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