Polytope of Type {8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1728d
if this polytope has a name.
Group : SmallGroup(1728,12762)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 72, 432, 108
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
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 : {4,12}*864b
3-fold quotients : {8,12}*576b
4-fold quotients : {4,6}*432a
6-fold quotients : {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}*64b
54-fold quotients : {4,4}*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)
( 55, 82)( 56, 84)( 57, 83)( 58,103)( 59,105)( 60,104)( 61, 99)( 62, 98)
( 63, 97)( 64,100)( 65,102)( 66,101)( 67, 94)( 68, 96)( 69, 95)( 70, 90)
( 71, 89)( 72, 88)( 73, 91)( 74, 93)( 75, 92)( 76, 85)( 77, 87)( 78, 86)
( 79,108)( 80,107)( 81,106)(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)(164,165)(166,184)
(167,186)(168,185)(169,180)(170,179)(171,178)(172,181)(173,183)(174,182)
(176,177)(187,189)(191,192)(193,211)(194,213)(195,212)(196,207)(197,206)
(198,205)(199,208)(200,210)(201,209)(203,204)(214,216)(218,219)(220,238)
(221,240)(222,239)(223,234)(224,233)(225,232)(226,235)(227,237)(228,236)
(230,231)(241,243)(245,246)(247,265)(248,267)(249,266)(250,261)(251,260)
(252,259)(253,262)(254,264)(255,263)(257,258)(268,270)(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)(325,352)(326,354)(327,353)(328,373)(329,375)(330,374)(331,369)
(332,368)(333,367)(334,370)(335,372)(336,371)(337,364)(338,366)(339,365)
(340,360)(341,359)(342,358)(343,361)(344,363)(345,362)(346,355)(347,357)
(348,356)(349,378)(350,377)(351,376)(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)(487,622)(488,624)(489,623)(490,643)(491,645)(492,644)
(493,639)(494,638)(495,637)(496,640)(497,642)(498,641)(499,634)(500,636)
(501,635)(502,630)(503,629)(504,628)(505,631)(506,633)(507,632)(508,625)
(509,627)(510,626)(511,648)(512,647)(513,646)(514,595)(515,597)(516,596)
(517,616)(518,618)(519,617)(520,612)(521,611)(522,610)(523,613)(524,615)
(525,614)(526,607)(527,609)(528,608)(529,603)(530,602)(531,601)(532,604)
(533,606)(534,605)(535,598)(536,600)(537,599)(538,621)(539,620)(540,619)
(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)(703,811)(704,813)
(705,812)(706,832)(707,834)(708,833)(709,828)(710,827)(711,826)(712,829)
(713,831)(714,830)(715,823)(716,825)(717,824)(718,819)(719,818)(720,817)
(721,820)(722,822)(723,821)(724,814)(725,816)(726,815)(727,837)(728,836)
(729,835)(730,838)(731,840)(732,839)(733,859)(734,861)(735,860)(736,855)
(737,854)(738,853)(739,856)(740,858)(741,857)(742,850)(743,852)(744,851)
(745,846)(746,845)(747,844)(748,847)(749,849)(750,848)(751,841)(752,843)
(753,842)(754,864)(755,863)(756,862);;
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 := ( 1,391)( 2,392)( 3,393)( 4,389)( 5,390)( 6,388)( 7,396)( 8,394)
( 9,395)( 10,384)( 11,382)( 12,383)( 13,379)( 14,380)( 15,381)( 16,386)
( 17,387)( 18,385)( 19,401)( 20,402)( 21,400)( 22,399)( 23,397)( 24,398)
( 25,403)( 26,404)( 27,405)( 28,418)( 29,419)( 30,420)( 31,416)( 32,417)
( 33,415)( 34,423)( 35,421)( 36,422)( 37,411)( 38,409)( 39,410)( 40,406)
( 41,407)( 42,408)( 43,413)( 44,414)( 45,412)( 46,428)( 47,429)( 48,427)
( 49,426)( 50,424)( 51,425)( 52,430)( 53,431)( 54,432)( 55,337)( 56,338)
( 57,339)( 58,335)( 59,336)( 60,334)( 61,342)( 62,340)( 63,341)( 64,330)
( 65,328)( 66,329)( 67,325)( 68,326)( 69,327)( 70,332)( 71,333)( 72,331)
( 73,347)( 74,348)( 75,346)( 76,345)( 77,343)( 78,344)( 79,349)( 80,350)
( 81,351)( 82,364)( 83,365)( 84,366)( 85,362)( 86,363)( 87,361)( 88,369)
( 89,367)( 90,368)( 91,357)( 92,355)( 93,356)( 94,352)( 95,353)( 96,354)
( 97,359)( 98,360)( 99,358)(100,374)(101,375)(102,373)(103,372)(104,370)
(105,371)(106,376)(107,377)(108,378)(109,283)(110,284)(111,285)(112,281)
(113,282)(114,280)(115,288)(116,286)(117,287)(118,276)(119,274)(120,275)
(121,271)(122,272)(123,273)(124,278)(125,279)(126,277)(127,293)(128,294)
(129,292)(130,291)(131,289)(132,290)(133,295)(134,296)(135,297)(136,310)
(137,311)(138,312)(139,308)(140,309)(141,307)(142,315)(143,313)(144,314)
(145,303)(146,301)(147,302)(148,298)(149,299)(150,300)(151,305)(152,306)
(153,304)(154,320)(155,321)(156,319)(157,318)(158,316)(159,317)(160,322)
(161,323)(162,324)(163,229)(164,230)(165,231)(166,227)(167,228)(168,226)
(169,234)(170,232)(171,233)(172,222)(173,220)(174,221)(175,217)(176,218)
(177,219)(178,224)(179,225)(180,223)(181,239)(182,240)(183,238)(184,237)
(185,235)(186,236)(187,241)(188,242)(189,243)(190,256)(191,257)(192,258)
(193,254)(194,255)(195,253)(196,261)(197,259)(198,260)(199,249)(200,247)
(201,248)(202,244)(203,245)(204,246)(205,251)(206,252)(207,250)(208,266)
(209,267)(210,265)(211,264)(212,262)(213,263)(214,268)(215,269)(216,270)
(433,823)(434,824)(435,825)(436,821)(437,822)(438,820)(439,828)(440,826)
(441,827)(442,816)(443,814)(444,815)(445,811)(446,812)(447,813)(448,818)
(449,819)(450,817)(451,833)(452,834)(453,832)(454,831)(455,829)(456,830)
(457,835)(458,836)(459,837)(460,850)(461,851)(462,852)(463,848)(464,849)
(465,847)(466,855)(467,853)(468,854)(469,843)(470,841)(471,842)(472,838)
(473,839)(474,840)(475,845)(476,846)(477,844)(478,860)(479,861)(480,859)
(481,858)(482,856)(483,857)(484,862)(485,863)(486,864)(487,769)(488,770)
(489,771)(490,767)(491,768)(492,766)(493,774)(494,772)(495,773)(496,762)
(497,760)(498,761)(499,757)(500,758)(501,759)(502,764)(503,765)(504,763)
(505,779)(506,780)(507,778)(508,777)(509,775)(510,776)(511,781)(512,782)
(513,783)(514,796)(515,797)(516,798)(517,794)(518,795)(519,793)(520,801)
(521,799)(522,800)(523,789)(524,787)(525,788)(526,784)(527,785)(528,786)
(529,791)(530,792)(531,790)(532,806)(533,807)(534,805)(535,804)(536,802)
(537,803)(538,808)(539,809)(540,810)(541,715)(542,716)(543,717)(544,713)
(545,714)(546,712)(547,720)(548,718)(549,719)(550,708)(551,706)(552,707)
(553,703)(554,704)(555,705)(556,710)(557,711)(558,709)(559,725)(560,726)
(561,724)(562,723)(563,721)(564,722)(565,727)(566,728)(567,729)(568,742)
(569,743)(570,744)(571,740)(572,741)(573,739)(574,747)(575,745)(576,746)
(577,735)(578,733)(579,734)(580,730)(581,731)(582,732)(583,737)(584,738)
(585,736)(586,752)(587,753)(588,751)(589,750)(590,748)(591,749)(592,754)
(593,755)(594,756)(595,661)(596,662)(597,663)(598,659)(599,660)(600,658)
(601,666)(602,664)(603,665)(604,654)(605,652)(606,653)(607,649)(608,650)
(609,651)(610,656)(611,657)(612,655)(613,671)(614,672)(615,670)(616,669)
(617,667)(618,668)(619,673)(620,674)(621,675)(622,688)(623,689)(624,690)
(625,686)(626,687)(627,685)(628,693)(629,691)(630,692)(631,681)(632,679)
(633,680)(634,676)(635,677)(636,678)(637,683)(638,684)(639,682)(640,698)
(641,699)(642,697)(643,696)(644,694)(645,695)(646,700)(647,701)(648,702);;
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,
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0 ];;
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)( 55, 82)( 56, 84)( 57, 83)( 58,103)( 59,105)( 60,104)( 61, 99)
( 62, 98)( 63, 97)( 64,100)( 65,102)( 66,101)( 67, 94)( 68, 96)( 69, 95)
( 70, 90)( 71, 89)( 72, 88)( 73, 91)( 74, 93)( 75, 92)( 76, 85)( 77, 87)
( 78, 86)( 79,108)( 80,107)( 81,106)(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)(164,165)
(166,184)(167,186)(168,185)(169,180)(170,179)(171,178)(172,181)(173,183)
(174,182)(176,177)(187,189)(191,192)(193,211)(194,213)(195,212)(196,207)
(197,206)(198,205)(199,208)(200,210)(201,209)(203,204)(214,216)(218,219)
(220,238)(221,240)(222,239)(223,234)(224,233)(225,232)(226,235)(227,237)
(228,236)(230,231)(241,243)(245,246)(247,265)(248,267)(249,266)(250,261)
(251,260)(252,259)(253,262)(254,264)(255,263)(257,258)(268,270)(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)(325,352)(326,354)(327,353)(328,373)(329,375)(330,374)
(331,369)(332,368)(333,367)(334,370)(335,372)(336,371)(337,364)(338,366)
(339,365)(340,360)(341,359)(342,358)(343,361)(344,363)(345,362)(346,355)
(347,357)(348,356)(349,378)(350,377)(351,376)(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)(487,622)(488,624)(489,623)(490,643)(491,645)
(492,644)(493,639)(494,638)(495,637)(496,640)(497,642)(498,641)(499,634)
(500,636)(501,635)(502,630)(503,629)(504,628)(505,631)(506,633)(507,632)
(508,625)(509,627)(510,626)(511,648)(512,647)(513,646)(514,595)(515,597)
(516,596)(517,616)(518,618)(519,617)(520,612)(521,611)(522,610)(523,613)
(524,615)(525,614)(526,607)(527,609)(528,608)(529,603)(530,602)(531,601)
(532,604)(533,606)(534,605)(535,598)(536,600)(537,599)(538,621)(539,620)
(540,619)(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)(703,811)
(704,813)(705,812)(706,832)(707,834)(708,833)(709,828)(710,827)(711,826)
(712,829)(713,831)(714,830)(715,823)(716,825)(717,824)(718,819)(719,818)
(720,817)(721,820)(722,822)(723,821)(724,814)(725,816)(726,815)(727,837)
(728,836)(729,835)(730,838)(731,840)(732,839)(733,859)(734,861)(735,860)
(736,855)(737,854)(738,853)(739,856)(740,858)(741,857)(742,850)(743,852)
(744,851)(745,846)(746,845)(747,844)(748,847)(749,849)(750,848)(751,841)
(752,843)(753,842)(754,864)(755,863)(756,862);
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)!( 1,391)( 2,392)( 3,393)( 4,389)( 5,390)( 6,388)( 7,396)
( 8,394)( 9,395)( 10,384)( 11,382)( 12,383)( 13,379)( 14,380)( 15,381)
( 16,386)( 17,387)( 18,385)( 19,401)( 20,402)( 21,400)( 22,399)( 23,397)
( 24,398)( 25,403)( 26,404)( 27,405)( 28,418)( 29,419)( 30,420)( 31,416)
( 32,417)( 33,415)( 34,423)( 35,421)( 36,422)( 37,411)( 38,409)( 39,410)
( 40,406)( 41,407)( 42,408)( 43,413)( 44,414)( 45,412)( 46,428)( 47,429)
( 48,427)( 49,426)( 50,424)( 51,425)( 52,430)( 53,431)( 54,432)( 55,337)
( 56,338)( 57,339)( 58,335)( 59,336)( 60,334)( 61,342)( 62,340)( 63,341)
( 64,330)( 65,328)( 66,329)( 67,325)( 68,326)( 69,327)( 70,332)( 71,333)
( 72,331)( 73,347)( 74,348)( 75,346)( 76,345)( 77,343)( 78,344)( 79,349)
( 80,350)( 81,351)( 82,364)( 83,365)( 84,366)( 85,362)( 86,363)( 87,361)
( 88,369)( 89,367)( 90,368)( 91,357)( 92,355)( 93,356)( 94,352)( 95,353)
( 96,354)( 97,359)( 98,360)( 99,358)(100,374)(101,375)(102,373)(103,372)
(104,370)(105,371)(106,376)(107,377)(108,378)(109,283)(110,284)(111,285)
(112,281)(113,282)(114,280)(115,288)(116,286)(117,287)(118,276)(119,274)
(120,275)(121,271)(122,272)(123,273)(124,278)(125,279)(126,277)(127,293)
(128,294)(129,292)(130,291)(131,289)(132,290)(133,295)(134,296)(135,297)
(136,310)(137,311)(138,312)(139,308)(140,309)(141,307)(142,315)(143,313)
(144,314)(145,303)(146,301)(147,302)(148,298)(149,299)(150,300)(151,305)
(152,306)(153,304)(154,320)(155,321)(156,319)(157,318)(158,316)(159,317)
(160,322)(161,323)(162,324)(163,229)(164,230)(165,231)(166,227)(167,228)
(168,226)(169,234)(170,232)(171,233)(172,222)(173,220)(174,221)(175,217)
(176,218)(177,219)(178,224)(179,225)(180,223)(181,239)(182,240)(183,238)
(184,237)(185,235)(186,236)(187,241)(188,242)(189,243)(190,256)(191,257)
(192,258)(193,254)(194,255)(195,253)(196,261)(197,259)(198,260)(199,249)
(200,247)(201,248)(202,244)(203,245)(204,246)(205,251)(206,252)(207,250)
(208,266)(209,267)(210,265)(211,264)(212,262)(213,263)(214,268)(215,269)
(216,270)(433,823)(434,824)(435,825)(436,821)(437,822)(438,820)(439,828)
(440,826)(441,827)(442,816)(443,814)(444,815)(445,811)(446,812)(447,813)
(448,818)(449,819)(450,817)(451,833)(452,834)(453,832)(454,831)(455,829)
(456,830)(457,835)(458,836)(459,837)(460,850)(461,851)(462,852)(463,848)
(464,849)(465,847)(466,855)(467,853)(468,854)(469,843)(470,841)(471,842)
(472,838)(473,839)(474,840)(475,845)(476,846)(477,844)(478,860)(479,861)
(480,859)(481,858)(482,856)(483,857)(484,862)(485,863)(486,864)(487,769)
(488,770)(489,771)(490,767)(491,768)(492,766)(493,774)(494,772)(495,773)
(496,762)(497,760)(498,761)(499,757)(500,758)(501,759)(502,764)(503,765)
(504,763)(505,779)(506,780)(507,778)(508,777)(509,775)(510,776)(511,781)
(512,782)(513,783)(514,796)(515,797)(516,798)(517,794)(518,795)(519,793)
(520,801)(521,799)(522,800)(523,789)(524,787)(525,788)(526,784)(527,785)
(528,786)(529,791)(530,792)(531,790)(532,806)(533,807)(534,805)(535,804)
(536,802)(537,803)(538,808)(539,809)(540,810)(541,715)(542,716)(543,717)
(544,713)(545,714)(546,712)(547,720)(548,718)(549,719)(550,708)(551,706)
(552,707)(553,703)(554,704)(555,705)(556,710)(557,711)(558,709)(559,725)
(560,726)(561,724)(562,723)(563,721)(564,722)(565,727)(566,728)(567,729)
(568,742)(569,743)(570,744)(571,740)(572,741)(573,739)(574,747)(575,745)
(576,746)(577,735)(578,733)(579,734)(580,730)(581,731)(582,732)(583,737)
(584,738)(585,736)(586,752)(587,753)(588,751)(589,750)(590,748)(591,749)
(592,754)(593,755)(594,756)(595,661)(596,662)(597,663)(598,659)(599,660)
(600,658)(601,666)(602,664)(603,665)(604,654)(605,652)(606,653)(607,649)
(608,650)(609,651)(610,656)(611,657)(612,655)(613,671)(614,672)(615,670)
(616,669)(617,667)(618,668)(619,673)(620,674)(621,675)(622,688)(623,689)
(624,690)(625,686)(626,687)(627,685)(628,693)(629,691)(630,692)(631,681)
(632,679)(633,680)(634,676)(635,677)(636,678)(637,683)(638,684)(639,682)
(640,698)(641,699)(642,697)(643,696)(644,694)(645,695)(646,700)(647,701)
(648,702);
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,
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0 >;
References : None.
to this polytope