Polytope of Type {174,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {174,4}*1392b
if this polytope has a name.
Group : SmallGroup(1392,188)
Rank : 3
Schlafli Type : {174,4}
Number of vertices, edges, etc : 174, 348, 4
Order of s0s1s2 : 174
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-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 : {87,4}*696
29-fold quotients : {6,4}*48c
58-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,113)( 6,114)( 7,116)( 8,115)( 9,109)( 10,110)( 11,112)
( 12,111)( 13,105)( 14,106)( 15,108)( 16,107)( 17,101)( 18,102)( 19,104)
( 20,103)( 21, 97)( 22, 98)( 23,100)( 24, 99)( 25, 93)( 26, 94)( 27, 96)
( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)( 33, 85)( 34, 86)( 35, 88)
( 36, 87)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)
( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 69)( 50, 70)( 51, 72)
( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)( 59, 64)
( 60, 63)(117,233)(118,234)(119,236)(120,235)(121,345)(122,346)(123,348)
(124,347)(125,341)(126,342)(127,344)(128,343)(129,337)(130,338)(131,340)
(132,339)(133,333)(134,334)(135,336)(136,335)(137,329)(138,330)(139,332)
(140,331)(141,325)(142,326)(143,328)(144,327)(145,321)(146,322)(147,324)
(148,323)(149,317)(150,318)(151,320)(152,319)(153,313)(154,314)(155,316)
(156,315)(157,309)(158,310)(159,312)(160,311)(161,305)(162,306)(163,308)
(164,307)(165,301)(166,302)(167,304)(168,303)(169,297)(170,298)(171,300)
(172,299)(173,293)(174,294)(175,296)(176,295)(177,289)(178,290)(179,292)
(180,291)(181,285)(182,286)(183,288)(184,287)(185,281)(186,282)(187,284)
(188,283)(189,277)(190,278)(191,280)(192,279)(193,273)(194,274)(195,276)
(196,275)(197,269)(198,270)(199,272)(200,271)(201,265)(202,266)(203,268)
(204,267)(205,261)(206,262)(207,264)(208,263)(209,257)(210,258)(211,260)
(212,259)(213,253)(214,254)(215,256)(216,255)(217,249)(218,250)(219,252)
(220,251)(221,245)(222,246)(223,248)(224,247)(225,241)(226,242)(227,244)
(228,243)(229,237)(230,238)(231,240)(232,239)(351,352)(353,461)(354,462)
(355,464)(356,463)(357,457)(358,458)(359,460)(360,459)(361,453)(362,454)
(363,456)(364,455)(365,449)(366,450)(367,452)(368,451)(369,445)(370,446)
(371,448)(372,447)(373,441)(374,442)(375,444)(376,443)(377,437)(378,438)
(379,440)(380,439)(381,433)(382,434)(383,436)(384,435)(385,429)(386,430)
(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)(393,421)(394,422)
(395,424)(396,423)(397,417)(398,418)(399,420)(400,419)(401,413)(402,414)
(403,416)(404,415)(405,409)(406,410)(407,412)(408,411)(465,581)(466,582)
(467,584)(468,583)(469,693)(470,694)(471,696)(472,695)(473,689)(474,690)
(475,692)(476,691)(477,685)(478,686)(479,688)(480,687)(481,681)(482,682)
(483,684)(484,683)(485,677)(486,678)(487,680)(488,679)(489,673)(490,674)
(491,676)(492,675)(493,669)(494,670)(495,672)(496,671)(497,665)(498,666)
(499,668)(500,667)(501,661)(502,662)(503,664)(504,663)(505,657)(506,658)
(507,660)(508,659)(509,653)(510,654)(511,656)(512,655)(513,649)(514,650)
(515,652)(516,651)(517,645)(518,646)(519,648)(520,647)(521,641)(522,642)
(523,644)(524,643)(525,637)(526,638)(527,640)(528,639)(529,633)(530,634)
(531,636)(532,635)(533,629)(534,630)(535,632)(536,631)(537,625)(538,626)
(539,628)(540,627)(541,621)(542,622)(543,624)(544,623)(545,617)(546,618)
(547,620)(548,619)(549,613)(550,614)(551,616)(552,615)(553,609)(554,610)
(555,612)(556,611)(557,605)(558,606)(559,608)(560,607)(561,601)(562,602)
(563,604)(564,603)(565,597)(566,598)(567,600)(568,599)(569,593)(570,594)
(571,596)(572,595)(573,589)(574,590)(575,592)(576,591)(577,585)(578,586)
(579,588)(580,587);;
s1 := ( 1,469)( 2,472)( 3,471)( 4,470)( 5,465)( 6,468)( 7,467)( 8,466)
( 9,577)( 10,580)( 11,579)( 12,578)( 13,573)( 14,576)( 15,575)( 16,574)
( 17,569)( 18,572)( 19,571)( 20,570)( 21,565)( 22,568)( 23,567)( 24,566)
( 25,561)( 26,564)( 27,563)( 28,562)( 29,557)( 30,560)( 31,559)( 32,558)
( 33,553)( 34,556)( 35,555)( 36,554)( 37,549)( 38,552)( 39,551)( 40,550)
( 41,545)( 42,548)( 43,547)( 44,546)( 45,541)( 46,544)( 47,543)( 48,542)
( 49,537)( 50,540)( 51,539)( 52,538)( 53,533)( 54,536)( 55,535)( 56,534)
( 57,529)( 58,532)( 59,531)( 60,530)( 61,525)( 62,528)( 63,527)( 64,526)
( 65,521)( 66,524)( 67,523)( 68,522)( 69,517)( 70,520)( 71,519)( 72,518)
( 73,513)( 74,516)( 75,515)( 76,514)( 77,509)( 78,512)( 79,511)( 80,510)
( 81,505)( 82,508)( 83,507)( 84,506)( 85,501)( 86,504)( 87,503)( 88,502)
( 89,497)( 90,500)( 91,499)( 92,498)( 93,493)( 94,496)( 95,495)( 96,494)
( 97,489)( 98,492)( 99,491)(100,490)(101,485)(102,488)(103,487)(104,486)
(105,481)(106,484)(107,483)(108,482)(109,477)(110,480)(111,479)(112,478)
(113,473)(114,476)(115,475)(116,474)(117,353)(118,356)(119,355)(120,354)
(121,349)(122,352)(123,351)(124,350)(125,461)(126,464)(127,463)(128,462)
(129,457)(130,460)(131,459)(132,458)(133,453)(134,456)(135,455)(136,454)
(137,449)(138,452)(139,451)(140,450)(141,445)(142,448)(143,447)(144,446)
(145,441)(146,444)(147,443)(148,442)(149,437)(150,440)(151,439)(152,438)
(153,433)(154,436)(155,435)(156,434)(157,429)(158,432)(159,431)(160,430)
(161,425)(162,428)(163,427)(164,426)(165,421)(166,424)(167,423)(168,422)
(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)(176,414)
(177,409)(178,412)(179,411)(180,410)(181,405)(182,408)(183,407)(184,406)
(185,401)(186,404)(187,403)(188,402)(189,397)(190,400)(191,399)(192,398)
(193,393)(194,396)(195,395)(196,394)(197,389)(198,392)(199,391)(200,390)
(201,385)(202,388)(203,387)(204,386)(205,381)(206,384)(207,383)(208,382)
(209,377)(210,380)(211,379)(212,378)(213,373)(214,376)(215,375)(216,374)
(217,369)(218,372)(219,371)(220,370)(221,365)(222,368)(223,367)(224,366)
(225,361)(226,364)(227,363)(228,362)(229,357)(230,360)(231,359)(232,358)
(233,585)(234,588)(235,587)(236,586)(237,581)(238,584)(239,583)(240,582)
(241,693)(242,696)(243,695)(244,694)(245,689)(246,692)(247,691)(248,690)
(249,685)(250,688)(251,687)(252,686)(253,681)(254,684)(255,683)(256,682)
(257,677)(258,680)(259,679)(260,678)(261,673)(262,676)(263,675)(264,674)
(265,669)(266,672)(267,671)(268,670)(269,665)(270,668)(271,667)(272,666)
(273,661)(274,664)(275,663)(276,662)(277,657)(278,660)(279,659)(280,658)
(281,653)(282,656)(283,655)(284,654)(285,649)(286,652)(287,651)(288,650)
(289,645)(290,648)(291,647)(292,646)(293,641)(294,644)(295,643)(296,642)
(297,637)(298,640)(299,639)(300,638)(301,633)(302,636)(303,635)(304,634)
(305,629)(306,632)(307,631)(308,630)(309,625)(310,628)(311,627)(312,626)
(313,621)(314,624)(315,623)(316,622)(317,617)(318,620)(319,619)(320,618)
(321,613)(322,616)(323,615)(324,614)(325,609)(326,612)(327,611)(328,610)
(329,605)(330,608)(331,607)(332,606)(333,601)(334,604)(335,603)(336,602)
(337,597)(338,600)(339,599)(340,598)(341,593)(342,596)(343,595)(344,594)
(345,589)(346,592)(347,591)(348,590);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)
(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)
(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)
(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)
(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)
(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)
(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)
(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)
(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)
(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)
(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)
(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)
(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)
(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)
(689,690)(691,692)(693,694)(695,696);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(696)!( 3, 4)( 5,113)( 6,114)( 7,116)( 8,115)( 9,109)( 10,110)
( 11,112)( 12,111)( 13,105)( 14,106)( 15,108)( 16,107)( 17,101)( 18,102)
( 19,104)( 20,103)( 21, 97)( 22, 98)( 23,100)( 24, 99)( 25, 93)( 26, 94)
( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)( 33, 85)( 34, 86)
( 35, 88)( 36, 87)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)
( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 69)( 50, 70)
( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)
( 59, 64)( 60, 63)(117,233)(118,234)(119,236)(120,235)(121,345)(122,346)
(123,348)(124,347)(125,341)(126,342)(127,344)(128,343)(129,337)(130,338)
(131,340)(132,339)(133,333)(134,334)(135,336)(136,335)(137,329)(138,330)
(139,332)(140,331)(141,325)(142,326)(143,328)(144,327)(145,321)(146,322)
(147,324)(148,323)(149,317)(150,318)(151,320)(152,319)(153,313)(154,314)
(155,316)(156,315)(157,309)(158,310)(159,312)(160,311)(161,305)(162,306)
(163,308)(164,307)(165,301)(166,302)(167,304)(168,303)(169,297)(170,298)
(171,300)(172,299)(173,293)(174,294)(175,296)(176,295)(177,289)(178,290)
(179,292)(180,291)(181,285)(182,286)(183,288)(184,287)(185,281)(186,282)
(187,284)(188,283)(189,277)(190,278)(191,280)(192,279)(193,273)(194,274)
(195,276)(196,275)(197,269)(198,270)(199,272)(200,271)(201,265)(202,266)
(203,268)(204,267)(205,261)(206,262)(207,264)(208,263)(209,257)(210,258)
(211,260)(212,259)(213,253)(214,254)(215,256)(216,255)(217,249)(218,250)
(219,252)(220,251)(221,245)(222,246)(223,248)(224,247)(225,241)(226,242)
(227,244)(228,243)(229,237)(230,238)(231,240)(232,239)(351,352)(353,461)
(354,462)(355,464)(356,463)(357,457)(358,458)(359,460)(360,459)(361,453)
(362,454)(363,456)(364,455)(365,449)(366,450)(367,452)(368,451)(369,445)
(370,446)(371,448)(372,447)(373,441)(374,442)(375,444)(376,443)(377,437)
(378,438)(379,440)(380,439)(381,433)(382,434)(383,436)(384,435)(385,429)
(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)(393,421)
(394,422)(395,424)(396,423)(397,417)(398,418)(399,420)(400,419)(401,413)
(402,414)(403,416)(404,415)(405,409)(406,410)(407,412)(408,411)(465,581)
(466,582)(467,584)(468,583)(469,693)(470,694)(471,696)(472,695)(473,689)
(474,690)(475,692)(476,691)(477,685)(478,686)(479,688)(480,687)(481,681)
(482,682)(483,684)(484,683)(485,677)(486,678)(487,680)(488,679)(489,673)
(490,674)(491,676)(492,675)(493,669)(494,670)(495,672)(496,671)(497,665)
(498,666)(499,668)(500,667)(501,661)(502,662)(503,664)(504,663)(505,657)
(506,658)(507,660)(508,659)(509,653)(510,654)(511,656)(512,655)(513,649)
(514,650)(515,652)(516,651)(517,645)(518,646)(519,648)(520,647)(521,641)
(522,642)(523,644)(524,643)(525,637)(526,638)(527,640)(528,639)(529,633)
(530,634)(531,636)(532,635)(533,629)(534,630)(535,632)(536,631)(537,625)
(538,626)(539,628)(540,627)(541,621)(542,622)(543,624)(544,623)(545,617)
(546,618)(547,620)(548,619)(549,613)(550,614)(551,616)(552,615)(553,609)
(554,610)(555,612)(556,611)(557,605)(558,606)(559,608)(560,607)(561,601)
(562,602)(563,604)(564,603)(565,597)(566,598)(567,600)(568,599)(569,593)
(570,594)(571,596)(572,595)(573,589)(574,590)(575,592)(576,591)(577,585)
(578,586)(579,588)(580,587);
s1 := Sym(696)!( 1,469)( 2,472)( 3,471)( 4,470)( 5,465)( 6,468)( 7,467)
( 8,466)( 9,577)( 10,580)( 11,579)( 12,578)( 13,573)( 14,576)( 15,575)
( 16,574)( 17,569)( 18,572)( 19,571)( 20,570)( 21,565)( 22,568)( 23,567)
( 24,566)( 25,561)( 26,564)( 27,563)( 28,562)( 29,557)( 30,560)( 31,559)
( 32,558)( 33,553)( 34,556)( 35,555)( 36,554)( 37,549)( 38,552)( 39,551)
( 40,550)( 41,545)( 42,548)( 43,547)( 44,546)( 45,541)( 46,544)( 47,543)
( 48,542)( 49,537)( 50,540)( 51,539)( 52,538)( 53,533)( 54,536)( 55,535)
( 56,534)( 57,529)( 58,532)( 59,531)( 60,530)( 61,525)( 62,528)( 63,527)
( 64,526)( 65,521)( 66,524)( 67,523)( 68,522)( 69,517)( 70,520)( 71,519)
( 72,518)( 73,513)( 74,516)( 75,515)( 76,514)( 77,509)( 78,512)( 79,511)
( 80,510)( 81,505)( 82,508)( 83,507)( 84,506)( 85,501)( 86,504)( 87,503)
( 88,502)( 89,497)( 90,500)( 91,499)( 92,498)( 93,493)( 94,496)( 95,495)
( 96,494)( 97,489)( 98,492)( 99,491)(100,490)(101,485)(102,488)(103,487)
(104,486)(105,481)(106,484)(107,483)(108,482)(109,477)(110,480)(111,479)
(112,478)(113,473)(114,476)(115,475)(116,474)(117,353)(118,356)(119,355)
(120,354)(121,349)(122,352)(123,351)(124,350)(125,461)(126,464)(127,463)
(128,462)(129,457)(130,460)(131,459)(132,458)(133,453)(134,456)(135,455)
(136,454)(137,449)(138,452)(139,451)(140,450)(141,445)(142,448)(143,447)
(144,446)(145,441)(146,444)(147,443)(148,442)(149,437)(150,440)(151,439)
(152,438)(153,433)(154,436)(155,435)(156,434)(157,429)(158,432)(159,431)
(160,430)(161,425)(162,428)(163,427)(164,426)(165,421)(166,424)(167,423)
(168,422)(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)
(176,414)(177,409)(178,412)(179,411)(180,410)(181,405)(182,408)(183,407)
(184,406)(185,401)(186,404)(187,403)(188,402)(189,397)(190,400)(191,399)
(192,398)(193,393)(194,396)(195,395)(196,394)(197,389)(198,392)(199,391)
(200,390)(201,385)(202,388)(203,387)(204,386)(205,381)(206,384)(207,383)
(208,382)(209,377)(210,380)(211,379)(212,378)(213,373)(214,376)(215,375)
(216,374)(217,369)(218,372)(219,371)(220,370)(221,365)(222,368)(223,367)
(224,366)(225,361)(226,364)(227,363)(228,362)(229,357)(230,360)(231,359)
(232,358)(233,585)(234,588)(235,587)(236,586)(237,581)(238,584)(239,583)
(240,582)(241,693)(242,696)(243,695)(244,694)(245,689)(246,692)(247,691)
(248,690)(249,685)(250,688)(251,687)(252,686)(253,681)(254,684)(255,683)
(256,682)(257,677)(258,680)(259,679)(260,678)(261,673)(262,676)(263,675)
(264,674)(265,669)(266,672)(267,671)(268,670)(269,665)(270,668)(271,667)
(272,666)(273,661)(274,664)(275,663)(276,662)(277,657)(278,660)(279,659)
(280,658)(281,653)(282,656)(283,655)(284,654)(285,649)(286,652)(287,651)
(288,650)(289,645)(290,648)(291,647)(292,646)(293,641)(294,644)(295,643)
(296,642)(297,637)(298,640)(299,639)(300,638)(301,633)(302,636)(303,635)
(304,634)(305,629)(306,632)(307,631)(308,630)(309,625)(310,628)(311,627)
(312,626)(313,621)(314,624)(315,623)(316,622)(317,617)(318,620)(319,619)
(320,618)(321,613)(322,616)(323,615)(324,614)(325,609)(326,612)(327,611)
(328,610)(329,605)(330,608)(331,607)(332,606)(333,601)(334,604)(335,603)
(336,602)(337,597)(338,600)(339,599)(340,598)(341,593)(342,596)(343,595)
(344,594)(345,589)(346,592)(347,591)(348,590);
s2 := Sym(696)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)
(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)
(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)
(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)
(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)
(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)
(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)
(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)
(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)
(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)
(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)
(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)
(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)
(687,688)(689,690)(691,692)(693,694)(695,696);
poly := sub<Sym(696)|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,
s2*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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