Polytope of Type {176,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {176,4}*1408b
if this polytope has a name.
Group : SmallGroup(1408,6458)
Rank : 3
Schlafli Type : {176,4}
Number of vertices, edges, etc : 176, 352, 4
Order of s0s1s2 : 176
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
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
4-fold quotients : {44,4}*352, {88,2}*352
8-fold quotients : {44,2}*176, {22,4}*176
11-fold quotients : {16,4}*128b
16-fold quotients : {22,2}*88
22-fold quotients : {8,4}*64a
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)( 45,408)( 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)( 67,419)( 68,429)( 69,428)( 70,427)( 71,426)( 72,425)
( 73,424)( 74,423)( 75,422)( 76,421)( 77,420)( 78,430)( 79,440)( 80,439)
( 81,438)( 82,437)( 83,436)( 84,435)( 85,434)( 86,433)( 87,432)( 88,431)
( 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)(199,562)(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)(221,584)(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)(243,595)(244,605)(245,604)(246,603)(247,602)(248,601)
(249,600)(250,599)(251,598)(252,597)(253,596)(254,606)(255,616)(256,615)
(257,614)(258,613)(259,612)(260,611)(261,610)(262,609)(263,608)(264,607)
(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, 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)(529,673)(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)(551,684)(552,683)(553,693)(554,692)
(555,691)(556,690)(557,689)(558,688)(559,687)(560,686)(561,685)(562,695)
(563,694)(564,704)(565,703)(566,702)(567,701)(568,700)(569,699)(570,698)
(571,697)(572,696)(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)
(595,640)(596,639)(597,649)(598,648)(599,647)(600,646)(601,645)(602,644)
(603,643)(604,642)(605,641)(606,651)(607,650)(608,660)(609,659)(610,658)
(611,657)(612,656)(613,655)(614,654)(615,653)(616,652);;
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)
( 89,276)( 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)(133,320)(134,321)(135,322)(136,323)
(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)(144,309)
(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)(152,317)
(153,318)(154,319)(155,342)(156,343)(157,344)(158,345)(159,346)(160,347)
(161,348)(162,349)(163,350)(164,351)(165,352)(166,331)(167,332)(168,333)
(169,334)(170,335)(171,336)(172,337)(173,338)(174,339)(175,340)(176,341)
(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)
(441,628)(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)(485,672)(486,673)(487,674)(488,675)
(489,676)(490,677)(491,678)(492,679)(493,680)(494,681)(495,682)(496,661)
(497,662)(498,663)(499,664)(500,665)(501,666)(502,667)(503,668)(504,669)
(505,670)(506,671)(507,694)(508,695)(509,696)(510,697)(511,698)(512,699)
(513,700)(514,701)(515,702)(516,703)(517,704)(518,683)(519,684)(520,685)
(521,686)(522,687)(523,688)(524,689)(525,690)(526,691)(527,692)(528,693);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*s2*s1*s0*s1*s0*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 ];;
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)( 45,408)( 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)( 67,419)( 68,429)( 69,428)( 70,427)( 71,426)
( 72,425)( 73,424)( 74,423)( 75,422)( 76,421)( 77,420)( 78,430)( 79,440)
( 80,439)( 81,438)( 82,437)( 83,436)( 84,435)( 85,434)( 86,433)( 87,432)
( 88,431)( 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)(199,562)
(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)(221,584)(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)(243,595)(244,605)(245,604)(246,603)(247,602)
(248,601)(249,600)(250,599)(251,598)(252,597)(253,596)(254,606)(255,616)
(256,615)(257,614)(258,613)(259,612)(260,611)(261,610)(262,609)(263,608)
(264,607)(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, 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)(529,673)
(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)(551,684)(552,683)(553,693)
(554,692)(555,691)(556,690)(557,689)(558,688)(559,687)(560,686)(561,685)
(562,695)(563,694)(564,704)(565,703)(566,702)(567,701)(568,700)(569,699)
(570,698)(571,697)(572,696)(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)(595,640)(596,639)(597,649)(598,648)(599,647)(600,646)(601,645)
(602,644)(603,643)(604,642)(605,641)(606,651)(607,650)(608,660)(609,659)
(610,658)(611,657)(612,656)(613,655)(614,654)(615,653)(616,652);
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)( 89,276)( 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)(133,320)(134,321)(135,322)
(136,323)(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)
(144,309)(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)
(152,317)(153,318)(154,319)(155,342)(156,343)(157,344)(158,345)(159,346)
(160,347)(161,348)(162,349)(163,350)(164,351)(165,352)(166,331)(167,332)
(168,333)(169,334)(170,335)(171,336)(172,337)(173,338)(174,339)(175,340)
(176,341)(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)(441,628)(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)(485,672)(486,673)(487,674)
(488,675)(489,676)(490,677)(491,678)(492,679)(493,680)(494,681)(495,682)
(496,661)(497,662)(498,663)(499,664)(500,665)(501,666)(502,667)(503,668)
(504,669)(505,670)(506,671)(507,694)(508,695)(509,696)(510,697)(511,698)
(512,699)(513,700)(514,701)(515,702)(516,703)(517,704)(518,683)(519,684)
(520,685)(521,686)(522,687)(523,688)(524,689)(525,690)(526,691)(527,692)
(528,693);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*s2*s1*s0*s1*s0*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 >;
References : None.
to this polytope