Polytope of Type {24,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1728m
if this polytope has a name.
Group : SmallGroup(1728,12762)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 72, 432, 36
Order of s0s1s2 : 8
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 : {12,12}*864e
3-fold quotients : {8,12}*576b
4-fold quotients : {12,6}*432f
6-fold quotients : {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}*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 := ( 1,434)( 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 := ( 1,391)( 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*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,
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*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2 ];;
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)!( 1,434)( 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)!( 1,391)( 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*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,
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*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2 >;
References : None.
to this polytope