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