Polytope of Type {8,88}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,88}*1408a
if this polytope has a name.
Group : SmallGroup(1408,3565)
Rank : 3
Schlafli Type : {8,88}
Number of vertices, edges, etc : 8, 352, 88
Order of s0s1s2 : 88
Order of s0s1s2s1 : 4
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}*704b, {8,44}*704a
4-fold quotients : {4,44}*352, {8,22}*352
8-fold quotients : {2,44}*176, {4,22}*176
11-fold quotients : {8,8}*128c
16-fold quotients : {2,22}*88
22-fold quotients : {8,4}*64a, {4,8}*64b
32-fold quotients : {2,11}*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)( 2,354)( 3,355)( 4,356)( 5,357)( 6,358)( 7,359)( 8,360)
( 9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)( 16,368)
( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,375)( 24,376)
( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)( 32,384)
( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)( 40,392)
( 41,393)( 42,394)( 43,395)( 44,396)( 45,408)( 46,409)( 47,410)( 48,411)
( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)( 56,397)
( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)( 64,405)
( 65,406)( 66,407)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)( 72,435)
( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)( 80,421)
( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)( 88,429)
( 89,463)( 90,464)( 91,465)( 92,466)( 93,467)( 94,468)( 95,469)( 96,470)
( 97,471)( 98,472)( 99,473)(100,474)(101,475)(102,476)(103,477)(104,478)
(105,479)(106,480)(107,481)(108,482)(109,483)(110,484)(111,441)(112,442)
(113,443)(114,444)(115,445)(116,446)(117,447)(118,448)(119,449)(120,450)
(121,451)(122,452)(123,453)(124,454)(125,455)(126,456)(127,457)(128,458)
(129,459)(130,460)(131,461)(132,462)(133,518)(134,519)(135,520)(136,521)
(137,522)(138,523)(139,524)(140,525)(141,526)(142,527)(143,528)(144,507)
(145,508)(146,509)(147,510)(148,511)(149,512)(150,513)(151,514)(152,515)
(153,516)(154,517)(155,496)(156,497)(157,498)(158,499)(159,500)(160,501)
(161,502)(162,503)(163,504)(164,505)(165,506)(166,485)(167,486)(168,487)
(169,488)(170,489)(171,490)(172,491)(173,492)(174,493)(175,494)(176,495)
(177,529)(178,530)(179,531)(180,532)(181,533)(182,534)(183,535)(184,536)
(185,537)(186,538)(187,539)(188,540)(189,541)(190,542)(191,543)(192,544)
(193,545)(194,546)(195,547)(196,548)(197,549)(198,550)(199,551)(200,552)
(201,553)(202,554)(203,555)(204,556)(205,557)(206,558)(207,559)(208,560)
(209,561)(210,562)(211,563)(212,564)(213,565)(214,566)(215,567)(216,568)
(217,569)(218,570)(219,571)(220,572)(221,584)(222,585)(223,586)(224,587)
(225,588)(226,589)(227,590)(228,591)(229,592)(230,593)(231,594)(232,573)
(233,574)(234,575)(235,576)(236,577)(237,578)(238,579)(239,580)(240,581)
(241,582)(242,583)(243,606)(244,607)(245,608)(246,609)(247,610)(248,611)
(249,612)(250,613)(251,614)(252,615)(253,616)(254,595)(255,596)(256,597)
(257,598)(258,599)(259,600)(260,601)(261,602)(262,603)(263,604)(264,605)
(265,639)(266,640)(267,641)(268,642)(269,643)(270,644)(271,645)(272,646)
(273,647)(274,648)(275,649)(276,650)(277,651)(278,652)(279,653)(280,654)
(281,655)(282,656)(283,657)(284,658)(285,659)(286,660)(287,617)(288,618)
(289,619)(290,620)(291,621)(292,622)(293,623)(294,624)(295,625)(296,626)
(297,627)(298,628)(299,629)(300,630)(301,631)(302,632)(303,633)(304,634)
(305,635)(306,636)(307,637)(308,638)(309,694)(310,695)(311,696)(312,697)
(313,698)(314,699)(315,700)(316,701)(317,702)(318,703)(319,704)(320,683)
(321,684)(322,685)(323,686)(324,687)(325,688)(326,689)(327,690)(328,691)
(329,692)(330,693)(331,672)(332,673)(333,674)(334,675)(335,676)(336,677)
(337,678)(338,679)(339,680)(340,681)(341,682)(342,661)(343,662)(344,663)
(345,664)(346,665)(347,666)(348,667)(349,668)(350,669)(351,670)(352,671);;
s1 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)( 48, 64)
( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 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)
(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)
(141,169)(142,168)(143,167)(144,155)(145,165)(146,164)(147,163)(148,162)
(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(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)(199,243)(200,253)(201,252)(202,251)
(203,250)(204,249)(205,248)(206,247)(207,246)(208,245)(209,244)(210,254)
(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,258)(218,257)
(219,256)(220,255)(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)(375,463)(376,473)(377,472)(378,471)
(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,474)
(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)
(395,476)(396,475)(397,496)(398,506)(399,505)(400,504)(401,503)(402,502)
(403,501)(404,500)(405,499)(406,498)(407,497)(408,485)(409,495)(410,494)
(411,493)(412,492)(413,491)(414,490)(415,489)(416,488)(417,487)(418,486)
(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)(529,672)(530,682)
(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)(538,674)
(539,673)(540,661)(541,671)(542,670)(543,669)(544,668)(545,667)(546,666)
(547,665)(548,664)(549,663)(550,662)(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)(573,628)(574,638)(575,637)(576,636)(577,635)(578,634)
(579,633)(580,632)(581,631)(582,630)(583,629)(584,617)(585,627)(586,626)
(587,625)(588,624)(589,623)(590,622)(591,621)(592,620)(593,619)(594,618)
(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 := ( 1,178)( 2,177)( 3,187)( 4,186)( 5,185)( 6,184)( 7,183)( 8,182)
( 9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)( 16,196)
( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,200)( 24,199)
( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,204)( 31,203)( 32,202)
( 33,201)( 34,211)( 35,210)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)
( 41,215)( 42,214)( 43,213)( 44,212)( 45,233)( 46,232)( 47,242)( 48,241)
( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)( 56,222)
( 57,221)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)( 64,225)
( 65,224)( 66,223)( 67,255)( 68,254)( 69,264)( 70,263)( 71,262)( 72,261)
( 73,260)( 74,259)( 75,258)( 76,257)( 77,256)( 78,244)( 79,243)( 80,253)
( 81,252)( 82,251)( 83,250)( 84,249)( 85,248)( 86,247)( 87,246)( 88,245)
( 89,277)( 90,276)( 91,286)( 92,285)( 93,284)( 94,283)( 95,282)( 96,281)
( 97,280)( 98,279)( 99,278)(100,266)(101,265)(102,275)(103,274)(104,273)
(105,272)(106,271)(107,270)(108,269)(109,268)(110,267)(111,299)(112,298)
(113,308)(114,307)(115,306)(116,305)(117,304)(118,303)(119,302)(120,301)
(121,300)(122,288)(123,287)(124,297)(125,296)(126,295)(127,294)(128,293)
(129,292)(130,291)(131,290)(132,289)(133,310)(134,309)(135,319)(136,318)
(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)(144,321)
(145,320)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)(152,324)
(153,323)(154,322)(155,332)(156,331)(157,341)(158,340)(159,339)(160,338)
(161,337)(162,336)(163,335)(164,334)(165,333)(166,343)(167,342)(168,352)
(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,344)
(353,530)(354,529)(355,539)(356,538)(357,537)(358,536)(359,535)(360,534)
(361,533)(362,532)(363,531)(364,541)(365,540)(366,550)(367,549)(368,548)
(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)(375,552)(376,551)
(377,561)(378,560)(379,559)(380,558)(381,557)(382,556)(383,555)(384,554)
(385,553)(386,563)(387,562)(388,572)(389,571)(390,570)(391,569)(392,568)
(393,567)(394,566)(395,565)(396,564)(397,585)(398,584)(399,594)(400,593)
(401,592)(402,591)(403,590)(404,589)(405,588)(406,587)(407,586)(408,574)
(409,573)(410,583)(411,582)(412,581)(413,580)(414,579)(415,578)(416,577)
(417,576)(418,575)(419,607)(420,606)(421,616)(422,615)(423,614)(424,613)
(425,612)(426,611)(427,610)(428,609)(429,608)(430,596)(431,595)(432,605)
(433,604)(434,603)(435,602)(436,601)(437,600)(438,599)(439,598)(440,597)
(441,629)(442,628)(443,638)(444,637)(445,636)(446,635)(447,634)(448,633)
(449,632)(450,631)(451,630)(452,618)(453,617)(454,627)(455,626)(456,625)
(457,624)(458,623)(459,622)(460,621)(461,620)(462,619)(463,651)(464,650)
(465,660)(466,659)(467,658)(468,657)(469,656)(470,655)(471,654)(472,653)
(473,652)(474,640)(475,639)(476,649)(477,648)(478,647)(479,646)(480,645)
(481,644)(482,643)(483,642)(484,641)(485,662)(486,661)(487,671)(488,670)
(489,669)(490,668)(491,667)(492,666)(493,665)(494,664)(495,663)(496,673)
(497,672)(498,682)(499,681)(500,680)(501,679)(502,678)(503,677)(504,676)
(505,675)(506,674)(507,684)(508,683)(509,693)(510,692)(511,691)(512,690)
(513,689)(514,688)(515,687)(516,686)(517,685)(518,695)(519,694)(520,704)
(521,703)(522,702)(523,701)(524,700)(525,699)(526,698)(527,697)(528,696);;
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*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(704)!( 1,353)( 2,354)( 3,355)( 4,356)( 5,357)( 6,358)( 7,359)
( 8,360)( 9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)
( 16,368)( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,375)
( 24,376)( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)
( 32,384)( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)
( 40,392)( 41,393)( 42,394)( 43,395)( 44,396)( 45,408)( 46,409)( 47,410)
( 48,411)( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)
( 56,397)( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)
( 64,405)( 65,406)( 66,407)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)
( 72,435)( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)
( 80,421)( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)
( 88,429)( 89,463)( 90,464)( 91,465)( 92,466)( 93,467)( 94,468)( 95,469)
( 96,470)( 97,471)( 98,472)( 99,473)(100,474)(101,475)(102,476)(103,477)
(104,478)(105,479)(106,480)(107,481)(108,482)(109,483)(110,484)(111,441)
(112,442)(113,443)(114,444)(115,445)(116,446)(117,447)(118,448)(119,449)
(120,450)(121,451)(122,452)(123,453)(124,454)(125,455)(126,456)(127,457)
(128,458)(129,459)(130,460)(131,461)(132,462)(133,518)(134,519)(135,520)
(136,521)(137,522)(138,523)(139,524)(140,525)(141,526)(142,527)(143,528)
(144,507)(145,508)(146,509)(147,510)(148,511)(149,512)(150,513)(151,514)
(152,515)(153,516)(154,517)(155,496)(156,497)(157,498)(158,499)(159,500)
(160,501)(161,502)(162,503)(163,504)(164,505)(165,506)(166,485)(167,486)
(168,487)(169,488)(170,489)(171,490)(172,491)(173,492)(174,493)(175,494)
(176,495)(177,529)(178,530)(179,531)(180,532)(181,533)(182,534)(183,535)
(184,536)(185,537)(186,538)(187,539)(188,540)(189,541)(190,542)(191,543)
(192,544)(193,545)(194,546)(195,547)(196,548)(197,549)(198,550)(199,551)
(200,552)(201,553)(202,554)(203,555)(204,556)(205,557)(206,558)(207,559)
(208,560)(209,561)(210,562)(211,563)(212,564)(213,565)(214,566)(215,567)
(216,568)(217,569)(218,570)(219,571)(220,572)(221,584)(222,585)(223,586)
(224,587)(225,588)(226,589)(227,590)(228,591)(229,592)(230,593)(231,594)
(232,573)(233,574)(234,575)(235,576)(236,577)(237,578)(238,579)(239,580)
(240,581)(241,582)(242,583)(243,606)(244,607)(245,608)(246,609)(247,610)
(248,611)(249,612)(250,613)(251,614)(252,615)(253,616)(254,595)(255,596)
(256,597)(257,598)(258,599)(259,600)(260,601)(261,602)(262,603)(263,604)
(264,605)(265,639)(266,640)(267,641)(268,642)(269,643)(270,644)(271,645)
(272,646)(273,647)(274,648)(275,649)(276,650)(277,651)(278,652)(279,653)
(280,654)(281,655)(282,656)(283,657)(284,658)(285,659)(286,660)(287,617)
(288,618)(289,619)(290,620)(291,621)(292,622)(293,623)(294,624)(295,625)
(296,626)(297,627)(298,628)(299,629)(300,630)(301,631)(302,632)(303,633)
(304,634)(305,635)(306,636)(307,637)(308,638)(309,694)(310,695)(311,696)
(312,697)(313,698)(314,699)(315,700)(316,701)(317,702)(318,703)(319,704)
(320,683)(321,684)(322,685)(323,686)(324,687)(325,688)(326,689)(327,690)
(328,691)(329,692)(330,693)(331,672)(332,673)(333,674)(334,675)(335,676)
(336,677)(337,678)(338,679)(339,680)(340,681)(341,682)(342,661)(343,662)
(344,663)(345,664)(346,665)(347,666)(348,667)(349,668)(350,669)(351,670)
(352,671);
s1 := Sym(704)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)
( 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)(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)
(140,170)(141,169)(142,168)(143,167)(144,155)(145,165)(146,164)(147,163)
(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(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)(199,243)(200,253)(201,252)
(202,251)(203,250)(204,249)(205,248)(206,247)(207,246)(208,245)(209,244)
(210,254)(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,258)
(218,257)(219,256)(220,255)(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)(375,463)(376,473)(377,472)
(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)
(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)
(394,477)(395,476)(396,475)(397,496)(398,506)(399,505)(400,504)(401,503)
(402,502)(403,501)(404,500)(405,499)(406,498)(407,497)(408,485)(409,495)
(410,494)(411,493)(412,492)(413,491)(414,490)(415,489)(416,488)(417,487)
(418,486)(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)(529,672)
(530,682)(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)
(538,674)(539,673)(540,661)(541,671)(542,670)(543,669)(544,668)(545,667)
(546,666)(547,665)(548,664)(549,663)(550,662)(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)(573,628)(574,638)(575,637)(576,636)(577,635)
(578,634)(579,633)(580,632)(581,631)(582,630)(583,629)(584,617)(585,627)
(586,626)(587,625)(588,624)(589,623)(590,622)(591,621)(592,620)(593,619)
(594,618)(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)!( 1,178)( 2,177)( 3,187)( 4,186)( 5,185)( 6,184)( 7,183)
( 8,182)( 9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)
( 16,196)( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,200)
( 24,199)( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,204)( 31,203)
( 32,202)( 33,201)( 34,211)( 35,210)( 36,220)( 37,219)( 38,218)( 39,217)
( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,233)( 46,232)( 47,242)
( 48,241)( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)
( 56,222)( 57,221)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)
( 64,225)( 65,224)( 66,223)( 67,255)( 68,254)( 69,264)( 70,263)( 71,262)
( 72,261)( 73,260)( 74,259)( 75,258)( 76,257)( 77,256)( 78,244)( 79,243)
( 80,253)( 81,252)( 82,251)( 83,250)( 84,249)( 85,248)( 86,247)( 87,246)
( 88,245)( 89,277)( 90,276)( 91,286)( 92,285)( 93,284)( 94,283)( 95,282)
( 96,281)( 97,280)( 98,279)( 99,278)(100,266)(101,265)(102,275)(103,274)
(104,273)(105,272)(106,271)(107,270)(108,269)(109,268)(110,267)(111,299)
(112,298)(113,308)(114,307)(115,306)(116,305)(117,304)(118,303)(119,302)
(120,301)(121,300)(122,288)(123,287)(124,297)(125,296)(126,295)(127,294)
(128,293)(129,292)(130,291)(131,290)(132,289)(133,310)(134,309)(135,319)
(136,318)(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)
(144,321)(145,320)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)
(152,324)(153,323)(154,322)(155,332)(156,331)(157,341)(158,340)(159,339)
(160,338)(161,337)(162,336)(163,335)(164,334)(165,333)(166,343)(167,342)
(168,352)(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)
(176,344)(353,530)(354,529)(355,539)(356,538)(357,537)(358,536)(359,535)
(360,534)(361,533)(362,532)(363,531)(364,541)(365,540)(366,550)(367,549)
(368,548)(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)(375,552)
(376,551)(377,561)(378,560)(379,559)(380,558)(381,557)(382,556)(383,555)
(384,554)(385,553)(386,563)(387,562)(388,572)(389,571)(390,570)(391,569)
(392,568)(393,567)(394,566)(395,565)(396,564)(397,585)(398,584)(399,594)
(400,593)(401,592)(402,591)(403,590)(404,589)(405,588)(406,587)(407,586)
(408,574)(409,573)(410,583)(411,582)(412,581)(413,580)(414,579)(415,578)
(416,577)(417,576)(418,575)(419,607)(420,606)(421,616)(422,615)(423,614)
(424,613)(425,612)(426,611)(427,610)(428,609)(429,608)(430,596)(431,595)
(432,605)(433,604)(434,603)(435,602)(436,601)(437,600)(438,599)(439,598)
(440,597)(441,629)(442,628)(443,638)(444,637)(445,636)(446,635)(447,634)
(448,633)(449,632)(450,631)(451,630)(452,618)(453,617)(454,627)(455,626)
(456,625)(457,624)(458,623)(459,622)(460,621)(461,620)(462,619)(463,651)
(464,650)(465,660)(466,659)(467,658)(468,657)(469,656)(470,655)(471,654)
(472,653)(473,652)(474,640)(475,639)(476,649)(477,648)(478,647)(479,646)
(480,645)(481,644)(482,643)(483,642)(484,641)(485,662)(486,661)(487,671)
(488,670)(489,669)(490,668)(491,667)(492,666)(493,665)(494,664)(495,663)
(496,673)(497,672)(498,682)(499,681)(500,680)(501,679)(502,678)(503,677)
(504,676)(505,675)(506,674)(507,684)(508,683)(509,693)(510,692)(511,691)
(512,690)(513,689)(514,688)(515,687)(516,686)(517,685)(518,695)(519,694)
(520,704)(521,703)(522,702)(523,701)(524,700)(525,699)(526,698)(527,697)
(528,696);
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*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope