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