Polytope of Type {28,32}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,32}*1792a
Also Known As : {28,32|2}. if this polytope has another name.
Group : SmallGroup(1792,90208)
Rank : 3
Schlafli Type : {28,32}
Number of vertices, edges, etc : 28, 448, 32
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 : {28,16}*896a, {14,32}*896
4-fold quotients : {28,8}*448a, {14,16}*448
7-fold quotients : {4,32}*256a
8-fold quotients : {28,4}*224, {14,8}*224
14-fold quotients : {4,16}*128a, {2,32}*128
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)
(113,337)(114,343)(115,342)(116,341)(117,340)(118,339)(119,338)(120,344)
(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,351)(128,357)
(129,356)(130,355)(131,354)(132,353)(133,352)(134,358)(135,364)(136,363)
(137,362)(138,361)(139,360)(140,359)(141,365)(142,371)(143,370)(144,369)
(145,368)(146,367)(147,366)(148,372)(149,378)(150,377)(151,376)(152,375)
(153,374)(154,373)(155,379)(156,385)(157,384)(158,383)(159,382)(160,381)
(161,380)(162,386)(163,392)(164,391)(165,390)(166,389)(167,388)(168,387)
(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)(176,400)
(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)(184,413)
(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)(192,419)
(193,418)(194,417)(195,416)(196,415)(197,421)(198,427)(199,426)(200,425)
(201,424)(202,423)(203,422)(204,428)(205,434)(206,433)(207,432)(208,431)
(209,430)(210,429)(211,435)(212,441)(213,440)(214,439)(215,438)(216,437)
(217,436)(218,442)(219,448)(220,447)(221,446)(222,445)(223,444)(224,443)
(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)
(561,785)(562,791)(563,790)(564,789)(565,788)(566,787)(567,786)(568,792)
(569,798)(570,797)(571,796)(572,795)(573,794)(574,793)(575,799)(576,805)
(577,804)(578,803)(579,802)(580,801)(581,800)(582,806)(583,812)(584,811)
(585,810)(586,809)(587,808)(588,807)(589,813)(590,819)(591,818)(592,817)
(593,816)(594,815)(595,814)(596,820)(597,826)(598,825)(599,824)(600,823)
(601,822)(602,821)(603,827)(604,833)(605,832)(606,831)(607,830)(608,829)
(609,828)(610,834)(611,840)(612,839)(613,838)(614,837)(615,836)(616,835)
(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)(624,848)
(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)(632,861)
(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)(640,867)
(641,866)(642,865)(643,864)(644,863)(645,869)(646,875)(647,874)(648,873)
(649,872)(650,871)(651,870)(652,876)(653,882)(654,881)(655,880)(656,879)
(657,878)(658,877)(659,883)(660,889)(661,888)(662,887)(663,886)(664,885)
(665,884)(666,890)(667,896)(668,895)(669,894)(670,893)(671,892)(672,891);;
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)(673,842)(674,841)
(675,847)(676,846)(677,845)(678,844)(679,843)(680,849)(681,848)(682,854)
(683,853)(684,852)(685,851)(686,850)(687,863)(688,862)(689,868)(690,867)
(691,866)(692,865)(693,864)(694,856)(695,855)(696,861)(697,860)(698,859)
(699,858)(700,857)(701,884)(702,883)(703,889)(704,888)(705,887)(706,886)
(707,885)(708,891)(709,890)(710,896)(711,895)(712,894)(713,893)(714,892)
(715,870)(716,869)(717,875)(718,874)(719,873)(720,872)(721,871)(722,877)
(723,876)(724,882)(725,881)(726,880)(727,879)(728,878)(729,786)(730,785)
(731,791)(732,790)(733,789)(734,788)(735,787)(736,793)(737,792)(738,798)
(739,797)(740,796)(741,795)(742,794)(743,807)(744,806)(745,812)(746,811)
(747,810)(748,809)(749,808)(750,800)(751,799)(752,805)(753,804)(754,803)
(755,802)(756,801)(757,828)(758,827)(759,833)(760,832)(761,831)(762,830)
(763,829)(764,835)(765,834)(766,840)(767,839)(768,838)(769,837)(770,836)
(771,814)(772,813)(773,819)(774,818)(775,817)(776,816)(777,815)(778,821)
(779,820)(780,826)(781,825)(782,824)(783,823)(784,822);;
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)
( 57,505)( 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);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)(113,337)(114,343)(115,342)(116,341)(117,340)(118,339)(119,338)
(120,344)(121,350)(122,349)(123,348)(124,347)(125,346)(126,345)(127,351)
(128,357)(129,356)(130,355)(131,354)(132,353)(133,352)(134,358)(135,364)
(136,363)(137,362)(138,361)(139,360)(140,359)(141,365)(142,371)(143,370)
(144,369)(145,368)(146,367)(147,366)(148,372)(149,378)(150,377)(151,376)
(152,375)(153,374)(154,373)(155,379)(156,385)(157,384)(158,383)(159,382)
(160,381)(161,380)(162,386)(163,392)(164,391)(165,390)(166,389)(167,388)
(168,387)(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)
(176,400)(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)
(184,413)(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)
(192,419)(193,418)(194,417)(195,416)(196,415)(197,421)(198,427)(199,426)
(200,425)(201,424)(202,423)(203,422)(204,428)(205,434)(206,433)(207,432)
(208,431)(209,430)(210,429)(211,435)(212,441)(213,440)(214,439)(215,438)
(216,437)(217,436)(218,442)(219,448)(220,447)(221,446)(222,445)(223,444)
(224,443)(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)(561,785)(562,791)(563,790)(564,789)(565,788)(566,787)(567,786)
(568,792)(569,798)(570,797)(571,796)(572,795)(573,794)(574,793)(575,799)
(576,805)(577,804)(578,803)(579,802)(580,801)(581,800)(582,806)(583,812)
(584,811)(585,810)(586,809)(587,808)(588,807)(589,813)(590,819)(591,818)
(592,817)(593,816)(594,815)(595,814)(596,820)(597,826)(598,825)(599,824)
(600,823)(601,822)(602,821)(603,827)(604,833)(605,832)(606,831)(607,830)
(608,829)(609,828)(610,834)(611,840)(612,839)(613,838)(614,837)(615,836)
(616,835)(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)
(624,848)(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)
(632,861)(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)
(640,867)(641,866)(642,865)(643,864)(644,863)(645,869)(646,875)(647,874)
(648,873)(649,872)(650,871)(651,870)(652,876)(653,882)(654,881)(655,880)
(656,879)(657,878)(658,877)(659,883)(660,889)(661,888)(662,887)(663,886)
(664,885)(665,884)(666,890)(667,896)(668,895)(669,894)(670,893)(671,892)
(672,891);
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)(673,842)
(674,841)(675,847)(676,846)(677,845)(678,844)(679,843)(680,849)(681,848)
(682,854)(683,853)(684,852)(685,851)(686,850)(687,863)(688,862)(689,868)
(690,867)(691,866)(692,865)(693,864)(694,856)(695,855)(696,861)(697,860)
(698,859)(699,858)(700,857)(701,884)(702,883)(703,889)(704,888)(705,887)
(706,886)(707,885)(708,891)(709,890)(710,896)(711,895)(712,894)(713,893)
(714,892)(715,870)(716,869)(717,875)(718,874)(719,873)(720,872)(721,871)
(722,877)(723,876)(724,882)(725,881)(726,880)(727,879)(728,878)(729,786)
(730,785)(731,791)(732,790)(733,789)(734,788)(735,787)(736,793)(737,792)
(738,798)(739,797)(740,796)(741,795)(742,794)(743,807)(744,806)(745,812)
(746,811)(747,810)(748,809)(749,808)(750,800)(751,799)(752,805)(753,804)
(754,803)(755,802)(756,801)(757,828)(758,827)(759,833)(760,832)(761,831)
(762,830)(763,829)(764,835)(765,834)(766,840)(767,839)(768,838)(769,837)
(770,836)(771,814)(772,813)(773,819)(774,818)(775,817)(776,816)(777,815)
(778,821)(779,820)(780,826)(781,825)(782,824)(783,823)(784,822);
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)( 57,505)( 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);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope