Questions?
See the FAQ
or other info.

Polytope of Type {24,4}

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