Polytope of Type {32,28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,28}*1792a
Also Known As : {32,28|2}. if this polytope has another name.
Group : SmallGroup(1792,90208)
Rank : 3
Schlafli Type : {32,28}
Number of vertices, edges, etc : 32, 448, 28
Order of s0s1s2 : 224
Order of s0s1s2s1 : 2
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, {32,14}*896
4-fold quotients : {8,28}*448a, {16,14}*448
7-fold quotients : {32,4}*256a
8-fold quotients : {4,28}*224, {8,14}*224
14-fold quotients : {16,4}*128a, {32,2}*128
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)
( 57,505)( 58,506)( 59,507)( 60,508)( 61,509)( 62,510)( 63,511)( 64,512)
( 65,513)( 66,514)( 67,515)( 68,516)( 69,517)( 70,518)( 71,526)( 72,527)
( 73,528)( 74,529)( 75,530)( 76,531)( 77,532)( 78,519)( 79,520)( 80,521)
( 81,522)( 82,523)( 83,524)( 84,525)( 85,547)( 86,548)( 87,549)( 88,550)
( 89,551)( 90,552)( 91,553)( 92,554)( 93,555)( 94,556)( 95,557)( 96,558)
( 97,559)( 98,560)( 99,533)(100,534)(101,535)(102,536)(103,537)(104,538)
(105,539)(106,540)(107,541)(108,542)(109,543)(110,544)(111,545)(112,546)
(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)
(169,645)(170,646)(171,647)(172,648)(173,649)(174,650)(175,651)(176,652)
(177,653)(178,654)(179,655)(180,656)(181,657)(182,658)(183,666)(184,667)
(185,668)(186,669)(187,670)(188,671)(189,672)(190,659)(191,660)(192,661)
(193,662)(194,663)(195,664)(196,665)(197,617)(198,618)(199,619)(200,620)
(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)(208,628)
(209,629)(210,630)(211,638)(212,639)(213,640)(214,641)(215,642)(216,643)
(217,644)(218,631)(219,632)(220,633)(221,634)(222,635)(223,636)(224,637)
(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)
(281,729)(282,730)(283,731)(284,732)(285,733)(286,734)(287,735)(288,736)
(289,737)(290,738)(291,739)(292,740)(293,741)(294,742)(295,750)(296,751)
(297,752)(298,753)(299,754)(300,755)(301,756)(302,743)(303,744)(304,745)
(305,746)(306,747)(307,748)(308,749)(309,771)(310,772)(311,773)(312,774)
(313,775)(314,776)(315,777)(316,778)(317,779)(318,780)(319,781)(320,782)
(321,783)(322,784)(323,757)(324,758)(325,759)(326,760)(327,761)(328,762)
(329,763)(330,764)(331,765)(332,766)(333,767)(334,768)(335,769)(336,770)
(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)
(393,869)(394,870)(395,871)(396,872)(397,873)(398,874)(399,875)(400,876)
(401,877)(402,878)(403,879)(404,880)(405,881)(406,882)(407,890)(408,891)
(409,892)(410,893)(411,894)(412,895)(413,896)(414,883)(415,884)(416,885)
(417,886)(418,887)(419,888)(420,889)(421,841)(422,842)(423,843)(424,844)
(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)(432,852)
(433,853)(434,854)(435,862)(436,863)(437,864)(438,865)(439,866)(440,867)
(441,868)(442,855)(443,856)(444,857)(445,858)(446,859)(447,860)(448,861);;
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)(673,841)(674,847)
(675,846)(676,845)(677,844)(678,843)(679,842)(680,848)(681,854)(682,853)
(683,852)(684,851)(685,850)(686,849)(687,862)(688,868)(689,867)(690,866)
(691,865)(692,864)(693,863)(694,855)(695,861)(696,860)(697,859)(698,858)
(699,857)(700,856)(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)
(707,884)(708,890)(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)
(715,869)(716,875)(717,874)(718,873)(719,872)(720,871)(721,870)(722,876)
(723,882)(724,881)(725,880)(726,879)(727,878)(728,877)(729,785)(730,791)
(731,790)(732,789)(733,788)(734,787)(735,786)(736,792)(737,798)(738,797)
(739,796)(740,795)(741,794)(742,793)(743,806)(744,812)(745,811)(746,810)
(747,809)(748,808)(749,807)(750,799)(751,805)(752,804)(753,803)(754,802)
(755,801)(756,800)(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)
(763,828)(764,834)(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)
(771,813)(772,819)(773,818)(774,817)(775,816)(776,815)(777,814)(778,820)
(779,826)(780,825)(781,824)(782,823)(783,822)(784,821);;
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)
(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)(120,345)
(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)(128,351)
(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)(136,364)
(137,363)(138,362)(139,361)(140,360)(141,366)(142,365)(143,371)(144,370)
(145,369)(146,368)(147,367)(148,373)(149,372)(150,378)(151,377)(152,376)
(153,375)(154,374)(155,380)(156,379)(157,385)(158,384)(159,383)(160,382)
(161,381)(162,387)(163,386)(164,392)(165,391)(166,390)(167,389)(168,388)
(169,394)(170,393)(171,399)(172,398)(173,397)(174,396)(175,395)(176,401)
(177,400)(178,406)(179,405)(180,404)(181,403)(182,402)(183,408)(184,407)
(185,413)(186,412)(187,411)(188,410)(189,409)(190,415)(191,414)(192,420)
(193,419)(194,418)(195,417)(196,416)(197,422)(198,421)(199,427)(200,426)
(201,425)(202,424)(203,423)(204,429)(205,428)(206,434)(207,433)(208,432)
(209,431)(210,430)(211,436)(212,435)(213,441)(214,440)(215,439)(216,438)
(217,437)(218,443)(219,442)(220,448)(221,447)(222,446)(223,445)(224,444)
(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)
(561,786)(562,785)(563,791)(564,790)(565,789)(566,788)(567,787)(568,793)
(569,792)(570,798)(571,797)(572,796)(573,795)(574,794)(575,800)(576,799)
(577,805)(578,804)(579,803)(580,802)(581,801)(582,807)(583,806)(584,812)
(585,811)(586,810)(587,809)(588,808)(589,814)(590,813)(591,819)(592,818)
(593,817)(594,816)(595,815)(596,821)(597,820)(598,826)(599,825)(600,824)
(601,823)(602,822)(603,828)(604,827)(605,833)(606,832)(607,831)(608,830)
(609,829)(610,835)(611,834)(612,840)(613,839)(614,838)(615,837)(616,836)
(617,842)(618,841)(619,847)(620,846)(621,845)(622,844)(623,843)(624,849)
(625,848)(626,854)(627,853)(628,852)(629,851)(630,850)(631,856)(632,855)
(633,861)(634,860)(635,859)(636,858)(637,857)(638,863)(639,862)(640,868)
(641,867)(642,866)(643,865)(644,864)(645,870)(646,869)(647,875)(648,874)
(649,873)(650,872)(651,871)(652,877)(653,876)(654,882)(655,881)(656,880)
(657,879)(658,878)(659,884)(660,883)(661,889)(662,888)(663,887)(664,886)
(665,885)(666,891)(667,890)(668,896)(669,895)(670,894)(671,893)(672,892);;
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, s0*s1*s2*s1*s0*s1*s2*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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(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)( 57,505)( 58,506)( 59,507)( 60,508)( 61,509)( 62,510)( 63,511)
( 64,512)( 65,513)( 66,514)( 67,515)( 68,516)( 69,517)( 70,518)( 71,526)
( 72,527)( 73,528)( 74,529)( 75,530)( 76,531)( 77,532)( 78,519)( 79,520)
( 80,521)( 81,522)( 82,523)( 83,524)( 84,525)( 85,547)( 86,548)( 87,549)
( 88,550)( 89,551)( 90,552)( 91,553)( 92,554)( 93,555)( 94,556)( 95,557)
( 96,558)( 97,559)( 98,560)( 99,533)(100,534)(101,535)(102,536)(103,537)
(104,538)(105,539)(106,540)(107,541)(108,542)(109,543)(110,544)(111,545)
(112,546)(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)(169,645)(170,646)(171,647)(172,648)(173,649)(174,650)(175,651)
(176,652)(177,653)(178,654)(179,655)(180,656)(181,657)(182,658)(183,666)
(184,667)(185,668)(186,669)(187,670)(188,671)(189,672)(190,659)(191,660)
(192,661)(193,662)(194,663)(195,664)(196,665)(197,617)(198,618)(199,619)
(200,620)(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)
(208,628)(209,629)(210,630)(211,638)(212,639)(213,640)(214,641)(215,642)
(216,643)(217,644)(218,631)(219,632)(220,633)(221,634)(222,635)(223,636)
(224,637)(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)(281,729)(282,730)(283,731)(284,732)(285,733)(286,734)(287,735)
(288,736)(289,737)(290,738)(291,739)(292,740)(293,741)(294,742)(295,750)
(296,751)(297,752)(298,753)(299,754)(300,755)(301,756)(302,743)(303,744)
(304,745)(305,746)(306,747)(307,748)(308,749)(309,771)(310,772)(311,773)
(312,774)(313,775)(314,776)(315,777)(316,778)(317,779)(318,780)(319,781)
(320,782)(321,783)(322,784)(323,757)(324,758)(325,759)(326,760)(327,761)
(328,762)(329,763)(330,764)(331,765)(332,766)(333,767)(334,768)(335,769)
(336,770)(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)(393,869)(394,870)(395,871)(396,872)(397,873)(398,874)(399,875)
(400,876)(401,877)(402,878)(403,879)(404,880)(405,881)(406,882)(407,890)
(408,891)(409,892)(410,893)(411,894)(412,895)(413,896)(414,883)(415,884)
(416,885)(417,886)(418,887)(419,888)(420,889)(421,841)(422,842)(423,843)
(424,844)(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)
(432,852)(433,853)(434,854)(435,862)(436,863)(437,864)(438,865)(439,866)
(440,867)(441,868)(442,855)(443,856)(444,857)(445,858)(446,859)(447,860)
(448,861);
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)(673,841)
(674,847)(675,846)(676,845)(677,844)(678,843)(679,842)(680,848)(681,854)
(682,853)(683,852)(684,851)(685,850)(686,849)(687,862)(688,868)(689,867)
(690,866)(691,865)(692,864)(693,863)(694,855)(695,861)(696,860)(697,859)
(698,858)(699,857)(700,856)(701,883)(702,889)(703,888)(704,887)(705,886)
(706,885)(707,884)(708,890)(709,896)(710,895)(711,894)(712,893)(713,892)
(714,891)(715,869)(716,875)(717,874)(718,873)(719,872)(720,871)(721,870)
(722,876)(723,882)(724,881)(725,880)(726,879)(727,878)(728,877)(729,785)
(730,791)(731,790)(732,789)(733,788)(734,787)(735,786)(736,792)(737,798)
(738,797)(739,796)(740,795)(741,794)(742,793)(743,806)(744,812)(745,811)
(746,810)(747,809)(748,808)(749,807)(750,799)(751,805)(752,804)(753,803)
(754,802)(755,801)(756,800)(757,827)(758,833)(759,832)(760,831)(761,830)
(762,829)(763,828)(764,834)(765,840)(766,839)(767,838)(768,837)(769,836)
(770,835)(771,813)(772,819)(773,818)(774,817)(775,816)(776,815)(777,814)
(778,820)(779,826)(780,825)(781,824)(782,823)(783,822)(784,821);
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)(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)
(120,345)(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)
(128,351)(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)
(136,364)(137,363)(138,362)(139,361)(140,360)(141,366)(142,365)(143,371)
(144,370)(145,369)(146,368)(147,367)(148,373)(149,372)(150,378)(151,377)
(152,376)(153,375)(154,374)(155,380)(156,379)(157,385)(158,384)(159,383)
(160,382)(161,381)(162,387)(163,386)(164,392)(165,391)(166,390)(167,389)
(168,388)(169,394)(170,393)(171,399)(172,398)(173,397)(174,396)(175,395)
(176,401)(177,400)(178,406)(179,405)(180,404)(181,403)(182,402)(183,408)
(184,407)(185,413)(186,412)(187,411)(188,410)(189,409)(190,415)(191,414)
(192,420)(193,419)(194,418)(195,417)(196,416)(197,422)(198,421)(199,427)
(200,426)(201,425)(202,424)(203,423)(204,429)(205,428)(206,434)(207,433)
(208,432)(209,431)(210,430)(211,436)(212,435)(213,441)(214,440)(215,439)
(216,438)(217,437)(218,443)(219,442)(220,448)(221,447)(222,446)(223,445)
(224,444)(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)(561,786)(562,785)(563,791)(564,790)(565,789)(566,788)(567,787)
(568,793)(569,792)(570,798)(571,797)(572,796)(573,795)(574,794)(575,800)
(576,799)(577,805)(578,804)(579,803)(580,802)(581,801)(582,807)(583,806)
(584,812)(585,811)(586,810)(587,809)(588,808)(589,814)(590,813)(591,819)
(592,818)(593,817)(594,816)(595,815)(596,821)(597,820)(598,826)(599,825)
(600,824)(601,823)(602,822)(603,828)(604,827)(605,833)(606,832)(607,831)
(608,830)(609,829)(610,835)(611,834)(612,840)(613,839)(614,838)(615,837)
(616,836)(617,842)(618,841)(619,847)(620,846)(621,845)(622,844)(623,843)
(624,849)(625,848)(626,854)(627,853)(628,852)(629,851)(630,850)(631,856)
(632,855)(633,861)(634,860)(635,859)(636,858)(637,857)(638,863)(639,862)
(640,868)(641,867)(642,866)(643,865)(644,864)(645,870)(646,869)(647,875)
(648,874)(649,873)(650,872)(651,871)(652,877)(653,876)(654,882)(655,881)
(656,880)(657,879)(658,878)(659,884)(660,883)(661,889)(662,888)(663,887)
(664,886)(665,885)(666,891)(667,890)(668,896)(669,895)(670,894)(671,893)
(672,892);
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, s0*s1*s2*s1*s0*s1*s2*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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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