Polytope of Type {8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1728a
if this polytope has a name.
Group : SmallGroup(1728,12653)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 72, 432, 108
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,6}*864a, {4,12}*864b
3-fold quotients : {8,12}*576a
4-fold quotients : {4,6}*432a
6-fold quotients : {8,6}*288, {4,12}*288
8-fold quotients : {4,6}*216
12-fold quotients : {4,6}*144
24-fold quotients : {4,6}*72
27-fold quotients : {8,4}*64a
54-fold quotients : {4,4}*32, {8,2}*32
108-fold quotients : {2,4}*16, {4,2}*16
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)
( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)
( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)
( 56, 57)( 58, 76)( 59, 78)( 60, 77)( 61, 72)( 62, 71)( 63, 70)( 64, 73)
( 65, 75)( 66, 74)( 68, 69)( 79, 81)( 83, 84)( 85,103)( 86,105)( 87,104)
( 88, 99)( 89, 98)( 90, 97)( 91,100)( 92,102)( 93,101)( 95, 96)(106,108)
(109,136)(110,138)(111,137)(112,157)(113,159)(114,158)(115,153)(116,152)
(117,151)(118,154)(119,156)(120,155)(121,148)(122,150)(123,149)(124,144)
(125,143)(126,142)(127,145)(128,147)(129,146)(130,139)(131,141)(132,140)
(133,162)(134,161)(135,160)(163,190)(164,192)(165,191)(166,211)(167,213)
(168,212)(169,207)(170,206)(171,205)(172,208)(173,210)(174,209)(175,202)
(176,204)(177,203)(178,198)(179,197)(180,196)(181,199)(182,201)(183,200)
(184,193)(185,195)(186,194)(187,216)(188,215)(189,214)(217,244)(218,246)
(219,245)(220,265)(221,267)(222,266)(223,261)(224,260)(225,259)(226,262)
(227,264)(228,263)(229,256)(230,258)(231,257)(232,252)(233,251)(234,250)
(235,253)(236,255)(237,254)(238,247)(239,249)(240,248)(241,270)(242,269)
(243,268)(271,298)(272,300)(273,299)(274,319)(275,321)(276,320)(277,315)
(278,314)(279,313)(280,316)(281,318)(282,317)(283,310)(284,312)(285,311)
(286,306)(287,305)(288,304)(289,307)(290,309)(291,308)(292,301)(293,303)
(294,302)(295,324)(296,323)(297,322)(326,327)(328,346)(329,348)(330,347)
(331,342)(332,341)(333,340)(334,343)(335,345)(336,344)(338,339)(349,351)
(353,354)(355,373)(356,375)(357,374)(358,369)(359,368)(360,367)(361,370)
(362,372)(363,371)(365,366)(376,378)(380,381)(382,400)(383,402)(384,401)
(385,396)(386,395)(387,394)(388,397)(389,399)(390,398)(392,393)(403,405)
(407,408)(409,427)(410,429)(411,428)(412,423)(413,422)(414,421)(415,424)
(416,426)(417,425)(419,420)(430,432)(433,541)(434,543)(435,542)(436,562)
(437,564)(438,563)(439,558)(440,557)(441,556)(442,559)(443,561)(444,560)
(445,553)(446,555)(447,554)(448,549)(449,548)(450,547)(451,550)(452,552)
(453,551)(454,544)(455,546)(456,545)(457,567)(458,566)(459,565)(460,568)
(461,570)(462,569)(463,589)(464,591)(465,590)(466,585)(467,584)(468,583)
(469,586)(470,588)(471,587)(472,580)(473,582)(474,581)(475,576)(476,575)
(477,574)(478,577)(479,579)(480,578)(481,571)(482,573)(483,572)(484,594)
(485,593)(486,592)(487,595)(488,597)(489,596)(490,616)(491,618)(492,617)
(493,612)(494,611)(495,610)(496,613)(497,615)(498,614)(499,607)(500,609)
(501,608)(502,603)(503,602)(504,601)(505,604)(506,606)(507,605)(508,598)
(509,600)(510,599)(511,621)(512,620)(513,619)(514,622)(515,624)(516,623)
(517,643)(518,645)(519,644)(520,639)(521,638)(522,637)(523,640)(524,642)
(525,641)(526,634)(527,636)(528,635)(529,630)(530,629)(531,628)(532,631)
(533,633)(534,632)(535,625)(536,627)(537,626)(538,648)(539,647)(540,646)
(649,784)(650,786)(651,785)(652,805)(653,807)(654,806)(655,801)(656,800)
(657,799)(658,802)(659,804)(660,803)(661,796)(662,798)(663,797)(664,792)
(665,791)(666,790)(667,793)(668,795)(669,794)(670,787)(671,789)(672,788)
(673,810)(674,809)(675,808)(676,757)(677,759)(678,758)(679,778)(680,780)
(681,779)(682,774)(683,773)(684,772)(685,775)(686,777)(687,776)(688,769)
(689,771)(690,770)(691,765)(692,764)(693,763)(694,766)(695,768)(696,767)
(697,760)(698,762)(699,761)(700,783)(701,782)(702,781)(703,838)(704,840)
(705,839)(706,859)(707,861)(708,860)(709,855)(710,854)(711,853)(712,856)
(713,858)(714,857)(715,850)(716,852)(717,851)(718,846)(719,845)(720,844)
(721,847)(722,849)(723,848)(724,841)(725,843)(726,842)(727,864)(728,863)
(729,862)(730,811)(731,813)(732,812)(733,832)(734,834)(735,833)(736,828)
(737,827)(738,826)(739,829)(740,831)(741,830)(742,823)(743,825)(744,824)
(745,819)(746,818)(747,817)(748,820)(749,822)(750,821)(751,814)(752,816)
(753,815)(754,837)(755,836)(756,835);;
s1 := ( 1,433)( 2,435)( 3,434)( 4,437)( 5,436)( 6,438)( 7,441)( 8,440)
( 9,439)( 10,457)( 11,459)( 12,458)( 13,452)( 14,451)( 15,453)( 16,456)
( 17,455)( 18,454)( 19,446)( 20,445)( 21,447)( 22,450)( 23,449)( 24,448)
( 25,442)( 26,444)( 27,443)( 28,460)( 29,462)( 30,461)( 31,464)( 32,463)
( 33,465)( 34,468)( 35,467)( 36,466)( 37,484)( 38,486)( 39,485)( 40,479)
( 41,478)( 42,480)( 43,483)( 44,482)( 45,481)( 46,473)( 47,472)( 48,474)
( 49,477)( 50,476)( 51,475)( 52,469)( 53,471)( 54,470)( 55,487)( 56,489)
( 57,488)( 58,491)( 59,490)( 60,492)( 61,495)( 62,494)( 63,493)( 64,511)
( 65,513)( 66,512)( 67,506)( 68,505)( 69,507)( 70,510)( 71,509)( 72,508)
( 73,500)( 74,499)( 75,501)( 76,504)( 77,503)( 78,502)( 79,496)( 80,498)
( 81,497)( 82,514)( 83,516)( 84,515)( 85,518)( 86,517)( 87,519)( 88,522)
( 89,521)( 90,520)( 91,538)( 92,540)( 93,539)( 94,533)( 95,532)( 96,534)
( 97,537)( 98,536)( 99,535)(100,527)(101,526)(102,528)(103,531)(104,530)
(105,529)(106,523)(107,525)(108,524)(109,568)(110,570)(111,569)(112,572)
(113,571)(114,573)(115,576)(116,575)(117,574)(118,592)(119,594)(120,593)
(121,587)(122,586)(123,588)(124,591)(125,590)(126,589)(127,581)(128,580)
(129,582)(130,585)(131,584)(132,583)(133,577)(134,579)(135,578)(136,541)
(137,543)(138,542)(139,545)(140,544)(141,546)(142,549)(143,548)(144,547)
(145,565)(146,567)(147,566)(148,560)(149,559)(150,561)(151,564)(152,563)
(153,562)(154,554)(155,553)(156,555)(157,558)(158,557)(159,556)(160,550)
(161,552)(162,551)(163,622)(164,624)(165,623)(166,626)(167,625)(168,627)
(169,630)(170,629)(171,628)(172,646)(173,648)(174,647)(175,641)(176,640)
(177,642)(178,645)(179,644)(180,643)(181,635)(182,634)(183,636)(184,639)
(185,638)(186,637)(187,631)(188,633)(189,632)(190,595)(191,597)(192,596)
(193,599)(194,598)(195,600)(196,603)(197,602)(198,601)(199,619)(200,621)
(201,620)(202,614)(203,613)(204,615)(205,618)(206,617)(207,616)(208,608)
(209,607)(210,609)(211,612)(212,611)(213,610)(214,604)(215,606)(216,605)
(217,703)(218,705)(219,704)(220,707)(221,706)(222,708)(223,711)(224,710)
(225,709)(226,727)(227,729)(228,728)(229,722)(230,721)(231,723)(232,726)
(233,725)(234,724)(235,716)(236,715)(237,717)(238,720)(239,719)(240,718)
(241,712)(242,714)(243,713)(244,730)(245,732)(246,731)(247,734)(248,733)
(249,735)(250,738)(251,737)(252,736)(253,754)(254,756)(255,755)(256,749)
(257,748)(258,750)(259,753)(260,752)(261,751)(262,743)(263,742)(264,744)
(265,747)(266,746)(267,745)(268,739)(269,741)(270,740)(271,649)(272,651)
(273,650)(274,653)(275,652)(276,654)(277,657)(278,656)(279,655)(280,673)
(281,675)(282,674)(283,668)(284,667)(285,669)(286,672)(287,671)(288,670)
(289,662)(290,661)(291,663)(292,666)(293,665)(294,664)(295,658)(296,660)
(297,659)(298,676)(299,678)(300,677)(301,680)(302,679)(303,681)(304,684)
(305,683)(306,682)(307,700)(308,702)(309,701)(310,695)(311,694)(312,696)
(313,699)(314,698)(315,697)(316,689)(317,688)(318,690)(319,693)(320,692)
(321,691)(322,685)(323,687)(324,686)(325,838)(326,840)(327,839)(328,842)
(329,841)(330,843)(331,846)(332,845)(333,844)(334,862)(335,864)(336,863)
(337,857)(338,856)(339,858)(340,861)(341,860)(342,859)(343,851)(344,850)
(345,852)(346,855)(347,854)(348,853)(349,847)(350,849)(351,848)(352,811)
(353,813)(354,812)(355,815)(356,814)(357,816)(358,819)(359,818)(360,817)
(361,835)(362,837)(363,836)(364,830)(365,829)(366,831)(367,834)(368,833)
(369,832)(370,824)(371,823)(372,825)(373,828)(374,827)(375,826)(376,820)
(377,822)(378,821)(379,784)(380,786)(381,785)(382,788)(383,787)(384,789)
(385,792)(386,791)(387,790)(388,808)(389,810)(390,809)(391,803)(392,802)
(393,804)(394,807)(395,806)(396,805)(397,797)(398,796)(399,798)(400,801)
(401,800)(402,799)(403,793)(404,795)(405,794)(406,757)(407,759)(408,758)
(409,761)(410,760)(411,762)(412,765)(413,764)(414,763)(415,781)(416,783)
(417,782)(418,776)(419,775)(420,777)(421,780)(422,779)(423,778)(424,770)
(425,769)(426,771)(427,774)(428,773)(429,772)(430,766)(431,768)(432,767);;
s2 := ( 1,337)( 2,338)( 3,339)( 4,335)( 5,336)( 6,334)( 7,342)( 8,340)
( 9,341)( 10,330)( 11,328)( 12,329)( 13,325)( 14,326)( 15,327)( 16,332)
( 17,333)( 18,331)( 19,347)( 20,348)( 21,346)( 22,345)( 23,343)( 24,344)
( 25,349)( 26,350)( 27,351)( 28,364)( 29,365)( 30,366)( 31,362)( 32,363)
( 33,361)( 34,369)( 35,367)( 36,368)( 37,357)( 38,355)( 39,356)( 40,352)
( 41,353)( 42,354)( 43,359)( 44,360)( 45,358)( 46,374)( 47,375)( 48,373)
( 49,372)( 50,370)( 51,371)( 52,376)( 53,377)( 54,378)( 55,391)( 56,392)
( 57,393)( 58,389)( 59,390)( 60,388)( 61,396)( 62,394)( 63,395)( 64,384)
( 65,382)( 66,383)( 67,379)( 68,380)( 69,381)( 70,386)( 71,387)( 72,385)
( 73,401)( 74,402)( 75,400)( 76,399)( 77,397)( 78,398)( 79,403)( 80,404)
( 81,405)( 82,418)( 83,419)( 84,420)( 85,416)( 86,417)( 87,415)( 88,423)
( 89,421)( 90,422)( 91,411)( 92,409)( 93,410)( 94,406)( 95,407)( 96,408)
( 97,413)( 98,414)( 99,412)(100,428)(101,429)(102,427)(103,426)(104,424)
(105,425)(106,430)(107,431)(108,432)(109,256)(110,257)(111,258)(112,254)
(113,255)(114,253)(115,261)(116,259)(117,260)(118,249)(119,247)(120,248)
(121,244)(122,245)(123,246)(124,251)(125,252)(126,250)(127,266)(128,267)
(129,265)(130,264)(131,262)(132,263)(133,268)(134,269)(135,270)(136,229)
(137,230)(138,231)(139,227)(140,228)(141,226)(142,234)(143,232)(144,233)
(145,222)(146,220)(147,221)(148,217)(149,218)(150,219)(151,224)(152,225)
(153,223)(154,239)(155,240)(156,238)(157,237)(158,235)(159,236)(160,241)
(161,242)(162,243)(163,310)(164,311)(165,312)(166,308)(167,309)(168,307)
(169,315)(170,313)(171,314)(172,303)(173,301)(174,302)(175,298)(176,299)
(177,300)(178,305)(179,306)(180,304)(181,320)(182,321)(183,319)(184,318)
(185,316)(186,317)(187,322)(188,323)(189,324)(190,283)(191,284)(192,285)
(193,281)(194,282)(195,280)(196,288)(197,286)(198,287)(199,276)(200,274)
(201,275)(202,271)(203,272)(204,273)(205,278)(206,279)(207,277)(208,293)
(209,294)(210,292)(211,291)(212,289)(213,290)(214,295)(215,296)(216,297)
(433,769)(434,770)(435,771)(436,767)(437,768)(438,766)(439,774)(440,772)
(441,773)(442,762)(443,760)(444,761)(445,757)(446,758)(447,759)(448,764)
(449,765)(450,763)(451,779)(452,780)(453,778)(454,777)(455,775)(456,776)
(457,781)(458,782)(459,783)(460,796)(461,797)(462,798)(463,794)(464,795)
(465,793)(466,801)(467,799)(468,800)(469,789)(470,787)(471,788)(472,784)
(473,785)(474,786)(475,791)(476,792)(477,790)(478,806)(479,807)(480,805)
(481,804)(482,802)(483,803)(484,808)(485,809)(486,810)(487,823)(488,824)
(489,825)(490,821)(491,822)(492,820)(493,828)(494,826)(495,827)(496,816)
(497,814)(498,815)(499,811)(500,812)(501,813)(502,818)(503,819)(504,817)
(505,833)(506,834)(507,832)(508,831)(509,829)(510,830)(511,835)(512,836)
(513,837)(514,850)(515,851)(516,852)(517,848)(518,849)(519,847)(520,855)
(521,853)(522,854)(523,843)(524,841)(525,842)(526,838)(527,839)(528,840)
(529,845)(530,846)(531,844)(532,860)(533,861)(534,859)(535,858)(536,856)
(537,857)(538,862)(539,863)(540,864)(541,688)(542,689)(543,690)(544,686)
(545,687)(546,685)(547,693)(548,691)(549,692)(550,681)(551,679)(552,680)
(553,676)(554,677)(555,678)(556,683)(557,684)(558,682)(559,698)(560,699)
(561,697)(562,696)(563,694)(564,695)(565,700)(566,701)(567,702)(568,661)
(569,662)(570,663)(571,659)(572,660)(573,658)(574,666)(575,664)(576,665)
(577,654)(578,652)(579,653)(580,649)(581,650)(582,651)(583,656)(584,657)
(585,655)(586,671)(587,672)(588,670)(589,669)(590,667)(591,668)(592,673)
(593,674)(594,675)(595,742)(596,743)(597,744)(598,740)(599,741)(600,739)
(601,747)(602,745)(603,746)(604,735)(605,733)(606,734)(607,730)(608,731)
(609,732)(610,737)(611,738)(612,736)(613,752)(614,753)(615,751)(616,750)
(617,748)(618,749)(619,754)(620,755)(621,756)(622,715)(623,716)(624,717)
(625,713)(626,714)(627,712)(628,720)(629,718)(630,719)(631,708)(632,706)
(633,707)(634,703)(635,704)(636,705)(637,710)(638,711)(639,709)(640,725)
(641,726)(642,724)(643,723)(644,721)(645,722)(646,727)(647,728)(648,729);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)
( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)
( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)
( 52, 54)( 56, 57)( 58, 76)( 59, 78)( 60, 77)( 61, 72)( 62, 71)( 63, 70)
( 64, 73)( 65, 75)( 66, 74)( 68, 69)( 79, 81)( 83, 84)( 85,103)( 86,105)
( 87,104)( 88, 99)( 89, 98)( 90, 97)( 91,100)( 92,102)( 93,101)( 95, 96)
(106,108)(109,136)(110,138)(111,137)(112,157)(113,159)(114,158)(115,153)
(116,152)(117,151)(118,154)(119,156)(120,155)(121,148)(122,150)(123,149)
(124,144)(125,143)(126,142)(127,145)(128,147)(129,146)(130,139)(131,141)
(132,140)(133,162)(134,161)(135,160)(163,190)(164,192)(165,191)(166,211)
(167,213)(168,212)(169,207)(170,206)(171,205)(172,208)(173,210)(174,209)
(175,202)(176,204)(177,203)(178,198)(179,197)(180,196)(181,199)(182,201)
(183,200)(184,193)(185,195)(186,194)(187,216)(188,215)(189,214)(217,244)
(218,246)(219,245)(220,265)(221,267)(222,266)(223,261)(224,260)(225,259)
(226,262)(227,264)(228,263)(229,256)(230,258)(231,257)(232,252)(233,251)
(234,250)(235,253)(236,255)(237,254)(238,247)(239,249)(240,248)(241,270)
(242,269)(243,268)(271,298)(272,300)(273,299)(274,319)(275,321)(276,320)
(277,315)(278,314)(279,313)(280,316)(281,318)(282,317)(283,310)(284,312)
(285,311)(286,306)(287,305)(288,304)(289,307)(290,309)(291,308)(292,301)
(293,303)(294,302)(295,324)(296,323)(297,322)(326,327)(328,346)(329,348)
(330,347)(331,342)(332,341)(333,340)(334,343)(335,345)(336,344)(338,339)
(349,351)(353,354)(355,373)(356,375)(357,374)(358,369)(359,368)(360,367)
(361,370)(362,372)(363,371)(365,366)(376,378)(380,381)(382,400)(383,402)
(384,401)(385,396)(386,395)(387,394)(388,397)(389,399)(390,398)(392,393)
(403,405)(407,408)(409,427)(410,429)(411,428)(412,423)(413,422)(414,421)
(415,424)(416,426)(417,425)(419,420)(430,432)(433,541)(434,543)(435,542)
(436,562)(437,564)(438,563)(439,558)(440,557)(441,556)(442,559)(443,561)
(444,560)(445,553)(446,555)(447,554)(448,549)(449,548)(450,547)(451,550)
(452,552)(453,551)(454,544)(455,546)(456,545)(457,567)(458,566)(459,565)
(460,568)(461,570)(462,569)(463,589)(464,591)(465,590)(466,585)(467,584)
(468,583)(469,586)(470,588)(471,587)(472,580)(473,582)(474,581)(475,576)
(476,575)(477,574)(478,577)(479,579)(480,578)(481,571)(482,573)(483,572)
(484,594)(485,593)(486,592)(487,595)(488,597)(489,596)(490,616)(491,618)
(492,617)(493,612)(494,611)(495,610)(496,613)(497,615)(498,614)(499,607)
(500,609)(501,608)(502,603)(503,602)(504,601)(505,604)(506,606)(507,605)
(508,598)(509,600)(510,599)(511,621)(512,620)(513,619)(514,622)(515,624)
(516,623)(517,643)(518,645)(519,644)(520,639)(521,638)(522,637)(523,640)
(524,642)(525,641)(526,634)(527,636)(528,635)(529,630)(530,629)(531,628)
(532,631)(533,633)(534,632)(535,625)(536,627)(537,626)(538,648)(539,647)
(540,646)(649,784)(650,786)(651,785)(652,805)(653,807)(654,806)(655,801)
(656,800)(657,799)(658,802)(659,804)(660,803)(661,796)(662,798)(663,797)
(664,792)(665,791)(666,790)(667,793)(668,795)(669,794)(670,787)(671,789)
(672,788)(673,810)(674,809)(675,808)(676,757)(677,759)(678,758)(679,778)
(680,780)(681,779)(682,774)(683,773)(684,772)(685,775)(686,777)(687,776)
(688,769)(689,771)(690,770)(691,765)(692,764)(693,763)(694,766)(695,768)
(696,767)(697,760)(698,762)(699,761)(700,783)(701,782)(702,781)(703,838)
(704,840)(705,839)(706,859)(707,861)(708,860)(709,855)(710,854)(711,853)
(712,856)(713,858)(714,857)(715,850)(716,852)(717,851)(718,846)(719,845)
(720,844)(721,847)(722,849)(723,848)(724,841)(725,843)(726,842)(727,864)
(728,863)(729,862)(730,811)(731,813)(732,812)(733,832)(734,834)(735,833)
(736,828)(737,827)(738,826)(739,829)(740,831)(741,830)(742,823)(743,825)
(744,824)(745,819)(746,818)(747,817)(748,820)(749,822)(750,821)(751,814)
(752,816)(753,815)(754,837)(755,836)(756,835);
s1 := Sym(864)!( 1,433)( 2,435)( 3,434)( 4,437)( 5,436)( 6,438)( 7,441)
( 8,440)( 9,439)( 10,457)( 11,459)( 12,458)( 13,452)( 14,451)( 15,453)
( 16,456)( 17,455)( 18,454)( 19,446)( 20,445)( 21,447)( 22,450)( 23,449)
( 24,448)( 25,442)( 26,444)( 27,443)( 28,460)( 29,462)( 30,461)( 31,464)
( 32,463)( 33,465)( 34,468)( 35,467)( 36,466)( 37,484)( 38,486)( 39,485)
( 40,479)( 41,478)( 42,480)( 43,483)( 44,482)( 45,481)( 46,473)( 47,472)
( 48,474)( 49,477)( 50,476)( 51,475)( 52,469)( 53,471)( 54,470)( 55,487)
( 56,489)( 57,488)( 58,491)( 59,490)( 60,492)( 61,495)( 62,494)( 63,493)
( 64,511)( 65,513)( 66,512)( 67,506)( 68,505)( 69,507)( 70,510)( 71,509)
( 72,508)( 73,500)( 74,499)( 75,501)( 76,504)( 77,503)( 78,502)( 79,496)
( 80,498)( 81,497)( 82,514)( 83,516)( 84,515)( 85,518)( 86,517)( 87,519)
( 88,522)( 89,521)( 90,520)( 91,538)( 92,540)( 93,539)( 94,533)( 95,532)
( 96,534)( 97,537)( 98,536)( 99,535)(100,527)(101,526)(102,528)(103,531)
(104,530)(105,529)(106,523)(107,525)(108,524)(109,568)(110,570)(111,569)
(112,572)(113,571)(114,573)(115,576)(116,575)(117,574)(118,592)(119,594)
(120,593)(121,587)(122,586)(123,588)(124,591)(125,590)(126,589)(127,581)
(128,580)(129,582)(130,585)(131,584)(132,583)(133,577)(134,579)(135,578)
(136,541)(137,543)(138,542)(139,545)(140,544)(141,546)(142,549)(143,548)
(144,547)(145,565)(146,567)(147,566)(148,560)(149,559)(150,561)(151,564)
(152,563)(153,562)(154,554)(155,553)(156,555)(157,558)(158,557)(159,556)
(160,550)(161,552)(162,551)(163,622)(164,624)(165,623)(166,626)(167,625)
(168,627)(169,630)(170,629)(171,628)(172,646)(173,648)(174,647)(175,641)
(176,640)(177,642)(178,645)(179,644)(180,643)(181,635)(182,634)(183,636)
(184,639)(185,638)(186,637)(187,631)(188,633)(189,632)(190,595)(191,597)
(192,596)(193,599)(194,598)(195,600)(196,603)(197,602)(198,601)(199,619)
(200,621)(201,620)(202,614)(203,613)(204,615)(205,618)(206,617)(207,616)
(208,608)(209,607)(210,609)(211,612)(212,611)(213,610)(214,604)(215,606)
(216,605)(217,703)(218,705)(219,704)(220,707)(221,706)(222,708)(223,711)
(224,710)(225,709)(226,727)(227,729)(228,728)(229,722)(230,721)(231,723)
(232,726)(233,725)(234,724)(235,716)(236,715)(237,717)(238,720)(239,719)
(240,718)(241,712)(242,714)(243,713)(244,730)(245,732)(246,731)(247,734)
(248,733)(249,735)(250,738)(251,737)(252,736)(253,754)(254,756)(255,755)
(256,749)(257,748)(258,750)(259,753)(260,752)(261,751)(262,743)(263,742)
(264,744)(265,747)(266,746)(267,745)(268,739)(269,741)(270,740)(271,649)
(272,651)(273,650)(274,653)(275,652)(276,654)(277,657)(278,656)(279,655)
(280,673)(281,675)(282,674)(283,668)(284,667)(285,669)(286,672)(287,671)
(288,670)(289,662)(290,661)(291,663)(292,666)(293,665)(294,664)(295,658)
(296,660)(297,659)(298,676)(299,678)(300,677)(301,680)(302,679)(303,681)
(304,684)(305,683)(306,682)(307,700)(308,702)(309,701)(310,695)(311,694)
(312,696)(313,699)(314,698)(315,697)(316,689)(317,688)(318,690)(319,693)
(320,692)(321,691)(322,685)(323,687)(324,686)(325,838)(326,840)(327,839)
(328,842)(329,841)(330,843)(331,846)(332,845)(333,844)(334,862)(335,864)
(336,863)(337,857)(338,856)(339,858)(340,861)(341,860)(342,859)(343,851)
(344,850)(345,852)(346,855)(347,854)(348,853)(349,847)(350,849)(351,848)
(352,811)(353,813)(354,812)(355,815)(356,814)(357,816)(358,819)(359,818)
(360,817)(361,835)(362,837)(363,836)(364,830)(365,829)(366,831)(367,834)
(368,833)(369,832)(370,824)(371,823)(372,825)(373,828)(374,827)(375,826)
(376,820)(377,822)(378,821)(379,784)(380,786)(381,785)(382,788)(383,787)
(384,789)(385,792)(386,791)(387,790)(388,808)(389,810)(390,809)(391,803)
(392,802)(393,804)(394,807)(395,806)(396,805)(397,797)(398,796)(399,798)
(400,801)(401,800)(402,799)(403,793)(404,795)(405,794)(406,757)(407,759)
(408,758)(409,761)(410,760)(411,762)(412,765)(413,764)(414,763)(415,781)
(416,783)(417,782)(418,776)(419,775)(420,777)(421,780)(422,779)(423,778)
(424,770)(425,769)(426,771)(427,774)(428,773)(429,772)(430,766)(431,768)
(432,767);
s2 := Sym(864)!( 1,337)( 2,338)( 3,339)( 4,335)( 5,336)( 6,334)( 7,342)
( 8,340)( 9,341)( 10,330)( 11,328)( 12,329)( 13,325)( 14,326)( 15,327)
( 16,332)( 17,333)( 18,331)( 19,347)( 20,348)( 21,346)( 22,345)( 23,343)
( 24,344)( 25,349)( 26,350)( 27,351)( 28,364)( 29,365)( 30,366)( 31,362)
( 32,363)( 33,361)( 34,369)( 35,367)( 36,368)( 37,357)( 38,355)( 39,356)
( 40,352)( 41,353)( 42,354)( 43,359)( 44,360)( 45,358)( 46,374)( 47,375)
( 48,373)( 49,372)( 50,370)( 51,371)( 52,376)( 53,377)( 54,378)( 55,391)
( 56,392)( 57,393)( 58,389)( 59,390)( 60,388)( 61,396)( 62,394)( 63,395)
( 64,384)( 65,382)( 66,383)( 67,379)( 68,380)( 69,381)( 70,386)( 71,387)
( 72,385)( 73,401)( 74,402)( 75,400)( 76,399)( 77,397)( 78,398)( 79,403)
( 80,404)( 81,405)( 82,418)( 83,419)( 84,420)( 85,416)( 86,417)( 87,415)
( 88,423)( 89,421)( 90,422)( 91,411)( 92,409)( 93,410)( 94,406)( 95,407)
( 96,408)( 97,413)( 98,414)( 99,412)(100,428)(101,429)(102,427)(103,426)
(104,424)(105,425)(106,430)(107,431)(108,432)(109,256)(110,257)(111,258)
(112,254)(113,255)(114,253)(115,261)(116,259)(117,260)(118,249)(119,247)
(120,248)(121,244)(122,245)(123,246)(124,251)(125,252)(126,250)(127,266)
(128,267)(129,265)(130,264)(131,262)(132,263)(133,268)(134,269)(135,270)
(136,229)(137,230)(138,231)(139,227)(140,228)(141,226)(142,234)(143,232)
(144,233)(145,222)(146,220)(147,221)(148,217)(149,218)(150,219)(151,224)
(152,225)(153,223)(154,239)(155,240)(156,238)(157,237)(158,235)(159,236)
(160,241)(161,242)(162,243)(163,310)(164,311)(165,312)(166,308)(167,309)
(168,307)(169,315)(170,313)(171,314)(172,303)(173,301)(174,302)(175,298)
(176,299)(177,300)(178,305)(179,306)(180,304)(181,320)(182,321)(183,319)
(184,318)(185,316)(186,317)(187,322)(188,323)(189,324)(190,283)(191,284)
(192,285)(193,281)(194,282)(195,280)(196,288)(197,286)(198,287)(199,276)
(200,274)(201,275)(202,271)(203,272)(204,273)(205,278)(206,279)(207,277)
(208,293)(209,294)(210,292)(211,291)(212,289)(213,290)(214,295)(215,296)
(216,297)(433,769)(434,770)(435,771)(436,767)(437,768)(438,766)(439,774)
(440,772)(441,773)(442,762)(443,760)(444,761)(445,757)(446,758)(447,759)
(448,764)(449,765)(450,763)(451,779)(452,780)(453,778)(454,777)(455,775)
(456,776)(457,781)(458,782)(459,783)(460,796)(461,797)(462,798)(463,794)
(464,795)(465,793)(466,801)(467,799)(468,800)(469,789)(470,787)(471,788)
(472,784)(473,785)(474,786)(475,791)(476,792)(477,790)(478,806)(479,807)
(480,805)(481,804)(482,802)(483,803)(484,808)(485,809)(486,810)(487,823)
(488,824)(489,825)(490,821)(491,822)(492,820)(493,828)(494,826)(495,827)
(496,816)(497,814)(498,815)(499,811)(500,812)(501,813)(502,818)(503,819)
(504,817)(505,833)(506,834)(507,832)(508,831)(509,829)(510,830)(511,835)
(512,836)(513,837)(514,850)(515,851)(516,852)(517,848)(518,849)(519,847)
(520,855)(521,853)(522,854)(523,843)(524,841)(525,842)(526,838)(527,839)
(528,840)(529,845)(530,846)(531,844)(532,860)(533,861)(534,859)(535,858)
(536,856)(537,857)(538,862)(539,863)(540,864)(541,688)(542,689)(543,690)
(544,686)(545,687)(546,685)(547,693)(548,691)(549,692)(550,681)(551,679)
(552,680)(553,676)(554,677)(555,678)(556,683)(557,684)(558,682)(559,698)
(560,699)(561,697)(562,696)(563,694)(564,695)(565,700)(566,701)(567,702)
(568,661)(569,662)(570,663)(571,659)(572,660)(573,658)(574,666)(575,664)
(576,665)(577,654)(578,652)(579,653)(580,649)(581,650)(582,651)(583,656)
(584,657)(585,655)(586,671)(587,672)(588,670)(589,669)(590,667)(591,668)
(592,673)(593,674)(594,675)(595,742)(596,743)(597,744)(598,740)(599,741)
(600,739)(601,747)(602,745)(603,746)(604,735)(605,733)(606,734)(607,730)
(608,731)(609,732)(610,737)(611,738)(612,736)(613,752)(614,753)(615,751)
(616,750)(617,748)(618,749)(619,754)(620,755)(621,756)(622,715)(623,716)
(624,717)(625,713)(626,714)(627,712)(628,720)(629,718)(630,719)(631,708)
(632,706)(633,707)(634,703)(635,704)(636,705)(637,710)(638,711)(639,709)
(640,725)(641,726)(642,724)(643,723)(644,721)(645,722)(646,727)(647,728)
(648,729);
poly := sub<Sym(864)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References : None.
to this polytope