Polytope of Type {16,28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,28}*1792a
if this polytope has a name.
Group : SmallGroup(1792,81666)
Rank : 3
Schlafli Type : {16,28}
Number of vertices, edges, etc : 32, 448, 56
Order of s0s1s2 : 112
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {8,28}*896a, {16,28}*896a, {16,28}*896b
4-fold quotients : {4,28}*448, {8,28}*448a, {8,28}*448b, {16,14}*448
7-fold quotients : {16,4}*256a
8-fold quotients : {4,28}*224, {8,14}*224
14-fold quotients : {8,4}*128a, {16,4}*128a, {16,4}*128b
16-fold quotients : {2,28}*112, {4,14}*112
28-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64, {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)( 15,463)( 16,464)
( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)
( 25,473)( 26,474)( 27,475)( 28,476)( 29,484)( 30,485)( 31,486)( 32,487)
( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)( 40,481)
( 41,482)( 42,483)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)( 48,503)
( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)( 56,497)
( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)( 64,526)
( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)( 72,506)
( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)( 80,514)
( 81,515)( 82,516)( 83,517)( 84,518)( 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)(127,603)(128,604)
(129,605)(130,606)(131,607)(132,608)(133,609)(134,610)(135,611)(136,612)
(137,613)(138,614)(139,615)(140,616)(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)(155,575)(156,576)(157,577)(158,578)(159,579)(160,580)
(161,581)(162,582)(163,583)(164,584)(165,585)(166,586)(167,587)(168,588)
(169,659)(170,660)(171,661)(172,662)(173,663)(174,664)(175,665)(176,666)
(177,667)(178,668)(179,669)(180,670)(181,671)(182,672)(183,645)(184,646)
(185,647)(186,648)(187,649)(188,650)(189,651)(190,652)(191,653)(192,654)
(193,655)(194,656)(195,657)(196,658)(197,631)(198,632)(199,633)(200,634)
(201,635)(202,636)(203,637)(204,638)(205,639)(206,640)(207,641)(208,642)
(209,643)(210,644)(211,617)(212,618)(213,619)(214,620)(215,621)(216,622)
(217,623)(218,624)(219,625)(220,626)(221,627)(222,628)(223,629)(224,630)
(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)(239,687)(240,688)
(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)(248,696)
(249,697)(250,698)(251,699)(252,700)(253,708)(254,709)(255,710)(256,711)
(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)
(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)
(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)
(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)(288,750)
(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)(296,730)
(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)(304,738)
(305,739)(306,740)(307,741)(308,742)(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)(351,827)(352,828)
(353,829)(354,830)(355,831)(356,832)(357,833)(358,834)(359,835)(360,836)
(361,837)(362,838)(363,839)(364,840)(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)(379,799)(380,800)(381,801)(382,802)(383,803)(384,804)
(385,805)(386,806)(387,807)(388,808)(389,809)(390,810)(391,811)(392,812)
(393,883)(394,884)(395,885)(396,886)(397,887)(398,888)(399,889)(400,890)
(401,891)(402,892)(403,893)(404,894)(405,895)(406,896)(407,869)(408,870)
(409,871)(410,872)(411,873)(412,874)(413,875)(414,876)(415,877)(416,878)
(417,879)(418,880)(419,881)(420,882)(421,855)(422,856)(423,857)(424,858)
(425,859)(426,860)(427,861)(428,862)(429,863)(430,864)(431,865)(432,866)
(433,867)(434,868)(435,841)(436,842)(437,843)(438,844)(439,845)(440,846)
(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)(448,854);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 36)( 30, 42)( 31, 41)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)
( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)
( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 85, 92)( 86, 98)
( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)( 99,106)(100,112)(101,111)
(102,110)(103,109)(104,108)(105,107)(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)(127,155)(128,161)(129,160)(130,159)(131,158)(132,157)
(133,156)(134,162)(135,168)(136,167)(137,166)(138,165)(139,164)(140,163)
(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)(183,211)(184,217)
(185,216)(186,215)(187,214)(188,213)(189,212)(190,218)(191,224)(192,223)
(193,222)(194,221)(195,220)(196,219)(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)(239,295)(240,301)(241,300)(242,299)(243,298)(244,297)
(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)(252,303)
(253,316)(254,322)(255,321)(256,320)(257,319)(258,318)(259,317)(260,309)
(261,315)(262,314)(263,313)(264,312)(265,311)(266,310)(267,330)(268,336)
(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)(276,328)
(277,327)(278,326)(279,325)(280,324)(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)(351,435)(352,441)(353,440)(354,439)(355,438)(356,437)
(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)(363,444)(364,443)
(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)(379,407)(380,413)
(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)(387,420)(388,419)
(389,418)(390,417)(391,416)(392,415)(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)(463,575)(464,581)(465,580)(466,579)(467,578)(468,577)
(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)(476,583)
(477,596)(478,602)(479,601)(480,600)(481,599)(482,598)(483,597)(484,589)
(485,595)(486,594)(487,593)(488,592)(489,591)(490,590)(491,610)(492,616)
(493,615)(494,614)(495,613)(496,612)(497,611)(498,603)(499,609)(500,608)
(501,607)(502,606)(503,605)(504,604)(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)(519,631)(520,637)(521,636)(522,635)(523,634)(524,633)
(525,632)(526,638)(527,644)(528,643)(529,642)(530,641)(531,640)(532,639)
(533,652)(534,658)(535,657)(536,656)(537,655)(538,654)(539,653)(540,645)
(541,651)(542,650)(543,649)(544,648)(545,647)(546,646)(547,666)(548,672)
(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)(556,664)
(557,663)(558,662)(559,661)(560,660)(673,855)(674,861)(675,860)(676,859)
(677,858)(678,857)(679,856)(680,862)(681,868)(682,867)(683,866)(684,865)
(685,864)(686,863)(687,841)(688,847)(689,846)(690,845)(691,844)(692,843)
(693,842)(694,848)(695,854)(696,853)(697,852)(698,851)(699,850)(700,849)
(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)(729,799)(730,805)(731,804)(732,803)
(733,802)(734,801)(735,800)(736,806)(737,812)(738,811)(739,810)(740,809)
(741,808)(742,807)(743,785)(744,791)(745,790)(746,789)(747,788)(748,787)
(749,786)(750,792)(751,798)(752,797)(753,796)(754,795)(755,794)(756,793)
(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)
(113,352)(114,351)(115,357)(116,356)(117,355)(118,354)(119,353)(120,359)
(121,358)(122,364)(123,363)(124,362)(125,361)(126,360)(127,338)(128,337)
(129,343)(130,342)(131,341)(132,340)(133,339)(134,345)(135,344)(136,350)
(137,349)(138,348)(139,347)(140,346)(141,380)(142,379)(143,385)(144,384)
(145,383)(146,382)(147,381)(148,387)(149,386)(150,392)(151,391)(152,390)
(153,389)(154,388)(155,366)(156,365)(157,371)(158,370)(159,369)(160,368)
(161,367)(162,373)(163,372)(164,378)(165,377)(166,376)(167,375)(168,374)
(169,408)(170,407)(171,413)(172,412)(173,411)(174,410)(175,409)(176,415)
(177,414)(178,420)(179,419)(180,418)(181,417)(182,416)(183,394)(184,393)
(185,399)(186,398)(187,397)(188,396)(189,395)(190,401)(191,400)(192,406)
(193,405)(194,404)(195,403)(196,402)(197,436)(198,435)(199,441)(200,440)
(201,439)(202,438)(203,437)(204,443)(205,442)(206,448)(207,447)(208,446)
(209,445)(210,444)(211,422)(212,421)(213,427)(214,426)(215,425)(216,424)
(217,423)(218,429)(219,428)(220,434)(221,433)(222,432)(223,431)(224,430)
(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)
(561,800)(562,799)(563,805)(564,804)(565,803)(566,802)(567,801)(568,807)
(569,806)(570,812)(571,811)(572,810)(573,809)(574,808)(575,786)(576,785)
(577,791)(578,790)(579,789)(580,788)(581,787)(582,793)(583,792)(584,798)
(585,797)(586,796)(587,795)(588,794)(589,828)(590,827)(591,833)(592,832)
(593,831)(594,830)(595,829)(596,835)(597,834)(598,840)(599,839)(600,838)
(601,837)(602,836)(603,814)(604,813)(605,819)(606,818)(607,817)(608,816)
(609,815)(610,821)(611,820)(612,826)(613,825)(614,824)(615,823)(616,822)
(617,856)(618,855)(619,861)(620,860)(621,859)(622,858)(623,857)(624,863)
(625,862)(626,868)(627,867)(628,866)(629,865)(630,864)(631,842)(632,841)
(633,847)(634,846)(635,845)(636,844)(637,843)(638,849)(639,848)(640,854)
(641,853)(642,852)(643,851)(644,850)(645,884)(646,883)(647,889)(648,888)
(649,887)(650,886)(651,885)(652,891)(653,890)(654,896)(655,895)(656,894)
(657,893)(658,892)(659,870)(660,869)(661,875)(662,874)(663,873)(664,872)
(665,871)(666,877)(667,876)(668,882)(669,881)(670,880)(671,879)(672,878);;
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*s1*s0*s1*s0*s1*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)( 15,463)
( 16,464)( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)
( 24,472)( 25,473)( 26,474)( 27,475)( 28,476)( 29,484)( 30,485)( 31,486)
( 32,487)( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)
( 40,481)( 41,482)( 42,483)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)
( 48,503)( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)
( 56,497)( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)
( 64,526)( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)
( 72,506)( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)
( 80,514)( 81,515)( 82,516)( 83,517)( 84,518)( 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)(127,603)
(128,604)(129,605)(130,606)(131,607)(132,608)(133,609)(134,610)(135,611)
(136,612)(137,613)(138,614)(139,615)(140,616)(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)(155,575)(156,576)(157,577)(158,578)(159,579)
(160,580)(161,581)(162,582)(163,583)(164,584)(165,585)(166,586)(167,587)
(168,588)(169,659)(170,660)(171,661)(172,662)(173,663)(174,664)(175,665)
(176,666)(177,667)(178,668)(179,669)(180,670)(181,671)(182,672)(183,645)
(184,646)(185,647)(186,648)(187,649)(188,650)(189,651)(190,652)(191,653)
(192,654)(193,655)(194,656)(195,657)(196,658)(197,631)(198,632)(199,633)
(200,634)(201,635)(202,636)(203,637)(204,638)(205,639)(206,640)(207,641)
(208,642)(209,643)(210,644)(211,617)(212,618)(213,619)(214,620)(215,621)
(216,622)(217,623)(218,624)(219,625)(220,626)(221,627)(222,628)(223,629)
(224,630)(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)(239,687)
(240,688)(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)
(248,696)(249,697)(250,698)(251,699)(252,700)(253,708)(254,709)(255,710)
(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)
(264,705)(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)
(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)
(280,721)(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)
(288,750)(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)
(296,730)(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)
(304,738)(305,739)(306,740)(307,741)(308,742)(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)(351,827)
(352,828)(353,829)(354,830)(355,831)(356,832)(357,833)(358,834)(359,835)
(360,836)(361,837)(362,838)(363,839)(364,840)(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)(379,799)(380,800)(381,801)(382,802)(383,803)
(384,804)(385,805)(386,806)(387,807)(388,808)(389,809)(390,810)(391,811)
(392,812)(393,883)(394,884)(395,885)(396,886)(397,887)(398,888)(399,889)
(400,890)(401,891)(402,892)(403,893)(404,894)(405,895)(406,896)(407,869)
(408,870)(409,871)(410,872)(411,873)(412,874)(413,875)(414,876)(415,877)
(416,878)(417,879)(418,880)(419,881)(420,882)(421,855)(422,856)(423,857)
(424,858)(425,859)(426,860)(427,861)(428,862)(429,863)(430,864)(431,865)
(432,866)(433,867)(434,868)(435,841)(436,842)(437,843)(438,844)(439,845)
(440,846)(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)
(448,854);
s1 := Sym(896)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 36)( 30, 42)( 31, 41)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)
( 47, 53)( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)
( 67, 68)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 85, 92)
( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)( 99,106)(100,112)
(101,111)(102,110)(103,109)(104,108)(105,107)(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)(127,155)(128,161)(129,160)(130,159)(131,158)
(132,157)(133,156)(134,162)(135,168)(136,167)(137,166)(138,165)(139,164)
(140,163)(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)(183,211)
(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)(190,218)(191,224)
(192,223)(193,222)(194,221)(195,220)(196,219)(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)(239,295)(240,301)(241,300)(242,299)(243,298)
(244,297)(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)
(252,303)(253,316)(254,322)(255,321)(256,320)(257,319)(258,318)(259,317)
(260,309)(261,315)(262,314)(263,313)(264,312)(265,311)(266,310)(267,330)
(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)
(276,328)(277,327)(278,326)(279,325)(280,324)(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)(351,435)(352,441)(353,440)(354,439)(355,438)
(356,437)(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)(363,444)
(364,443)(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)(379,407)
(380,413)(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)(387,420)
(388,419)(389,418)(390,417)(391,416)(392,415)(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)(463,575)(464,581)(465,580)(466,579)(467,578)
(468,577)(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)
(476,583)(477,596)(478,602)(479,601)(480,600)(481,599)(482,598)(483,597)
(484,589)(485,595)(486,594)(487,593)(488,592)(489,591)(490,590)(491,610)
(492,616)(493,615)(494,614)(495,613)(496,612)(497,611)(498,603)(499,609)
(500,608)(501,607)(502,606)(503,605)(504,604)(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)(519,631)(520,637)(521,636)(522,635)(523,634)
(524,633)(525,632)(526,638)(527,644)(528,643)(529,642)(530,641)(531,640)
(532,639)(533,652)(534,658)(535,657)(536,656)(537,655)(538,654)(539,653)
(540,645)(541,651)(542,650)(543,649)(544,648)(545,647)(546,646)(547,666)
(548,672)(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)
(556,664)(557,663)(558,662)(559,661)(560,660)(673,855)(674,861)(675,860)
(676,859)(677,858)(678,857)(679,856)(680,862)(681,868)(682,867)(683,866)
(684,865)(685,864)(686,863)(687,841)(688,847)(689,846)(690,845)(691,844)
(692,843)(693,842)(694,848)(695,854)(696,853)(697,852)(698,851)(699,850)
(700,849)(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)(729,799)(730,805)(731,804)
(732,803)(733,802)(734,801)(735,800)(736,806)(737,812)(738,811)(739,810)
(740,809)(741,808)(742,807)(743,785)(744,791)(745,790)(746,789)(747,788)
(748,787)(749,786)(750,792)(751,798)(752,797)(753,796)(754,795)(755,794)
(756,793)(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)(113,352)(114,351)(115,357)(116,356)(117,355)(118,354)(119,353)
(120,359)(121,358)(122,364)(123,363)(124,362)(125,361)(126,360)(127,338)
(128,337)(129,343)(130,342)(131,341)(132,340)(133,339)(134,345)(135,344)
(136,350)(137,349)(138,348)(139,347)(140,346)(141,380)(142,379)(143,385)
(144,384)(145,383)(146,382)(147,381)(148,387)(149,386)(150,392)(151,391)
(152,390)(153,389)(154,388)(155,366)(156,365)(157,371)(158,370)(159,369)
(160,368)(161,367)(162,373)(163,372)(164,378)(165,377)(166,376)(167,375)
(168,374)(169,408)(170,407)(171,413)(172,412)(173,411)(174,410)(175,409)
(176,415)(177,414)(178,420)(179,419)(180,418)(181,417)(182,416)(183,394)
(184,393)(185,399)(186,398)(187,397)(188,396)(189,395)(190,401)(191,400)
(192,406)(193,405)(194,404)(195,403)(196,402)(197,436)(198,435)(199,441)
(200,440)(201,439)(202,438)(203,437)(204,443)(205,442)(206,448)(207,447)
(208,446)(209,445)(210,444)(211,422)(212,421)(213,427)(214,426)(215,425)
(216,424)(217,423)(218,429)(219,428)(220,434)(221,433)(222,432)(223,431)
(224,430)(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)(561,800)(562,799)(563,805)(564,804)(565,803)(566,802)(567,801)
(568,807)(569,806)(570,812)(571,811)(572,810)(573,809)(574,808)(575,786)
(576,785)(577,791)(578,790)(579,789)(580,788)(581,787)(582,793)(583,792)
(584,798)(585,797)(586,796)(587,795)(588,794)(589,828)(590,827)(591,833)
(592,832)(593,831)(594,830)(595,829)(596,835)(597,834)(598,840)(599,839)
(600,838)(601,837)(602,836)(603,814)(604,813)(605,819)(606,818)(607,817)
(608,816)(609,815)(610,821)(611,820)(612,826)(613,825)(614,824)(615,823)
(616,822)(617,856)(618,855)(619,861)(620,860)(621,859)(622,858)(623,857)
(624,863)(625,862)(626,868)(627,867)(628,866)(629,865)(630,864)(631,842)
(632,841)(633,847)(634,846)(635,845)(636,844)(637,843)(638,849)(639,848)
(640,854)(641,853)(642,852)(643,851)(644,850)(645,884)(646,883)(647,889)
(648,888)(649,887)(650,886)(651,885)(652,891)(653,890)(654,896)(655,895)
(656,894)(657,893)(658,892)(659,870)(660,869)(661,875)(662,874)(663,873)
(664,872)(665,871)(666,877)(667,876)(668,882)(669,881)(670,880)(671,879)
(672,878);
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*s1*s0*s1*s0*s1*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