Polytope of Type {24,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1728g
if this polytope has a name.
Group : SmallGroup(1728,12653)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 72, 432, 36
Order of s0s1s2 : 8
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 : {24,6}*864e, {12,12}*864e
3-fold quotients : {8,12}*576a
4-fold quotients : {12,6}*432f
6-fold quotients : {8,6}*288, {4,12}*288
8-fold quotients : {12,6}*216a
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 := ( 1,434)( 2,433)( 3,435)( 4,438)( 5,437)( 6,436)( 7,439)( 8,441)
( 9,440)( 10,458)( 11,457)( 12,459)( 13,453)( 14,452)( 15,451)( 16,454)
( 17,456)( 18,455)( 19,447)( 20,446)( 21,445)( 22,448)( 23,450)( 24,449)
( 25,443)( 26,442)( 27,444)( 28,461)( 29,460)( 30,462)( 31,465)( 32,464)
( 33,463)( 34,466)( 35,468)( 36,467)( 37,485)( 38,484)( 39,486)( 40,480)
( 41,479)( 42,478)( 43,481)( 44,483)( 45,482)( 46,474)( 47,473)( 48,472)
( 49,475)( 50,477)( 51,476)( 52,470)( 53,469)( 54,471)( 55,488)( 56,487)
( 57,489)( 58,492)( 59,491)( 60,490)( 61,493)( 62,495)( 63,494)( 64,512)
( 65,511)( 66,513)( 67,507)( 68,506)( 69,505)( 70,508)( 71,510)( 72,509)
( 73,501)( 74,500)( 75,499)( 76,502)( 77,504)( 78,503)( 79,497)( 80,496)
( 81,498)( 82,515)( 83,514)( 84,516)( 85,519)( 86,518)( 87,517)( 88,520)
( 89,522)( 90,521)( 91,539)( 92,538)( 93,540)( 94,534)( 95,533)( 96,532)
( 97,535)( 98,537)( 99,536)(100,528)(101,527)(102,526)(103,529)(104,531)
(105,530)(106,524)(107,523)(108,525)(109,569)(110,568)(111,570)(112,573)
(113,572)(114,571)(115,574)(116,576)(117,575)(118,593)(119,592)(120,594)
(121,588)(122,587)(123,586)(124,589)(125,591)(126,590)(127,582)(128,581)
(129,580)(130,583)(131,585)(132,584)(133,578)(134,577)(135,579)(136,542)
(137,541)(138,543)(139,546)(140,545)(141,544)(142,547)(143,549)(144,548)
(145,566)(146,565)(147,567)(148,561)(149,560)(150,559)(151,562)(152,564)
(153,563)(154,555)(155,554)(156,553)(157,556)(158,558)(159,557)(160,551)
(161,550)(162,552)(163,623)(164,622)(165,624)(166,627)(167,626)(168,625)
(169,628)(170,630)(171,629)(172,647)(173,646)(174,648)(175,642)(176,641)
(177,640)(178,643)(179,645)(180,644)(181,636)(182,635)(183,634)(184,637)
(185,639)(186,638)(187,632)(188,631)(189,633)(190,596)(191,595)(192,597)
(193,600)(194,599)(195,598)(196,601)(197,603)(198,602)(199,620)(200,619)
(201,621)(202,615)(203,614)(204,613)(205,616)(206,618)(207,617)(208,609)
(209,608)(210,607)(211,610)(212,612)(213,611)(214,605)(215,604)(216,606)
(217,704)(218,703)(219,705)(220,708)(221,707)(222,706)(223,709)(224,711)
(225,710)(226,728)(227,727)(228,729)(229,723)(230,722)(231,721)(232,724)
(233,726)(234,725)(235,717)(236,716)(237,715)(238,718)(239,720)(240,719)
(241,713)(242,712)(243,714)(244,731)(245,730)(246,732)(247,735)(248,734)
(249,733)(250,736)(251,738)(252,737)(253,755)(254,754)(255,756)(256,750)
(257,749)(258,748)(259,751)(260,753)(261,752)(262,744)(263,743)(264,742)
(265,745)(266,747)(267,746)(268,740)(269,739)(270,741)(271,650)(272,649)
(273,651)(274,654)(275,653)(276,652)(277,655)(278,657)(279,656)(280,674)
(281,673)(282,675)(283,669)(284,668)(285,667)(286,670)(287,672)(288,671)
(289,663)(290,662)(291,661)(292,664)(293,666)(294,665)(295,659)(296,658)
(297,660)(298,677)(299,676)(300,678)(301,681)(302,680)(303,679)(304,682)
(305,684)(306,683)(307,701)(308,700)(309,702)(310,696)(311,695)(312,694)
(313,697)(314,699)(315,698)(316,690)(317,689)(318,688)(319,691)(320,693)
(321,692)(322,686)(323,685)(324,687)(325,839)(326,838)(327,840)(328,843)
(329,842)(330,841)(331,844)(332,846)(333,845)(334,863)(335,862)(336,864)
(337,858)(338,857)(339,856)(340,859)(341,861)(342,860)(343,852)(344,851)
(345,850)(346,853)(347,855)(348,854)(349,848)(350,847)(351,849)(352,812)
(353,811)(354,813)(355,816)(356,815)(357,814)(358,817)(359,819)(360,818)
(361,836)(362,835)(363,837)(364,831)(365,830)(366,829)(367,832)(368,834)
(369,833)(370,825)(371,824)(372,823)(373,826)(374,828)(375,827)(376,821)
(377,820)(378,822)(379,785)(380,784)(381,786)(382,789)(383,788)(384,787)
(385,790)(386,792)(387,791)(388,809)(389,808)(390,810)(391,804)(392,803)
(393,802)(394,805)(395,807)(396,806)(397,798)(398,797)(399,796)(400,799)
(401,801)(402,800)(403,794)(404,793)(405,795)(406,758)(407,757)(408,759)
(409,762)(410,761)(411,760)(412,763)(413,765)(414,764)(415,782)(416,781)
(417,783)(418,777)(419,776)(420,775)(421,778)(422,780)(423,779)(424,771)
(425,770)(426,769)(427,772)(428,774)(429,773)(430,767)(431,766)(432,768);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*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)!( 1,434)( 2,433)( 3,435)( 4,438)( 5,437)( 6,436)( 7,439)
( 8,441)( 9,440)( 10,458)( 11,457)( 12,459)( 13,453)( 14,452)( 15,451)
( 16,454)( 17,456)( 18,455)( 19,447)( 20,446)( 21,445)( 22,448)( 23,450)
( 24,449)( 25,443)( 26,442)( 27,444)( 28,461)( 29,460)( 30,462)( 31,465)
( 32,464)( 33,463)( 34,466)( 35,468)( 36,467)( 37,485)( 38,484)( 39,486)
( 40,480)( 41,479)( 42,478)( 43,481)( 44,483)( 45,482)( 46,474)( 47,473)
( 48,472)( 49,475)( 50,477)( 51,476)( 52,470)( 53,469)( 54,471)( 55,488)
( 56,487)( 57,489)( 58,492)( 59,491)( 60,490)( 61,493)( 62,495)( 63,494)
( 64,512)( 65,511)( 66,513)( 67,507)( 68,506)( 69,505)( 70,508)( 71,510)
( 72,509)( 73,501)( 74,500)( 75,499)( 76,502)( 77,504)( 78,503)( 79,497)
( 80,496)( 81,498)( 82,515)( 83,514)( 84,516)( 85,519)( 86,518)( 87,517)
( 88,520)( 89,522)( 90,521)( 91,539)( 92,538)( 93,540)( 94,534)( 95,533)
( 96,532)( 97,535)( 98,537)( 99,536)(100,528)(101,527)(102,526)(103,529)
(104,531)(105,530)(106,524)(107,523)(108,525)(109,569)(110,568)(111,570)
(112,573)(113,572)(114,571)(115,574)(116,576)(117,575)(118,593)(119,592)
(120,594)(121,588)(122,587)(123,586)(124,589)(125,591)(126,590)(127,582)
(128,581)(129,580)(130,583)(131,585)(132,584)(133,578)(134,577)(135,579)
(136,542)(137,541)(138,543)(139,546)(140,545)(141,544)(142,547)(143,549)
(144,548)(145,566)(146,565)(147,567)(148,561)(149,560)(150,559)(151,562)
(152,564)(153,563)(154,555)(155,554)(156,553)(157,556)(158,558)(159,557)
(160,551)(161,550)(162,552)(163,623)(164,622)(165,624)(166,627)(167,626)
(168,625)(169,628)(170,630)(171,629)(172,647)(173,646)(174,648)(175,642)
(176,641)(177,640)(178,643)(179,645)(180,644)(181,636)(182,635)(183,634)
(184,637)(185,639)(186,638)(187,632)(188,631)(189,633)(190,596)(191,595)
(192,597)(193,600)(194,599)(195,598)(196,601)(197,603)(198,602)(199,620)
(200,619)(201,621)(202,615)(203,614)(204,613)(205,616)(206,618)(207,617)
(208,609)(209,608)(210,607)(211,610)(212,612)(213,611)(214,605)(215,604)
(216,606)(217,704)(218,703)(219,705)(220,708)(221,707)(222,706)(223,709)
(224,711)(225,710)(226,728)(227,727)(228,729)(229,723)(230,722)(231,721)
(232,724)(233,726)(234,725)(235,717)(236,716)(237,715)(238,718)(239,720)
(240,719)(241,713)(242,712)(243,714)(244,731)(245,730)(246,732)(247,735)
(248,734)(249,733)(250,736)(251,738)(252,737)(253,755)(254,754)(255,756)
(256,750)(257,749)(258,748)(259,751)(260,753)(261,752)(262,744)(263,743)
(264,742)(265,745)(266,747)(267,746)(268,740)(269,739)(270,741)(271,650)
(272,649)(273,651)(274,654)(275,653)(276,652)(277,655)(278,657)(279,656)
(280,674)(281,673)(282,675)(283,669)(284,668)(285,667)(286,670)(287,672)
(288,671)(289,663)(290,662)(291,661)(292,664)(293,666)(294,665)(295,659)
(296,658)(297,660)(298,677)(299,676)(300,678)(301,681)(302,680)(303,679)
(304,682)(305,684)(306,683)(307,701)(308,700)(309,702)(310,696)(311,695)
(312,694)(313,697)(314,699)(315,698)(316,690)(317,689)(318,688)(319,691)
(320,693)(321,692)(322,686)(323,685)(324,687)(325,839)(326,838)(327,840)
(328,843)(329,842)(330,841)(331,844)(332,846)(333,845)(334,863)(335,862)
(336,864)(337,858)(338,857)(339,856)(340,859)(341,861)(342,860)(343,852)
(344,851)(345,850)(346,853)(347,855)(348,854)(349,848)(350,847)(351,849)
(352,812)(353,811)(354,813)(355,816)(356,815)(357,814)(358,817)(359,819)
(360,818)(361,836)(362,835)(363,837)(364,831)(365,830)(366,829)(367,832)
(368,834)(369,833)(370,825)(371,824)(372,823)(373,826)(374,828)(375,827)
(376,821)(377,820)(378,822)(379,785)(380,784)(381,786)(382,789)(383,788)
(384,787)(385,790)(386,792)(387,791)(388,809)(389,808)(390,810)(391,804)
(392,803)(393,802)(394,805)(395,807)(396,806)(397,798)(398,797)(399,796)
(400,799)(401,801)(402,800)(403,794)(404,793)(405,795)(406,758)(407,757)
(408,759)(409,762)(410,761)(411,760)(412,763)(413,765)(414,764)(415,782)
(416,781)(417,783)(418,777)(419,776)(420,775)(421,778)(422,780)(423,779)
(424,771)(425,770)(426,769)(427,772)(428,774)(429,773)(430,767)(431,766)
(432,768);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*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