Polytope of Type {4,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*1728g
if this polytope has a name.
Group : SmallGroup(1728,31293)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 36, 432, 216
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12}*864c
3-fold quotients : {4,24}*576b
4-fold quotients : {4,6}*432b
6-fold quotients : {4,12}*288
9-fold quotients : {4,24}*192b
12-fold quotients : {4,6}*144
18-fold quotients : {4,12}*96a
24-fold quotients : {4,6}*72
27-fold quotients : {4,8}*64b
36-fold quotients : {2,12}*48, {4,6}*48a
54-fold quotients : {4,4}*32
72-fold quotients : {2,6}*24
108-fold quotients : {2,4}*16, {4,2}*16
144-fold quotients : {2,3}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)( 60, 84)
( 61, 85)( 62, 83)( 63, 90)( 64, 91)( 65, 98)( 66, 96)( 67, 97)( 68, 95)
( 69, 93)( 70, 94)( 71, 92)( 72, 99)( 73,100)( 74,107)( 75,105)( 76,106)
( 77,104)( 78,102)( 79,103)( 80,101)( 81,108)(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)(163,190)
(164,197)(165,195)(166,196)(167,194)(168,192)(169,193)(170,191)(171,198)
(172,199)(173,206)(174,204)(175,205)(176,203)(177,201)(178,202)(179,200)
(180,207)(181,208)(182,215)(183,213)(184,214)(185,212)(186,210)(187,211)
(188,209)(189,216)(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)(271,298)(272,305)(273,303)(274,304)
(275,302)(276,300)(277,301)(278,299)(279,306)(280,307)(281,314)(282,312)
(283,313)(284,311)(285,309)(286,310)(287,308)(288,315)(289,316)(290,323)
(291,321)(292,322)(293,320)(294,318)(295,319)(296,317)(297,324)(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)(379,406)(380,413)(381,411)(382,412)(383,410)(384,408)(385,409)
(386,407)(387,414)(388,415)(389,422)(390,420)(391,421)(392,419)(393,417)
(394,418)(395,416)(396,423)(397,424)(398,431)(399,429)(400,430)(401,428)
(402,426)(403,427)(404,425)(405,432)(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)(487,622)(488,629)(489,627)(490,628)(491,626)(492,624)
(493,625)(494,623)(495,630)(496,631)(497,638)(498,636)(499,637)(500,635)
(501,633)(502,634)(503,632)(504,639)(505,640)(506,647)(507,645)(508,646)
(509,644)(510,642)(511,643)(512,641)(513,648)(514,595)(515,602)(516,600)
(517,601)(518,599)(519,597)(520,598)(521,596)(522,603)(523,604)(524,611)
(525,609)(526,610)(527,608)(528,606)(529,607)(530,605)(531,612)(532,613)
(533,620)(534,618)(535,619)(536,617)(537,615)(538,616)(539,614)(540,621)
(649,784)(650,791)(651,789)(652,790)(653,788)(654,786)(655,787)(656,785)
(657,792)(658,793)(659,800)(660,798)(661,799)(662,797)(663,795)(664,796)
(665,794)(666,801)(667,802)(668,809)(669,807)(670,808)(671,806)(672,804)
(673,805)(674,803)(675,810)(676,757)(677,764)(678,762)(679,763)(680,761)
(681,759)(682,760)(683,758)(684,765)(685,766)(686,773)(687,771)(688,772)
(689,770)(690,768)(691,769)(692,767)(693,774)(694,775)(695,782)(696,780)
(697,781)(698,779)(699,777)(700,778)(701,776)(702,783)(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);;
s1 := ( 1,649)( 2,650)( 3,651)( 4,657)( 5,655)( 6,656)( 7,653)( 8,654)
( 9,652)( 10,667)( 11,668)( 12,669)( 13,675)( 14,673)( 15,674)( 16,671)
( 17,672)( 18,670)( 19,658)( 20,659)( 21,660)( 22,666)( 23,664)( 24,665)
( 25,662)( 26,663)( 27,661)( 28,676)( 29,677)( 30,678)( 31,684)( 32,682)
( 33,683)( 34,680)( 35,681)( 36,679)( 37,694)( 38,695)( 39,696)( 40,702)
( 41,700)( 42,701)( 43,698)( 44,699)( 45,697)( 46,685)( 47,686)( 48,687)
( 49,693)( 50,691)( 51,692)( 52,689)( 53,690)( 54,688)( 55,730)( 56,731)
( 57,732)( 58,738)( 59,736)( 60,737)( 61,734)( 62,735)( 63,733)( 64,748)
( 65,749)( 66,750)( 67,756)( 68,754)( 69,755)( 70,752)( 71,753)( 72,751)
( 73,739)( 74,740)( 75,741)( 76,747)( 77,745)( 78,746)( 79,743)( 80,744)
( 81,742)( 82,703)( 83,704)( 84,705)( 85,711)( 86,709)( 87,710)( 88,707)
( 89,708)( 90,706)( 91,721)( 92,722)( 93,723)( 94,729)( 95,727)( 96,728)
( 97,725)( 98,726)( 99,724)(100,712)(101,713)(102,714)(103,720)(104,718)
(105,719)(106,716)(107,717)(108,715)(109,757)(110,758)(111,759)(112,765)
(113,763)(114,764)(115,761)(116,762)(117,760)(118,775)(119,776)(120,777)
(121,783)(122,781)(123,782)(124,779)(125,780)(126,778)(127,766)(128,767)
(129,768)(130,774)(131,772)(132,773)(133,770)(134,771)(135,769)(136,784)
(137,785)(138,786)(139,792)(140,790)(141,791)(142,788)(143,789)(144,787)
(145,802)(146,803)(147,804)(148,810)(149,808)(150,809)(151,806)(152,807)
(153,805)(154,793)(155,794)(156,795)(157,801)(158,799)(159,800)(160,797)
(161,798)(162,796)(163,838)(164,839)(165,840)(166,846)(167,844)(168,845)
(169,842)(170,843)(171,841)(172,856)(173,857)(174,858)(175,864)(176,862)
(177,863)(178,860)(179,861)(180,859)(181,847)(182,848)(183,849)(184,855)
(185,853)(186,854)(187,851)(188,852)(189,850)(190,811)(191,812)(192,813)
(193,819)(194,817)(195,818)(196,815)(197,816)(198,814)(199,829)(200,830)
(201,831)(202,837)(203,835)(204,836)(205,833)(206,834)(207,832)(208,820)
(209,821)(210,822)(211,828)(212,826)(213,827)(214,824)(215,825)(216,823)
(217,514)(218,515)(219,516)(220,522)(221,520)(222,521)(223,518)(224,519)
(225,517)(226,532)(227,533)(228,534)(229,540)(230,538)(231,539)(232,536)
(233,537)(234,535)(235,523)(236,524)(237,525)(238,531)(239,529)(240,530)
(241,527)(242,528)(243,526)(244,487)(245,488)(246,489)(247,495)(248,493)
(249,494)(250,491)(251,492)(252,490)(253,505)(254,506)(255,507)(256,513)
(257,511)(258,512)(259,509)(260,510)(261,508)(262,496)(263,497)(264,498)
(265,504)(266,502)(267,503)(268,500)(269,501)(270,499)(271,460)(272,461)
(273,462)(274,468)(275,466)(276,467)(277,464)(278,465)(279,463)(280,478)
(281,479)(282,480)(283,486)(284,484)(285,485)(286,482)(287,483)(288,481)
(289,469)(290,470)(291,471)(292,477)(293,475)(294,476)(295,473)(296,474)
(297,472)(298,433)(299,434)(300,435)(301,441)(302,439)(303,440)(304,437)
(305,438)(306,436)(307,451)(308,452)(309,453)(310,459)(311,457)(312,458)
(313,455)(314,456)(315,454)(316,442)(317,443)(318,444)(319,450)(320,448)
(321,449)(322,446)(323,447)(324,445)(325,622)(326,623)(327,624)(328,630)
(329,628)(330,629)(331,626)(332,627)(333,625)(334,640)(335,641)(336,642)
(337,648)(338,646)(339,647)(340,644)(341,645)(342,643)(343,631)(344,632)
(345,633)(346,639)(347,637)(348,638)(349,635)(350,636)(351,634)(352,595)
(353,596)(354,597)(355,603)(356,601)(357,602)(358,599)(359,600)(360,598)
(361,613)(362,614)(363,615)(364,621)(365,619)(366,620)(367,617)(368,618)
(369,616)(370,604)(371,605)(372,606)(373,612)(374,610)(375,611)(376,608)
(377,609)(378,607)(379,568)(380,569)(381,570)(382,576)(383,574)(384,575)
(385,572)(386,573)(387,571)(388,586)(389,587)(390,588)(391,594)(392,592)
(393,593)(394,590)(395,591)(396,589)(397,577)(398,578)(399,579)(400,585)
(401,583)(402,584)(403,581)(404,582)(405,580)(406,541)(407,542)(408,543)
(409,549)(410,547)(411,548)(412,545)(413,546)(414,544)(415,559)(416,560)
(417,561)(418,567)(419,565)(420,566)(421,563)(422,564)(423,562)(424,550)
(425,551)(426,552)(427,558)(428,556)(429,557)(430,554)(431,555)(432,553);;
s2 := ( 1,338)( 2,337)( 3,339)( 4,335)( 5,334)( 6,336)( 7,341)( 8,340)
( 9,342)( 10,329)( 11,328)( 12,330)( 13,326)( 14,325)( 15,327)( 16,332)
( 17,331)( 18,333)( 19,347)( 20,346)( 21,348)( 22,344)( 23,343)( 24,345)
( 25,350)( 26,349)( 27,351)( 28,365)( 29,364)( 30,366)( 31,362)( 32,361)
( 33,363)( 34,368)( 35,367)( 36,369)( 37,356)( 38,355)( 39,357)( 40,353)
( 41,352)( 42,354)( 43,359)( 44,358)( 45,360)( 46,374)( 47,373)( 48,375)
( 49,371)( 50,370)( 51,372)( 52,377)( 53,376)( 54,378)( 55,419)( 56,418)
( 57,420)( 58,416)( 59,415)( 60,417)( 61,422)( 62,421)( 63,423)( 64,410)
( 65,409)( 66,411)( 67,407)( 68,406)( 69,408)( 70,413)( 71,412)( 72,414)
( 73,428)( 74,427)( 75,429)( 76,425)( 77,424)( 78,426)( 79,431)( 80,430)
( 81,432)( 82,392)( 83,391)( 84,393)( 85,389)( 86,388)( 87,390)( 88,395)
( 89,394)( 90,396)( 91,383)( 92,382)( 93,384)( 94,380)( 95,379)( 96,381)
( 97,386)( 98,385)( 99,387)(100,401)(101,400)(102,402)(103,398)(104,397)
(105,399)(106,404)(107,403)(108,405)(109,257)(110,256)(111,258)(112,254)
(113,253)(114,255)(115,260)(116,259)(117,261)(118,248)(119,247)(120,249)
(121,245)(122,244)(123,246)(124,251)(125,250)(126,252)(127,266)(128,265)
(129,267)(130,263)(131,262)(132,264)(133,269)(134,268)(135,270)(136,230)
(137,229)(138,231)(139,227)(140,226)(141,228)(142,233)(143,232)(144,234)
(145,221)(146,220)(147,222)(148,218)(149,217)(150,219)(151,224)(152,223)
(153,225)(154,239)(155,238)(156,240)(157,236)(158,235)(159,237)(160,242)
(161,241)(162,243)(163,284)(164,283)(165,285)(166,281)(167,280)(168,282)
(169,287)(170,286)(171,288)(172,275)(173,274)(174,276)(175,272)(176,271)
(177,273)(178,278)(179,277)(180,279)(181,293)(182,292)(183,294)(184,290)
(185,289)(186,291)(187,296)(188,295)(189,297)(190,311)(191,310)(192,312)
(193,308)(194,307)(195,309)(196,314)(197,313)(198,315)(199,302)(200,301)
(201,303)(202,299)(203,298)(204,300)(205,305)(206,304)(207,306)(208,320)
(209,319)(210,321)(211,317)(212,316)(213,318)(214,323)(215,322)(216,324)
(433,770)(434,769)(435,771)(436,767)(437,766)(438,768)(439,773)(440,772)
(441,774)(442,761)(443,760)(444,762)(445,758)(446,757)(447,759)(448,764)
(449,763)(450,765)(451,779)(452,778)(453,780)(454,776)(455,775)(456,777)
(457,782)(458,781)(459,783)(460,797)(461,796)(462,798)(463,794)(464,793)
(465,795)(466,800)(467,799)(468,801)(469,788)(470,787)(471,789)(472,785)
(473,784)(474,786)(475,791)(476,790)(477,792)(478,806)(479,805)(480,807)
(481,803)(482,802)(483,804)(484,809)(485,808)(486,810)(487,851)(488,850)
(489,852)(490,848)(491,847)(492,849)(493,854)(494,853)(495,855)(496,842)
(497,841)(498,843)(499,839)(500,838)(501,840)(502,845)(503,844)(504,846)
(505,860)(506,859)(507,861)(508,857)(509,856)(510,858)(511,863)(512,862)
(513,864)(514,824)(515,823)(516,825)(517,821)(518,820)(519,822)(520,827)
(521,826)(522,828)(523,815)(524,814)(525,816)(526,812)(527,811)(528,813)
(529,818)(530,817)(531,819)(532,833)(533,832)(534,834)(535,830)(536,829)
(537,831)(538,836)(539,835)(540,837)(541,689)(542,688)(543,690)(544,686)
(545,685)(546,687)(547,692)(548,691)(549,693)(550,680)(551,679)(552,681)
(553,677)(554,676)(555,678)(556,683)(557,682)(558,684)(559,698)(560,697)
(561,699)(562,695)(563,694)(564,696)(565,701)(566,700)(567,702)(568,662)
(569,661)(570,663)(571,659)(572,658)(573,660)(574,665)(575,664)(576,666)
(577,653)(578,652)(579,654)(580,650)(581,649)(582,651)(583,656)(584,655)
(585,657)(586,671)(587,670)(588,672)(589,668)(590,667)(591,669)(592,674)
(593,673)(594,675)(595,716)(596,715)(597,717)(598,713)(599,712)(600,714)
(601,719)(602,718)(603,720)(604,707)(605,706)(606,708)(607,704)(608,703)
(609,705)(610,710)(611,709)(612,711)(613,725)(614,724)(615,726)(616,722)
(617,721)(618,723)(619,728)(620,727)(621,729)(622,743)(623,742)(624,744)
(625,740)(626,739)(627,741)(628,746)(629,745)(630,747)(631,734)(632,733)
(633,735)(634,731)(635,730)(636,732)(637,737)(638,736)(639,738)(640,752)
(641,751)(642,753)(643,749)(644,748)(645,750)(646,755)(647,754)(648,756);;
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)
( 60, 84)( 61, 85)( 62, 83)( 63, 90)( 64, 91)( 65, 98)( 66, 96)( 67, 97)
( 68, 95)( 69, 93)( 70, 94)( 71, 92)( 72, 99)( 73,100)( 74,107)( 75,105)
( 76,106)( 77,104)( 78,102)( 79,103)( 80,101)( 81,108)(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)
(163,190)(164,197)(165,195)(166,196)(167,194)(168,192)(169,193)(170,191)
(171,198)(172,199)(173,206)(174,204)(175,205)(176,203)(177,201)(178,202)
(179,200)(180,207)(181,208)(182,215)(183,213)(184,214)(185,212)(186,210)
(187,211)(188,209)(189,216)(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)(271,298)(272,305)(273,303)
(274,304)(275,302)(276,300)(277,301)(278,299)(279,306)(280,307)(281,314)
(282,312)(283,313)(284,311)(285,309)(286,310)(287,308)(288,315)(289,316)
(290,323)(291,321)(292,322)(293,320)(294,318)(295,319)(296,317)(297,324)
(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)(379,406)(380,413)(381,411)(382,412)(383,410)(384,408)
(385,409)(386,407)(387,414)(388,415)(389,422)(390,420)(391,421)(392,419)
(393,417)(394,418)(395,416)(396,423)(397,424)(398,431)(399,429)(400,430)
(401,428)(402,426)(403,427)(404,425)(405,432)(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)(487,622)(488,629)(489,627)(490,628)(491,626)
(492,624)(493,625)(494,623)(495,630)(496,631)(497,638)(498,636)(499,637)
(500,635)(501,633)(502,634)(503,632)(504,639)(505,640)(506,647)(507,645)
(508,646)(509,644)(510,642)(511,643)(512,641)(513,648)(514,595)(515,602)
(516,600)(517,601)(518,599)(519,597)(520,598)(521,596)(522,603)(523,604)
(524,611)(525,609)(526,610)(527,608)(528,606)(529,607)(530,605)(531,612)
(532,613)(533,620)(534,618)(535,619)(536,617)(537,615)(538,616)(539,614)
(540,621)(649,784)(650,791)(651,789)(652,790)(653,788)(654,786)(655,787)
(656,785)(657,792)(658,793)(659,800)(660,798)(661,799)(662,797)(663,795)
(664,796)(665,794)(666,801)(667,802)(668,809)(669,807)(670,808)(671,806)
(672,804)(673,805)(674,803)(675,810)(676,757)(677,764)(678,762)(679,763)
(680,761)(681,759)(682,760)(683,758)(684,765)(685,766)(686,773)(687,771)
(688,772)(689,770)(690,768)(691,769)(692,767)(693,774)(694,775)(695,782)
(696,780)(697,781)(698,779)(699,777)(700,778)(701,776)(702,783)(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);
s1 := Sym(864)!( 1,649)( 2,650)( 3,651)( 4,657)( 5,655)( 6,656)( 7,653)
( 8,654)( 9,652)( 10,667)( 11,668)( 12,669)( 13,675)( 14,673)( 15,674)
( 16,671)( 17,672)( 18,670)( 19,658)( 20,659)( 21,660)( 22,666)( 23,664)
( 24,665)( 25,662)( 26,663)( 27,661)( 28,676)( 29,677)( 30,678)( 31,684)
( 32,682)( 33,683)( 34,680)( 35,681)( 36,679)( 37,694)( 38,695)( 39,696)
( 40,702)( 41,700)( 42,701)( 43,698)( 44,699)( 45,697)( 46,685)( 47,686)
( 48,687)( 49,693)( 50,691)( 51,692)( 52,689)( 53,690)( 54,688)( 55,730)
( 56,731)( 57,732)( 58,738)( 59,736)( 60,737)( 61,734)( 62,735)( 63,733)
( 64,748)( 65,749)( 66,750)( 67,756)( 68,754)( 69,755)( 70,752)( 71,753)
( 72,751)( 73,739)( 74,740)( 75,741)( 76,747)( 77,745)( 78,746)( 79,743)
( 80,744)( 81,742)( 82,703)( 83,704)( 84,705)( 85,711)( 86,709)( 87,710)
( 88,707)( 89,708)( 90,706)( 91,721)( 92,722)( 93,723)( 94,729)( 95,727)
( 96,728)( 97,725)( 98,726)( 99,724)(100,712)(101,713)(102,714)(103,720)
(104,718)(105,719)(106,716)(107,717)(108,715)(109,757)(110,758)(111,759)
(112,765)(113,763)(114,764)(115,761)(116,762)(117,760)(118,775)(119,776)
(120,777)(121,783)(122,781)(123,782)(124,779)(125,780)(126,778)(127,766)
(128,767)(129,768)(130,774)(131,772)(132,773)(133,770)(134,771)(135,769)
(136,784)(137,785)(138,786)(139,792)(140,790)(141,791)(142,788)(143,789)
(144,787)(145,802)(146,803)(147,804)(148,810)(149,808)(150,809)(151,806)
(152,807)(153,805)(154,793)(155,794)(156,795)(157,801)(158,799)(159,800)
(160,797)(161,798)(162,796)(163,838)(164,839)(165,840)(166,846)(167,844)
(168,845)(169,842)(170,843)(171,841)(172,856)(173,857)(174,858)(175,864)
(176,862)(177,863)(178,860)(179,861)(180,859)(181,847)(182,848)(183,849)
(184,855)(185,853)(186,854)(187,851)(188,852)(189,850)(190,811)(191,812)
(192,813)(193,819)(194,817)(195,818)(196,815)(197,816)(198,814)(199,829)
(200,830)(201,831)(202,837)(203,835)(204,836)(205,833)(206,834)(207,832)
(208,820)(209,821)(210,822)(211,828)(212,826)(213,827)(214,824)(215,825)
(216,823)(217,514)(218,515)(219,516)(220,522)(221,520)(222,521)(223,518)
(224,519)(225,517)(226,532)(227,533)(228,534)(229,540)(230,538)(231,539)
(232,536)(233,537)(234,535)(235,523)(236,524)(237,525)(238,531)(239,529)
(240,530)(241,527)(242,528)(243,526)(244,487)(245,488)(246,489)(247,495)
(248,493)(249,494)(250,491)(251,492)(252,490)(253,505)(254,506)(255,507)
(256,513)(257,511)(258,512)(259,509)(260,510)(261,508)(262,496)(263,497)
(264,498)(265,504)(266,502)(267,503)(268,500)(269,501)(270,499)(271,460)
(272,461)(273,462)(274,468)(275,466)(276,467)(277,464)(278,465)(279,463)
(280,478)(281,479)(282,480)(283,486)(284,484)(285,485)(286,482)(287,483)
(288,481)(289,469)(290,470)(291,471)(292,477)(293,475)(294,476)(295,473)
(296,474)(297,472)(298,433)(299,434)(300,435)(301,441)(302,439)(303,440)
(304,437)(305,438)(306,436)(307,451)(308,452)(309,453)(310,459)(311,457)
(312,458)(313,455)(314,456)(315,454)(316,442)(317,443)(318,444)(319,450)
(320,448)(321,449)(322,446)(323,447)(324,445)(325,622)(326,623)(327,624)
(328,630)(329,628)(330,629)(331,626)(332,627)(333,625)(334,640)(335,641)
(336,642)(337,648)(338,646)(339,647)(340,644)(341,645)(342,643)(343,631)
(344,632)(345,633)(346,639)(347,637)(348,638)(349,635)(350,636)(351,634)
(352,595)(353,596)(354,597)(355,603)(356,601)(357,602)(358,599)(359,600)
(360,598)(361,613)(362,614)(363,615)(364,621)(365,619)(366,620)(367,617)
(368,618)(369,616)(370,604)(371,605)(372,606)(373,612)(374,610)(375,611)
(376,608)(377,609)(378,607)(379,568)(380,569)(381,570)(382,576)(383,574)
(384,575)(385,572)(386,573)(387,571)(388,586)(389,587)(390,588)(391,594)
(392,592)(393,593)(394,590)(395,591)(396,589)(397,577)(398,578)(399,579)
(400,585)(401,583)(402,584)(403,581)(404,582)(405,580)(406,541)(407,542)
(408,543)(409,549)(410,547)(411,548)(412,545)(413,546)(414,544)(415,559)
(416,560)(417,561)(418,567)(419,565)(420,566)(421,563)(422,564)(423,562)
(424,550)(425,551)(426,552)(427,558)(428,556)(429,557)(430,554)(431,555)
(432,553);
s2 := Sym(864)!( 1,338)( 2,337)( 3,339)( 4,335)( 5,334)( 6,336)( 7,341)
( 8,340)( 9,342)( 10,329)( 11,328)( 12,330)( 13,326)( 14,325)( 15,327)
( 16,332)( 17,331)( 18,333)( 19,347)( 20,346)( 21,348)( 22,344)( 23,343)
( 24,345)( 25,350)( 26,349)( 27,351)( 28,365)( 29,364)( 30,366)( 31,362)
( 32,361)( 33,363)( 34,368)( 35,367)( 36,369)( 37,356)( 38,355)( 39,357)
( 40,353)( 41,352)( 42,354)( 43,359)( 44,358)( 45,360)( 46,374)( 47,373)
( 48,375)( 49,371)( 50,370)( 51,372)( 52,377)( 53,376)( 54,378)( 55,419)
( 56,418)( 57,420)( 58,416)( 59,415)( 60,417)( 61,422)( 62,421)( 63,423)
( 64,410)( 65,409)( 66,411)( 67,407)( 68,406)( 69,408)( 70,413)( 71,412)
( 72,414)( 73,428)( 74,427)( 75,429)( 76,425)( 77,424)( 78,426)( 79,431)
( 80,430)( 81,432)( 82,392)( 83,391)( 84,393)( 85,389)( 86,388)( 87,390)
( 88,395)( 89,394)( 90,396)( 91,383)( 92,382)( 93,384)( 94,380)( 95,379)
( 96,381)( 97,386)( 98,385)( 99,387)(100,401)(101,400)(102,402)(103,398)
(104,397)(105,399)(106,404)(107,403)(108,405)(109,257)(110,256)(111,258)
(112,254)(113,253)(114,255)(115,260)(116,259)(117,261)(118,248)(119,247)
(120,249)(121,245)(122,244)(123,246)(124,251)(125,250)(126,252)(127,266)
(128,265)(129,267)(130,263)(131,262)(132,264)(133,269)(134,268)(135,270)
(136,230)(137,229)(138,231)(139,227)(140,226)(141,228)(142,233)(143,232)
(144,234)(145,221)(146,220)(147,222)(148,218)(149,217)(150,219)(151,224)
(152,223)(153,225)(154,239)(155,238)(156,240)(157,236)(158,235)(159,237)
(160,242)(161,241)(162,243)(163,284)(164,283)(165,285)(166,281)(167,280)
(168,282)(169,287)(170,286)(171,288)(172,275)(173,274)(174,276)(175,272)
(176,271)(177,273)(178,278)(179,277)(180,279)(181,293)(182,292)(183,294)
(184,290)(185,289)(186,291)(187,296)(188,295)(189,297)(190,311)(191,310)
(192,312)(193,308)(194,307)(195,309)(196,314)(197,313)(198,315)(199,302)
(200,301)(201,303)(202,299)(203,298)(204,300)(205,305)(206,304)(207,306)
(208,320)(209,319)(210,321)(211,317)(212,316)(213,318)(214,323)(215,322)
(216,324)(433,770)(434,769)(435,771)(436,767)(437,766)(438,768)(439,773)
(440,772)(441,774)(442,761)(443,760)(444,762)(445,758)(446,757)(447,759)
(448,764)(449,763)(450,765)(451,779)(452,778)(453,780)(454,776)(455,775)
(456,777)(457,782)(458,781)(459,783)(460,797)(461,796)(462,798)(463,794)
(464,793)(465,795)(466,800)(467,799)(468,801)(469,788)(470,787)(471,789)
(472,785)(473,784)(474,786)(475,791)(476,790)(477,792)(478,806)(479,805)
(480,807)(481,803)(482,802)(483,804)(484,809)(485,808)(486,810)(487,851)
(488,850)(489,852)(490,848)(491,847)(492,849)(493,854)(494,853)(495,855)
(496,842)(497,841)(498,843)(499,839)(500,838)(501,840)(502,845)(503,844)
(504,846)(505,860)(506,859)(507,861)(508,857)(509,856)(510,858)(511,863)
(512,862)(513,864)(514,824)(515,823)(516,825)(517,821)(518,820)(519,822)
(520,827)(521,826)(522,828)(523,815)(524,814)(525,816)(526,812)(527,811)
(528,813)(529,818)(530,817)(531,819)(532,833)(533,832)(534,834)(535,830)
(536,829)(537,831)(538,836)(539,835)(540,837)(541,689)(542,688)(543,690)
(544,686)(545,685)(546,687)(547,692)(548,691)(549,693)(550,680)(551,679)
(552,681)(553,677)(554,676)(555,678)(556,683)(557,682)(558,684)(559,698)
(560,697)(561,699)(562,695)(563,694)(564,696)(565,701)(566,700)(567,702)
(568,662)(569,661)(570,663)(571,659)(572,658)(573,660)(574,665)(575,664)
(576,666)(577,653)(578,652)(579,654)(580,650)(581,649)(582,651)(583,656)
(584,655)(585,657)(586,671)(587,670)(588,672)(589,668)(590,667)(591,669)
(592,674)(593,673)(594,675)(595,716)(596,715)(597,717)(598,713)(599,712)
(600,714)(601,719)(602,718)(603,720)(604,707)(605,706)(606,708)(607,704)
(608,703)(609,705)(610,710)(611,709)(612,711)(613,725)(614,724)(615,726)
(616,722)(617,721)(618,723)(619,728)(620,727)(621,729)(622,743)(623,742)
(624,744)(625,740)(626,739)(627,741)(628,746)(629,745)(630,747)(631,734)
(632,733)(633,735)(634,731)(635,730)(636,732)(637,737)(638,736)(639,738)
(640,752)(641,751)(642,753)(643,749)(644,748)(645,750)(646,755)(647,754)
(648,756);
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;
References : None.
to this polytope