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Polytope of Type {88,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {88,8}*1408b
if this polytope has a name.
Group : SmallGroup(1408,3566)
Rank : 3
Schlafli Type : {88,8}
Number of vertices, edges, etc : 88, 352, 8
Order of s0s1s2 : 88
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {88,4}*704a, {44,8}*704b
   4-fold quotients : {44,4}*352, {88,2}*352
   8-fold quotients : {44,2}*176, {22,4}*176
   11-fold quotients : {8,8}*128c
   16-fold quotients : {22,2}*88
   22-fold quotients : {8,4}*64a, {4,8}*64b
   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)( 23,375)( 24,385)
( 25,384)( 26,383)( 27,382)( 28,381)( 29,380)( 30,379)( 31,378)( 32,377)
( 33,376)( 34,386)( 35,396)( 36,395)( 37,394)( 38,393)( 39,392)( 40,391)
( 41,390)( 42,389)( 43,388)( 44,387)( 45,408)( 46,418)( 47,417)( 48,416)
( 49,415)( 50,414)( 51,413)( 52,412)( 53,411)( 54,410)( 55,409)( 56,397)
( 57,407)( 58,406)( 59,405)( 60,404)( 61,403)( 62,402)( 63,401)( 64,400)
( 65,399)( 66,398)( 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)(133,518)(134,528)(135,527)(136,526)
(137,525)(138,524)(139,523)(140,522)(141,521)(142,520)(143,519)(144,507)
(145,517)(146,516)(147,515)(148,514)(149,513)(150,512)(151,511)(152,510)
(153,509)(154,508)(155,496)(156,506)(157,505)(158,504)(159,503)(160,502)
(161,501)(162,500)(163,499)(164,498)(165,497)(166,485)(167,495)(168,494)
(169,493)(170,492)(171,491)(172,490)(173,489)(174,488)(175,487)(176,486)
(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)(199,551)(200,561)
(201,560)(202,559)(203,558)(204,557)(205,556)(206,555)(207,554)(208,553)
(209,552)(210,562)(211,572)(212,571)(213,570)(214,569)(215,568)(216,567)
(217,566)(218,565)(219,564)(220,563)(221,584)(222,594)(223,593)(224,592)
(225,591)(226,590)(227,589)(228,588)(229,587)(230,586)(231,585)(232,573)
(233,583)(234,582)(235,581)(236,580)(237,579)(238,578)(239,577)(240,576)
(241,575)(242,574)(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)(309,694)(310,704)(311,703)(312,702)
(313,701)(314,700)(315,699)(316,698)(317,697)(318,696)(319,695)(320,683)
(321,693)(322,692)(323,691)(324,690)(325,689)(326,688)(327,687)(328,686)
(329,685)(330,684)(331,672)(332,682)(333,681)(334,680)(335,679)(336,678)
(337,677)(338,676)(339,675)(340,674)(341,673)(342,661)(343,671)(344,670)
(345,669)(346,668)(347,667)(348,666)(349,665)(350,664)(351,663)(352,662);;
s1 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)
( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 57)( 46, 56)( 47, 66)( 48, 65)
( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 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)
(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)
(141,170)(142,169)(143,168)(144,156)(145,155)(146,165)(147,164)(148,163)
(149,162)(150,161)(151,160)(152,159)(153,158)(154,157)(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)(199,244)(200,243)(201,253)(202,252)
(203,251)(204,250)(205,249)(206,248)(207,247)(208,246)(209,245)(210,255)
(211,254)(212,264)(213,263)(214,262)(215,261)(216,260)(217,259)(218,258)
(219,257)(220,256)(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)(375,464)(376,463)(377,473)(378,472)
(379,471)(380,470)(381,469)(382,468)(383,467)(384,466)(385,465)(386,475)
(387,474)(388,484)(389,483)(390,482)(391,481)(392,480)(393,479)(394,478)
(395,477)(396,476)(397,497)(398,496)(399,506)(400,505)(401,504)(402,503)
(403,502)(404,501)(405,500)(406,499)(407,498)(408,486)(409,485)(410,495)
(411,494)(412,493)(413,492)(414,491)(415,490)(416,489)(417,488)(418,487)
(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)(529,673)(530,672)
(531,682)(532,681)(533,680)(534,679)(535,678)(536,677)(537,676)(538,675)
(539,674)(540,662)(541,661)(542,671)(543,670)(544,669)(545,668)(546,667)
(547,666)(548,665)(549,664)(550,663)(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)(573,629)(574,628)(575,638)(576,637)(577,636)(578,635)
(579,634)(580,633)(581,632)(582,631)(583,630)(584,618)(585,617)(586,627)
(587,626)(588,625)(589,624)(590,623)(591,622)(592,621)(593,620)(594,619)
(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)( 45,232)( 46,233)( 47,234)( 48,235)
( 49,236)( 50,237)( 51,238)( 52,239)( 53,240)( 54,241)( 55,242)( 56,221)
( 57,222)( 58,223)( 59,224)( 60,225)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,231)( 67,254)( 68,255)( 69,256)( 70,257)( 71,258)( 72,259)
( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,243)( 79,244)( 80,245)
( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)( 88,253)
( 89,276)( 90,277)( 91,278)( 92,279)( 93,280)( 94,281)( 95,282)( 96,283)
( 97,284)( 98,285)( 99,286)(100,265)(101,266)(102,267)(103,268)(104,269)
(105,270)(106,271)(107,272)(108,273)(109,274)(110,275)(111,298)(112,299)
(113,300)(114,301)(115,302)(116,303)(117,304)(118,305)(119,306)(120,307)
(121,308)(122,287)(123,288)(124,289)(125,290)(126,291)(127,292)(128,293)
(129,294)(130,295)(131,296)(132,297)(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)(397,584)(398,585)(399,586)(400,587)
(401,588)(402,589)(403,590)(404,591)(405,592)(406,593)(407,594)(408,573)
(409,574)(410,575)(411,576)(412,577)(413,578)(414,579)(415,580)(416,581)
(417,582)(418,583)(419,606)(420,607)(421,608)(422,609)(423,610)(424,611)
(425,612)(426,613)(427,614)(428,615)(429,616)(430,595)(431,596)(432,597)
(433,598)(434,599)(435,600)(436,601)(437,602)(438,603)(439,604)(440,605)
(441,628)(442,629)(443,630)(444,631)(445,632)(446,633)(447,634)(448,635)
(449,636)(450,637)(451,638)(452,617)(453,618)(454,619)(455,620)(456,621)
(457,622)(458,623)(459,624)(460,625)(461,626)(462,627)(463,650)(464,651)
(465,652)(466,653)(467,654)(468,655)(469,656)(470,657)(471,658)(472,659)
(473,660)(474,639)(475,640)(476,641)(477,642)(478,643)(479,644)(480,645)
(481,646)(482,647)(483,648)(484,649)(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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 23,375)
( 24,385)( 25,384)( 26,383)( 27,382)( 28,381)( 29,380)( 30,379)( 31,378)
( 32,377)( 33,376)( 34,386)( 35,396)( 36,395)( 37,394)( 38,393)( 39,392)
( 40,391)( 41,390)( 42,389)( 43,388)( 44,387)( 45,408)( 46,418)( 47,417)
( 48,416)( 49,415)( 50,414)( 51,413)( 52,412)( 53,411)( 54,410)( 55,409)
( 56,397)( 57,407)( 58,406)( 59,405)( 60,404)( 61,403)( 62,402)( 63,401)
( 64,400)( 65,399)( 66,398)( 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)(133,518)(134,528)(135,527)
(136,526)(137,525)(138,524)(139,523)(140,522)(141,521)(142,520)(143,519)
(144,507)(145,517)(146,516)(147,515)(148,514)(149,513)(150,512)(151,511)
(152,510)(153,509)(154,508)(155,496)(156,506)(157,505)(158,504)(159,503)
(160,502)(161,501)(162,500)(163,499)(164,498)(165,497)(166,485)(167,495)
(168,494)(169,493)(170,492)(171,491)(172,490)(173,489)(174,488)(175,487)
(176,486)(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)(199,551)
(200,561)(201,560)(202,559)(203,558)(204,557)(205,556)(206,555)(207,554)
(208,553)(209,552)(210,562)(211,572)(212,571)(213,570)(214,569)(215,568)
(216,567)(217,566)(218,565)(219,564)(220,563)(221,584)(222,594)(223,593)
(224,592)(225,591)(226,590)(227,589)(228,588)(229,587)(230,586)(231,585)
(232,573)(233,583)(234,582)(235,581)(236,580)(237,579)(238,578)(239,577)
(240,576)(241,575)(242,574)(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)(309,694)(310,704)(311,703)
(312,702)(313,701)(314,700)(315,699)(316,698)(317,697)(318,696)(319,695)
(320,683)(321,693)(322,692)(323,691)(324,690)(325,689)(326,688)(327,687)
(328,686)(329,685)(330,684)(331,672)(332,682)(333,681)(334,680)(335,679)
(336,678)(337,677)(338,676)(339,675)(340,674)(341,673)(342,661)(343,671)
(344,670)(345,669)(346,668)(347,667)(348,666)(349,665)(350,664)(351,663)
(352,662);
s1 := Sym(704)!(  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)
( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 57)( 46, 56)( 47, 66)
( 48, 65)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)
( 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)(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)
(140,171)(141,170)(142,169)(143,168)(144,156)(145,155)(146,165)(147,164)
(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157)(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)(199,244)(200,243)(201,253)
(202,252)(203,251)(204,250)(205,249)(206,248)(207,247)(208,246)(209,245)
(210,255)(211,254)(212,264)(213,263)(214,262)(215,261)(216,260)(217,259)
(218,258)(219,257)(220,256)(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)(375,464)(376,463)(377,473)
(378,472)(379,471)(380,470)(381,469)(382,468)(383,467)(384,466)(385,465)
(386,475)(387,474)(388,484)(389,483)(390,482)(391,481)(392,480)(393,479)
(394,478)(395,477)(396,476)(397,497)(398,496)(399,506)(400,505)(401,504)
(402,503)(403,502)(404,501)(405,500)(406,499)(407,498)(408,486)(409,485)
(410,495)(411,494)(412,493)(413,492)(414,491)(415,490)(416,489)(417,488)
(418,487)(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)(529,673)
(530,672)(531,682)(532,681)(533,680)(534,679)(535,678)(536,677)(537,676)
(538,675)(539,674)(540,662)(541,661)(542,671)(543,670)(544,669)(545,668)
(546,667)(547,666)(548,665)(549,664)(550,663)(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)(573,629)(574,628)(575,638)(576,637)(577,636)
(578,635)(579,634)(580,633)(581,632)(582,631)(583,630)(584,618)(585,617)
(586,627)(587,626)(588,625)(589,624)(590,623)(591,622)(592,621)(593,620)
(594,619)(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)( 45,232)( 46,233)( 47,234)
( 48,235)( 49,236)( 50,237)( 51,238)( 52,239)( 53,240)( 54,241)( 55,242)
( 56,221)( 57,222)( 58,223)( 59,224)( 60,225)( 61,226)( 62,227)( 63,228)
( 64,229)( 65,230)( 66,231)( 67,254)( 68,255)( 69,256)( 70,257)( 71,258)
( 72,259)( 73,260)( 74,261)( 75,262)( 76,263)( 77,264)( 78,243)( 79,244)
( 80,245)( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)
( 88,253)( 89,276)( 90,277)( 91,278)( 92,279)( 93,280)( 94,281)( 95,282)
( 96,283)( 97,284)( 98,285)( 99,286)(100,265)(101,266)(102,267)(103,268)
(104,269)(105,270)(106,271)(107,272)(108,273)(109,274)(110,275)(111,298)
(112,299)(113,300)(114,301)(115,302)(116,303)(117,304)(118,305)(119,306)
(120,307)(121,308)(122,287)(123,288)(124,289)(125,290)(126,291)(127,292)
(128,293)(129,294)(130,295)(131,296)(132,297)(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)(397,584)(398,585)(399,586)
(400,587)(401,588)(402,589)(403,590)(404,591)(405,592)(406,593)(407,594)
(408,573)(409,574)(410,575)(411,576)(412,577)(413,578)(414,579)(415,580)
(416,581)(417,582)(418,583)(419,606)(420,607)(421,608)(422,609)(423,610)
(424,611)(425,612)(426,613)(427,614)(428,615)(429,616)(430,595)(431,596)
(432,597)(433,598)(434,599)(435,600)(436,601)(437,602)(438,603)(439,604)
(440,605)(441,628)(442,629)(443,630)(444,631)(445,632)(446,633)(447,634)
(448,635)(449,636)(450,637)(451,638)(452,617)(453,618)(454,619)(455,620)
(456,621)(457,622)(458,623)(459,624)(460,625)(461,626)(462,627)(463,650)
(464,651)(465,652)(466,653)(467,654)(468,655)(469,656)(470,657)(471,658)
(472,659)(473,660)(474,639)(475,640)(476,641)(477,642)(478,643)(479,644)
(480,645)(481,646)(482,647)(483,648)(484,649)(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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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