Polytope of Type {24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*1728h
if this polytope has a name.
Group : SmallGroup(1728,31293)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 216, 432, 36
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 : {12,4}*864c
3-fold quotients : {8,4}*576b
4-fold quotients : {12,4}*432b
6-fold quotients : {4,4}*288
9-fold quotients : {24,4}*192b
12-fold quotients : {4,4}*144
18-fold quotients : {12,4}*96a
24-fold quotients : {4,4}*72
27-fold quotients : {8,4}*64b
36-fold quotients : {12,2}*48, {6,4}*48a
54-fold quotients : {4,4}*32
72-fold quotients : {6,2}*24
108-fold quotients : {2,4}*16, {4,2}*16
144-fold quotients : {3,2}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,325)( 2,330)( 3,332)( 4,328)( 5,333)( 6,326)( 7,331)( 8,327)
( 9,329)( 10,343)( 11,348)( 12,350)( 13,346)( 14,351)( 15,344)( 16,349)
( 17,345)( 18,347)( 19,334)( 20,339)( 21,341)( 22,337)( 23,342)( 24,335)
( 25,340)( 26,336)( 27,338)( 28,352)( 29,357)( 30,359)( 31,355)( 32,360)
( 33,353)( 34,358)( 35,354)( 36,356)( 37,370)( 38,375)( 39,377)( 40,373)
( 41,378)( 42,371)( 43,376)( 44,372)( 45,374)( 46,361)( 47,366)( 48,368)
( 49,364)( 50,369)( 51,362)( 52,367)( 53,363)( 54,365)( 55,379)( 56,384)
( 57,386)( 58,382)( 59,387)( 60,380)( 61,385)( 62,381)( 63,383)( 64,397)
( 65,402)( 66,404)( 67,400)( 68,405)( 69,398)( 70,403)( 71,399)( 72,401)
( 73,388)( 74,393)( 75,395)( 76,391)( 77,396)( 78,389)( 79,394)( 80,390)
( 81,392)( 82,406)( 83,411)( 84,413)( 85,409)( 86,414)( 87,407)( 88,412)
( 89,408)( 90,410)( 91,424)( 92,429)( 93,431)( 94,427)( 95,432)( 96,425)
( 97,430)( 98,426)( 99,428)(100,415)(101,420)(102,422)(103,418)(104,423)
(105,416)(106,421)(107,417)(108,419)(109,244)(110,249)(111,251)(112,247)
(113,252)(114,245)(115,250)(116,246)(117,248)(118,262)(119,267)(120,269)
(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,253)(128,258)
(129,260)(130,256)(131,261)(132,254)(133,259)(134,255)(135,257)(136,217)
(137,222)(138,224)(139,220)(140,225)(141,218)(142,223)(143,219)(144,221)
(145,235)(146,240)(147,242)(148,238)(149,243)(150,236)(151,241)(152,237)
(153,239)(154,226)(155,231)(156,233)(157,229)(158,234)(159,227)(160,232)
(161,228)(162,230)(163,298)(164,303)(165,305)(166,301)(167,306)(168,299)
(169,304)(170,300)(171,302)(172,316)(173,321)(174,323)(175,319)(176,324)
(177,317)(178,322)(179,318)(180,320)(181,307)(182,312)(183,314)(184,310)
(185,315)(186,308)(187,313)(188,309)(189,311)(190,271)(191,276)(192,278)
(193,274)(194,279)(195,272)(196,277)(197,273)(198,275)(199,289)(200,294)
(201,296)(202,292)(203,297)(204,290)(205,295)(206,291)(207,293)(208,280)
(209,285)(210,287)(211,283)(212,288)(213,281)(214,286)(215,282)(216,284)
(433,676)(434,681)(435,683)(436,679)(437,684)(438,677)(439,682)(440,678)
(441,680)(442,694)(443,699)(444,701)(445,697)(446,702)(447,695)(448,700)
(449,696)(450,698)(451,685)(452,690)(453,692)(454,688)(455,693)(456,686)
(457,691)(458,687)(459,689)(460,649)(461,654)(462,656)(463,652)(464,657)
(465,650)(466,655)(467,651)(468,653)(469,667)(470,672)(471,674)(472,670)
(473,675)(474,668)(475,673)(476,669)(477,671)(478,658)(479,663)(480,665)
(481,661)(482,666)(483,659)(484,664)(485,660)(486,662)(487,730)(488,735)
(489,737)(490,733)(491,738)(492,731)(493,736)(494,732)(495,734)(496,748)
(497,753)(498,755)(499,751)(500,756)(501,749)(502,754)(503,750)(504,752)
(505,739)(506,744)(507,746)(508,742)(509,747)(510,740)(511,745)(512,741)
(513,743)(514,703)(515,708)(516,710)(517,706)(518,711)(519,704)(520,709)
(521,705)(522,707)(523,721)(524,726)(525,728)(526,724)(527,729)(528,722)
(529,727)(530,723)(531,725)(532,712)(533,717)(534,719)(535,715)(536,720)
(537,713)(538,718)(539,714)(540,716)(541,757)(542,762)(543,764)(544,760)
(545,765)(546,758)(547,763)(548,759)(549,761)(550,775)(551,780)(552,782)
(553,778)(554,783)(555,776)(556,781)(557,777)(558,779)(559,766)(560,771)
(561,773)(562,769)(563,774)(564,767)(565,772)(566,768)(567,770)(568,784)
(569,789)(570,791)(571,787)(572,792)(573,785)(574,790)(575,786)(576,788)
(577,802)(578,807)(579,809)(580,805)(581,810)(582,803)(583,808)(584,804)
(585,806)(586,793)(587,798)(588,800)(589,796)(590,801)(591,794)(592,799)
(593,795)(594,797)(595,811)(596,816)(597,818)(598,814)(599,819)(600,812)
(601,817)(602,813)(603,815)(604,829)(605,834)(606,836)(607,832)(608,837)
(609,830)(610,835)(611,831)(612,833)(613,820)(614,825)(615,827)(616,823)
(617,828)(618,821)(619,826)(620,822)(621,824)(622,838)(623,843)(624,845)
(625,841)(626,846)(627,839)(628,844)(629,840)(630,842)(631,856)(632,861)
(633,863)(634,859)(635,864)(636,857)(637,862)(638,858)(639,860)(640,847)
(641,852)(642,854)(643,850)(644,855)(645,848)(646,853)(647,849)(648,851);;
s1 := ( 1,658)( 2,659)( 3,660)( 4,666)( 5,664)( 6,665)( 7,662)( 8,663)
( 9,661)( 10,649)( 11,650)( 12,651)( 13,657)( 14,655)( 15,656)( 16,653)
( 17,654)( 18,652)( 19,667)( 20,668)( 21,669)( 22,675)( 23,673)( 24,674)
( 25,671)( 26,672)( 27,670)( 28,685)( 29,686)( 30,687)( 31,693)( 32,691)
( 33,692)( 34,689)( 35,690)( 36,688)( 37,676)( 38,677)( 39,678)( 40,684)
( 41,682)( 42,683)( 43,680)( 44,681)( 45,679)( 46,694)( 47,695)( 48,696)
( 49,702)( 50,700)( 51,701)( 52,698)( 53,699)( 54,697)( 55,739)( 56,740)
( 57,741)( 58,747)( 59,745)( 60,746)( 61,743)( 62,744)( 63,742)( 64,730)
( 65,731)( 66,732)( 67,738)( 68,736)( 69,737)( 70,734)( 71,735)( 72,733)
( 73,748)( 74,749)( 75,750)( 76,756)( 77,754)( 78,755)( 79,752)( 80,753)
( 81,751)( 82,712)( 83,713)( 84,714)( 85,720)( 86,718)( 87,719)( 88,716)
( 89,717)( 90,715)( 91,703)( 92,704)( 93,705)( 94,711)( 95,709)( 96,710)
( 97,707)( 98,708)( 99,706)(100,721)(101,722)(102,723)(103,729)(104,727)
(105,728)(106,725)(107,726)(108,724)(109,766)(110,767)(111,768)(112,774)
(113,772)(114,773)(115,770)(116,771)(117,769)(118,757)(119,758)(120,759)
(121,765)(122,763)(123,764)(124,761)(125,762)(126,760)(127,775)(128,776)
(129,777)(130,783)(131,781)(132,782)(133,779)(134,780)(135,778)(136,793)
(137,794)(138,795)(139,801)(140,799)(141,800)(142,797)(143,798)(144,796)
(145,784)(146,785)(147,786)(148,792)(149,790)(150,791)(151,788)(152,789)
(153,787)(154,802)(155,803)(156,804)(157,810)(158,808)(159,809)(160,806)
(161,807)(162,805)(163,847)(164,848)(165,849)(166,855)(167,853)(168,854)
(169,851)(170,852)(171,850)(172,838)(173,839)(174,840)(175,846)(176,844)
(177,845)(178,842)(179,843)(180,841)(181,856)(182,857)(183,858)(184,864)
(185,862)(186,863)(187,860)(188,861)(189,859)(190,820)(191,821)(192,822)
(193,828)(194,826)(195,827)(196,824)(197,825)(198,823)(199,811)(200,812)
(201,813)(202,819)(203,817)(204,818)(205,815)(206,816)(207,814)(208,829)
(209,830)(210,831)(211,837)(212,835)(213,836)(214,833)(215,834)(216,832)
(217,523)(218,524)(219,525)(220,531)(221,529)(222,530)(223,527)(224,528)
(225,526)(226,514)(227,515)(228,516)(229,522)(230,520)(231,521)(232,518)
(233,519)(234,517)(235,532)(236,533)(237,534)(238,540)(239,538)(240,539)
(241,536)(242,537)(243,535)(244,496)(245,497)(246,498)(247,504)(248,502)
(249,503)(250,500)(251,501)(252,499)(253,487)(254,488)(255,489)(256,495)
(257,493)(258,494)(259,491)(260,492)(261,490)(262,505)(263,506)(264,507)
(265,513)(266,511)(267,512)(268,509)(269,510)(270,508)(271,469)(272,470)
(273,471)(274,477)(275,475)(276,476)(277,473)(278,474)(279,472)(280,460)
(281,461)(282,462)(283,468)(284,466)(285,467)(286,464)(287,465)(288,463)
(289,478)(290,479)(291,480)(292,486)(293,484)(294,485)(295,482)(296,483)
(297,481)(298,442)(299,443)(300,444)(301,450)(302,448)(303,449)(304,446)
(305,447)(306,445)(307,433)(308,434)(309,435)(310,441)(311,439)(312,440)
(313,437)(314,438)(315,436)(316,451)(317,452)(318,453)(319,459)(320,457)
(321,458)(322,455)(323,456)(324,454)(325,631)(326,632)(327,633)(328,639)
(329,637)(330,638)(331,635)(332,636)(333,634)(334,622)(335,623)(336,624)
(337,630)(338,628)(339,629)(340,626)(341,627)(342,625)(343,640)(344,641)
(345,642)(346,648)(347,646)(348,647)(349,644)(350,645)(351,643)(352,604)
(353,605)(354,606)(355,612)(356,610)(357,611)(358,608)(359,609)(360,607)
(361,595)(362,596)(363,597)(364,603)(365,601)(366,602)(367,599)(368,600)
(369,598)(370,613)(371,614)(372,615)(373,621)(374,619)(375,620)(376,617)
(377,618)(378,616)(379,577)(380,578)(381,579)(382,585)(383,583)(384,584)
(385,581)(386,582)(387,580)(388,568)(389,569)(390,570)(391,576)(392,574)
(393,575)(394,572)(395,573)(396,571)(397,586)(398,587)(399,588)(400,594)
(401,592)(402,593)(403,590)(404,591)(405,589)(406,550)(407,551)(408,552)
(409,558)(410,556)(411,557)(412,554)(413,555)(414,553)(415,541)(416,542)
(417,543)(418,549)(419,547)(420,548)(421,545)(422,546)(423,544)(424,559)
(425,560)(426,561)(427,567)(428,565)(429,566)(430,563)(431,564)(432,562);;
s2 := ( 1, 4)( 3, 9)( 5, 8)( 10, 13)( 12, 18)( 14, 17)( 19, 22)( 21, 27)
( 23, 26)( 28, 31)( 30, 36)( 32, 35)( 37, 40)( 39, 45)( 41, 44)( 46, 49)
( 48, 54)( 50, 53)( 55, 85)( 56, 83)( 57, 90)( 58, 82)( 59, 89)( 60, 87)
( 61, 88)( 62, 86)( 63, 84)( 64, 94)( 65, 92)( 66, 99)( 67, 91)( 68, 98)
( 69, 96)( 70, 97)( 71, 95)( 72, 93)( 73,103)( 74,101)( 75,108)( 76,100)
( 77,107)( 78,105)( 79,106)( 80,104)( 81,102)(109,112)(111,117)(113,116)
(118,121)(120,126)(122,125)(127,130)(129,135)(131,134)(136,139)(138,144)
(140,143)(145,148)(147,153)(149,152)(154,157)(156,162)(158,161)(163,193)
(164,191)(165,198)(166,190)(167,197)(168,195)(169,196)(170,194)(171,192)
(172,202)(173,200)(174,207)(175,199)(176,206)(177,204)(178,205)(179,203)
(180,201)(181,211)(182,209)(183,216)(184,208)(185,215)(186,213)(187,214)
(188,212)(189,210)(217,220)(219,225)(221,224)(226,229)(228,234)(230,233)
(235,238)(237,243)(239,242)(244,247)(246,252)(248,251)(253,256)(255,261)
(257,260)(262,265)(264,270)(266,269)(271,301)(272,299)(273,306)(274,298)
(275,305)(276,303)(277,304)(278,302)(279,300)(280,310)(281,308)(282,315)
(283,307)(284,314)(285,312)(286,313)(287,311)(288,309)(289,319)(290,317)
(291,324)(292,316)(293,323)(294,321)(295,322)(296,320)(297,318)(325,328)
(327,333)(329,332)(334,337)(336,342)(338,341)(343,346)(345,351)(347,350)
(352,355)(354,360)(356,359)(361,364)(363,369)(365,368)(370,373)(372,378)
(374,377)(379,409)(380,407)(381,414)(382,406)(383,413)(384,411)(385,412)
(386,410)(387,408)(388,418)(389,416)(390,423)(391,415)(392,422)(393,420)
(394,421)(395,419)(396,417)(397,427)(398,425)(399,432)(400,424)(401,431)
(402,429)(403,430)(404,428)(405,426)(433,544)(434,542)(435,549)(436,541)
(437,548)(438,546)(439,547)(440,545)(441,543)(442,553)(443,551)(444,558)
(445,550)(446,557)(447,555)(448,556)(449,554)(450,552)(451,562)(452,560)
(453,567)(454,559)(455,566)(456,564)(457,565)(458,563)(459,561)(460,571)
(461,569)(462,576)(463,568)(464,575)(465,573)(466,574)(467,572)(468,570)
(469,580)(470,578)(471,585)(472,577)(473,584)(474,582)(475,583)(476,581)
(477,579)(478,589)(479,587)(480,594)(481,586)(482,593)(483,591)(484,592)
(485,590)(486,588)(487,625)(488,623)(489,630)(490,622)(491,629)(492,627)
(493,628)(494,626)(495,624)(496,634)(497,632)(498,639)(499,631)(500,638)
(501,636)(502,637)(503,635)(504,633)(505,643)(506,641)(507,648)(508,640)
(509,647)(510,645)(511,646)(512,644)(513,642)(514,598)(515,596)(516,603)
(517,595)(518,602)(519,600)(520,601)(521,599)(522,597)(523,607)(524,605)
(525,612)(526,604)(527,611)(528,609)(529,610)(530,608)(531,606)(532,616)
(533,614)(534,621)(535,613)(536,620)(537,618)(538,619)(539,617)(540,615)
(649,787)(650,785)(651,792)(652,784)(653,791)(654,789)(655,790)(656,788)
(657,786)(658,796)(659,794)(660,801)(661,793)(662,800)(663,798)(664,799)
(665,797)(666,795)(667,805)(668,803)(669,810)(670,802)(671,809)(672,807)
(673,808)(674,806)(675,804)(676,760)(677,758)(678,765)(679,757)(680,764)
(681,762)(682,763)(683,761)(684,759)(685,769)(686,767)(687,774)(688,766)
(689,773)(690,771)(691,772)(692,770)(693,768)(694,778)(695,776)(696,783)
(697,775)(698,782)(699,780)(700,781)(701,779)(702,777)(703,814)(704,812)
(705,819)(706,811)(707,818)(708,816)(709,817)(710,815)(711,813)(712,823)
(713,821)(714,828)(715,820)(716,827)(717,825)(718,826)(719,824)(720,822)
(721,832)(722,830)(723,837)(724,829)(725,836)(726,834)(727,835)(728,833)
(729,831)(730,841)(731,839)(732,846)(733,838)(734,845)(735,843)(736,844)
(737,842)(738,840)(739,850)(740,848)(741,855)(742,847)(743,854)(744,852)
(745,853)(746,851)(747,849)(748,859)(749,857)(750,864)(751,856)(752,863)
(753,861)(754,862)(755,860)(756,858);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,325)( 2,330)( 3,332)( 4,328)( 5,333)( 6,326)( 7,331)
( 8,327)( 9,329)( 10,343)( 11,348)( 12,350)( 13,346)( 14,351)( 15,344)
( 16,349)( 17,345)( 18,347)( 19,334)( 20,339)( 21,341)( 22,337)( 23,342)
( 24,335)( 25,340)( 26,336)( 27,338)( 28,352)( 29,357)( 30,359)( 31,355)
( 32,360)( 33,353)( 34,358)( 35,354)( 36,356)( 37,370)( 38,375)( 39,377)
( 40,373)( 41,378)( 42,371)( 43,376)( 44,372)( 45,374)( 46,361)( 47,366)
( 48,368)( 49,364)( 50,369)( 51,362)( 52,367)( 53,363)( 54,365)( 55,379)
( 56,384)( 57,386)( 58,382)( 59,387)( 60,380)( 61,385)( 62,381)( 63,383)
( 64,397)( 65,402)( 66,404)( 67,400)( 68,405)( 69,398)( 70,403)( 71,399)
( 72,401)( 73,388)( 74,393)( 75,395)( 76,391)( 77,396)( 78,389)( 79,394)
( 80,390)( 81,392)( 82,406)( 83,411)( 84,413)( 85,409)( 86,414)( 87,407)
( 88,412)( 89,408)( 90,410)( 91,424)( 92,429)( 93,431)( 94,427)( 95,432)
( 96,425)( 97,430)( 98,426)( 99,428)(100,415)(101,420)(102,422)(103,418)
(104,423)(105,416)(106,421)(107,417)(108,419)(109,244)(110,249)(111,251)
(112,247)(113,252)(114,245)(115,250)(116,246)(117,248)(118,262)(119,267)
(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,253)
(128,258)(129,260)(130,256)(131,261)(132,254)(133,259)(134,255)(135,257)
(136,217)(137,222)(138,224)(139,220)(140,225)(141,218)(142,223)(143,219)
(144,221)(145,235)(146,240)(147,242)(148,238)(149,243)(150,236)(151,241)
(152,237)(153,239)(154,226)(155,231)(156,233)(157,229)(158,234)(159,227)
(160,232)(161,228)(162,230)(163,298)(164,303)(165,305)(166,301)(167,306)
(168,299)(169,304)(170,300)(171,302)(172,316)(173,321)(174,323)(175,319)
(176,324)(177,317)(178,322)(179,318)(180,320)(181,307)(182,312)(183,314)
(184,310)(185,315)(186,308)(187,313)(188,309)(189,311)(190,271)(191,276)
(192,278)(193,274)(194,279)(195,272)(196,277)(197,273)(198,275)(199,289)
(200,294)(201,296)(202,292)(203,297)(204,290)(205,295)(206,291)(207,293)
(208,280)(209,285)(210,287)(211,283)(212,288)(213,281)(214,286)(215,282)
(216,284)(433,676)(434,681)(435,683)(436,679)(437,684)(438,677)(439,682)
(440,678)(441,680)(442,694)(443,699)(444,701)(445,697)(446,702)(447,695)
(448,700)(449,696)(450,698)(451,685)(452,690)(453,692)(454,688)(455,693)
(456,686)(457,691)(458,687)(459,689)(460,649)(461,654)(462,656)(463,652)
(464,657)(465,650)(466,655)(467,651)(468,653)(469,667)(470,672)(471,674)
(472,670)(473,675)(474,668)(475,673)(476,669)(477,671)(478,658)(479,663)
(480,665)(481,661)(482,666)(483,659)(484,664)(485,660)(486,662)(487,730)
(488,735)(489,737)(490,733)(491,738)(492,731)(493,736)(494,732)(495,734)
(496,748)(497,753)(498,755)(499,751)(500,756)(501,749)(502,754)(503,750)
(504,752)(505,739)(506,744)(507,746)(508,742)(509,747)(510,740)(511,745)
(512,741)(513,743)(514,703)(515,708)(516,710)(517,706)(518,711)(519,704)
(520,709)(521,705)(522,707)(523,721)(524,726)(525,728)(526,724)(527,729)
(528,722)(529,727)(530,723)(531,725)(532,712)(533,717)(534,719)(535,715)
(536,720)(537,713)(538,718)(539,714)(540,716)(541,757)(542,762)(543,764)
(544,760)(545,765)(546,758)(547,763)(548,759)(549,761)(550,775)(551,780)
(552,782)(553,778)(554,783)(555,776)(556,781)(557,777)(558,779)(559,766)
(560,771)(561,773)(562,769)(563,774)(564,767)(565,772)(566,768)(567,770)
(568,784)(569,789)(570,791)(571,787)(572,792)(573,785)(574,790)(575,786)
(576,788)(577,802)(578,807)(579,809)(580,805)(581,810)(582,803)(583,808)
(584,804)(585,806)(586,793)(587,798)(588,800)(589,796)(590,801)(591,794)
(592,799)(593,795)(594,797)(595,811)(596,816)(597,818)(598,814)(599,819)
(600,812)(601,817)(602,813)(603,815)(604,829)(605,834)(606,836)(607,832)
(608,837)(609,830)(610,835)(611,831)(612,833)(613,820)(614,825)(615,827)
(616,823)(617,828)(618,821)(619,826)(620,822)(621,824)(622,838)(623,843)
(624,845)(625,841)(626,846)(627,839)(628,844)(629,840)(630,842)(631,856)
(632,861)(633,863)(634,859)(635,864)(636,857)(637,862)(638,858)(639,860)
(640,847)(641,852)(642,854)(643,850)(644,855)(645,848)(646,853)(647,849)
(648,851);
s1 := Sym(864)!( 1,658)( 2,659)( 3,660)( 4,666)( 5,664)( 6,665)( 7,662)
( 8,663)( 9,661)( 10,649)( 11,650)( 12,651)( 13,657)( 14,655)( 15,656)
( 16,653)( 17,654)( 18,652)( 19,667)( 20,668)( 21,669)( 22,675)( 23,673)
( 24,674)( 25,671)( 26,672)( 27,670)( 28,685)( 29,686)( 30,687)( 31,693)
( 32,691)( 33,692)( 34,689)( 35,690)( 36,688)( 37,676)( 38,677)( 39,678)
( 40,684)( 41,682)( 42,683)( 43,680)( 44,681)( 45,679)( 46,694)( 47,695)
( 48,696)( 49,702)( 50,700)( 51,701)( 52,698)( 53,699)( 54,697)( 55,739)
( 56,740)( 57,741)( 58,747)( 59,745)( 60,746)( 61,743)( 62,744)( 63,742)
( 64,730)( 65,731)( 66,732)( 67,738)( 68,736)( 69,737)( 70,734)( 71,735)
( 72,733)( 73,748)( 74,749)( 75,750)( 76,756)( 77,754)( 78,755)( 79,752)
( 80,753)( 81,751)( 82,712)( 83,713)( 84,714)( 85,720)( 86,718)( 87,719)
( 88,716)( 89,717)( 90,715)( 91,703)( 92,704)( 93,705)( 94,711)( 95,709)
( 96,710)( 97,707)( 98,708)( 99,706)(100,721)(101,722)(102,723)(103,729)
(104,727)(105,728)(106,725)(107,726)(108,724)(109,766)(110,767)(111,768)
(112,774)(113,772)(114,773)(115,770)(116,771)(117,769)(118,757)(119,758)
(120,759)(121,765)(122,763)(123,764)(124,761)(125,762)(126,760)(127,775)
(128,776)(129,777)(130,783)(131,781)(132,782)(133,779)(134,780)(135,778)
(136,793)(137,794)(138,795)(139,801)(140,799)(141,800)(142,797)(143,798)
(144,796)(145,784)(146,785)(147,786)(148,792)(149,790)(150,791)(151,788)
(152,789)(153,787)(154,802)(155,803)(156,804)(157,810)(158,808)(159,809)
(160,806)(161,807)(162,805)(163,847)(164,848)(165,849)(166,855)(167,853)
(168,854)(169,851)(170,852)(171,850)(172,838)(173,839)(174,840)(175,846)
(176,844)(177,845)(178,842)(179,843)(180,841)(181,856)(182,857)(183,858)
(184,864)(185,862)(186,863)(187,860)(188,861)(189,859)(190,820)(191,821)
(192,822)(193,828)(194,826)(195,827)(196,824)(197,825)(198,823)(199,811)
(200,812)(201,813)(202,819)(203,817)(204,818)(205,815)(206,816)(207,814)
(208,829)(209,830)(210,831)(211,837)(212,835)(213,836)(214,833)(215,834)
(216,832)(217,523)(218,524)(219,525)(220,531)(221,529)(222,530)(223,527)
(224,528)(225,526)(226,514)(227,515)(228,516)(229,522)(230,520)(231,521)
(232,518)(233,519)(234,517)(235,532)(236,533)(237,534)(238,540)(239,538)
(240,539)(241,536)(242,537)(243,535)(244,496)(245,497)(246,498)(247,504)
(248,502)(249,503)(250,500)(251,501)(252,499)(253,487)(254,488)(255,489)
(256,495)(257,493)(258,494)(259,491)(260,492)(261,490)(262,505)(263,506)
(264,507)(265,513)(266,511)(267,512)(268,509)(269,510)(270,508)(271,469)
(272,470)(273,471)(274,477)(275,475)(276,476)(277,473)(278,474)(279,472)
(280,460)(281,461)(282,462)(283,468)(284,466)(285,467)(286,464)(287,465)
(288,463)(289,478)(290,479)(291,480)(292,486)(293,484)(294,485)(295,482)
(296,483)(297,481)(298,442)(299,443)(300,444)(301,450)(302,448)(303,449)
(304,446)(305,447)(306,445)(307,433)(308,434)(309,435)(310,441)(311,439)
(312,440)(313,437)(314,438)(315,436)(316,451)(317,452)(318,453)(319,459)
(320,457)(321,458)(322,455)(323,456)(324,454)(325,631)(326,632)(327,633)
(328,639)(329,637)(330,638)(331,635)(332,636)(333,634)(334,622)(335,623)
(336,624)(337,630)(338,628)(339,629)(340,626)(341,627)(342,625)(343,640)
(344,641)(345,642)(346,648)(347,646)(348,647)(349,644)(350,645)(351,643)
(352,604)(353,605)(354,606)(355,612)(356,610)(357,611)(358,608)(359,609)
(360,607)(361,595)(362,596)(363,597)(364,603)(365,601)(366,602)(367,599)
(368,600)(369,598)(370,613)(371,614)(372,615)(373,621)(374,619)(375,620)
(376,617)(377,618)(378,616)(379,577)(380,578)(381,579)(382,585)(383,583)
(384,584)(385,581)(386,582)(387,580)(388,568)(389,569)(390,570)(391,576)
(392,574)(393,575)(394,572)(395,573)(396,571)(397,586)(398,587)(399,588)
(400,594)(401,592)(402,593)(403,590)(404,591)(405,589)(406,550)(407,551)
(408,552)(409,558)(410,556)(411,557)(412,554)(413,555)(414,553)(415,541)
(416,542)(417,543)(418,549)(419,547)(420,548)(421,545)(422,546)(423,544)
(424,559)(425,560)(426,561)(427,567)(428,565)(429,566)(430,563)(431,564)
(432,562);
s2 := Sym(864)!( 1, 4)( 3, 9)( 5, 8)( 10, 13)( 12, 18)( 14, 17)( 19, 22)
( 21, 27)( 23, 26)( 28, 31)( 30, 36)( 32, 35)( 37, 40)( 39, 45)( 41, 44)
( 46, 49)( 48, 54)( 50, 53)( 55, 85)( 56, 83)( 57, 90)( 58, 82)( 59, 89)
( 60, 87)( 61, 88)( 62, 86)( 63, 84)( 64, 94)( 65, 92)( 66, 99)( 67, 91)
( 68, 98)( 69, 96)( 70, 97)( 71, 95)( 72, 93)( 73,103)( 74,101)( 75,108)
( 76,100)( 77,107)( 78,105)( 79,106)( 80,104)( 81,102)(109,112)(111,117)
(113,116)(118,121)(120,126)(122,125)(127,130)(129,135)(131,134)(136,139)
(138,144)(140,143)(145,148)(147,153)(149,152)(154,157)(156,162)(158,161)
(163,193)(164,191)(165,198)(166,190)(167,197)(168,195)(169,196)(170,194)
(171,192)(172,202)(173,200)(174,207)(175,199)(176,206)(177,204)(178,205)
(179,203)(180,201)(181,211)(182,209)(183,216)(184,208)(185,215)(186,213)
(187,214)(188,212)(189,210)(217,220)(219,225)(221,224)(226,229)(228,234)
(230,233)(235,238)(237,243)(239,242)(244,247)(246,252)(248,251)(253,256)
(255,261)(257,260)(262,265)(264,270)(266,269)(271,301)(272,299)(273,306)
(274,298)(275,305)(276,303)(277,304)(278,302)(279,300)(280,310)(281,308)
(282,315)(283,307)(284,314)(285,312)(286,313)(287,311)(288,309)(289,319)
(290,317)(291,324)(292,316)(293,323)(294,321)(295,322)(296,320)(297,318)
(325,328)(327,333)(329,332)(334,337)(336,342)(338,341)(343,346)(345,351)
(347,350)(352,355)(354,360)(356,359)(361,364)(363,369)(365,368)(370,373)
(372,378)(374,377)(379,409)(380,407)(381,414)(382,406)(383,413)(384,411)
(385,412)(386,410)(387,408)(388,418)(389,416)(390,423)(391,415)(392,422)
(393,420)(394,421)(395,419)(396,417)(397,427)(398,425)(399,432)(400,424)
(401,431)(402,429)(403,430)(404,428)(405,426)(433,544)(434,542)(435,549)
(436,541)(437,548)(438,546)(439,547)(440,545)(441,543)(442,553)(443,551)
(444,558)(445,550)(446,557)(447,555)(448,556)(449,554)(450,552)(451,562)
(452,560)(453,567)(454,559)(455,566)(456,564)(457,565)(458,563)(459,561)
(460,571)(461,569)(462,576)(463,568)(464,575)(465,573)(466,574)(467,572)
(468,570)(469,580)(470,578)(471,585)(472,577)(473,584)(474,582)(475,583)
(476,581)(477,579)(478,589)(479,587)(480,594)(481,586)(482,593)(483,591)
(484,592)(485,590)(486,588)(487,625)(488,623)(489,630)(490,622)(491,629)
(492,627)(493,628)(494,626)(495,624)(496,634)(497,632)(498,639)(499,631)
(500,638)(501,636)(502,637)(503,635)(504,633)(505,643)(506,641)(507,648)
(508,640)(509,647)(510,645)(511,646)(512,644)(513,642)(514,598)(515,596)
(516,603)(517,595)(518,602)(519,600)(520,601)(521,599)(522,597)(523,607)
(524,605)(525,612)(526,604)(527,611)(528,609)(529,610)(530,608)(531,606)
(532,616)(533,614)(534,621)(535,613)(536,620)(537,618)(538,619)(539,617)
(540,615)(649,787)(650,785)(651,792)(652,784)(653,791)(654,789)(655,790)
(656,788)(657,786)(658,796)(659,794)(660,801)(661,793)(662,800)(663,798)
(664,799)(665,797)(666,795)(667,805)(668,803)(669,810)(670,802)(671,809)
(672,807)(673,808)(674,806)(675,804)(676,760)(677,758)(678,765)(679,757)
(680,764)(681,762)(682,763)(683,761)(684,759)(685,769)(686,767)(687,774)
(688,766)(689,773)(690,771)(691,772)(692,770)(693,768)(694,778)(695,776)
(696,783)(697,775)(698,782)(699,780)(700,781)(701,779)(702,777)(703,814)
(704,812)(705,819)(706,811)(707,818)(708,816)(709,817)(710,815)(711,813)
(712,823)(713,821)(714,828)(715,820)(716,827)(717,825)(718,826)(719,824)
(720,822)(721,832)(722,830)(723,837)(724,829)(725,836)(726,834)(727,835)
(728,833)(729,831)(730,841)(731,839)(732,846)(733,838)(734,845)(735,843)
(736,844)(737,842)(738,840)(739,850)(740,848)(741,855)(742,847)(743,854)
(744,852)(745,853)(746,851)(747,849)(748,859)(749,857)(750,864)(751,856)
(752,863)(753,861)(754,862)(755,860)(756,858);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >;
References : None.
to this polytope