)(134,501)(135,499)(136,500)
(137,489)(138,490)(139,495)(140,496)(141,494)(142,493)(143,491)(144,492)
(145,481)(146,482)(147,487)(148,488)(149,486)(150,485)(151,483)(152,484)
(153,473)(154,474)(155,479)(156,480)(157,478)(158,477)(159,475)(160,476)
(161,465)(162,466)(163,471)(164,472)(165,470)(166,469)(167,467)(168,468)
(169,570)(170,569)(171,576)(172,575)(173,573)(174,574)(175,572)(176,571)
(177,562)(178,561)(179,568)(180,567)(181,565)(182,566)(183,564)(184,563)
(185,610)(186,609)(187,616)(188,615)(189,613)(190,614)(191,612)(192,611)
(193,602)(194,601)(195,608)(196,607)(197,605)(198,606)(199,604)(200,603)
(201,594)(202,593)(203,600)(204,599)(205,597)(206,598)(207,596)(208,595)
(209,586)(210,585)(211,592)(212,591)(213,589)(214,590)(215,588)(216,587)
(217,578)(218,577)(219,584)(220,583)(221,581)(222,582)(223,580)(224,579)
(225,514)(226,513)(227,520)(228,519)(229,517)(230,518)(231,516)(232,515)
(233,506)(234,505)(235,512)(236,511)(237,509)(238,510)(239,508)(240,507)
(241,554)(242,553)(243,560)(244,559)(245,557)(246,558)(247,556)(248,555)
(249,546)(250,545)(251,552)(252,551)(253,549)(254,550)(255,548)(256,547)
(257,538)(258,537)(259,544)(260,543)(261,541)(262,542)(263,540)(264,539)
(265,530)(266,529)(267,536)(268,535)(269,533)(270,534)(271,532)(272,531)
(273,522)(274,521)(275,528)(276,527)(277,525)(278,526)(279,524)(280,523)
(281,626)(282,625)(283,632)(284,631)(285,629)(286,630)(287,628)(288,627)
(289,618)(290,617)(291,624)(292,623)(293,621)(294,622)(295,620)(296,619)
(297,666)(298,665)(299,672)(300,671)(301,669)(302,670)(303,668)(304,667)
(305,658)(306,657)(307,664)(308,663)(309,661)(310,662)(311,660)(312,659)
(313,650)(314,649)(315,656)(316,655)(317,653)(318,654)(319,652)(320,651)
(321,642)(322,641)(323,648)(324,647)(325,645)(326,646)(327,644)(328,643)
(329,634)(330,633)(331,640)(332,639)(333,637)(334,638)(335,636)(336,635);;
s2 := (  1,171)(  2,172)(  3,170)(  4,169)(  5,175)(  6,176)(  7,174)(  8,173)
(  9,179)( 10,180)( 11,178)( 12,177)( 13,183)( 14,184)( 15,182)( 16,181)
( 17,187)( 18,188)( 19,186)( 20,185)( 21,191)( 22,192)( 23,190)( 24,189)
( 25,195)( 26,196)( 27,194)( 28,193)( 29,199)( 30,200)( 31,198)( 32,197)
( 33,203)( 34,204)( 35,202)( 36,201)( 37,207)( 38,208)( 39,206)( 40,205)
( 41,211)( 42,212)( 43,210)( 44,209)( 45,215)( 46,216)( 47,214)( 48,213)
( 49,219)( 50,220)( 51,218)( 52,217)( 53,223)( 54,224)( 55,222)( 56,221)
( 57,227)( 58,228)( 59,226)( 60,225)( 61,231)( 62,232)( 63,230)( 64,229)
( 65,235)( 66,236)( 67,234)( 68,233)( 69,239)( 70,240)( 71,238)( 72,237)
( 73,243)( 74,244)( 75,242)( 76,241)( 77,247)( 78,248)( 79,246)( 80,245)
( 81,251)( 82,252)( 83,250)( 84,249)( 85,255)( 86,256)( 87,254)( 88,253)
( 89,259)( 90,260)( 91,258)( 92,257)( 93,263)( 94,264)( 95,262)( 96,261)
( 97,267)( 98,268)( 99,266)(100,265)(101,271)(102,272)(103,270)(104,269)
(105,275)(106,276)(107,274)(108,273)(109,279)(110,280)(111,278)(112,277)
(113,283)(114,284)(115,282)(116,281)(117,287)(118,288)(119,286)(120,285)
(121,291)(122,292)(123,290)(124,289)(125,295)(126,296)(127,294)(128,293)
(129,299)(130,300)(131,298)(132,297)(133,303)(134,304)(135,302)(136,301)
(137,307)(138,308)(139,306)(140,305)(141,311)(142,312)(143,310)(144,309)
(145,315)(146,316)(147,314)(148,313)(149,319)(150,320)(151,318)(152,317)
(153,323)(154,324)(155,322)(156,321)(157,327)(158,328)(159,326)(160,325)
(161,331)(162,332)(163,330)(164,329)(165,335)(166,336)(167,334)(168,333)
(337,507)(338,508)(339,506)(340,505)(341,511)(342,512)(343,510)(344,509)
(345,515)(346,516)(347,514)(348,513)(349,519)(350,520)(351,518)(352,517)
(353,523)(354,524)(355,522)(356,521)(357,527)(358,528)(359,526)(360,525)
(361,531)(362,532)(363,530)(364,529)(365,535)(366,536)(367,534)(368,533)
(369,539)(370,540)(371,538)(372,537)(373,543)(374,544)(375,542)(376,541)
(377,547)(378,548)(379,546)(380,545)(381,551)(382,552)(383,550)(384,549)
(385,555)(386,556)(387,554)(388,553)(389,559)(390,560)(391,558)(392,557)
(393,563)(394,564)(395,562)(396,561)(397,567)(398,568)(399,566)(400,565)
(401,571)(402,572)(403,570)(404,569)(405,575)(406,576)(407,574)(408,573)
(409,579)(410,580)(411,578)(412,577)(413,583)(414,584)(415,582)(416,581)
(417,587)(418,588)(419,586)(420,585)(421,591)(422,592)(423,590)(424,589)
(425,595)(426,596)(427,594)(428,593)(429,599)(430,600)(431,598)(432,597)
(433,603)(434,604)(435,602)(436,601)(437,607)(438,608)(439,606)(440,605)
(441,611)(442,612)(443,610)(444,609)(445,615)(446,616)(447,614)(448,613)
(449,619)(450,620)(451,618)(452,617)(453,623)(454,624)(455,622)(456,621)
(457,627)(458,628)(459,626)(460,625)(461,631)(462,632)(463,630)(464,629)
(465,635)(466,636)(467,634)(468,633)(469,639)(470,640)(471,638)(472,637)
(473,643)(474,644)(475,642)(476,641)(477,647)(478,648)(479,646)(480,645)
(481,651)(482,652)(483,650)(484,649)(485,655)(486,656)(487,654)(488,653)
(489,659)(490,660)(491,658)(492,657)(493,663)(494,664)(495,662)(496,661)
(497,667)(498,668)(499,666)(500,665)(501,671)(502,672)(503,670)(504,669);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*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*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)!(  3,  4)(  5,  7)(  6,  8)(  9, 49)( 10, 50)( 11, 52)( 12, 51)
( 13, 55)( 14, 56)( 15, 53)( 16, 54)( 17, 41)( 18, 42)( 19, 44)( 20, 43)
( 21, 47)( 22, 48)( 23, 45)( 24, 46)( 25, 33)( 26, 34)( 27, 36)( 28, 35)
( 29, 39)( 30, 40)( 31, 37)( 32, 38)( 57,113)( 58,114)( 59,116)( 60,115)
( 61,119)( 62,120)( 63,117)( 64,118)( 65,161)( 66,162)( 67,164)( 68,163)
( 69,167)( 70,168)( 71,165)( 72,166)( 73,153)( 74,154)( 75,156)( 76,155)
( 77,159)( 78,160)( 79,157)( 80,158)( 81,145)( 82,146)( 83,148)( 84,147)
( 85,151)( 86,152)( 87,149)( 88,150)( 89,137)( 90,138)( 91,140)( 92,139)
( 93,143)( 94,144)( 95,141)( 96,142)( 97,129)( 98,130)( 99,132)(100,131)
(101,135)(102,136)(103,133)(104,134)(105,121)(106,122)(107,124)(108,123)
(109,127)(110,128)(111,125)(112,126)(169,170)(173,176)(174,175)(177,218)
(178,217)(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,210)
(186,209)(187,211)(188,212)(189,216)(190,215)(191,214)(192,213)(193,202)
(194,201)(195,203)(196,204)(197,208)(198,207)(199,206)(200,205)(225,282)
(226,281)(227,283)(228,284)(229,288)(230,287)(231,286)(232,285)(233,330)
(234,329)(235,331)(236,332)(237,336)(238,335)(239,334)(240,333)(241,322)
(242,321)(243,323)(244,324)(245,328)(246,327)(247,326)(248,325)(249,314)
(250,313)(251,315)(252,316)(253,320)(254,319)(255,318)(256,317)(257,306)
(258,305)(259,307)(260,308)(261,312)(262,311)(263,310)(264,309)(265,298)
(266,297)(267,299)(268,300)(269,304)(270,303)(271,302)(272,301)(273,290)
(274,289)(275,291)(276,292)(277,296)(278,295)(279,294)(280,293)(339,340)
(341,343)(342,344)(345,385)(346,386)(347,388)(348,387)(349,391)(350,392)
(351,389)(352,390)(353,377)(354,378)(355,380)(356,379)(357,383)(358,384)
(359,381)(360,382)(361,369)(362,370)(363,372)(364,371)(365,375)(366,376)
(367,373)(368,374)(393,449)(394,450)(395,452)(396,451)(397,455)(398,456)
(399,453)(400,454)(401,497)(402,498)(403,500)(404,499)(405,503)(406,504)
(407,501)(408,502)(409,489)(410,490)(411,492)(412,491)(413,495)(414,496)
(415,493)(416,494)(417,481)(418,482)(419,484)(420,483)(421,487)(422,488)
(423,485)(424,486)(425,473)(426,474)(427,476)(428,475)(429,479)(430,480)
(431,477)(432,478)(433,465)(434,466)(435,468)(436,467)(437,471)(438,472)
(439,469)(440,470)(441,457)(442,458)(443,460)(444,459)(445,463)(446,464)
(447,461)(448,462)(505,506)(509,512)(510,511)(513,554)(514,553)(515,555)
(516,556)(517,560)(518,559)(519,558)(520,557)(521,546)(522,545)(523,547)
(524,548)(525,552)(526,551)(527,550)(528,549)(529,538)(530,537)(531,539)
(532,540)(533,544)(534,543)(535,542)(536,541)(561,618)(562,617)(563,619)
(564,620)(565,624)(566,623)(567,622)(568,621)(569,666)(570,665)(571,667)
(572,668)(573,672)(574,671)(575,670)(576,669)(577,658)(578,657)(579,659)
(580,660)(581,664)(582,663)(583,662)(584,661)(585,650)(586,649)(587,651)
(588,652)(589,656)(590,655)(591,654)(592,653)(593,642)(594,641)(595,643)
(596,644)(597,648)(598,647)(599,646)(600,645)(601,634)(602,633)(603,635)
(604,636)(605,640)(606,639)(607,638)(608,637)(609,626)(610,625)(611,627)
(612,628)(613,632)(614,631)(615,630)(616,629);
s1 := Sym(672)!(  1,401)(  2,402)(  3,407)(  4,408)(  5,406)(  6,405)(  7,403)
(  8,404)(  9,393)( 10,394)( 11,399)( 12,400)( 13,398)( 14,397)( 15,395)
( 16,396)( 17,441)( 18,442)( 19,447)( 20,448)( 21,446)( 22,445)( 23,443)
( 24,444)( 25,433)( 26,434)( 27,439)( 28,440)( 29,438)( 30,437)( 31,435)
( 32,436)( 33,425)( 34,426)( 35,431)( 36,432)( 37,430)( 38,429)( 39,427)
( 40,428)( 41,417)( 42,418)( 43,423)( 44,424)( 45,422)( 46,421)( 47,419)
( 48,420)( 49,409)( 50,410)( 51,415)( 52,416)( 53,414)( 54,413)( 55,411)
( 56,412)( 57,345)( 58,346)( 59,351)( 60,352)( 61,350)( 62,349)( 63,347)
( 64,348)( 65,337)( 66,338)( 67,343)( 68,344)( 69,342)( 70,341)( 71,339)
( 72,340)( 73,385)( 74,386)( 75,391)( 76,392)( 77,390)( 78,389)( 79,387)
( 80,388)( 81,377)( 82,378)( 83,383)( 84,384)( 85,382)( 86,381)( 87,379)
( 88,380)( 89,369)( 90,370)( 91,375)( 92,376)( 93,374)( 94,373)( 95,371)
( 96,372)( 97,361)( 98,362)( 99,367)(100,368)(101,366)(102,365)(103,363)
(104,364)(105,353)(106,354)(107,359)(108,360)(109,358)(110,357)(111,355)
(112,356)(113,457)(114,458)(115,463)(116,464)(117,462)(118,461)(119,459)
(120,460)(121,449)(122,450)(123,455)(124,456)(125,454)(126,453)(127,451)
(128,452)(129,497)(130,498)(131,503)(132,504)(133,502)(134,501)(135,499)
(136,500)(137,489)(138,490)(139,495)(140,496)(141,494)(142,493)(143,491)
(144,492)(145,481)(146,482)(147,487)(148,488)(149,486)(150,485)(151,483)
(152,484)(153,473)(154,474)(155,479)(156,480)(157,478)(158,477)(159,475)
(160,476)(161,465)(162,466)(163,471)(164,472)(165,470)(166,469)(167,467)
(168,468)(169,570)(170,569)(171,576)(172,575)(173,573)(174,574)(175,572)
(176,571)(177,562)(178,561)(179,568)(180,567)(181,565)(182,566)(183,564)
(184,563)(185,610)(186,609)(187,616)(188,615)(189,613)(190,614)(191,612)
(192,611)(193,602)(194,601)(195,608)(196,607)(197,605)(198,606)(199,604)
(200,603)(201,594)(202,593)(203,600)(204,599)(205,597)(206,598)(207,596)
(208,595)(209,586)(210,585)(211,592)(212,591)(213,589)(214,590)(215,588)
(216,587)(217,578)(218,577)(219,584)(220,583)(221,581)(222,582)(223,580)
(224,579)(225,514)(226,513)(227,520)(228,519)(229,517)(230,518)(231,516)
(232,515)(233,506)(234,505)(235,512)(236,511)(237,509)(238,510)(239,508)
(240,507)(241,554)(242,553)(243,560)(244,559)(245,557)(246,558)(247,556)
(248,555)(249,546)(250,545)(251,552)(252,551)(253,549)(254,550)(255,548)
(256,547)(257,538)(258,537)(259,544)(260,543)(261,541)(262,542)(263,540)
(264,539)(265,530)(266,529)(267,536)(268,535)(269,533)(270,534)(271,532)
(272,531)(273,522)(274,521)(275,528)(276,527)(277,525)(278,526)(279,524)
(280,523)(281,626)(282,625)(283,632)(284,631)(285,629)(286,630)(287,628)
(288,627)(289,618)(290,617)(291,624)(292,623)(293,621)(294,622)(295,620)
(296,619)(297,666)(298,665)(299,672)(300,671)(301,669)(302,670)(303,668)
(304,667)(305,658)(306,657)(307,664)(308,663)(309,661)(310,662)(311,660)
(312,659)(313,650)(314,649)(315,656)(316,655)(317,653)(318,654)(319,652)
(320,651)(321,642)(322,641)(323,648)(324,647)(325,645)(326,646)(327,644)
(328,643)(329,634)(330,633)(331,640)(332,639)(333,637)(334,638)(335,636)
(336,635);
s2 := Sym(672)!(  1,171)(  2,172)(  3,170)(  4,169)(  5,175)(  6,176)(  7,174)
(  8,173)(  9,179)( 10,180)( 11,178)( 12,177)( 13,183)( 14,184)( 15,182)
( 16,181)( 17,187)( 18,188)( 19,186)( 20,185)( 21,191)( 22,192)( 23,190)
( 24,189)( 25,195)( 26,196)( 27,194)( 28,193)( 29,199)( 30,200)( 31,198)
( 32,197)( 33,203)( 34,204)( 35,202)( 36,201)( 37,207)( 38,208)( 39,206)
( 40,205)( 41,211)( 42,212)( 43,210)( 44,209)( 45,215)( 46,216)( 47,214)
( 48,213)( 49,219)( 50,220)( 51,218)( 52,217)( 53,223)( 54,224)( 55,222)
( 56,221)( 57,227)( 58,228)( 59,226)( 60,225)( 61,231)( 62,232)( 63,230)
( 64,229)( 65,235)( 66,236)( 67,234)( 68,233)( 69,239)( 70,240)( 71,238)
( 72,237)( 73,243)( 74,244)( 75,242)( 76,241)( 77,247)( 78,248)( 79,246)
( 80,245)( 81,251)( 82,252)( 83,250)( 84,249)( 85,255)( 86,256)( 87,254)
( 88,253)( 89,259)( 90,260)( 91,258)( 92,257)( 93,263)( 94,264)( 95,262)
( 96,261)( 97,267)( 98,268)( 99,266)(100,265)(101,271)(102,272)(103,270)
(104,269)(105,275)(106,276)(107,274)(108,273)(109,279)(110,280)(111,278)
(112,277)(113,283)(114,284)(115,282)(116,281)(117,287)(118,288)(119,286)
(120,285)(121,291)(122,292)(123,290)(124,289)(125,295)(126,296)(127,294)
(128,293)(129,299)(130,300)(131,298)(132,297)(133,303)(134,304)(135,302)
(136,301)(137,307)(138,308)(139,306)(140,305)(141,311)(142,312)(143,310)
(144,309)(145,315)(146,316)(147,314)(148,313)(149,319)(150,320)(151,318)
(152,317)(153,323)(154,324)(155,322)(156,321)(157,327)(158,328)(159,326)
(160,325)(161,331)(162,332)(163,330)(164,329)(165,335)(166,336)(167,334)
(168,333)(337,507)(338,508)(339,506)(340,505)(341,511)(342,512)(343,510)
(344,509)(345,515)(346,516)(347,514)(348,513)(349,519)(350,520)(351,518)
(352,517)(353,523)(354,524)(355,522)(356,521)(357,527)(358,528)(359,526)
(360,525)(361,531)(362,532)(363,530)(364,529)(365,535)(366,536)(367,534)
(368,533)(369,539)(370,540)(371,538)(372,537)(373,543)(374,544)(375,542)
(376,541)(377,547)(378,548)(379,546)(380,545)(381,551)(382,552)(383,550)
(384,549)(385,555)(386,556)(387,554)(388,553)(389,559)(390,560)(391,558)
(392,557)(393,563)(394,564)(395,562)(396,561)(397,567)(398,568)(399,566)
(400,565)(401,571)(402,572)(403,570)(404,569)(405,575)(406,576)(407,574)
(408,573)(409,579)(410,580)(411,578)(412,577)(413,583)(414,584)(415,582)
(416,581)(417,587)(418,588)(419,586)(420,585)(421,591)(422,592)(423,590)
(424,589)(425,595)(426,596)(427,594)(428,593)(429,599)(430,600)(431,598)
(432,597)(433,603)(434,604)(435,602)(436,601)(437,607)(438,608)(439,606)
(440,605)(441,611)(442,612)(443,610)(444,609)(445,615)(446,616)(447,614)
(448,613)(449,619)(450,620)(451,618)(452,617)(453,623)(454,624)(455,622)
(456,621)(457,627)(458,628)(459,626)(460,625)(461,631)(462,632)(463,630)
(464,629)(465,635)(466,636)(467,634)(468,633)(469,639)(470,640)(471,638)
(472,637)(473,643)(474,644)(475,642)(476,641)(477,647)(478,648)(479,646)
(480,645)(481,651)(482,652)(483,650)(484,649)(485,655)(486,656)(487,654)
(488,653)(489,659)(490,660)(491,658)(492,657)(493,663)(494,664)(495,662)
(496,661)(497,667)(498,668)(499,666)(500,665)(501,671)(502,672)(503,670)
(504,669);
poly := sub<Sym(672)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*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*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