Polytope of Type {4,176}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,176}*1408a
Also Known As : {4,176|2}. if this polytope has another name.
Group : SmallGroup(1408,6424)
Rank : 3
Schlafli Type : {4,176}
Number of vertices, edges, etc : 4, 352, 176
Order of s₀s₁s₂ : 176
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,88}*704a, {2,176}*704
   4-fold quotients : {4,44}*352, {2,88}*352
   8-fold quotients : {2,44}*176, {4,22}*176
   11-fold quotients : {4,16}*128a
   16-fold quotients : {2,22}*88
   22-fold quotients : {4,8}*64a, {2,16}*64
   32-fold quotients : {2,11}*44
   44-fold quotients : {4,4}*32, {2,8}*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 := (  1,177)(  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);;
s1 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)
( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 67, 78)
( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)
( 76, 80)( 77, 79)( 89,111)( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)
( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,122)(101,132)(102,131)
(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)
(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)(140,159)
(141,158)(142,157)(143,156)(144,166)(145,176)(146,175)(147,174)(148,173)
(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(177,221)(178,231)
(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)
(187,222)(188,232)(189,242)(190,241)(191,240)(192,239)(193,238)(194,237)
(195,236)(196,235)(197,234)(198,233)(199,254)(200,264)(201,263)(202,262)
(203,261)(204,260)(205,259)(206,258)(207,257)(208,256)(209,255)(210,243)
(211,253)(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)(218,246)
(219,245)(220,244)(265,331)(266,341)(267,340)(268,339)(269,338)(270,337)
(271,336)(272,335)(273,334)(274,333)(275,332)(276,342)(277,352)(278,351)
(279,350)(280,349)(281,348)(282,347)(283,346)(284,345)(285,344)(286,343)
(287,309)(288,319)(289,318)(290,317)(291,316)(292,315)(293,314)(294,313)
(295,312)(296,311)(297,310)(298,320)(299,330)(300,329)(301,328)(302,327)
(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)(353,441)(354,451)
(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)
(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)
(371,456)(372,455)(373,454)(374,453)(375,474)(376,484)(377,483)(378,482)
(379,481)(380,480)(381,479)(382,478)(383,477)(384,476)(385,475)(386,463)
(387,473)(388,472)(389,471)(390,470)(391,469)(392,468)(393,467)(394,466)
(395,465)(396,464)(397,485)(398,495)(399,494)(400,493)(401,492)(402,491)
(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)(410,505)
(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)
(419,518)(420,528)(421,527)(422,526)(423,525)(424,524)(425,523)(426,522)
(427,521)(428,520)(429,519)(430,507)(431,517)(432,516)(433,515)(434,514)
(435,513)(436,512)(437,511)(438,510)(439,509)(440,508)(529,661)(530,671)
(531,670)(532,669)(533,668)(534,667)(535,666)(536,665)(537,664)(538,663)
(539,662)(540,672)(541,682)(542,681)(543,680)(544,679)(545,678)(546,677)
(547,676)(548,675)(549,674)(550,673)(551,694)(552,704)(553,703)(554,702)
(555,701)(556,700)(557,699)(558,698)(559,697)(560,696)(561,695)(562,683)
(563,693)(564,692)(565,691)(566,690)(567,689)(568,688)(569,687)(570,686)
(571,685)(572,684)(573,617)(574,627)(575,626)(576,625)(577,624)(578,623)
(579,622)(580,621)(581,620)(582,619)(583,618)(584,628)(585,638)(586,637)
(587,636)(588,635)(589,634)(590,633)(591,632)(592,631)(593,630)(594,629)
(595,650)(596,660)(597,659)(598,658)(599,657)(600,656)(601,655)(602,654)
(603,653)(604,652)(605,651)(606,639)(607,649)(608,648)(609,647)(610,646)
(611,645)(612,644)(613,643)(614,642)(615,641)(616,640);;
s2 := (  1,354)(  2,353)(  3,363)(  4,362)(  5,361)(  6,360)(  7,359)(  8,358)
(  9,357)( 10,356)( 11,355)( 12,365)( 13,364)( 14,374)( 15,373)( 16,372)
( 17,371)( 18,370)( 19,369)( 20,368)( 21,367)( 22,366)( 23,387)( 24,386)
( 25,396)( 26,395)( 27,394)( 28,393)( 29,392)( 30,391)( 31,390)( 32,389)
( 33,388)( 34,376)( 35,375)( 36,385)( 37,384)( 38,383)( 39,382)( 40,381)
( 41,380)( 42,379)( 43,378)( 44,377)( 45,398)( 46,397)( 47,407)( 48,406)
( 49,405)( 50,404)( 51,403)( 52,402)( 53,401)( 54,400)( 55,399)( 56,409)
( 57,408)( 58,418)( 59,417)( 60,416)( 61,415)( 62,414)( 63,413)( 64,412)
( 65,411)( 66,410)( 67,431)( 68,430)( 69,440)( 70,439)( 71,438)( 72,437)
( 73,436)( 74,435)( 75,434)( 76,433)( 77,432)( 78,420)( 79,419)( 80,429)
( 81,428)( 82,427)( 83,426)( 84,425)( 85,424)( 86,423)( 87,422)( 88,421)
( 89,464)( 90,463)( 91,473)( 92,472)( 93,471)( 94,470)( 95,469)( 96,468)
( 97,467)( 98,466)( 99,465)(100,475)(101,474)(102,484)(103,483)(104,482)
(105,481)(106,480)(107,479)(108,478)(109,477)(110,476)(111,442)(112,441)
(113,451)(114,450)(115,449)(116,448)(117,447)(118,446)(119,445)(120,444)
(121,443)(122,453)(123,452)(124,462)(125,461)(126,460)(127,459)(128,458)
(129,457)(130,456)(131,455)(132,454)(133,508)(134,507)(135,517)(136,516)
(137,515)(138,514)(139,513)(140,512)(141,511)(142,510)(143,509)(144,519)
(145,518)(146,528)(147,527)(148,526)(149,525)(150,524)(151,523)(152,522)
(153,521)(154,520)(155,486)(156,485)(157,495)(158,494)(159,493)(160,492)
(161,491)(162,490)(163,489)(164,488)(165,487)(166,497)(167,496)(168,506)
(169,505)(170,504)(171,503)(172,502)(173,501)(174,500)(175,499)(176,498)
(177,530)(178,529)(179,539)(180,538)(181,537)(182,536)(183,535)(184,534)
(185,533)(186,532)(187,531)(188,541)(189,540)(190,550)(191,549)(192,548)
(193,547)(194,546)(195,545)(196,544)(197,543)(198,542)(199,563)(200,562)
(201,572)(202,571)(203,570)(204,569)(205,568)(206,567)(207,566)(208,565)
(209,564)(210,552)(211,551)(212,561)(213,560)(214,559)(215,558)(216,557)
(217,556)(218,555)(219,554)(220,553)(221,574)(222,573)(223,583)(224,582)
(225,581)(226,580)(227,579)(228,578)(229,577)(230,576)(231,575)(232,585)
(233,584)(234,594)(235,593)(236,592)(237,591)(238,590)(239,589)(240,588)
(241,587)(242,586)(243,607)(244,606)(245,616)(246,615)(247,614)(248,613)
(249,612)(250,611)(251,610)(252,609)(253,608)(254,596)(255,595)(256,605)
(257,604)(258,603)(259,602)(260,601)(261,600)(262,599)(263,598)(264,597)
(265,640)(266,639)(267,649)(268,648)(269,647)(270,646)(271,645)(272,644)
(273,643)(274,642)(275,641)(276,651)(277,650)(278,660)(279,659)(280,658)
(281,657)(282,656)(283,655)(284,654)(285,653)(286,652)(287,618)(288,617)
(289,627)(290,626)(291,625)(292,624)(293,623)(294,622)(295,621)(296,620)
(297,619)(298,629)(299,628)(300,638)(301,637)(302,636)(303,635)(304,634)
(305,633)(306,632)(307,631)(308,630)(309,684)(310,683)(311,693)(312,692)
(313,691)(314,690)(315,689)(316,688)(317,687)(318,686)(319,685)(320,695)
(321,694)(322,704)(323,703)(324,702)(325,701)(326,700)(327,699)(328,698)
(329,697)(330,696)(331,662)(332,661)(333,671)(334,670)(335,669)(336,668)
(337,667)(338,666)(339,665)(340,664)(341,663)(342,673)(343,672)(344,682)
(345,681)(346,680)(347,679)(348,678)(349,677)(350,676)(351,675)(352,674);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*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*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*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*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*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*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*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*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*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*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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := 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);
s1 := Sym(704)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)
( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 46, 55)( 47, 54)
( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)
( 67, 78)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)
( 75, 81)( 76, 80)( 77, 79)( 89,111)( 90,121)( 91,120)( 92,119)( 93,118)
( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,122)(101,132)
(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)
(110,123)(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)
(140,159)(141,158)(142,157)(143,156)(144,166)(145,176)(146,175)(147,174)
(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(177,221)
(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)
(186,223)(187,222)(188,232)(189,242)(190,241)(191,240)(192,239)(193,238)
(194,237)(195,236)(196,235)(197,234)(198,233)(199,254)(200,264)(201,263)
(202,262)(203,261)(204,260)(205,259)(206,258)(207,257)(208,256)(209,255)
(210,243)(211,253)(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)
(218,246)(219,245)(220,244)(265,331)(266,341)(267,340)(268,339)(269,338)
(270,337)(271,336)(272,335)(273,334)(274,333)(275,332)(276,342)(277,352)
(278,351)(279,350)(280,349)(281,348)(282,347)(283,346)(284,345)(285,344)
(286,343)(287,309)(288,319)(289,318)(290,317)(291,316)(292,315)(293,314)
(294,313)(295,312)(296,311)(297,310)(298,320)(299,330)(300,329)(301,328)
(302,327)(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)(353,441)
(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)
(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)
(370,457)(371,456)(372,455)(373,454)(374,453)(375,474)(376,484)(377,483)
(378,482)(379,481)(380,480)(381,479)(382,478)(383,477)(384,476)(385,475)
(386,463)(387,473)(388,472)(389,471)(390,470)(391,469)(392,468)(393,467)
(394,466)(395,465)(396,464)(397,485)(398,495)(399,494)(400,493)(401,492)
(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)
(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)
(418,497)(419,518)(420,528)(421,527)(422,526)(423,525)(424,524)(425,523)
(426,522)(427,521)(428,520)(429,519)(430,507)(431,517)(432,516)(433,515)
(434,514)(435,513)(436,512)(437,511)(438,510)(439,509)(440,508)(529,661)
(530,671)(531,670)(532,669)(533,668)(534,667)(535,666)(536,665)(537,664)
(538,663)(539,662)(540,672)(541,682)(542,681)(543,680)(544,679)(545,678)
(546,677)(547,676)(548,675)(549,674)(550,673)(551,694)(552,704)(553,703)
(554,702)(555,701)(556,700)(557,699)(558,698)(559,697)(560,696)(561,695)
(562,683)(563,693)(564,692)(565,691)(566,690)(567,689)(568,688)(569,687)
(570,686)(571,685)(572,684)(573,617)(574,627)(575,626)(576,625)(577,624)
(578,623)(579,622)(580,621)(581,620)(582,619)(583,618)(584,628)(585,638)
(586,637)(587,636)(588,635)(589,634)(590,633)(591,632)(592,631)(593,630)
(594,629)(595,650)(596,660)(597,659)(598,658)(599,657)(600,656)(601,655)
(602,654)(603,653)(604,652)(605,651)(606,639)(607,649)(608,648)(609,647)
(610,646)(611,645)(612,644)(613,643)(614,642)(615,641)(616,640);
s2 := Sym(704)!(  1,354)(  2,353)(  3,363)(  4,362)(  5,361)(  6,360)(  7,359)
(  8,358)(  9,357)( 10,356)( 11,355)( 12,365)( 13,364)( 14,374)( 15,373)
( 16,372)( 17,371)( 18,370)( 19,369)( 20,368)( 21,367)( 22,366)( 23,387)
( 24,386)( 25,396)( 26,395)( 27,394)( 28,393)( 29,392)( 30,391)( 31,390)
( 32,389)( 33,388)( 34,376)( 35,375)( 36,385)( 37,384)( 38,383)( 39,382)
( 40,381)( 41,380)( 42,379)( 43,378)( 44,377)( 45,398)( 46,397)( 47,407)
( 48,406)( 49,405)( 50,404)( 51,403)( 52,402)( 53,401)( 54,400)( 55,399)
( 56,409)( 57,408)( 58,418)( 59,417)( 60,416)( 61,415)( 62,414)( 63,413)
( 64,412)( 65,411)( 66,410)( 67,431)( 68,430)( 69,440)( 70,439)( 71,438)
( 72,437)( 73,436)( 74,435)( 75,434)( 76,433)( 77,432)( 78,420)( 79,419)
( 80,429)( 81,428)( 82,427)( 83,426)( 84,425)( 85,424)( 86,423)( 87,422)
( 88,421)( 89,464)( 90,463)( 91,473)( 92,472)( 93,471)( 94,470)( 95,469)
( 96,468)( 97,467)( 98,466)( 99,465)(100,475)(101,474)(102,484)(103,483)
(104,482)(105,481)(106,480)(107,479)(108,478)(109,477)(110,476)(111,442)
(112,441)(113,451)(114,450)(115,449)(116,448)(117,447)(118,446)(119,445)
(120,444)(121,443)(122,453)(123,452)(124,462)(125,461)(126,460)(127,459)
(128,458)(129,457)(130,456)(131,455)(132,454)(133,508)(134,507)(135,517)
(136,516)(137,515)(138,514)(139,513)(140,512)(141,511)(142,510)(143,509)
(144,519)(145,518)(146,528)(147,527)(148,526)(149,525)(150,524)(151,523)
(152,522)(153,521)(154,520)(155,486)(156,485)(157,495)(158,494)(159,493)
(160,492)(161,491)(162,490)(163,489)(164,488)(165,487)(166,497)(167,496)
(168,506)(169,505)(170,504)(171,503)(172,502)(173,501)(174,500)(175,499)
(176,498)(177,530)(178,529)(179,539)(180,538)(181,537)(182,536)(183,535)
(184,534)(185,533)(186,532)(187,531)(188,541)(189,540)(190,550)(191,549)
(192,548)(193,547)(194,546)(195,545)(196,544)(197,543)(198,542)(199,563)
(200,562)(201,572)(202,571)(203,570)(204,569)(205,568)(206,567)(207,566)
(208,565)(209,564)(210,552)(211,551)(212,561)(213,560)(214,559)(215,558)
(216,557)(217,556)(218,555)(219,554)(220,553)(221,574)(222,573)(223,583)
(224,582)(225,581)(226,580)(227,579)(228,578)(229,577)(230,576)(231,575)
(232,585)(233,584)(234,594)(235,593)(236,592)(237,591)(238,590)(239,589)
(240,588)(241,587)(242,586)(243,607)(244,606)(245,616)(246,615)(247,614)
(248,613)(249,612)(250,611)(251,610)(252,609)(253,608)(254,596)(255,595)
(256,605)(257,604)(258,603)(259,602)(260,601)(261,600)(262,599)(263,598)
(264,597)(265,640)(266,639)(267,649)(268,648)(269,647)(270,646)(271,645)
(272,644)(273,643)(274,642)(275,641)(276,651)(277,650)(278,660)(279,659)
(280,658)(281,657)(282,656)(283,655)(284,654)(285,653)(286,652)(287,618)
(288,617)(289,627)(290,626)(291,625)(292,624)(293,623)(294,622)(295,621)
(296,620)(297,619)(298,629)(299,628)(300,638)(301,637)(302,636)(303,635)
(304,634)(305,633)(306,632)(307,631)(308,630)(309,684)(310,683)(311,693)
(312,692)(313,691)(314,690)(315,689)(316,688)(317,687)(318,686)(319,685)
(320,695)(321,694)(322,704)(323,703)(324,702)(325,701)(326,700)(327,699)
(328,698)(329,697)(330,696)(331,662)(332,661)(333,671)(334,670)(335,669)
(336,668)(337,667)(338,666)(339,665)(340,664)(341,663)(342,673)(343,672)
(344,682)(345,681)(346,680)(347,679)(348,678)(349,677)(350,676)(351,675)
(352,674);
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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*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*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*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*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*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*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*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*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*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*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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope