Polytope of Type {32,28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,28}*1792b
if this polytope has a name.
Group : SmallGroup(1792,90242)
Rank : 3
Schlafli Type : {32,28}
Number of vertices, edges, etc : 32, 448, 28
Order of s0s1s2 : 224
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 : {16,28}*896a
4-fold quotients : {8,28}*448a, {16,14}*448
7-fold quotients : {32,4}*256b
8-fold quotients : {4,28}*224, {8,14}*224
14-fold quotients : {16,4}*128a
16-fold quotients : {2,28}*112, {4,14}*112
28-fold quotients : {8,4}*64a, {16,2}*64
32-fold quotients : {2,14}*56
56-fold quotients : {4,4}*32, {8,2}*32
64-fold quotients : {2,7}*28
112-fold quotients : {2,4}*16, {4,2}*16
224-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,449)( 2,450)( 3,451)( 4,452)( 5,453)( 6,454)( 7,455)( 8,456)
( 9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,470)( 16,471)
( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)( 24,465)
( 25,466)( 26,467)( 27,468)( 28,469)( 29,491)( 30,492)( 31,493)( 32,494)
( 33,495)( 34,496)( 35,497)( 36,498)( 37,499)( 38,500)( 39,501)( 40,502)
( 41,503)( 42,504)( 43,477)( 44,478)( 45,479)( 46,480)( 47,481)( 48,482)
( 49,483)( 50,484)( 51,485)( 52,486)( 53,487)( 54,488)( 55,489)( 56,490)
( 57,512)( 58,513)( 59,514)( 60,515)( 61,516)( 62,517)( 63,518)( 64,505)
( 65,506)( 66,507)( 67,508)( 68,509)( 69,510)( 70,511)( 71,519)( 72,520)
( 73,521)( 74,522)( 75,523)( 76,524)( 77,525)( 78,526)( 79,527)( 80,528)
( 81,529)( 82,530)( 83,531)( 84,532)( 85,554)( 86,555)( 87,556)( 88,557)
( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)
( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)
(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)
(113,589)(114,590)(115,591)(116,592)(117,593)(118,594)(119,595)(120,596)
(121,597)(122,598)(123,599)(124,600)(125,601)(126,602)(127,610)(128,611)
(129,612)(130,613)(131,614)(132,615)(133,616)(134,603)(135,604)(136,605)
(137,606)(138,607)(139,608)(140,609)(141,561)(142,562)(143,563)(144,564)
(145,565)(146,566)(147,567)(148,568)(149,569)(150,570)(151,571)(152,572)
(153,573)(154,574)(155,582)(156,583)(157,584)(158,585)(159,586)(160,587)
(161,588)(162,575)(163,576)(164,577)(165,578)(166,579)(167,580)(168,581)
(169,652)(170,653)(171,654)(172,655)(173,656)(174,657)(175,658)(176,645)
(177,646)(178,647)(179,648)(180,649)(181,650)(182,651)(183,659)(184,660)
(185,661)(186,662)(187,663)(188,664)(189,665)(190,666)(191,667)(192,668)
(193,669)(194,670)(195,671)(196,672)(197,624)(198,625)(199,626)(200,627)
(201,628)(202,629)(203,630)(204,617)(205,618)(206,619)(207,620)(208,621)
(209,622)(210,623)(211,631)(212,632)(213,633)(214,634)(215,635)(216,636)
(217,637)(218,638)(219,639)(220,640)(221,641)(222,642)(223,643)(224,644)
(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)
(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,694)(240,695)
(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)
(249,690)(250,691)(251,692)(252,693)(253,715)(254,716)(255,717)(256,718)
(257,719)(258,720)(259,721)(260,722)(261,723)(262,724)(263,725)(264,726)
(265,727)(266,728)(267,701)(268,702)(269,703)(270,704)(271,705)(272,706)
(273,707)(274,708)(275,709)(276,710)(277,711)(278,712)(279,713)(280,714)
(281,736)(282,737)(283,738)(284,739)(285,740)(286,741)(287,742)(288,729)
(289,730)(290,731)(291,732)(292,733)(293,734)(294,735)(295,743)(296,744)
(297,745)(298,746)(299,747)(300,748)(301,749)(302,750)(303,751)(304,752)
(305,753)(306,754)(307,755)(308,756)(309,778)(310,779)(311,780)(312,781)
(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)
(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)
(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)
(337,813)(338,814)(339,815)(340,816)(341,817)(342,818)(343,819)(344,820)
(345,821)(346,822)(347,823)(348,824)(349,825)(350,826)(351,834)(352,835)
(353,836)(354,837)(355,838)(356,839)(357,840)(358,827)(359,828)(360,829)
(361,830)(362,831)(363,832)(364,833)(365,785)(366,786)(367,787)(368,788)
(369,789)(370,790)(371,791)(372,792)(373,793)(374,794)(375,795)(376,796)
(377,797)(378,798)(379,806)(380,807)(381,808)(382,809)(383,810)(384,811)
(385,812)(386,799)(387,800)(388,801)(389,802)(390,803)(391,804)(392,805)
(393,876)(394,877)(395,878)(396,879)(397,880)(398,881)(399,882)(400,869)
(401,870)(402,871)(403,872)(404,873)(405,874)(406,875)(407,883)(408,884)
(409,885)(410,886)(411,887)(412,888)(413,889)(414,890)(415,891)(416,892)
(417,893)(418,894)(419,895)(420,896)(421,848)(422,849)(423,850)(424,851)
(425,852)(426,853)(427,854)(428,841)(429,842)(430,843)(431,844)(432,845)
(433,846)(434,847)(435,855)(436,856)(437,857)(438,858)(439,859)(440,860)
(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)(448,868);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)
( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 29, 43)( 30, 49)( 31, 48)
( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)
( 40, 53)( 41, 52)( 42, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)
( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)( 92,106)
( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)(113,141)(114,147)
(115,146)(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)(122,153)
(123,152)(124,151)(125,150)(126,149)(127,162)(128,168)(129,167)(130,166)
(131,165)(132,164)(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)
(139,157)(140,156)(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)
(175,198)(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)
(183,218)(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)
(191,217)(192,216)(193,215)(194,214)(195,213)(196,212)(225,281)(226,287)
(227,286)(228,285)(229,284)(230,283)(231,282)(232,288)(233,294)(234,293)
(235,292)(236,291)(237,290)(238,289)(239,302)(240,308)(241,307)(242,306)
(243,305)(244,304)(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)
(251,297)(252,296)(253,323)(254,329)(255,328)(256,327)(257,326)(258,325)
(259,324)(260,330)(261,336)(262,335)(263,334)(264,333)(265,332)(266,331)
(267,309)(268,315)(269,314)(270,313)(271,312)(272,311)(273,310)(274,316)
(275,322)(276,321)(277,320)(278,319)(279,318)(280,317)(337,421)(338,427)
(339,426)(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)(346,433)
(347,432)(348,431)(349,430)(350,429)(351,442)(352,448)(353,447)(354,446)
(355,445)(356,444)(357,443)(358,435)(359,441)(360,440)(361,439)(362,438)
(363,437)(364,436)(365,393)(366,399)(367,398)(368,397)(369,396)(370,395)
(371,394)(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)(378,401)
(379,414)(380,420)(381,419)(382,418)(383,417)(384,416)(385,415)(386,407)
(387,413)(388,412)(389,411)(390,410)(391,409)(392,408)(449,561)(450,567)
(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)(458,573)
(459,572)(460,571)(461,570)(462,569)(463,582)(464,588)(465,587)(466,586)
(467,585)(468,584)(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)
(475,577)(476,576)(477,603)(478,609)(479,608)(480,607)(481,606)(482,605)
(483,604)(484,610)(485,616)(486,615)(487,614)(488,613)(489,612)(490,611)
(491,589)(492,595)(493,594)(494,593)(495,592)(496,591)(497,590)(498,596)
(499,602)(500,601)(501,600)(502,599)(503,598)(504,597)(505,617)(506,623)
(507,622)(508,621)(509,620)(510,619)(511,618)(512,624)(513,630)(514,629)
(515,628)(516,627)(517,626)(518,625)(519,638)(520,644)(521,643)(522,642)
(523,641)(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)
(531,633)(532,632)(533,659)(534,665)(535,664)(536,663)(537,662)(538,661)
(539,660)(540,666)(541,672)(542,671)(543,670)(544,669)(545,668)(546,667)
(547,645)(548,651)(549,650)(550,649)(551,648)(552,647)(553,646)(554,652)
(555,658)(556,657)(557,656)(558,655)(559,654)(560,653)(673,848)(674,854)
(675,853)(676,852)(677,851)(678,850)(679,849)(680,841)(681,847)(682,846)
(683,845)(684,844)(685,843)(686,842)(687,855)(688,861)(689,860)(690,859)
(691,858)(692,857)(693,856)(694,862)(695,868)(696,867)(697,866)(698,865)
(699,864)(700,863)(701,890)(702,896)(703,895)(704,894)(705,893)(706,892)
(707,891)(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)(714,884)
(715,876)(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)(722,869)
(723,875)(724,874)(725,873)(726,872)(727,871)(728,870)(729,792)(730,798)
(731,797)(732,796)(733,795)(734,794)(735,793)(736,785)(737,791)(738,790)
(739,789)(740,788)(741,787)(742,786)(743,799)(744,805)(745,804)(746,803)
(747,802)(748,801)(749,800)(750,806)(751,812)(752,811)(753,810)(754,809)
(755,808)(756,807)(757,834)(758,840)(759,839)(760,838)(761,837)(762,836)
(763,835)(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)(770,828)
(771,820)(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)(778,813)
(779,819)(780,818)(781,817)(782,816)(783,815)(784,814);;
s2 := ( 1,226)( 2,225)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)( 8,233)
( 9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)( 24,252)
( 25,251)( 26,250)( 27,249)( 28,248)( 29,254)( 30,253)( 31,259)( 32,258)
( 33,257)( 34,256)( 35,255)( 36,261)( 37,260)( 38,266)( 39,265)( 40,264)
( 41,263)( 42,262)( 43,268)( 44,267)( 45,273)( 46,272)( 47,271)( 48,270)
( 49,269)( 50,275)( 51,274)( 52,280)( 53,279)( 54,278)( 55,277)( 56,276)
( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)( 64,289)
( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,296)( 72,295)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)( 80,308)
( 81,307)( 82,306)( 83,305)( 84,304)( 85,310)( 86,309)( 87,315)( 88,314)
( 89,313)( 90,312)( 91,311)( 92,317)( 93,316)( 94,322)( 95,321)( 96,320)
( 97,319)( 98,318)( 99,324)(100,323)(101,329)(102,328)(103,327)(104,326)
(105,325)(106,331)(107,330)(108,336)(109,335)(110,334)(111,333)(112,332)
(113,345)(114,344)(115,350)(116,349)(117,348)(118,347)(119,346)(120,338)
(121,337)(122,343)(123,342)(124,341)(125,340)(126,339)(127,359)(128,358)
(129,364)(130,363)(131,362)(132,361)(133,360)(134,352)(135,351)(136,357)
(137,356)(138,355)(139,354)(140,353)(141,373)(142,372)(143,378)(144,377)
(145,376)(146,375)(147,374)(148,366)(149,365)(150,371)(151,370)(152,369)
(153,368)(154,367)(155,387)(156,386)(157,392)(158,391)(159,390)(160,389)
(161,388)(162,380)(163,379)(164,385)(165,384)(166,383)(167,382)(168,381)
(169,401)(170,400)(171,406)(172,405)(173,404)(174,403)(175,402)(176,394)
(177,393)(178,399)(179,398)(180,397)(181,396)(182,395)(183,415)(184,414)
(185,420)(186,419)(187,418)(188,417)(189,416)(190,408)(191,407)(192,413)
(193,412)(194,411)(195,410)(196,409)(197,429)(198,428)(199,434)(200,433)
(201,432)(202,431)(203,430)(204,422)(205,421)(206,427)(207,426)(208,425)
(209,424)(210,423)(211,443)(212,442)(213,448)(214,447)(215,446)(216,445)
(217,444)(218,436)(219,435)(220,441)(221,440)(222,439)(223,438)(224,437)
(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)(456,681)
(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,688)(464,687)
(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)(472,700)
(473,699)(474,698)(475,697)(476,696)(477,702)(478,701)(479,707)(480,706)
(481,705)(482,704)(483,703)(484,709)(485,708)(486,714)(487,713)(488,712)
(489,711)(490,710)(491,716)(492,715)(493,721)(494,720)(495,719)(496,718)
(497,717)(498,723)(499,722)(500,728)(501,727)(502,726)(503,725)(504,724)
(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)(512,737)
(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(519,744)(520,743)
(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)(528,756)
(529,755)(530,754)(531,753)(532,752)(533,758)(534,757)(535,763)(536,762)
(537,761)(538,760)(539,759)(540,765)(541,764)(542,770)(543,769)(544,768)
(545,767)(546,766)(547,772)(548,771)(549,777)(550,776)(551,775)(552,774)
(553,773)(554,779)(555,778)(556,784)(557,783)(558,782)(559,781)(560,780)
(561,793)(562,792)(563,798)(564,797)(565,796)(566,795)(567,794)(568,786)
(569,785)(570,791)(571,790)(572,789)(573,788)(574,787)(575,807)(576,806)
(577,812)(578,811)(579,810)(580,809)(581,808)(582,800)(583,799)(584,805)
(585,804)(586,803)(587,802)(588,801)(589,821)(590,820)(591,826)(592,825)
(593,824)(594,823)(595,822)(596,814)(597,813)(598,819)(599,818)(600,817)
(601,816)(602,815)(603,835)(604,834)(605,840)(606,839)(607,838)(608,837)
(609,836)(610,828)(611,827)(612,833)(613,832)(614,831)(615,830)(616,829)
(617,849)(618,848)(619,854)(620,853)(621,852)(622,851)(623,850)(624,842)
(625,841)(626,847)(627,846)(628,845)(629,844)(630,843)(631,863)(632,862)
(633,868)(634,867)(635,866)(636,865)(637,864)(638,856)(639,855)(640,861)
(641,860)(642,859)(643,858)(644,857)(645,877)(646,876)(647,882)(648,881)
(649,880)(650,879)(651,878)(652,870)(653,869)(654,875)(655,874)(656,873)
(657,872)(658,871)(659,891)(660,890)(661,896)(662,895)(663,894)(664,893)
(665,892)(666,884)(667,883)(668,889)(669,888)(670,887)(671,886)(672,885);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(896)!( 1,449)( 2,450)( 3,451)( 4,452)( 5,453)( 6,454)( 7,455)
( 8,456)( 9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,470)
( 16,471)( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)
( 24,465)( 25,466)( 26,467)( 27,468)( 28,469)( 29,491)( 30,492)( 31,493)
( 32,494)( 33,495)( 34,496)( 35,497)( 36,498)( 37,499)( 38,500)( 39,501)
( 40,502)( 41,503)( 42,504)( 43,477)( 44,478)( 45,479)( 46,480)( 47,481)
( 48,482)( 49,483)( 50,484)( 51,485)( 52,486)( 53,487)( 54,488)( 55,489)
( 56,490)( 57,512)( 58,513)( 59,514)( 60,515)( 61,516)( 62,517)( 63,518)
( 64,505)( 65,506)( 66,507)( 67,508)( 68,509)( 69,510)( 70,511)( 71,519)
( 72,520)( 73,521)( 74,522)( 75,523)( 76,524)( 77,525)( 78,526)( 79,527)
( 80,528)( 81,529)( 82,530)( 83,531)( 84,532)( 85,554)( 86,555)( 87,556)
( 88,557)( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)
( 96,551)( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)
(104,545)(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)
(112,539)(113,589)(114,590)(115,591)(116,592)(117,593)(118,594)(119,595)
(120,596)(121,597)(122,598)(123,599)(124,600)(125,601)(126,602)(127,610)
(128,611)(129,612)(130,613)(131,614)(132,615)(133,616)(134,603)(135,604)
(136,605)(137,606)(138,607)(139,608)(140,609)(141,561)(142,562)(143,563)
(144,564)(145,565)(146,566)(147,567)(148,568)(149,569)(150,570)(151,571)
(152,572)(153,573)(154,574)(155,582)(156,583)(157,584)(158,585)(159,586)
(160,587)(161,588)(162,575)(163,576)(164,577)(165,578)(166,579)(167,580)
(168,581)(169,652)(170,653)(171,654)(172,655)(173,656)(174,657)(175,658)
(176,645)(177,646)(178,647)(179,648)(180,649)(181,650)(182,651)(183,659)
(184,660)(185,661)(186,662)(187,663)(188,664)(189,665)(190,666)(191,667)
(192,668)(193,669)(194,670)(195,671)(196,672)(197,624)(198,625)(199,626)
(200,627)(201,628)(202,629)(203,630)(204,617)(205,618)(206,619)(207,620)
(208,621)(209,622)(210,623)(211,631)(212,632)(213,633)(214,634)(215,635)
(216,636)(217,637)(218,638)(219,639)(220,640)(221,641)(222,642)(223,643)
(224,644)(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)
(232,680)(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,694)
(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)
(248,689)(249,690)(250,691)(251,692)(252,693)(253,715)(254,716)(255,717)
(256,718)(257,719)(258,720)(259,721)(260,722)(261,723)(262,724)(263,725)
(264,726)(265,727)(266,728)(267,701)(268,702)(269,703)(270,704)(271,705)
(272,706)(273,707)(274,708)(275,709)(276,710)(277,711)(278,712)(279,713)
(280,714)(281,736)(282,737)(283,738)(284,739)(285,740)(286,741)(287,742)
(288,729)(289,730)(290,731)(291,732)(292,733)(293,734)(294,735)(295,743)
(296,744)(297,745)(298,746)(299,747)(300,748)(301,749)(302,750)(303,751)
(304,752)(305,753)(306,754)(307,755)(308,756)(309,778)(310,779)(311,780)
(312,781)(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)
(320,775)(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)
(328,769)(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)
(336,763)(337,813)(338,814)(339,815)(340,816)(341,817)(342,818)(343,819)
(344,820)(345,821)(346,822)(347,823)(348,824)(349,825)(350,826)(351,834)
(352,835)(353,836)(354,837)(355,838)(356,839)(357,840)(358,827)(359,828)
(360,829)(361,830)(362,831)(363,832)(364,833)(365,785)(366,786)(367,787)
(368,788)(369,789)(370,790)(371,791)(372,792)(373,793)(374,794)(375,795)
(376,796)(377,797)(378,798)(379,806)(380,807)(381,808)(382,809)(383,810)
(384,811)(385,812)(386,799)(387,800)(388,801)(389,802)(390,803)(391,804)
(392,805)(393,876)(394,877)(395,878)(396,879)(397,880)(398,881)(399,882)
(400,869)(401,870)(402,871)(403,872)(404,873)(405,874)(406,875)(407,883)
(408,884)(409,885)(410,886)(411,887)(412,888)(413,889)(414,890)(415,891)
(416,892)(417,893)(418,894)(419,895)(420,896)(421,848)(422,849)(423,850)
(424,851)(425,852)(426,853)(427,854)(428,841)(429,842)(430,843)(431,844)
(432,845)(433,846)(434,847)(435,855)(436,856)(437,857)(438,858)(439,859)
(440,860)(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)
(448,868);
s1 := Sym(896)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 15, 22)
( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 29, 43)( 30, 49)
( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)
( 39, 54)( 40, 53)( 41, 52)( 42, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)
( 66, 69)( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)
( 92,106)( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)(113,141)
(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)
(122,153)(123,152)(124,151)(125,150)(126,149)(127,162)(128,168)(129,167)
(130,166)(131,165)(132,164)(133,163)(134,155)(135,161)(136,160)(137,159)
(138,158)(139,157)(140,156)(169,197)(170,203)(171,202)(172,201)(173,200)
(174,199)(175,198)(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)
(182,205)(183,218)(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)
(190,211)(191,217)(192,216)(193,215)(194,214)(195,213)(196,212)(225,281)
(226,287)(227,286)(228,285)(229,284)(230,283)(231,282)(232,288)(233,294)
(234,293)(235,292)(236,291)(237,290)(238,289)(239,302)(240,308)(241,307)
(242,306)(243,305)(244,304)(245,303)(246,295)(247,301)(248,300)(249,299)
(250,298)(251,297)(252,296)(253,323)(254,329)(255,328)(256,327)(257,326)
(258,325)(259,324)(260,330)(261,336)(262,335)(263,334)(264,333)(265,332)
(266,331)(267,309)(268,315)(269,314)(270,313)(271,312)(272,311)(273,310)
(274,316)(275,322)(276,321)(277,320)(278,319)(279,318)(280,317)(337,421)
(338,427)(339,426)(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)
(346,433)(347,432)(348,431)(349,430)(350,429)(351,442)(352,448)(353,447)
(354,446)(355,445)(356,444)(357,443)(358,435)(359,441)(360,440)(361,439)
(362,438)(363,437)(364,436)(365,393)(366,399)(367,398)(368,397)(369,396)
(370,395)(371,394)(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)
(378,401)(379,414)(380,420)(381,419)(382,418)(383,417)(384,416)(385,415)
(386,407)(387,413)(388,412)(389,411)(390,410)(391,409)(392,408)(449,561)
(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)
(458,573)(459,572)(460,571)(461,570)(462,569)(463,582)(464,588)(465,587)
(466,586)(467,585)(468,584)(469,583)(470,575)(471,581)(472,580)(473,579)
(474,578)(475,577)(476,576)(477,603)(478,609)(479,608)(480,607)(481,606)
(482,605)(483,604)(484,610)(485,616)(486,615)(487,614)(488,613)(489,612)
(490,611)(491,589)(492,595)(493,594)(494,593)(495,592)(496,591)(497,590)
(498,596)(499,602)(500,601)(501,600)(502,599)(503,598)(504,597)(505,617)
(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)(512,624)(513,630)
(514,629)(515,628)(516,627)(517,626)(518,625)(519,638)(520,644)(521,643)
(522,642)(523,641)(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)
(530,634)(531,633)(532,632)(533,659)(534,665)(535,664)(536,663)(537,662)
(538,661)(539,660)(540,666)(541,672)(542,671)(543,670)(544,669)(545,668)
(546,667)(547,645)(548,651)(549,650)(550,649)(551,648)(552,647)(553,646)
(554,652)(555,658)(556,657)(557,656)(558,655)(559,654)(560,653)(673,848)
(674,854)(675,853)(676,852)(677,851)(678,850)(679,849)(680,841)(681,847)
(682,846)(683,845)(684,844)(685,843)(686,842)(687,855)(688,861)(689,860)
(690,859)(691,858)(692,857)(693,856)(694,862)(695,868)(696,867)(697,866)
(698,865)(699,864)(700,863)(701,890)(702,896)(703,895)(704,894)(705,893)
(706,892)(707,891)(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)
(714,884)(715,876)(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)
(722,869)(723,875)(724,874)(725,873)(726,872)(727,871)(728,870)(729,792)
(730,798)(731,797)(732,796)(733,795)(734,794)(735,793)(736,785)(737,791)
(738,790)(739,789)(740,788)(741,787)(742,786)(743,799)(744,805)(745,804)
(746,803)(747,802)(748,801)(749,800)(750,806)(751,812)(752,811)(753,810)
(754,809)(755,808)(756,807)(757,834)(758,840)(759,839)(760,838)(761,837)
(762,836)(763,835)(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)
(770,828)(771,820)(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)
(778,813)(779,819)(780,818)(781,817)(782,816)(783,815)(784,814);
s2 := Sym(896)!( 1,226)( 2,225)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)
( 8,233)( 9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)
( 16,239)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)
( 24,252)( 25,251)( 26,250)( 27,249)( 28,248)( 29,254)( 30,253)( 31,259)
( 32,258)( 33,257)( 34,256)( 35,255)( 36,261)( 37,260)( 38,266)( 39,265)
( 40,264)( 41,263)( 42,262)( 43,268)( 44,267)( 45,273)( 46,272)( 47,271)
( 48,270)( 49,269)( 50,275)( 51,274)( 52,280)( 53,279)( 54,278)( 55,277)
( 56,276)( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)
( 64,289)( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,296)
( 72,295)( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)
( 80,308)( 81,307)( 82,306)( 83,305)( 84,304)( 85,310)( 86,309)( 87,315)
( 88,314)( 89,313)( 90,312)( 91,311)( 92,317)( 93,316)( 94,322)( 95,321)
( 96,320)( 97,319)( 98,318)( 99,324)(100,323)(101,329)(102,328)(103,327)
(104,326)(105,325)(106,331)(107,330)(108,336)(109,335)(110,334)(111,333)
(112,332)(113,345)(114,344)(115,350)(116,349)(117,348)(118,347)(119,346)
(120,338)(121,337)(122,343)(123,342)(124,341)(125,340)(126,339)(127,359)
(128,358)(129,364)(130,363)(131,362)(132,361)(133,360)(134,352)(135,351)
(136,357)(137,356)(138,355)(139,354)(140,353)(141,373)(142,372)(143,378)
(144,377)(145,376)(146,375)(147,374)(148,366)(149,365)(150,371)(151,370)
(152,369)(153,368)(154,367)(155,387)(156,386)(157,392)(158,391)(159,390)
(160,389)(161,388)(162,380)(163,379)(164,385)(165,384)(166,383)(167,382)
(168,381)(169,401)(170,400)(171,406)(172,405)(173,404)(174,403)(175,402)
(176,394)(177,393)(178,399)(179,398)(180,397)(181,396)(182,395)(183,415)
(184,414)(185,420)(186,419)(187,418)(188,417)(189,416)(190,408)(191,407)
(192,413)(193,412)(194,411)(195,410)(196,409)(197,429)(198,428)(199,434)
(200,433)(201,432)(202,431)(203,430)(204,422)(205,421)(206,427)(207,426)
(208,425)(209,424)(210,423)(211,443)(212,442)(213,448)(214,447)(215,446)
(216,445)(217,444)(218,436)(219,435)(220,441)(221,440)(222,439)(223,438)
(224,437)(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)
(456,681)(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,688)
(464,687)(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)
(472,700)(473,699)(474,698)(475,697)(476,696)(477,702)(478,701)(479,707)
(480,706)(481,705)(482,704)(483,703)(484,709)(485,708)(486,714)(487,713)
(488,712)(489,711)(490,710)(491,716)(492,715)(493,721)(494,720)(495,719)
(496,718)(497,717)(498,723)(499,722)(500,728)(501,727)(502,726)(503,725)
(504,724)(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)
(512,737)(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(519,744)
(520,743)(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)
(528,756)(529,755)(530,754)(531,753)(532,752)(533,758)(534,757)(535,763)
(536,762)(537,761)(538,760)(539,759)(540,765)(541,764)(542,770)(543,769)
(544,768)(545,767)(546,766)(547,772)(548,771)(549,777)(550,776)(551,775)
(552,774)(553,773)(554,779)(555,778)(556,784)(557,783)(558,782)(559,781)
(560,780)(561,793)(562,792)(563,798)(564,797)(565,796)(566,795)(567,794)
(568,786)(569,785)(570,791)(571,790)(572,789)(573,788)(574,787)(575,807)
(576,806)(577,812)(578,811)(579,810)(580,809)(581,808)(582,800)(583,799)
(584,805)(585,804)(586,803)(587,802)(588,801)(589,821)(590,820)(591,826)
(592,825)(593,824)(594,823)(595,822)(596,814)(597,813)(598,819)(599,818)
(600,817)(601,816)(602,815)(603,835)(604,834)(605,840)(606,839)(607,838)
(608,837)(609,836)(610,828)(611,827)(612,833)(613,832)(614,831)(615,830)
(616,829)(617,849)(618,848)(619,854)(620,853)(621,852)(622,851)(623,850)
(624,842)(625,841)(626,847)(627,846)(628,845)(629,844)(630,843)(631,863)
(632,862)(633,868)(634,867)(635,866)(636,865)(637,864)(638,856)(639,855)
(640,861)(641,860)(642,859)(643,858)(644,857)(645,877)(646,876)(647,882)
(648,881)(649,880)(650,879)(651,878)(652,870)(653,869)(654,875)(655,874)
(656,873)(657,872)(658,871)(659,891)(660,890)(661,896)(662,895)(663,894)
(664,893)(665,892)(666,884)(667,883)(668,889)(669,888)(670,887)(671,886)
(672,885);
poly := sub<Sym(896)|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*s2*s1*s0*s1*s0*s1*s0*s1*s2*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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