Polytope of Type {24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*1728f
if this polytope has a name.
Group : SmallGroup(1728,31257)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 216, 432, 36
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,4}*864d
3-fold quotients : {24,4}*576a
4-fold quotients : {6,4}*432b
6-fold quotients : {12,4}*288
9-fold quotients : {24,4}*192a
12-fold quotients : {6,4}*144
18-fold quotients : {12,4}*96a, {24,2}*96
24-fold quotients : {6,4}*72
27-fold quotients : {8,4}*64a
36-fold quotients : {12,2}*48, {6,4}*48a
54-fold quotients : {4,4}*32, {8,2}*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)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)
( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)
( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)
( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)
( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)( 40,376)
( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)( 48,362)
( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,406)( 56,408)
( 57,407)( 58,412)( 59,414)( 60,413)( 61,409)( 62,411)( 63,410)( 64,424)
( 65,426)( 66,425)( 67,430)( 68,432)( 69,431)( 70,427)( 71,429)( 72,428)
( 73,415)( 74,417)( 75,416)( 76,421)( 77,423)( 78,422)( 79,418)( 80,420)
( 81,419)( 82,379)( 83,381)( 84,380)( 85,385)( 86,387)( 87,386)( 88,382)
( 89,384)( 90,383)( 91,397)( 92,399)( 93,398)( 94,403)( 95,405)( 96,404)
( 97,400)( 98,402)( 99,401)(100,388)(101,390)(102,389)(103,394)(104,396)
(105,395)(106,391)(107,393)(108,392)(109,217)(110,219)(111,218)(112,223)
(113,225)(114,224)(115,220)(116,222)(117,221)(118,235)(119,237)(120,236)
(121,241)(122,243)(123,242)(124,238)(125,240)(126,239)(127,226)(128,228)
(129,227)(130,232)(131,234)(132,233)(133,229)(134,231)(135,230)(136,244)
(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)(144,248)
(145,262)(146,264)(147,263)(148,268)(149,270)(150,269)(151,265)(152,267)
(153,266)(154,253)(155,255)(156,254)(157,259)(158,261)(159,260)(160,256)
(161,258)(162,257)(163,298)(164,300)(165,299)(166,304)(167,306)(168,305)
(169,301)(170,303)(171,302)(172,316)(173,318)(174,317)(175,322)(176,324)
(177,323)(178,319)(179,321)(180,320)(181,307)(182,309)(183,308)(184,313)
(185,315)(186,314)(187,310)(188,312)(189,311)(190,271)(191,273)(192,272)
(193,277)(194,279)(195,278)(196,274)(197,276)(198,275)(199,289)(200,291)
(201,290)(202,295)(203,297)(204,296)(205,292)(206,294)(207,293)(208,280)
(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)(216,284)
(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)
(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)(448,778)
(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)(456,773)
(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)(464,792)
(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)(472,808)
(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)(480,794)
(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,838)(488,840)
(489,839)(490,844)(491,846)(492,845)(493,841)(494,843)(495,842)(496,856)
(497,858)(498,857)(499,862)(500,864)(501,863)(502,859)(503,861)(504,860)
(505,847)(506,849)(507,848)(508,853)(509,855)(510,854)(511,850)(512,852)
(513,851)(514,811)(515,813)(516,812)(517,817)(518,819)(519,818)(520,814)
(521,816)(522,815)(523,829)(524,831)(525,830)(526,835)(527,837)(528,836)
(529,832)(530,834)(531,833)(532,820)(533,822)(534,821)(535,826)(536,828)
(537,827)(538,823)(539,825)(540,824)(541,649)(542,651)(543,650)(544,655)
(545,657)(546,656)(547,652)(548,654)(549,653)(550,667)(551,669)(552,668)
(553,673)(554,675)(555,674)(556,670)(557,672)(558,671)(559,658)(560,660)
(561,659)(562,664)(563,666)(564,665)(565,661)(566,663)(567,662)(568,676)
(569,678)(570,677)(571,682)(572,684)(573,683)(574,679)(575,681)(576,680)
(577,694)(578,696)(579,695)(580,700)(581,702)(582,701)(583,697)(584,699)
(585,698)(586,685)(587,687)(588,686)(589,691)(590,693)(591,692)(592,688)
(593,690)(594,689)(595,730)(596,732)(597,731)(598,736)(599,738)(600,737)
(601,733)(602,735)(603,734)(604,748)(605,750)(606,749)(607,754)(608,756)
(609,755)(610,751)(611,753)(612,752)(613,739)(614,741)(615,740)(616,745)
(617,747)(618,746)(619,742)(620,744)(621,743)(622,703)(623,705)(624,704)
(625,709)(626,711)(627,710)(628,706)(629,708)(630,707)(631,721)(632,723)
(633,722)(634,727)(635,729)(636,728)(637,724)(638,726)(639,725)(640,712)
(641,714)(642,713)(643,718)(644,720)(645,719)(646,715)(647,717)(648,716);;
s1 := ( 1,767)( 2,766)( 3,768)( 4,771)( 5,770)( 6,769)( 7,772)( 8,774)
( 9,773)( 10,758)( 11,757)( 12,759)( 13,762)( 14,761)( 15,760)( 16,763)
( 17,765)( 18,764)( 19,776)( 20,775)( 21,777)( 22,780)( 23,779)( 24,778)
( 25,781)( 26,783)( 27,782)( 28,794)( 29,793)( 30,795)( 31,798)( 32,797)
( 33,796)( 34,799)( 35,801)( 36,800)( 37,785)( 38,784)( 39,786)( 40,789)
( 41,788)( 42,787)( 43,790)( 44,792)( 45,791)( 46,803)( 47,802)( 48,804)
( 49,807)( 50,806)( 51,805)( 52,808)( 53,810)( 54,809)( 55,848)( 56,847)
( 57,849)( 58,852)( 59,851)( 60,850)( 61,853)( 62,855)( 63,854)( 64,839)
( 65,838)( 66,840)( 67,843)( 68,842)( 69,841)( 70,844)( 71,846)( 72,845)
( 73,857)( 74,856)( 75,858)( 76,861)( 77,860)( 78,859)( 79,862)( 80,864)
( 81,863)( 82,821)( 83,820)( 84,822)( 85,825)( 86,824)( 87,823)( 88,826)
( 89,828)( 90,827)( 91,812)( 92,811)( 93,813)( 94,816)( 95,815)( 96,814)
( 97,817)( 98,819)( 99,818)(100,830)(101,829)(102,831)(103,834)(104,833)
(105,832)(106,835)(107,837)(108,836)(109,659)(110,658)(111,660)(112,663)
(113,662)(114,661)(115,664)(116,666)(117,665)(118,650)(119,649)(120,651)
(121,654)(122,653)(123,652)(124,655)(125,657)(126,656)(127,668)(128,667)
(129,669)(130,672)(131,671)(132,670)(133,673)(134,675)(135,674)(136,686)
(137,685)(138,687)(139,690)(140,689)(141,688)(142,691)(143,693)(144,692)
(145,677)(146,676)(147,678)(148,681)(149,680)(150,679)(151,682)(152,684)
(153,683)(154,695)(155,694)(156,696)(157,699)(158,698)(159,697)(160,700)
(161,702)(162,701)(163,740)(164,739)(165,741)(166,744)(167,743)(168,742)
(169,745)(170,747)(171,746)(172,731)(173,730)(174,732)(175,735)(176,734)
(177,733)(178,736)(179,738)(180,737)(181,749)(182,748)(183,750)(184,753)
(185,752)(186,751)(187,754)(188,756)(189,755)(190,713)(191,712)(192,714)
(193,717)(194,716)(195,715)(196,718)(197,720)(198,719)(199,704)(200,703)
(201,705)(202,708)(203,707)(204,706)(205,709)(206,711)(207,710)(208,722)
(209,721)(210,723)(211,726)(212,725)(213,724)(214,727)(215,729)(216,728)
(217,632)(218,631)(219,633)(220,636)(221,635)(222,634)(223,637)(224,639)
(225,638)(226,623)(227,622)(228,624)(229,627)(230,626)(231,625)(232,628)
(233,630)(234,629)(235,641)(236,640)(237,642)(238,645)(239,644)(240,643)
(241,646)(242,648)(243,647)(244,605)(245,604)(246,606)(247,609)(248,608)
(249,607)(250,610)(251,612)(252,611)(253,596)(254,595)(255,597)(256,600)
(257,599)(258,598)(259,601)(260,603)(261,602)(262,614)(263,613)(264,615)
(265,618)(266,617)(267,616)(268,619)(269,621)(270,620)(271,578)(272,577)
(273,579)(274,582)(275,581)(276,580)(277,583)(278,585)(279,584)(280,569)
(281,568)(282,570)(283,573)(284,572)(285,571)(286,574)(287,576)(288,575)
(289,587)(290,586)(291,588)(292,591)(293,590)(294,589)(295,592)(296,594)
(297,593)(298,551)(299,550)(300,552)(301,555)(302,554)(303,553)(304,556)
(305,558)(306,557)(307,542)(308,541)(309,543)(310,546)(311,545)(312,544)
(313,547)(314,549)(315,548)(316,560)(317,559)(318,561)(319,564)(320,563)
(321,562)(322,565)(323,567)(324,566)(325,524)(326,523)(327,525)(328,528)
(329,527)(330,526)(331,529)(332,531)(333,530)(334,515)(335,514)(336,516)
(337,519)(338,518)(339,517)(340,520)(341,522)(342,521)(343,533)(344,532)
(345,534)(346,537)(347,536)(348,535)(349,538)(350,540)(351,539)(352,497)
(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)(360,503)
(361,488)(362,487)(363,489)(364,492)(365,491)(366,490)(367,493)(368,495)
(369,494)(370,506)(371,505)(372,507)(373,510)(374,509)(375,508)(376,511)
(377,513)(378,512)(379,470)(380,469)(381,471)(382,474)(383,473)(384,472)
(385,475)(386,477)(387,476)(388,461)(389,460)(390,462)(391,465)(392,464)
(393,463)(394,466)(395,468)(396,467)(397,479)(398,478)(399,480)(400,483)
(401,482)(402,481)(403,484)(404,486)(405,485)(406,443)(407,442)(408,444)
(409,447)(410,446)(411,445)(412,448)(413,450)(414,449)(415,434)(416,433)
(417,435)(418,438)(419,437)(420,436)(421,439)(422,441)(423,440)(424,452)
(425,451)(426,453)(427,456)(428,455)(429,454)(430,457)(431,459)(432,458);;
s2 := ( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)( 21, 24)
( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)( 47, 53)
( 48, 51)( 49, 52)( 56, 62)( 57, 60)( 58, 61)( 65, 71)( 66, 69)( 67, 70)
( 74, 80)( 75, 78)( 76, 79)( 83, 89)( 84, 87)( 85, 88)( 92, 98)( 93, 96)
( 94, 97)(101,107)(102,105)(103,106)(110,116)(111,114)(112,115)(119,125)
(120,123)(121,124)(128,134)(129,132)(130,133)(137,143)(138,141)(139,142)
(146,152)(147,150)(148,151)(155,161)(156,159)(157,160)(164,170)(165,168)
(166,169)(173,179)(174,177)(175,178)(182,188)(183,186)(184,187)(191,197)
(192,195)(193,196)(200,206)(201,204)(202,205)(209,215)(210,213)(211,214)
(218,224)(219,222)(220,223)(227,233)(228,231)(229,232)(236,242)(237,240)
(238,241)(245,251)(246,249)(247,250)(254,260)(255,258)(256,259)(263,269)
(264,267)(265,268)(272,278)(273,276)(274,277)(281,287)(282,285)(283,286)
(290,296)(291,294)(292,295)(299,305)(300,303)(301,304)(308,314)(309,312)
(310,313)(317,323)(318,321)(319,322)(326,332)(327,330)(328,331)(335,341)
(336,339)(337,340)(344,350)(345,348)(346,349)(353,359)(354,357)(355,358)
(362,368)(363,366)(364,367)(371,377)(372,375)(373,376)(380,386)(381,384)
(382,385)(389,395)(390,393)(391,394)(398,404)(399,402)(400,403)(407,413)
(408,411)(409,412)(416,422)(417,420)(418,421)(425,431)(426,429)(427,430)
(433,541)(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)(440,542)
(441,549)(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)(448,553)
(449,551)(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)(456,561)
(457,562)(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)(464,572)
(465,570)(466,571)(467,569)(468,576)(469,577)(470,584)(471,582)(472,583)
(473,581)(474,579)(475,580)(476,578)(477,585)(478,586)(479,593)(480,591)
(481,592)(482,590)(483,588)(484,589)(485,587)(486,594)(487,595)(488,602)
(489,600)(490,601)(491,599)(492,597)(493,598)(494,596)(495,603)(496,604)
(497,611)(498,609)(499,610)(500,608)(501,606)(502,607)(503,605)(504,612)
(505,613)(506,620)(507,618)(508,619)(509,617)(510,615)(511,616)(512,614)
(513,621)(514,622)(515,629)(516,627)(517,628)(518,626)(519,624)(520,625)
(521,623)(522,630)(523,631)(524,638)(525,636)(526,637)(527,635)(528,633)
(529,634)(530,632)(531,639)(532,640)(533,647)(534,645)(535,646)(536,644)
(537,642)(538,643)(539,641)(540,648)(649,757)(650,764)(651,762)(652,763)
(653,761)(654,759)(655,760)(656,758)(657,765)(658,766)(659,773)(660,771)
(661,772)(662,770)(663,768)(664,769)(665,767)(666,774)(667,775)(668,782)
(669,780)(670,781)(671,779)(672,777)(673,778)(674,776)(675,783)(676,784)
(677,791)(678,789)(679,790)(680,788)(681,786)(682,787)(683,785)(684,792)
(685,793)(686,800)(687,798)(688,799)(689,797)(690,795)(691,796)(692,794)
(693,801)(694,802)(695,809)(696,807)(697,808)(698,806)(699,804)(700,805)
(701,803)(702,810)(703,811)(704,818)(705,816)(706,817)(707,815)(708,813)
(709,814)(710,812)(711,819)(712,820)(713,827)(714,825)(715,826)(716,824)
(717,822)(718,823)(719,821)(720,828)(721,829)(722,836)(723,834)(724,835)
(725,833)(726,831)(727,832)(728,830)(729,837)(730,838)(731,845)(732,843)
(733,844)(734,842)(735,840)(736,841)(737,839)(738,846)(739,847)(740,854)
(741,852)(742,853)(743,851)(744,849)(745,850)(746,848)(747,855)(748,856)
(749,863)(750,861)(751,862)(752,860)(753,858)(754,859)(755,857)(756,864);;
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,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)
( 8,330)( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)
( 16,346)( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)
( 24,341)( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)
( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)
( 40,376)( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)
( 48,362)( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,406)
( 56,408)( 57,407)( 58,412)( 59,414)( 60,413)( 61,409)( 62,411)( 63,410)
( 64,424)( 65,426)( 66,425)( 67,430)( 68,432)( 69,431)( 70,427)( 71,429)
( 72,428)( 73,415)( 74,417)( 75,416)( 76,421)( 77,423)( 78,422)( 79,418)
( 80,420)( 81,419)( 82,379)( 83,381)( 84,380)( 85,385)( 86,387)( 87,386)
( 88,382)( 89,384)( 90,383)( 91,397)( 92,399)( 93,398)( 94,403)( 95,405)
( 96,404)( 97,400)( 98,402)( 99,401)(100,388)(101,390)(102,389)(103,394)
(104,396)(105,395)(106,391)(107,393)(108,392)(109,217)(110,219)(111,218)
(112,223)(113,225)(114,224)(115,220)(116,222)(117,221)(118,235)(119,237)
(120,236)(121,241)(122,243)(123,242)(124,238)(125,240)(126,239)(127,226)
(128,228)(129,227)(130,232)(131,234)(132,233)(133,229)(134,231)(135,230)
(136,244)(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)
(144,248)(145,262)(146,264)(147,263)(148,268)(149,270)(150,269)(151,265)
(152,267)(153,266)(154,253)(155,255)(156,254)(157,259)(158,261)(159,260)
(160,256)(161,258)(162,257)(163,298)(164,300)(165,299)(166,304)(167,306)
(168,305)(169,301)(170,303)(171,302)(172,316)(173,318)(174,317)(175,322)
(176,324)(177,323)(178,319)(179,321)(180,320)(181,307)(182,309)(183,308)
(184,313)(185,315)(186,314)(187,310)(188,312)(189,311)(190,271)(191,273)
(192,272)(193,277)(194,279)(195,278)(196,274)(197,276)(198,275)(199,289)
(200,291)(201,290)(202,295)(203,297)(204,296)(205,292)(206,294)(207,293)
(208,280)(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)
(216,284)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)
(440,762)(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)
(448,778)(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)
(456,773)(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)
(464,792)(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)
(472,808)(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)
(480,794)(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,838)
(488,840)(489,839)(490,844)(491,846)(492,845)(493,841)(494,843)(495,842)
(496,856)(497,858)(498,857)(499,862)(500,864)(501,863)(502,859)(503,861)
(504,860)(505,847)(506,849)(507,848)(508,853)(509,855)(510,854)(511,850)
(512,852)(513,851)(514,811)(515,813)(516,812)(517,817)(518,819)(519,818)
(520,814)(521,816)(522,815)(523,829)(524,831)(525,830)(526,835)(527,837)
(528,836)(529,832)(530,834)(531,833)(532,820)(533,822)(534,821)(535,826)
(536,828)(537,827)(538,823)(539,825)(540,824)(541,649)(542,651)(543,650)
(544,655)(545,657)(546,656)(547,652)(548,654)(549,653)(550,667)(551,669)
(552,668)(553,673)(554,675)(555,674)(556,670)(557,672)(558,671)(559,658)
(560,660)(561,659)(562,664)(563,666)(564,665)(565,661)(566,663)(567,662)
(568,676)(569,678)(570,677)(571,682)(572,684)(573,683)(574,679)(575,681)
(576,680)(577,694)(578,696)(579,695)(580,700)(581,702)(582,701)(583,697)
(584,699)(585,698)(586,685)(587,687)(588,686)(589,691)(590,693)(591,692)
(592,688)(593,690)(594,689)(595,730)(596,732)(597,731)(598,736)(599,738)
(600,737)(601,733)(602,735)(603,734)(604,748)(605,750)(606,749)(607,754)
(608,756)(609,755)(610,751)(611,753)(612,752)(613,739)(614,741)(615,740)
(616,745)(617,747)(618,746)(619,742)(620,744)(621,743)(622,703)(623,705)
(624,704)(625,709)(626,711)(627,710)(628,706)(629,708)(630,707)(631,721)
(632,723)(633,722)(634,727)(635,729)(636,728)(637,724)(638,726)(639,725)
(640,712)(641,714)(642,713)(643,718)(644,720)(645,719)(646,715)(647,717)
(648,716);
s1 := Sym(864)!( 1,767)( 2,766)( 3,768)( 4,771)( 5,770)( 6,769)( 7,772)
( 8,774)( 9,773)( 10,758)( 11,757)( 12,759)( 13,762)( 14,761)( 15,760)
( 16,763)( 17,765)( 18,764)( 19,776)( 20,775)( 21,777)( 22,780)( 23,779)
( 24,778)( 25,781)( 26,783)( 27,782)( 28,794)( 29,793)( 30,795)( 31,798)
( 32,797)( 33,796)( 34,799)( 35,801)( 36,800)( 37,785)( 38,784)( 39,786)
( 40,789)( 41,788)( 42,787)( 43,790)( 44,792)( 45,791)( 46,803)( 47,802)
( 48,804)( 49,807)( 50,806)( 51,805)( 52,808)( 53,810)( 54,809)( 55,848)
( 56,847)( 57,849)( 58,852)( 59,851)( 60,850)( 61,853)( 62,855)( 63,854)
( 64,839)( 65,838)( 66,840)( 67,843)( 68,842)( 69,841)( 70,844)( 71,846)
( 72,845)( 73,857)( 74,856)( 75,858)( 76,861)( 77,860)( 78,859)( 79,862)
( 80,864)( 81,863)( 82,821)( 83,820)( 84,822)( 85,825)( 86,824)( 87,823)
( 88,826)( 89,828)( 90,827)( 91,812)( 92,811)( 93,813)( 94,816)( 95,815)
( 96,814)( 97,817)( 98,819)( 99,818)(100,830)(101,829)(102,831)(103,834)
(104,833)(105,832)(106,835)(107,837)(108,836)(109,659)(110,658)(111,660)
(112,663)(113,662)(114,661)(115,664)(116,666)(117,665)(118,650)(119,649)
(120,651)(121,654)(122,653)(123,652)(124,655)(125,657)(126,656)(127,668)
(128,667)(129,669)(130,672)(131,671)(132,670)(133,673)(134,675)(135,674)
(136,686)(137,685)(138,687)(139,690)(140,689)(141,688)(142,691)(143,693)
(144,692)(145,677)(146,676)(147,678)(148,681)(149,680)(150,679)(151,682)
(152,684)(153,683)(154,695)(155,694)(156,696)(157,699)(158,698)(159,697)
(160,700)(161,702)(162,701)(163,740)(164,739)(165,741)(166,744)(167,743)
(168,742)(169,745)(170,747)(171,746)(172,731)(173,730)(174,732)(175,735)
(176,734)(177,733)(178,736)(179,738)(180,737)(181,749)(182,748)(183,750)
(184,753)(185,752)(186,751)(187,754)(188,756)(189,755)(190,713)(191,712)
(192,714)(193,717)(194,716)(195,715)(196,718)(197,720)(198,719)(199,704)
(200,703)(201,705)(202,708)(203,707)(204,706)(205,709)(206,711)(207,710)
(208,722)(209,721)(210,723)(211,726)(212,725)(213,724)(214,727)(215,729)
(216,728)(217,632)(218,631)(219,633)(220,636)(221,635)(222,634)(223,637)
(224,639)(225,638)(226,623)(227,622)(228,624)(229,627)(230,626)(231,625)
(232,628)(233,630)(234,629)(235,641)(236,640)(237,642)(238,645)(239,644)
(240,643)(241,646)(242,648)(243,647)(244,605)(245,604)(246,606)(247,609)
(248,608)(249,607)(250,610)(251,612)(252,611)(253,596)(254,595)(255,597)
(256,600)(257,599)(258,598)(259,601)(260,603)(261,602)(262,614)(263,613)
(264,615)(265,618)(266,617)(267,616)(268,619)(269,621)(270,620)(271,578)
(272,577)(273,579)(274,582)(275,581)(276,580)(277,583)(278,585)(279,584)
(280,569)(281,568)(282,570)(283,573)(284,572)(285,571)(286,574)(287,576)
(288,575)(289,587)(290,586)(291,588)(292,591)(293,590)(294,589)(295,592)
(296,594)(297,593)(298,551)(299,550)(300,552)(301,555)(302,554)(303,553)
(304,556)(305,558)(306,557)(307,542)(308,541)(309,543)(310,546)(311,545)
(312,544)(313,547)(314,549)(315,548)(316,560)(317,559)(318,561)(319,564)
(320,563)(321,562)(322,565)(323,567)(324,566)(325,524)(326,523)(327,525)
(328,528)(329,527)(330,526)(331,529)(332,531)(333,530)(334,515)(335,514)
(336,516)(337,519)(338,518)(339,517)(340,520)(341,522)(342,521)(343,533)
(344,532)(345,534)(346,537)(347,536)(348,535)(349,538)(350,540)(351,539)
(352,497)(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)
(360,503)(361,488)(362,487)(363,489)(364,492)(365,491)(366,490)(367,493)
(368,495)(369,494)(370,506)(371,505)(372,507)(373,510)(374,509)(375,508)
(376,511)(377,513)(378,512)(379,470)(380,469)(381,471)(382,474)(383,473)
(384,472)(385,475)(386,477)(387,476)(388,461)(389,460)(390,462)(391,465)
(392,464)(393,463)(394,466)(395,468)(396,467)(397,479)(398,478)(399,480)
(400,483)(401,482)(402,481)(403,484)(404,486)(405,485)(406,443)(407,442)
(408,444)(409,447)(410,446)(411,445)(412,448)(413,450)(414,449)(415,434)
(416,433)(417,435)(418,438)(419,437)(420,436)(421,439)(422,441)(423,440)
(424,452)(425,451)(426,453)(427,456)(428,455)(429,454)(430,457)(431,459)
(432,458);
s2 := Sym(864)!( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)
( 21, 24)( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)
( 47, 53)( 48, 51)( 49, 52)( 56, 62)( 57, 60)( 58, 61)( 65, 71)( 66, 69)
( 67, 70)( 74, 80)( 75, 78)( 76, 79)( 83, 89)( 84, 87)( 85, 88)( 92, 98)
( 93, 96)( 94, 97)(101,107)(102,105)(103,106)(110,116)(111,114)(112,115)
(119,125)(120,123)(121,124)(128,134)(129,132)(130,133)(137,143)(138,141)
(139,142)(146,152)(147,150)(148,151)(155,161)(156,159)(157,160)(164,170)
(165,168)(166,169)(173,179)(174,177)(175,178)(182,188)(183,186)(184,187)
(191,197)(192,195)(193,196)(200,206)(201,204)(202,205)(209,215)(210,213)
(211,214)(218,224)(219,222)(220,223)(227,233)(228,231)(229,232)(236,242)
(237,240)(238,241)(245,251)(246,249)(247,250)(254,260)(255,258)(256,259)
(263,269)(264,267)(265,268)(272,278)(273,276)(274,277)(281,287)(282,285)
(283,286)(290,296)(291,294)(292,295)(299,305)(300,303)(301,304)(308,314)
(309,312)(310,313)(317,323)(318,321)(319,322)(326,332)(327,330)(328,331)
(335,341)(336,339)(337,340)(344,350)(345,348)(346,349)(353,359)(354,357)
(355,358)(362,368)(363,366)(364,367)(371,377)(372,375)(373,376)(380,386)
(381,384)(382,385)(389,395)(390,393)(391,394)(398,404)(399,402)(400,403)
(407,413)(408,411)(409,412)(416,422)(417,420)(418,421)(425,431)(426,429)
(427,430)(433,541)(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)
(440,542)(441,549)(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)
(448,553)(449,551)(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)
(456,561)(457,562)(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)
(464,572)(465,570)(466,571)(467,569)(468,576)(469,577)(470,584)(471,582)
(472,583)(473,581)(474,579)(475,580)(476,578)(477,585)(478,586)(479,593)
(480,591)(481,592)(482,590)(483,588)(484,589)(485,587)(486,594)(487,595)
(488,602)(489,600)(490,601)(491,599)(492,597)(493,598)(494,596)(495,603)
(496,604)(497,611)(498,609)(499,610)(500,608)(501,606)(502,607)(503,605)
(504,612)(505,613)(506,620)(507,618)(508,619)(509,617)(510,615)(511,616)
(512,614)(513,621)(514,622)(515,629)(516,627)(517,628)(518,626)(519,624)
(520,625)(521,623)(522,630)(523,631)(524,638)(525,636)(526,637)(527,635)
(528,633)(529,634)(530,632)(531,639)(532,640)(533,647)(534,645)(535,646)
(536,644)(537,642)(538,643)(539,641)(540,648)(649,757)(650,764)(651,762)
(652,763)(653,761)(654,759)(655,760)(656,758)(657,765)(658,766)(659,773)
(660,771)(661,772)(662,770)(663,768)(664,769)(665,767)(666,774)(667,775)
(668,782)(669,780)(670,781)(671,779)(672,777)(673,778)(674,776)(675,783)
(676,784)(677,791)(678,789)(679,790)(680,788)(681,786)(682,787)(683,785)
(684,792)(685,793)(686,800)(687,798)(688,799)(689,797)(690,795)(691,796)
(692,794)(693,801)(694,802)(695,809)(696,807)(697,808)(698,806)(699,804)
(700,805)(701,803)(702,810)(703,811)(704,818)(705,816)(706,817)(707,815)
(708,813)(709,814)(710,812)(711,819)(712,820)(713,827)(714,825)(715,826)
(716,824)(717,822)(718,823)(719,821)(720,828)(721,829)(722,836)(723,834)
(724,835)(725,833)(726,831)(727,832)(728,830)(729,837)(730,838)(731,845)
(732,843)(733,844)(734,842)(735,840)(736,841)(737,839)(738,846)(739,847)
(740,854)(741,852)(742,853)(743,851)(744,849)(745,850)(746,848)(747,855)
(748,856)(749,863)(750,861)(751,862)(752,860)(753,858)(754,859)(755,857)
(756,864);
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,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope