Polytope of Type {6,4,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,24}*1728
if this polytope has a name.
Group : SmallGroup(1728,31257)
Rank : 4
Schlafli Type : {6,4,24}
Number of vertices, edges, etc : 9, 18, 72, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
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 : {6,4,12}*864
3-fold quotients : {6,4,8}*576
4-fold quotients : {6,4,6}*432a
6-fold quotients : {6,4,4}*288
12-fold quotients : {6,4,2}*144
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,109)( 2,111)( 3,110)( 4,115)( 5,117)( 6,116)( 7,112)( 8,114)
( 9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)( 16,121)
( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)( 24,134)
( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)( 32,144)
( 33,143)( 34,139)( 35,141)( 36,140)( 37,145)( 38,147)( 39,146)( 40,151)
( 41,153)( 42,152)( 43,148)( 44,150)( 45,149)( 46,154)( 47,156)( 48,155)
( 49,160)( 50,162)( 51,161)( 52,157)( 53,159)( 54,158)( 55,163)( 56,165)
( 57,164)( 58,169)( 59,171)( 60,170)( 61,166)( 62,168)( 63,167)( 64,172)
( 65,174)( 66,173)( 67,178)( 68,180)( 69,179)( 70,175)( 71,177)( 72,176)
( 73,181)( 74,183)( 75,182)( 76,187)( 77,189)( 78,188)( 79,184)( 80,186)
( 81,185)( 82,190)( 83,192)( 84,191)( 85,196)( 86,198)( 87,197)( 88,193)
( 89,195)( 90,194)( 91,199)( 92,201)( 93,200)( 94,205)( 95,207)( 96,206)
( 97,202)( 98,204)( 99,203)(100,208)(101,210)(102,209)(103,214)(104,216)
(105,215)(106,211)(107,213)(108,212)(217,325)(218,327)(219,326)(220,331)
(221,333)(222,332)(223,328)(224,330)(225,329)(226,334)(227,336)(228,335)
(229,340)(230,342)(231,341)(232,337)(233,339)(234,338)(235,343)(236,345)
(237,344)(238,349)(239,351)(240,350)(241,346)(242,348)(243,347)(244,352)
(245,354)(246,353)(247,358)(248,360)(249,359)(250,355)(251,357)(252,356)
(253,361)(254,363)(255,362)(256,367)(257,369)(258,368)(259,364)(260,366)
(261,365)(262,370)(263,372)(264,371)(265,376)(266,378)(267,377)(268,373)
(269,375)(270,374)(271,379)(272,381)(273,380)(274,385)(275,387)(276,386)
(277,382)(278,384)(279,383)(280,388)(281,390)(282,389)(283,394)(284,396)
(285,395)(286,391)(287,393)(288,392)(289,397)(290,399)(291,398)(292,403)
(293,405)(294,404)(295,400)(296,402)(297,401)(298,406)(299,408)(300,407)
(301,412)(302,414)(303,413)(304,409)(305,411)(306,410)(307,415)(308,417)
(309,416)(310,421)(311,423)(312,422)(313,418)(314,420)(315,419)(316,424)
(317,426)(318,425)(319,430)(320,432)(321,431)(322,427)(323,429)(324,428)
(433,541)(434,543)(435,542)(436,547)(437,549)(438,548)(439,544)(440,546)
(441,545)(442,550)(443,552)(444,551)(445,556)(446,558)(447,557)(448,553)
(449,555)(450,554)(451,559)(452,561)(453,560)(454,565)(455,567)(456,566)
(457,562)(458,564)(459,563)(460,568)(461,570)(462,569)(463,574)(464,576)
(465,575)(466,571)(467,573)(468,572)(469,577)(470,579)(471,578)(472,583)
(473,585)(474,584)(475,580)(476,582)(477,581)(478,586)(479,588)(480,587)
(481,592)(482,594)(483,593)(484,589)(485,591)(486,590)(487,595)(488,597)
(489,596)(490,601)(491,603)(492,602)(493,598)(494,600)(495,599)(496,604)
(497,606)(498,605)(499,610)(500,612)(501,611)(502,607)(503,609)(504,608)
(505,613)(506,615)(507,614)(508,619)(509,621)(510,620)(511,616)(512,618)
(513,617)(514,622)(515,624)(516,623)(517,628)(518,630)(519,629)(520,625)
(521,627)(522,626)(523,631)(524,633)(525,632)(526,637)(527,639)(528,638)
(529,634)(530,636)(531,635)(532,640)(533,642)(534,641)(535,646)(536,648)
(537,647)(538,643)(539,645)(540,644)(649,757)(650,759)(651,758)(652,763)
(653,765)(654,764)(655,760)(656,762)(657,761)(658,766)(659,768)(660,767)
(661,772)(662,774)(663,773)(664,769)(665,771)(666,770)(667,775)(668,777)
(669,776)(670,781)(671,783)(672,782)(673,778)(674,780)(675,779)(676,784)
(677,786)(678,785)(679,790)(680,792)(681,791)(682,787)(683,789)(684,788)
(685,793)(686,795)(687,794)(688,799)(689,801)(690,800)(691,796)(692,798)
(693,797)(694,802)(695,804)(696,803)(697,808)(698,810)(699,809)(700,805)
(701,807)(702,806)(703,811)(704,813)(705,812)(706,817)(707,819)(708,818)
(709,814)(710,816)(711,815)(712,820)(713,822)(714,821)(715,826)(716,828)
(717,827)(718,823)(719,825)(720,824)(721,829)(722,831)(723,830)(724,835)
(725,837)(726,836)(727,832)(728,834)(729,833)(730,838)(731,840)(732,839)
(733,844)(734,846)(735,845)(736,841)(737,843)(738,842)(739,847)(740,849)
(741,848)(742,853)(743,855)(744,854)(745,850)(746,852)(747,851)(748,856)
(749,858)(750,857)(751,862)(752,864)(753,863)(754,859)(755,861)(756,860);;
s1 := ( 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, 58)( 57, 63)( 59, 62)( 64, 67)( 66, 72)( 68, 71)
( 73, 76)( 75, 81)( 77, 80)( 82, 85)( 84, 90)( 86, 89)( 91, 94)( 93, 99)
( 95, 98)(100,103)(102,108)(104,107)(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)(163,166)(165,171)
(167,170)(172,175)(174,180)(176,179)(181,184)(183,189)(185,188)(190,193)
(192,198)(194,197)(199,202)(201,207)(203,206)(208,211)(210,216)(212,215)
(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)(271,274)(273,279)(275,278)(280,283)(282,288)(284,287)
(289,292)(291,297)(293,296)(298,301)(300,306)(302,305)(307,310)(309,315)
(311,314)(316,319)(318,324)(320,323)(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)(379,382)(381,387)
(383,386)(388,391)(390,396)(392,395)(397,400)(399,405)(401,404)(406,409)
(408,414)(410,413)(415,418)(417,423)(419,422)(424,427)(426,432)(428,431)
(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)(487,598)(488,596)
(489,603)(490,595)(491,602)(492,600)(493,601)(494,599)(495,597)(496,607)
(497,605)(498,612)(499,604)(500,611)(501,609)(502,610)(503,608)(504,606)
(505,616)(506,614)(507,621)(508,613)(509,620)(510,618)(511,619)(512,617)
(513,615)(514,625)(515,623)(516,630)(517,622)(518,629)(519,627)(520,628)
(521,626)(522,624)(523,634)(524,632)(525,639)(526,631)(527,638)(528,636)
(529,637)(530,635)(531,633)(532,643)(533,641)(534,648)(535,640)(536,647)
(537,645)(538,646)(539,644)(540,642)(649,760)(650,758)(651,765)(652,757)
(653,764)(654,762)(655,763)(656,761)(657,759)(658,769)(659,767)(660,774)
(661,766)(662,773)(663,771)(664,772)(665,770)(666,768)(667,778)(668,776)
(669,783)(670,775)(671,782)(672,780)(673,781)(674,779)(675,777)(676,787)
(677,785)(678,792)(679,784)(680,791)(681,789)(682,790)(683,788)(684,786)
(685,796)(686,794)(687,801)(688,793)(689,800)(690,798)(691,799)(692,797)
(693,795)(694,805)(695,803)(696,810)(697,802)(698,809)(699,807)(700,808)
(701,806)(702,804)(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);;
s2 := ( 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);;
s3 := ( 1,226)( 2,227)( 3,228)( 4,229)( 5,230)( 6,231)( 7,232)( 8,233)
( 9,234)( 10,217)( 11,218)( 12,219)( 13,220)( 14,221)( 15,222)( 16,223)
( 17,224)( 18,225)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,253)( 29,254)( 30,255)( 31,256)( 32,257)
( 33,258)( 34,259)( 35,260)( 36,261)( 37,244)( 38,245)( 39,246)( 40,247)
( 41,248)( 42,249)( 43,250)( 44,251)( 45,252)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,307)( 56,308)
( 57,309)( 58,310)( 59,311)( 60,312)( 61,313)( 62,314)( 63,315)( 64,298)
( 65,299)( 66,300)( 67,301)( 68,302)( 69,303)( 70,304)( 71,305)( 72,306)
( 73,316)( 74,317)( 75,318)( 76,319)( 77,320)( 78,321)( 79,322)( 80,323)
( 81,324)( 82,280)( 83,281)( 84,282)( 85,283)( 86,284)( 87,285)( 88,286)
( 89,287)( 90,288)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)( 96,276)
( 97,277)( 98,278)( 99,279)(100,289)(101,290)(102,291)(103,292)(104,293)
(105,294)(106,295)(107,296)(108,297)(109,334)(110,335)(111,336)(112,337)
(113,338)(114,339)(115,340)(116,341)(117,342)(118,325)(119,326)(120,327)
(121,328)(122,329)(123,330)(124,331)(125,332)(126,333)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,361)
(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)(144,369)
(145,352)(146,353)(147,354)(148,355)(149,356)(150,357)(151,358)(152,359)
(153,360)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,415)(164,416)(165,417)(166,418)(167,419)(168,420)
(169,421)(170,422)(171,423)(172,406)(173,407)(174,408)(175,409)(176,410)
(177,411)(178,412)(179,413)(180,414)(181,424)(182,425)(183,426)(184,427)
(185,428)(186,429)(187,430)(188,431)(189,432)(190,388)(191,389)(192,390)
(193,391)(194,392)(195,393)(196,394)(197,395)(198,396)(199,379)(200,380)
(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)(208,397)
(209,398)(210,399)(211,400)(212,401)(213,402)(214,403)(215,404)(216,405)
(433,658)(434,659)(435,660)(436,661)(437,662)(438,663)(439,664)(440,665)
(441,666)(442,649)(443,650)(444,651)(445,652)(446,653)(447,654)(448,655)
(449,656)(450,657)(451,667)(452,668)(453,669)(454,670)(455,671)(456,672)
(457,673)(458,674)(459,675)(460,685)(461,686)(462,687)(463,688)(464,689)
(465,690)(466,691)(467,692)(468,693)(469,676)(470,677)(471,678)(472,679)
(473,680)(474,681)(475,682)(476,683)(477,684)(478,694)(479,695)(480,696)
(481,697)(482,698)(483,699)(484,700)(485,701)(486,702)(487,739)(488,740)
(489,741)(490,742)(491,743)(492,744)(493,745)(494,746)(495,747)(496,730)
(497,731)(498,732)(499,733)(500,734)(501,735)(502,736)(503,737)(504,738)
(505,748)(506,749)(507,750)(508,751)(509,752)(510,753)(511,754)(512,755)
(513,756)(514,712)(515,713)(516,714)(517,715)(518,716)(519,717)(520,718)
(521,719)(522,720)(523,703)(524,704)(525,705)(526,706)(527,707)(528,708)
(529,709)(530,710)(531,711)(532,721)(533,722)(534,723)(535,724)(536,725)
(537,726)(538,727)(539,728)(540,729)(541,766)(542,767)(543,768)(544,769)
(545,770)(546,771)(547,772)(548,773)(549,774)(550,757)(551,758)(552,759)
(553,760)(554,761)(555,762)(556,763)(557,764)(558,765)(559,775)(560,776)
(561,777)(562,778)(563,779)(564,780)(565,781)(566,782)(567,783)(568,793)
(569,794)(570,795)(571,796)(572,797)(573,798)(574,799)(575,800)(576,801)
(577,784)(578,785)(579,786)(580,787)(581,788)(582,789)(583,790)(584,791)
(585,792)(586,802)(587,803)(588,804)(589,805)(590,806)(591,807)(592,808)
(593,809)(594,810)(595,847)(596,848)(597,849)(598,850)(599,851)(600,852)
(601,853)(602,854)(603,855)(604,838)(605,839)(606,840)(607,841)(608,842)
(609,843)(610,844)(611,845)(612,846)(613,856)(614,857)(615,858)(616,859)
(617,860)(618,861)(619,862)(620,863)(621,864)(622,820)(623,821)(624,822)
(625,823)(626,824)(627,825)(628,826)(629,827)(630,828)(631,811)(632,812)
(633,813)(634,814)(635,815)(636,816)(637,817)(638,818)(639,819)(640,829)
(641,830)(642,831)(643,832)(644,833)(645,834)(646,835)(647,836)(648,837);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,109)( 2,111)( 3,110)( 4,115)( 5,117)( 6,116)( 7,112)
( 8,114)( 9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)
( 16,121)( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)
( 24,134)( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)
( 32,144)( 33,143)( 34,139)( 35,141)( 36,140)( 37,145)( 38,147)( 39,146)
( 40,151)( 41,153)( 42,152)( 43,148)( 44,150)( 45,149)( 46,154)( 47,156)
( 48,155)( 49,160)( 50,162)( 51,161)( 52,157)( 53,159)( 54,158)( 55,163)
( 56,165)( 57,164)( 58,169)( 59,171)( 60,170)( 61,166)( 62,168)( 63,167)
( 64,172)( 65,174)( 66,173)( 67,178)( 68,180)( 69,179)( 70,175)( 71,177)
( 72,176)( 73,181)( 74,183)( 75,182)( 76,187)( 77,189)( 78,188)( 79,184)
( 80,186)( 81,185)( 82,190)( 83,192)( 84,191)( 85,196)( 86,198)( 87,197)
( 88,193)( 89,195)( 90,194)( 91,199)( 92,201)( 93,200)( 94,205)( 95,207)
( 96,206)( 97,202)( 98,204)( 99,203)(100,208)(101,210)(102,209)(103,214)
(104,216)(105,215)(106,211)(107,213)(108,212)(217,325)(218,327)(219,326)
(220,331)(221,333)(222,332)(223,328)(224,330)(225,329)(226,334)(227,336)
(228,335)(229,340)(230,342)(231,341)(232,337)(233,339)(234,338)(235,343)
(236,345)(237,344)(238,349)(239,351)(240,350)(241,346)(242,348)(243,347)
(244,352)(245,354)(246,353)(247,358)(248,360)(249,359)(250,355)(251,357)
(252,356)(253,361)(254,363)(255,362)(256,367)(257,369)(258,368)(259,364)
(260,366)(261,365)(262,370)(263,372)(264,371)(265,376)(266,378)(267,377)
(268,373)(269,375)(270,374)(271,379)(272,381)(273,380)(274,385)(275,387)
(276,386)(277,382)(278,384)(279,383)(280,388)(281,390)(282,389)(283,394)
(284,396)(285,395)(286,391)(287,393)(288,392)(289,397)(290,399)(291,398)
(292,403)(293,405)(294,404)(295,400)(296,402)(297,401)(298,406)(299,408)
(300,407)(301,412)(302,414)(303,413)(304,409)(305,411)(306,410)(307,415)
(308,417)(309,416)(310,421)(311,423)(312,422)(313,418)(314,420)(315,419)
(316,424)(317,426)(318,425)(319,430)(320,432)(321,431)(322,427)(323,429)
(324,428)(433,541)(434,543)(435,542)(436,547)(437,549)(438,548)(439,544)
(440,546)(441,545)(442,550)(443,552)(444,551)(445,556)(446,558)(447,557)
(448,553)(449,555)(450,554)(451,559)(452,561)(453,560)(454,565)(455,567)
(456,566)(457,562)(458,564)(459,563)(460,568)(461,570)(462,569)(463,574)
(464,576)(465,575)(466,571)(467,573)(468,572)(469,577)(470,579)(471,578)
(472,583)(473,585)(474,584)(475,580)(476,582)(477,581)(478,586)(479,588)
(480,587)(481,592)(482,594)(483,593)(484,589)(485,591)(486,590)(487,595)
(488,597)(489,596)(490,601)(491,603)(492,602)(493,598)(494,600)(495,599)
(496,604)(497,606)(498,605)(499,610)(500,612)(501,611)(502,607)(503,609)
(504,608)(505,613)(506,615)(507,614)(508,619)(509,621)(510,620)(511,616)
(512,618)(513,617)(514,622)(515,624)(516,623)(517,628)(518,630)(519,629)
(520,625)(521,627)(522,626)(523,631)(524,633)(525,632)(526,637)(527,639)
(528,638)(529,634)(530,636)(531,635)(532,640)(533,642)(534,641)(535,646)
(536,648)(537,647)(538,643)(539,645)(540,644)(649,757)(650,759)(651,758)
(652,763)(653,765)(654,764)(655,760)(656,762)(657,761)(658,766)(659,768)
(660,767)(661,772)(662,774)(663,773)(664,769)(665,771)(666,770)(667,775)
(668,777)(669,776)(670,781)(671,783)(672,782)(673,778)(674,780)(675,779)
(676,784)(677,786)(678,785)(679,790)(680,792)(681,791)(682,787)(683,789)
(684,788)(685,793)(686,795)(687,794)(688,799)(689,801)(690,800)(691,796)
(692,798)(693,797)(694,802)(695,804)(696,803)(697,808)(698,810)(699,809)
(700,805)(701,807)(702,806)(703,811)(704,813)(705,812)(706,817)(707,819)
(708,818)(709,814)(710,816)(711,815)(712,820)(713,822)(714,821)(715,826)
(716,828)(717,827)(718,823)(719,825)(720,824)(721,829)(722,831)(723,830)
(724,835)(725,837)(726,836)(727,832)(728,834)(729,833)(730,838)(731,840)
(732,839)(733,844)(734,846)(735,845)(736,841)(737,843)(738,842)(739,847)
(740,849)(741,848)(742,853)(743,855)(744,854)(745,850)(746,852)(747,851)
(748,856)(749,858)(750,857)(751,862)(752,864)(753,863)(754,859)(755,861)
(756,860);
s1 := 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, 58)( 57, 63)( 59, 62)( 64, 67)( 66, 72)
( 68, 71)( 73, 76)( 75, 81)( 77, 80)( 82, 85)( 84, 90)( 86, 89)( 91, 94)
( 93, 99)( 95, 98)(100,103)(102,108)(104,107)(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)(163,166)
(165,171)(167,170)(172,175)(174,180)(176,179)(181,184)(183,189)(185,188)
(190,193)(192,198)(194,197)(199,202)(201,207)(203,206)(208,211)(210,216)
(212,215)(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)(271,274)(273,279)(275,278)(280,283)(282,288)
(284,287)(289,292)(291,297)(293,296)(298,301)(300,306)(302,305)(307,310)
(309,315)(311,314)(316,319)(318,324)(320,323)(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)(379,382)
(381,387)(383,386)(388,391)(390,396)(392,395)(397,400)(399,405)(401,404)
(406,409)(408,414)(410,413)(415,418)(417,423)(419,422)(424,427)(426,432)
(428,431)(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)(487,598)
(488,596)(489,603)(490,595)(491,602)(492,600)(493,601)(494,599)(495,597)
(496,607)(497,605)(498,612)(499,604)(500,611)(501,609)(502,610)(503,608)
(504,606)(505,616)(506,614)(507,621)(508,613)(509,620)(510,618)(511,619)
(512,617)(513,615)(514,625)(515,623)(516,630)(517,622)(518,629)(519,627)
(520,628)(521,626)(522,624)(523,634)(524,632)(525,639)(526,631)(527,638)
(528,636)(529,637)(530,635)(531,633)(532,643)(533,641)(534,648)(535,640)
(536,647)(537,645)(538,646)(539,644)(540,642)(649,760)(650,758)(651,765)
(652,757)(653,764)(654,762)(655,763)(656,761)(657,759)(658,769)(659,767)
(660,774)(661,766)(662,773)(663,771)(664,772)(665,770)(666,768)(667,778)
(668,776)(669,783)(670,775)(671,782)(672,780)(673,781)(674,779)(675,777)
(676,787)(677,785)(678,792)(679,784)(680,791)(681,789)(682,790)(683,788)
(684,786)(685,796)(686,794)(687,801)(688,793)(689,800)(690,798)(691,799)
(692,797)(693,795)(694,805)(695,803)(696,810)(697,802)(698,809)(699,807)
(700,808)(701,806)(702,804)(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);
s2 := 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);
s3 := Sym(864)!( 1,226)( 2,227)( 3,228)( 4,229)( 5,230)( 6,231)( 7,232)
( 8,233)( 9,234)( 10,217)( 11,218)( 12,219)( 13,220)( 14,221)( 15,222)
( 16,223)( 17,224)( 18,225)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,253)( 29,254)( 30,255)( 31,256)
( 32,257)( 33,258)( 34,259)( 35,260)( 36,261)( 37,244)( 38,245)( 39,246)
( 40,247)( 41,248)( 42,249)( 43,250)( 44,251)( 45,252)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,307)
( 56,308)( 57,309)( 58,310)( 59,311)( 60,312)( 61,313)( 62,314)( 63,315)
( 64,298)( 65,299)( 66,300)( 67,301)( 68,302)( 69,303)( 70,304)( 71,305)
( 72,306)( 73,316)( 74,317)( 75,318)( 76,319)( 77,320)( 78,321)( 79,322)
( 80,323)( 81,324)( 82,280)( 83,281)( 84,282)( 85,283)( 86,284)( 87,285)
( 88,286)( 89,287)( 90,288)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)
( 96,276)( 97,277)( 98,278)( 99,279)(100,289)(101,290)(102,291)(103,292)
(104,293)(105,294)(106,295)(107,296)(108,297)(109,334)(110,335)(111,336)
(112,337)(113,338)(114,339)(115,340)(116,341)(117,342)(118,325)(119,326)
(120,327)(121,328)(122,329)(123,330)(124,331)(125,332)(126,333)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,361)(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)
(144,369)(145,352)(146,353)(147,354)(148,355)(149,356)(150,357)(151,358)
(152,359)(153,360)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,415)(164,416)(165,417)(166,418)(167,419)
(168,420)(169,421)(170,422)(171,423)(172,406)(173,407)(174,408)(175,409)
(176,410)(177,411)(178,412)(179,413)(180,414)(181,424)(182,425)(183,426)
(184,427)(185,428)(186,429)(187,430)(188,431)(189,432)(190,388)(191,389)
(192,390)(193,391)(194,392)(195,393)(196,394)(197,395)(198,396)(199,379)
(200,380)(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)
(208,397)(209,398)(210,399)(211,400)(212,401)(213,402)(214,403)(215,404)
(216,405)(433,658)(434,659)(435,660)(436,661)(437,662)(438,663)(439,664)
(440,665)(441,666)(442,649)(443,650)(444,651)(445,652)(446,653)(447,654)
(448,655)(449,656)(450,657)(451,667)(452,668)(453,669)(454,670)(455,671)
(456,672)(457,673)(458,674)(459,675)(460,685)(461,686)(462,687)(463,688)
(464,689)(465,690)(466,691)(467,692)(468,693)(469,676)(470,677)(471,678)
(472,679)(473,680)(474,681)(475,682)(476,683)(477,684)(478,694)(479,695)
(480,696)(481,697)(482,698)(483,699)(484,700)(485,701)(486,702)(487,739)
(488,740)(489,741)(490,742)(491,743)(492,744)(493,745)(494,746)(495,747)
(496,730)(497,731)(498,732)(499,733)(500,734)(501,735)(502,736)(503,737)
(504,738)(505,748)(506,749)(507,750)(508,751)(509,752)(510,753)(511,754)
(512,755)(513,756)(514,712)(515,713)(516,714)(517,715)(518,716)(519,717)
(520,718)(521,719)(522,720)(523,703)(524,704)(525,705)(526,706)(527,707)
(528,708)(529,709)(530,710)(531,711)(532,721)(533,722)(534,723)(535,724)
(536,725)(537,726)(538,727)(539,728)(540,729)(541,766)(542,767)(543,768)
(544,769)(545,770)(546,771)(547,772)(548,773)(549,774)(550,757)(551,758)
(552,759)(553,760)(554,761)(555,762)(556,763)(557,764)(558,765)(559,775)
(560,776)(561,777)(562,778)(563,779)(564,780)(565,781)(566,782)(567,783)
(568,793)(569,794)(570,795)(571,796)(572,797)(573,798)(574,799)(575,800)
(576,801)(577,784)(578,785)(579,786)(580,787)(581,788)(582,789)(583,790)
(584,791)(585,792)(586,802)(587,803)(588,804)(589,805)(590,806)(591,807)
(592,808)(593,809)(594,810)(595,847)(596,848)(597,849)(598,850)(599,851)
(600,852)(601,853)(602,854)(603,855)(604,838)(605,839)(606,840)(607,841)
(608,842)(609,843)(610,844)(611,845)(612,846)(613,856)(614,857)(615,858)
(616,859)(617,860)(618,861)(619,862)(620,863)(621,864)(622,820)(623,821)
(624,822)(625,823)(626,824)(627,825)(628,826)(629,827)(630,828)(631,811)
(632,812)(633,813)(634,814)(635,815)(636,816)(637,817)(638,818)(639,819)
(640,829)(641,830)(642,831)(643,832)(644,833)(645,834)(646,835)(647,836)
(648,837);
poly := sub<Sym(864)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope