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Polytope of Type {176,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {176,4}*1408a
Also Known As : {176,4|2}. if this polytope has another name.
Group : SmallGroup(1408,6424)
Rank : 3
Schlafli Type : {176,4}
Number of vertices, edges, etc : 176, 352, 4
Order of s0s1s2 : 176
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {88,4}*704a, {176,2}*704
   4-fold quotients : {44,4}*352, {88,2}*352
   8-fold quotients : {44,2}*176, {22,4}*176
   11-fold quotients : {16,4}*128a
   16-fold quotients : {22,2}*88
   22-fold quotients : {8,4}*64a, {16,2}*64
   32-fold quotients : {11,2}*44
   44-fold quotients : {4,4}*32, {8,2}*32
   88-fold quotients : {2,4}*16, {4,2}*16
   176-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,353)(  2,363)(  3,362)(  4,361)(  5,360)(  6,359)(  7,358)(  8,357)
(  9,356)( 10,355)( 11,354)( 12,364)( 13,374)( 14,373)( 15,372)( 16,371)
( 17,370)( 18,369)( 19,368)( 20,367)( 21,366)( 22,365)( 23,386)( 24,396)
( 25,395)( 26,394)( 27,393)( 28,392)( 29,391)( 30,390)( 31,389)( 32,388)
( 33,387)( 34,375)( 35,385)( 36,384)( 37,383)( 38,382)( 39,381)( 40,380)
( 41,379)( 42,378)( 43,377)( 44,376)( 45,397)( 46,407)( 47,406)( 48,405)
( 49,404)( 50,403)( 51,402)( 52,401)( 53,400)( 54,399)( 55,398)( 56,408)
( 57,418)( 58,417)( 59,416)( 60,415)( 61,414)( 62,413)( 63,412)( 64,411)
( 65,410)( 66,409)( 67,430)( 68,440)( 69,439)( 70,438)( 71,437)( 72,436)
( 73,435)( 74,434)( 75,433)( 76,432)( 77,431)( 78,419)( 79,429)( 80,428)
( 81,427)( 82,426)( 83,425)( 84,424)( 85,423)( 86,422)( 87,421)( 88,420)
( 89,463)( 90,473)( 91,472)( 92,471)( 93,470)( 94,469)( 95,468)( 96,467)
( 97,466)( 98,465)( 99,464)(100,474)(101,484)(102,483)(103,482)(104,481)
(105,480)(106,479)(107,478)(108,477)(109,476)(110,475)(111,441)(112,451)
(113,450)(114,449)(115,448)(116,447)(117,446)(118,445)(119,444)(120,443)
(121,442)(122,452)(123,462)(124,461)(125,460)(126,459)(127,458)(128,457)
(129,456)(130,455)(131,454)(132,453)(133,507)(134,517)(135,516)(136,515)
(137,514)(138,513)(139,512)(140,511)(141,510)(142,509)(143,508)(144,518)
(145,528)(146,527)(147,526)(148,525)(149,524)(150,523)(151,522)(152,521)
(153,520)(154,519)(155,485)(156,495)(157,494)(158,493)(159,492)(160,491)
(161,490)(162,489)(163,488)(164,487)(165,486)(166,496)(167,506)(168,505)
(169,504)(170,503)(171,502)(172,501)(173,500)(174,499)(175,498)(176,497)
(177,529)(178,539)(179,538)(180,537)(181,536)(182,535)(183,534)(184,533)
(185,532)(186,531)(187,530)(188,540)(189,550)(190,549)(191,548)(192,547)
(193,546)(194,545)(195,544)(196,543)(197,542)(198,541)(199,562)(200,572)
(201,571)(202,570)(203,569)(204,568)(205,567)(206,566)(207,565)(208,564)
(209,563)(210,551)(211,561)(212,560)(213,559)(214,558)(215,557)(216,556)
(217,555)(218,554)(219,553)(220,552)(221,573)(222,583)(223,582)(224,581)
(225,580)(226,579)(227,578)(228,577)(229,576)(230,575)(231,574)(232,584)
(233,594)(234,593)(235,592)(236,591)(237,590)(238,589)(239,588)(240,587)
(241,586)(242,585)(243,606)(244,616)(245,615)(246,614)(247,613)(248,612)
(249,611)(250,610)(251,609)(252,608)(253,607)(254,595)(255,605)(256,604)
(257,603)(258,602)(259,601)(260,600)(261,599)(262,598)(263,597)(264,596)
(265,639)(266,649)(267,648)(268,647)(269,646)(270,645)(271,644)(272,643)
(273,642)(274,641)(275,640)(276,650)(277,660)(278,659)(279,658)(280,657)
(281,656)(282,655)(283,654)(284,653)(285,652)(286,651)(287,617)(288,627)
(289,626)(290,625)(291,624)(292,623)(293,622)(294,621)(295,620)(296,619)
(297,618)(298,628)(299,638)(300,637)(301,636)(302,635)(303,634)(304,633)
(305,632)(306,631)(307,630)(308,629)(309,683)(310,693)(311,692)(312,691)
(313,690)(314,689)(315,688)(316,687)(317,686)(318,685)(319,684)(320,694)
(321,704)(322,703)(323,702)(324,701)(325,700)(326,699)(327,698)(328,697)
(329,696)(330,695)(331,661)(332,671)(333,670)(334,669)(335,668)(336,667)
(337,666)(338,665)(339,664)(340,663)(341,662)(342,672)(343,682)(344,681)
(345,680)(346,679)(347,678)(348,677)(349,676)(350,675)(351,674)(352,673);;
s1 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)
( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 46)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 79)
( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)
( 76, 81)( 77, 80)( 89,112)( 90,111)( 91,121)( 92,120)( 93,119)( 94,118)
( 95,117)( 96,116)( 97,115)( 98,114)( 99,113)(100,123)(101,122)(102,132)
(103,131)(104,130)(105,129)(106,128)(107,127)(108,126)(109,125)(110,124)
(133,156)(134,155)(135,165)(136,164)(137,163)(138,162)(139,161)(140,160)
(141,159)(142,158)(143,157)(144,167)(145,166)(146,176)(147,175)(148,174)
(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(177,222)(178,221)
(179,231)(180,230)(181,229)(182,228)(183,227)(184,226)(185,225)(186,224)
(187,223)(188,233)(189,232)(190,242)(191,241)(192,240)(193,239)(194,238)
(195,237)(196,236)(197,235)(198,234)(199,255)(200,254)(201,264)(202,263)
(203,262)(204,261)(205,260)(206,259)(207,258)(208,257)(209,256)(210,244)
(211,243)(212,253)(213,252)(214,251)(215,250)(216,249)(217,248)(218,247)
(219,246)(220,245)(265,332)(266,331)(267,341)(268,340)(269,339)(270,338)
(271,337)(272,336)(273,335)(274,334)(275,333)(276,343)(277,342)(278,352)
(279,351)(280,350)(281,349)(282,348)(283,347)(284,346)(285,345)(286,344)
(287,310)(288,309)(289,319)(290,318)(291,317)(292,316)(293,315)(294,314)
(295,313)(296,312)(297,311)(298,321)(299,320)(300,330)(301,329)(302,328)
(303,327)(304,326)(305,325)(306,324)(307,323)(308,322)(353,442)(354,441)
(355,451)(356,450)(357,449)(358,448)(359,447)(360,446)(361,445)(362,444)
(363,443)(364,453)(365,452)(366,462)(367,461)(368,460)(369,459)(370,458)
(371,457)(372,456)(373,455)(374,454)(375,475)(376,474)(377,484)(378,483)
(379,482)(380,481)(381,480)(382,479)(383,478)(384,477)(385,476)(386,464)
(387,463)(388,473)(389,472)(390,471)(391,470)(392,469)(393,468)(394,467)
(395,466)(396,465)(397,486)(398,485)(399,495)(400,494)(401,493)(402,492)
(403,491)(404,490)(405,489)(406,488)(407,487)(408,497)(409,496)(410,506)
(411,505)(412,504)(413,503)(414,502)(415,501)(416,500)(417,499)(418,498)
(419,519)(420,518)(421,528)(422,527)(423,526)(424,525)(425,524)(426,523)
(427,522)(428,521)(429,520)(430,508)(431,507)(432,517)(433,516)(434,515)
(435,514)(436,513)(437,512)(438,511)(439,510)(440,509)(529,662)(530,661)
(531,671)(532,670)(533,669)(534,668)(535,667)(536,666)(537,665)(538,664)
(539,663)(540,673)(541,672)(542,682)(543,681)(544,680)(545,679)(546,678)
(547,677)(548,676)(549,675)(550,674)(551,695)(552,694)(553,704)(554,703)
(555,702)(556,701)(557,700)(558,699)(559,698)(560,697)(561,696)(562,684)
(563,683)(564,693)(565,692)(566,691)(567,690)(568,689)(569,688)(570,687)
(571,686)(572,685)(573,618)(574,617)(575,627)(576,626)(577,625)(578,624)
(579,623)(580,622)(581,621)(582,620)(583,619)(584,629)(585,628)(586,638)
(587,637)(588,636)(589,635)(590,634)(591,633)(592,632)(593,631)(594,630)
(595,651)(596,650)(597,660)(598,659)(599,658)(600,657)(601,656)(602,655)
(603,654)(604,653)(605,652)(606,640)(607,639)(608,649)(609,648)(610,647)
(611,646)(612,645)(613,644)(614,643)(615,642)(616,641);;
s2 := (  1,177)(  2,178)(  3,179)(  4,180)(  5,181)(  6,182)(  7,183)(  8,184)
(  9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)( 16,192)
( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)( 24,200)
( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)( 32,208)
( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)( 40,216)
( 41,217)( 42,218)( 43,219)( 44,220)( 45,221)( 46,222)( 47,223)( 48,224)
( 49,225)( 50,226)( 51,227)( 52,228)( 53,229)( 54,230)( 55,231)( 56,232)
( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)( 64,240)
( 65,241)( 66,242)( 67,243)( 68,244)( 69,245)( 70,246)( 71,247)( 72,248)
( 73,249)( 74,250)( 75,251)( 76,252)( 77,253)( 78,254)( 79,255)( 80,256)
( 81,257)( 82,258)( 83,259)( 84,260)( 85,261)( 86,262)( 87,263)( 88,264)
( 89,265)( 90,266)( 91,267)( 92,268)( 93,269)( 94,270)( 95,271)( 96,272)
( 97,273)( 98,274)( 99,275)(100,276)(101,277)(102,278)(103,279)(104,280)
(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)(112,288)
(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)(120,296)
(121,297)(122,298)(123,299)(124,300)(125,301)(126,302)(127,303)(128,304)
(129,305)(130,306)(131,307)(132,308)(133,309)(134,310)(135,311)(136,312)
(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)(144,320)
(145,321)(146,322)(147,323)(148,324)(149,325)(150,326)(151,327)(152,328)
(153,329)(154,330)(155,331)(156,332)(157,333)(158,334)(159,335)(160,336)
(161,337)(162,338)(163,339)(164,340)(165,341)(166,342)(167,343)(168,344)
(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)(176,352)
(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)(360,536)
(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)(368,544)
(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)(376,552)
(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)(384,560)
(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)(392,568)
(393,569)(394,570)(395,571)(396,572)(397,573)(398,574)(399,575)(400,576)
(401,577)(402,578)(403,579)(404,580)(405,581)(406,582)(407,583)(408,584)
(409,585)(410,586)(411,587)(412,588)(413,589)(414,590)(415,591)(416,592)
(417,593)(418,594)(419,595)(420,596)(421,597)(422,598)(423,599)(424,600)
(425,601)(426,602)(427,603)(428,604)(429,605)(430,606)(431,607)(432,608)
(433,609)(434,610)(435,611)(436,612)(437,613)(438,614)(439,615)(440,616)
(441,617)(442,618)(443,619)(444,620)(445,621)(446,622)(447,623)(448,624)
(449,625)(450,626)(451,627)(452,628)(453,629)(454,630)(455,631)(456,632)
(457,633)(458,634)(459,635)(460,636)(461,637)(462,638)(463,639)(464,640)
(465,641)(466,642)(467,643)(468,644)(469,645)(470,646)(471,647)(472,648)
(473,649)(474,650)(475,651)(476,652)(477,653)(478,654)(479,655)(480,656)
(481,657)(482,658)(483,659)(484,660)(485,661)(486,662)(487,663)(488,664)
(489,665)(490,666)(491,667)(492,668)(493,669)(494,670)(495,671)(496,672)
(497,673)(498,674)(499,675)(500,676)(501,677)(502,678)(503,679)(504,680)
(505,681)(506,682)(507,683)(508,684)(509,685)(510,686)(511,687)(512,688)
(513,689)(514,690)(515,691)(516,692)(517,693)(518,694)(519,695)(520,696)
(521,697)(522,698)(523,699)(524,700)(525,701)(526,702)(527,703)(528,704);;
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*s2*s1, 
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*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*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*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*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(704)!(  1,353)(  2,363)(  3,362)(  4,361)(  5,360)(  6,359)(  7,358)
(  8,357)(  9,356)( 10,355)( 11,354)( 12,364)( 13,374)( 14,373)( 15,372)
( 16,371)( 17,370)( 18,369)( 19,368)( 20,367)( 21,366)( 22,365)( 23,386)
( 24,396)( 25,395)( 26,394)( 27,393)( 28,392)( 29,391)( 30,390)( 31,389)
( 32,388)( 33,387)( 34,375)( 35,385)( 36,384)( 37,383)( 38,382)( 39,381)
( 40,380)( 41,379)( 42,378)( 43,377)( 44,376)( 45,397)( 46,407)( 47,406)
( 48,405)( 49,404)( 50,403)( 51,402)( 52,401)( 53,400)( 54,399)( 55,398)
( 56,408)( 57,418)( 58,417)( 59,416)( 60,415)( 61,414)( 62,413)( 63,412)
( 64,411)( 65,410)( 66,409)( 67,430)( 68,440)( 69,439)( 70,438)( 71,437)
( 72,436)( 73,435)( 74,434)( 75,433)( 76,432)( 77,431)( 78,419)( 79,429)
( 80,428)( 81,427)( 82,426)( 83,425)( 84,424)( 85,423)( 86,422)( 87,421)
( 88,420)( 89,463)( 90,473)( 91,472)( 92,471)( 93,470)( 94,469)( 95,468)
( 96,467)( 97,466)( 98,465)( 99,464)(100,474)(101,484)(102,483)(103,482)
(104,481)(105,480)(106,479)(107,478)(108,477)(109,476)(110,475)(111,441)
(112,451)(113,450)(114,449)(115,448)(116,447)(117,446)(118,445)(119,444)
(120,443)(121,442)(122,452)(123,462)(124,461)(125,460)(126,459)(127,458)
(128,457)(129,456)(130,455)(131,454)(132,453)(133,507)(134,517)(135,516)
(136,515)(137,514)(138,513)(139,512)(140,511)(141,510)(142,509)(143,508)
(144,518)(145,528)(146,527)(147,526)(148,525)(149,524)(150,523)(151,522)
(152,521)(153,520)(154,519)(155,485)(156,495)(157,494)(158,493)(159,492)
(160,491)(161,490)(162,489)(163,488)(164,487)(165,486)(166,496)(167,506)
(168,505)(169,504)(170,503)(171,502)(172,501)(173,500)(174,499)(175,498)
(176,497)(177,529)(178,539)(179,538)(180,537)(181,536)(182,535)(183,534)
(184,533)(185,532)(186,531)(187,530)(188,540)(189,550)(190,549)(191,548)
(192,547)(193,546)(194,545)(195,544)(196,543)(197,542)(198,541)(199,562)
(200,572)(201,571)(202,570)(203,569)(204,568)(205,567)(206,566)(207,565)
(208,564)(209,563)(210,551)(211,561)(212,560)(213,559)(214,558)(215,557)
(216,556)(217,555)(218,554)(219,553)(220,552)(221,573)(222,583)(223,582)
(224,581)(225,580)(226,579)(227,578)(228,577)(229,576)(230,575)(231,574)
(232,584)(233,594)(234,593)(235,592)(236,591)(237,590)(238,589)(239,588)
(240,587)(241,586)(242,585)(243,606)(244,616)(245,615)(246,614)(247,613)
(248,612)(249,611)(250,610)(251,609)(252,608)(253,607)(254,595)(255,605)
(256,604)(257,603)(258,602)(259,601)(260,600)(261,599)(262,598)(263,597)
(264,596)(265,639)(266,649)(267,648)(268,647)(269,646)(270,645)(271,644)
(272,643)(273,642)(274,641)(275,640)(276,650)(277,660)(278,659)(279,658)
(280,657)(281,656)(282,655)(283,654)(284,653)(285,652)(286,651)(287,617)
(288,627)(289,626)(290,625)(291,624)(292,623)(293,622)(294,621)(295,620)
(296,619)(297,618)(298,628)(299,638)(300,637)(301,636)(302,635)(303,634)
(304,633)(305,632)(306,631)(307,630)(308,629)(309,683)(310,693)(311,692)
(312,691)(313,690)(314,689)(315,688)(316,687)(317,686)(318,685)(319,684)
(320,694)(321,704)(322,703)(323,702)(324,701)(325,700)(326,699)(327,698)
(328,697)(329,696)(330,695)(331,661)(332,671)(333,670)(334,669)(335,668)
(336,667)(337,666)(338,665)(339,664)(340,663)(341,662)(342,672)(343,682)
(344,681)(345,680)(346,679)(347,678)(348,677)(349,676)(350,675)(351,674)
(352,673);
s1 := Sym(704)!(  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)
( 15, 21)( 16, 20)( 17, 19)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)
( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 46)( 47, 55)
( 48, 54)( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)
( 67, 79)( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)
( 75, 82)( 76, 81)( 77, 80)( 89,112)( 90,111)( 91,121)( 92,120)( 93,119)
( 94,118)( 95,117)( 96,116)( 97,115)( 98,114)( 99,113)(100,123)(101,122)
(102,132)(103,131)(104,130)(105,129)(106,128)(107,127)(108,126)(109,125)
(110,124)(133,156)(134,155)(135,165)(136,164)(137,163)(138,162)(139,161)
(140,160)(141,159)(142,158)(143,157)(144,167)(145,166)(146,176)(147,175)
(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(177,222)
(178,221)(179,231)(180,230)(181,229)(182,228)(183,227)(184,226)(185,225)
(186,224)(187,223)(188,233)(189,232)(190,242)(191,241)(192,240)(193,239)
(194,238)(195,237)(196,236)(197,235)(198,234)(199,255)(200,254)(201,264)
(202,263)(203,262)(204,261)(205,260)(206,259)(207,258)(208,257)(209,256)
(210,244)(211,243)(212,253)(213,252)(214,251)(215,250)(216,249)(217,248)
(218,247)(219,246)(220,245)(265,332)(266,331)(267,341)(268,340)(269,339)
(270,338)(271,337)(272,336)(273,335)(274,334)(275,333)(276,343)(277,342)
(278,352)(279,351)(280,350)(281,349)(282,348)(283,347)(284,346)(285,345)
(286,344)(287,310)(288,309)(289,319)(290,318)(291,317)(292,316)(293,315)
(294,314)(295,313)(296,312)(297,311)(298,321)(299,320)(300,330)(301,329)
(302,328)(303,327)(304,326)(305,325)(306,324)(307,323)(308,322)(353,442)
(354,441)(355,451)(356,450)(357,449)(358,448)(359,447)(360,446)(361,445)
(362,444)(363,443)(364,453)(365,452)(366,462)(367,461)(368,460)(369,459)
(370,458)(371,457)(372,456)(373,455)(374,454)(375,475)(376,474)(377,484)
(378,483)(379,482)(380,481)(381,480)(382,479)(383,478)(384,477)(385,476)
(386,464)(387,463)(388,473)(389,472)(390,471)(391,470)(392,469)(393,468)
(394,467)(395,466)(396,465)(397,486)(398,485)(399,495)(400,494)(401,493)
(402,492)(403,491)(404,490)(405,489)(406,488)(407,487)(408,497)(409,496)
(410,506)(411,505)(412,504)(413,503)(414,502)(415,501)(416,500)(417,499)
(418,498)(419,519)(420,518)(421,528)(422,527)(423,526)(424,525)(425,524)
(426,523)(427,522)(428,521)(429,520)(430,508)(431,507)(432,517)(433,516)
(434,515)(435,514)(436,513)(437,512)(438,511)(439,510)(440,509)(529,662)
(530,661)(531,671)(532,670)(533,669)(534,668)(535,667)(536,666)(537,665)
(538,664)(539,663)(540,673)(541,672)(542,682)(543,681)(544,680)(545,679)
(546,678)(547,677)(548,676)(549,675)(550,674)(551,695)(552,694)(553,704)
(554,703)(555,702)(556,701)(557,700)(558,699)(559,698)(560,697)(561,696)
(562,684)(563,683)(564,693)(565,692)(566,691)(567,690)(568,689)(569,688)
(570,687)(571,686)(572,685)(573,618)(574,617)(575,627)(576,626)(577,625)
(578,624)(579,623)(580,622)(581,621)(582,620)(583,619)(584,629)(585,628)
(586,638)(587,637)(588,636)(589,635)(590,634)(591,633)(592,632)(593,631)
(594,630)(595,651)(596,650)(597,660)(598,659)(599,658)(600,657)(601,656)
(602,655)(603,654)(604,653)(605,652)(606,640)(607,639)(608,649)(609,648)
(610,647)(611,646)(612,645)(613,644)(614,643)(615,642)(616,641);
s2 := Sym(704)!(  1,177)(  2,178)(  3,179)(  4,180)(  5,181)(  6,182)(  7,183)
(  8,184)(  9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)
( 16,192)( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)
( 24,200)( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)
( 32,208)( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)
( 40,216)( 41,217)( 42,218)( 43,219)( 44,220)( 45,221)( 46,222)( 47,223)
( 48,224)( 49,225)( 50,226)( 51,227)( 52,228)( 53,229)( 54,230)( 55,231)
( 56,232)( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)
( 64,240)( 65,241)( 66,242)( 67,243)( 68,244)( 69,245)( 70,246)( 71,247)
( 72,248)( 73,249)( 74,250)( 75,251)( 76,252)( 77,253)( 78,254)( 79,255)
( 80,256)( 81,257)( 82,258)( 83,259)( 84,260)( 85,261)( 86,262)( 87,263)
( 88,264)( 89,265)( 90,266)( 91,267)( 92,268)( 93,269)( 94,270)( 95,271)
( 96,272)( 97,273)( 98,274)( 99,275)(100,276)(101,277)(102,278)(103,279)
(104,280)(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)
(112,288)(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)
(120,296)(121,297)(122,298)(123,299)(124,300)(125,301)(126,302)(127,303)
(128,304)(129,305)(130,306)(131,307)(132,308)(133,309)(134,310)(135,311)
(136,312)(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)
(144,320)(145,321)(146,322)(147,323)(148,324)(149,325)(150,326)(151,327)
(152,328)(153,329)(154,330)(155,331)(156,332)(157,333)(158,334)(159,335)
(160,336)(161,337)(162,338)(163,339)(164,340)(165,341)(166,342)(167,343)
(168,344)(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)
(176,352)(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)
(360,536)(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)
(368,544)(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)
(376,552)(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)
(384,560)(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)
(392,568)(393,569)(394,570)(395,571)(396,572)(397,573)(398,574)(399,575)
(400,576)(401,577)(402,578)(403,579)(404,580)(405,581)(406,582)(407,583)
(408,584)(409,585)(410,586)(411,587)(412,588)(413,589)(414,590)(415,591)
(416,592)(417,593)(418,594)(419,595)(420,596)(421,597)(422,598)(423,599)
(424,600)(425,601)(426,602)(427,603)(428,604)(429,605)(430,606)(431,607)
(432,608)(433,609)(434,610)(435,611)(436,612)(437,613)(438,614)(439,615)
(440,616)(441,617)(442,618)(443,619)(444,620)(445,621)(446,622)(447,623)
(448,624)(449,625)(450,626)(451,627)(452,628)(453,629)(454,630)(455,631)
(456,632)(457,633)(458,634)(459,635)(460,636)(461,637)(462,638)(463,639)
(464,640)(465,641)(466,642)(467,643)(468,644)(469,645)(470,646)(471,647)
(472,648)(473,649)(474,650)(475,651)(476,652)(477,653)(478,654)(479,655)
(480,656)(481,657)(482,658)(483,659)(484,660)(485,661)(486,662)(487,663)
(488,664)(489,665)(490,666)(491,667)(492,668)(493,669)(494,670)(495,671)
(496,672)(497,673)(498,674)(499,675)(500,676)(501,677)(502,678)(503,679)
(504,680)(505,681)(506,682)(507,683)(508,684)(509,685)(510,686)(511,687)
(512,688)(513,689)(514,690)(515,691)(516,692)(517,693)(518,694)(519,695)
(520,696)(521,697)(522,698)(523,699)(524,700)(525,701)(526,702)(527,703)
(528,704);
poly := sub<Sym(704)|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*s2*s1, 
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*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*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*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*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