Polytope of Type {12,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,6}*1728a
Also Known As : {{12,4|2},{4,6}4}. if this polytope has another name.
Group : SmallGroup(1728,46611)
Rank : 4
Schlafli Type : {12,4,6}
Number of vertices, edges, etc : 12, 72, 36, 18
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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, {6,4,6}*864a
3-fold quotients : {4,4,6}*576
4-fold quotients : {6,4,6}*432b
6-fold quotients : {4,4,6}*288, {2,4,6}*288
9-fold quotients : {12,4,2}*192a
12-fold quotients : {2,4,6}*144
18-fold quotients : {12,2,2}*96, {6,4,2}*96a
27-fold quotients : {4,4,2}*64
36-fold quotients : {6,2,2}*48
54-fold quotients : {2,4,2}*32, {4,2,2}*32
72-fold quotients : {3,2,2}*24
108-fold quotients : {2,2,2}*16
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)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,289)
( 65,290)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,296)( 72,297)
( 73,280)( 74,281)( 75,282)( 76,283)( 77,284)( 78,285)( 79,286)( 80,287)
( 81,288)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,316)( 92,317)( 93,318)( 94,319)( 95,320)( 96,321)
( 97,322)( 98,323)( 99,324)(100,307)(101,308)(102,309)(103,310)(104,311)
(105,312)(106,313)(107,314)(108,315)(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)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)
(169,385)(170,386)(171,387)(172,397)(173,398)(174,399)(175,400)(176,401)
(177,402)(178,403)(179,404)(180,405)(181,388)(182,389)(183,390)(184,391)
(185,392)(186,393)(187,394)(188,395)(189,396)(190,406)(191,407)(192,408)
(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,424)(200,425)
(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,415)
(209,416)(210,417)(211,418)(212,419)(213,420)(214,421)(215,422)(216,423)
(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)(487,703)(488,704)
(489,705)(490,706)(491,707)(492,708)(493,709)(494,710)(495,711)(496,721)
(497,722)(498,723)(499,724)(500,725)(501,726)(502,727)(503,728)(504,729)
(505,712)(506,713)(507,714)(508,715)(509,716)(510,717)(511,718)(512,719)
(513,720)(514,730)(515,731)(516,732)(517,733)(518,734)(519,735)(520,736)
(521,737)(522,738)(523,748)(524,749)(525,750)(526,751)(527,752)(528,753)
(529,754)(530,755)(531,756)(532,739)(533,740)(534,741)(535,742)(536,743)
(537,744)(538,745)(539,746)(540,747)(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)(595,811)(596,812)(597,813)(598,814)(599,815)(600,816)
(601,817)(602,818)(603,819)(604,829)(605,830)(606,831)(607,832)(608,833)
(609,834)(610,835)(611,836)(612,837)(613,820)(614,821)(615,822)(616,823)
(617,824)(618,825)(619,826)(620,827)(621,828)(622,838)(623,839)(624,840)
(625,841)(626,842)(627,843)(628,844)(629,845)(630,846)(631,856)(632,857)
(633,858)(634,859)(635,860)(636,861)(637,862)(638,863)(639,864)(640,847)
(641,848)(642,849)(643,850)(644,851)(645,852)(646,853)(647,854)(648,855);;
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)( 55,712)( 56,713)
( 57,714)( 58,720)( 59,718)( 60,719)( 61,716)( 62,717)( 63,715)( 64,703)
( 65,704)( 66,705)( 67,711)( 68,709)( 69,710)( 70,707)( 71,708)( 72,706)
( 73,721)( 74,722)( 75,723)( 76,729)( 77,727)( 78,728)( 79,725)( 80,726)
( 81,724)( 82,739)( 83,740)( 84,741)( 85,747)( 86,745)( 87,746)( 88,743)
( 89,744)( 90,742)( 91,730)( 92,731)( 93,732)( 94,738)( 95,736)( 96,737)
( 97,734)( 98,735)( 99,733)(100,748)(101,749)(102,750)(103,756)(104,754)
(105,755)(106,752)(107,753)(108,751)(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)(163,820)(164,821)(165,822)(166,828)(167,826)(168,827)
(169,824)(170,825)(171,823)(172,811)(173,812)(174,813)(175,819)(176,817)
(177,818)(178,815)(179,816)(180,814)(181,829)(182,830)(183,831)(184,837)
(185,835)(186,836)(187,833)(188,834)(189,832)(190,847)(191,848)(192,849)
(193,855)(194,853)(195,854)(196,851)(197,852)(198,850)(199,838)(200,839)
(201,840)(202,846)(203,844)(204,845)(205,842)(206,843)(207,841)(208,856)
(209,857)(210,858)(211,864)(212,862)(213,863)(214,860)(215,861)(216,859)
(217,469)(218,470)(219,471)(220,477)(221,475)(222,476)(223,473)(224,474)
(225,472)(226,460)(227,461)(228,462)(229,468)(230,466)(231,467)(232,464)
(233,465)(234,463)(235,478)(236,479)(237,480)(238,486)(239,484)(240,485)
(241,482)(242,483)(243,481)(244,442)(245,443)(246,444)(247,450)(248,448)
(249,449)(250,446)(251,447)(252,445)(253,433)(254,434)(255,435)(256,441)
(257,439)(258,440)(259,437)(260,438)(261,436)(262,451)(263,452)(264,453)
(265,459)(266,457)(267,458)(268,455)(269,456)(270,454)(271,523)(272,524)
(273,525)(274,531)(275,529)(276,530)(277,527)(278,528)(279,526)(280,514)
(281,515)(282,516)(283,522)(284,520)(285,521)(286,518)(287,519)(288,517)
(289,532)(290,533)(291,534)(292,540)(293,538)(294,539)(295,536)(296,537)
(297,535)(298,496)(299,497)(300,498)(301,504)(302,502)(303,503)(304,500)
(305,501)(306,499)(307,487)(308,488)(309,489)(310,495)(311,493)(312,494)
(313,491)(314,492)(315,490)(316,505)(317,506)(318,507)(319,513)(320,511)
(321,512)(322,509)(323,510)(324,508)(325,577)(326,578)(327,579)(328,585)
(329,583)(330,584)(331,581)(332,582)(333,580)(334,568)(335,569)(336,570)
(337,576)(338,574)(339,575)(340,572)(341,573)(342,571)(343,586)(344,587)
(345,588)(346,594)(347,592)(348,593)(349,590)(350,591)(351,589)(352,550)
(353,551)(354,552)(355,558)(356,556)(357,557)(358,554)(359,555)(360,553)
(361,541)(362,542)(363,543)(364,549)(365,547)(366,548)(367,545)(368,546)
(369,544)(370,559)(371,560)(372,561)(373,567)(374,565)(375,566)(376,563)
(377,564)(378,562)(379,631)(380,632)(381,633)(382,639)(383,637)(384,638)
(385,635)(386,636)(387,634)(388,622)(389,623)(390,624)(391,630)(392,628)
(393,629)(394,626)(395,627)(396,625)(397,640)(398,641)(399,642)(400,648)
(401,646)(402,647)(403,644)(404,645)(405,643)(406,604)(407,605)(408,606)
(409,612)(410,610)(411,611)(412,608)(413,609)(414,607)(415,595)(416,596)
(417,597)(418,603)(419,601)(420,602)(421,599)(422,600)(423,598)(424,613)
(425,614)(426,615)(427,621)(428,619)(429,620)(430,617)(431,618)(432,616);;
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)
(433,487)(434,494)(435,492)(436,493)(437,491)(438,489)(439,490)(440,488)
(441,495)(442,496)(443,503)(444,501)(445,502)(446,500)(447,498)(448,499)
(449,497)(450,504)(451,505)(452,512)(453,510)(454,511)(455,509)(456,507)
(457,508)(458,506)(459,513)(460,514)(461,521)(462,519)(463,520)(464,518)
(465,516)(466,517)(467,515)(468,522)(469,523)(470,530)(471,528)(472,529)
(473,527)(474,525)(475,526)(476,524)(477,531)(478,532)(479,539)(480,537)
(481,538)(482,536)(483,534)(484,535)(485,533)(486,540)(541,595)(542,602)
(543,600)(544,601)(545,599)(546,597)(547,598)(548,596)(549,603)(550,604)
(551,611)(552,609)(553,610)(554,608)(555,606)(556,607)(557,605)(558,612)
(559,613)(560,620)(561,618)(562,619)(563,617)(564,615)(565,616)(566,614)
(567,621)(568,622)(569,629)(570,627)(571,628)(572,626)(573,624)(574,625)
(575,623)(576,630)(577,631)(578,638)(579,636)(580,637)(581,635)(582,633)
(583,634)(584,632)(585,639)(586,640)(587,647)(588,645)(589,646)(590,644)
(591,642)(592,643)(593,641)(594,648)(649,703)(650,710)(651,708)(652,709)
(653,707)(654,705)(655,706)(656,704)(657,711)(658,712)(659,719)(660,717)
(661,718)(662,716)(663,714)(664,715)(665,713)(666,720)(667,721)(668,728)
(669,726)(670,727)(671,725)(672,723)(673,724)(674,722)(675,729)(676,730)
(677,737)(678,735)(679,736)(680,734)(681,732)(682,733)(683,731)(684,738)
(685,739)(686,746)(687,744)(688,745)(689,743)(690,741)(691,742)(692,740)
(693,747)(694,748)(695,755)(696,753)(697,754)(698,752)(699,750)(700,751)
(701,749)(702,756)(757,811)(758,818)(759,816)(760,817)(761,815)(762,813)
(763,814)(764,812)(765,819)(766,820)(767,827)(768,825)(769,826)(770,824)
(771,822)(772,823)(773,821)(774,828)(775,829)(776,836)(777,834)(778,835)
(779,833)(780,831)(781,832)(782,830)(783,837)(784,838)(785,845)(786,843)
(787,844)(788,842)(789,840)(790,841)(791,839)(792,846)(793,847)(794,854)
(795,852)(796,853)(797,851)(798,849)(799,850)(800,848)(801,855)(802,856)
(803,863)(804,861)(805,862)(806,860)(807,858)(808,859)(809,857)(810,864);;
s3 := ( 1,164)( 2,163)( 3,165)( 4,170)( 5,169)( 6,171)( 7,167)( 8,166)
( 9,168)( 10,173)( 11,172)( 12,174)( 13,179)( 14,178)( 15,180)( 16,176)
( 17,175)( 18,177)( 19,182)( 20,181)( 21,183)( 22,188)( 23,187)( 24,189)
( 25,185)( 26,184)( 27,186)( 28,191)( 29,190)( 30,192)( 31,197)( 32,196)
( 33,198)( 34,194)( 35,193)( 36,195)( 37,200)( 38,199)( 39,201)( 40,206)
( 41,205)( 42,207)( 43,203)( 44,202)( 45,204)( 46,209)( 47,208)( 48,210)
( 49,215)( 50,214)( 51,216)( 52,212)( 53,211)( 54,213)( 55,110)( 56,109)
( 57,111)( 58,116)( 59,115)( 60,117)( 61,113)( 62,112)( 63,114)( 64,119)
( 65,118)( 66,120)( 67,125)( 68,124)( 69,126)( 70,122)( 71,121)( 72,123)
( 73,128)( 74,127)( 75,129)( 76,134)( 77,133)( 78,135)( 79,131)( 80,130)
( 81,132)( 82,137)( 83,136)( 84,138)( 85,143)( 86,142)( 87,144)( 88,140)
( 89,139)( 90,141)( 91,146)( 92,145)( 93,147)( 94,152)( 95,151)( 96,153)
( 97,149)( 98,148)( 99,150)(100,155)(101,154)(102,156)(103,161)(104,160)
(105,162)(106,158)(107,157)(108,159)(217,380)(218,379)(219,381)(220,386)
(221,385)(222,387)(223,383)(224,382)(225,384)(226,389)(227,388)(228,390)
(229,395)(230,394)(231,396)(232,392)(233,391)(234,393)(235,398)(236,397)
(237,399)(238,404)(239,403)(240,405)(241,401)(242,400)(243,402)(244,407)
(245,406)(246,408)(247,413)(248,412)(249,414)(250,410)(251,409)(252,411)
(253,416)(254,415)(255,417)(256,422)(257,421)(258,423)(259,419)(260,418)
(261,420)(262,425)(263,424)(264,426)(265,431)(266,430)(267,432)(268,428)
(269,427)(270,429)(271,326)(272,325)(273,327)(274,332)(275,331)(276,333)
(277,329)(278,328)(279,330)(280,335)(281,334)(282,336)(283,341)(284,340)
(285,342)(286,338)(287,337)(288,339)(289,344)(290,343)(291,345)(292,350)
(293,349)(294,351)(295,347)(296,346)(297,348)(298,353)(299,352)(300,354)
(301,359)(302,358)(303,360)(304,356)(305,355)(306,357)(307,362)(308,361)
(309,363)(310,368)(311,367)(312,369)(313,365)(314,364)(315,366)(316,371)
(317,370)(318,372)(319,377)(320,376)(321,378)(322,374)(323,373)(324,375)
(433,596)(434,595)(435,597)(436,602)(437,601)(438,603)(439,599)(440,598)
(441,600)(442,605)(443,604)(444,606)(445,611)(446,610)(447,612)(448,608)
(449,607)(450,609)(451,614)(452,613)(453,615)(454,620)(455,619)(456,621)
(457,617)(458,616)(459,618)(460,623)(461,622)(462,624)(463,629)(464,628)
(465,630)(466,626)(467,625)(468,627)(469,632)(470,631)(471,633)(472,638)
(473,637)(474,639)(475,635)(476,634)(477,636)(478,641)(479,640)(480,642)
(481,647)(482,646)(483,648)(484,644)(485,643)(486,645)(487,542)(488,541)
(489,543)(490,548)(491,547)(492,549)(493,545)(494,544)(495,546)(496,551)
(497,550)(498,552)(499,557)(500,556)(501,558)(502,554)(503,553)(504,555)
(505,560)(506,559)(507,561)(508,566)(509,565)(510,567)(511,563)(512,562)
(513,564)(514,569)(515,568)(516,570)(517,575)(518,574)(519,576)(520,572)
(521,571)(522,573)(523,578)(524,577)(525,579)(526,584)(527,583)(528,585)
(529,581)(530,580)(531,582)(532,587)(533,586)(534,588)(535,593)(536,592)
(537,594)(538,590)(539,589)(540,591)(649,812)(650,811)(651,813)(652,818)
(653,817)(654,819)(655,815)(656,814)(657,816)(658,821)(659,820)(660,822)
(661,827)(662,826)(663,828)(664,824)(665,823)(666,825)(667,830)(668,829)
(669,831)(670,836)(671,835)(672,837)(673,833)(674,832)(675,834)(676,839)
(677,838)(678,840)(679,845)(680,844)(681,846)(682,842)(683,841)(684,843)
(685,848)(686,847)(687,849)(688,854)(689,853)(690,855)(691,851)(692,850)
(693,852)(694,857)(695,856)(696,858)(697,863)(698,862)(699,864)(700,860)
(701,859)(702,861)(703,758)(704,757)(705,759)(706,764)(707,763)(708,765)
(709,761)(710,760)(711,762)(712,767)(713,766)(714,768)(715,773)(716,772)
(717,774)(718,770)(719,769)(720,771)(721,776)(722,775)(723,777)(724,782)
(725,781)(726,783)(727,779)(728,778)(729,780)(730,785)(731,784)(732,786)
(733,791)(734,790)(735,792)(736,788)(737,787)(738,789)(739,794)(740,793)
(741,795)(742,800)(743,799)(744,801)(745,797)(746,796)(747,798)(748,803)
(749,802)(750,804)(751,809)(752,808)(753,810)(754,806)(755,805)(756,807);;
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,
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)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,289)( 65,290)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,296)
( 72,297)( 73,280)( 74,281)( 75,282)( 76,283)( 77,284)( 78,285)( 79,286)
( 80,287)( 81,288)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,316)( 92,317)( 93,318)( 94,319)( 95,320)
( 96,321)( 97,322)( 98,323)( 99,324)(100,307)(101,308)(102,309)(103,310)
(104,311)(105,312)(106,313)(107,314)(108,315)(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)(163,379)(164,380)(165,381)(166,382)(167,383)
(168,384)(169,385)(170,386)(171,387)(172,397)(173,398)(174,399)(175,400)
(176,401)(177,402)(178,403)(179,404)(180,405)(181,388)(182,389)(183,390)
(184,391)(185,392)(186,393)(187,394)(188,395)(189,396)(190,406)(191,407)
(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,424)
(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)
(208,415)(209,416)(210,417)(211,418)(212,419)(213,420)(214,421)(215,422)
(216,423)(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)(487,703)
(488,704)(489,705)(490,706)(491,707)(492,708)(493,709)(494,710)(495,711)
(496,721)(497,722)(498,723)(499,724)(500,725)(501,726)(502,727)(503,728)
(504,729)(505,712)(506,713)(507,714)(508,715)(509,716)(510,717)(511,718)
(512,719)(513,720)(514,730)(515,731)(516,732)(517,733)(518,734)(519,735)
(520,736)(521,737)(522,738)(523,748)(524,749)(525,750)(526,751)(527,752)
(528,753)(529,754)(530,755)(531,756)(532,739)(533,740)(534,741)(535,742)
(536,743)(537,744)(538,745)(539,746)(540,747)(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)(595,811)(596,812)(597,813)(598,814)(599,815)
(600,816)(601,817)(602,818)(603,819)(604,829)(605,830)(606,831)(607,832)
(608,833)(609,834)(610,835)(611,836)(612,837)(613,820)(614,821)(615,822)
(616,823)(617,824)(618,825)(619,826)(620,827)(621,828)(622,838)(623,839)
(624,840)(625,841)(626,842)(627,843)(628,844)(629,845)(630,846)(631,856)
(632,857)(633,858)(634,859)(635,860)(636,861)(637,862)(638,863)(639,864)
(640,847)(641,848)(642,849)(643,850)(644,851)(645,852)(646,853)(647,854)
(648,855);
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)( 55,712)
( 56,713)( 57,714)( 58,720)( 59,718)( 60,719)( 61,716)( 62,717)( 63,715)
( 64,703)( 65,704)( 66,705)( 67,711)( 68,709)( 69,710)( 70,707)( 71,708)
( 72,706)( 73,721)( 74,722)( 75,723)( 76,729)( 77,727)( 78,728)( 79,725)
( 80,726)( 81,724)( 82,739)( 83,740)( 84,741)( 85,747)( 86,745)( 87,746)
( 88,743)( 89,744)( 90,742)( 91,730)( 92,731)( 93,732)( 94,738)( 95,736)
( 96,737)( 97,734)( 98,735)( 99,733)(100,748)(101,749)(102,750)(103,756)
(104,754)(105,755)(106,752)(107,753)(108,751)(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)(163,820)(164,821)(165,822)(166,828)(167,826)
(168,827)(169,824)(170,825)(171,823)(172,811)(173,812)(174,813)(175,819)
(176,817)(177,818)(178,815)(179,816)(180,814)(181,829)(182,830)(183,831)
(184,837)(185,835)(186,836)(187,833)(188,834)(189,832)(190,847)(191,848)
(192,849)(193,855)(194,853)(195,854)(196,851)(197,852)(198,850)(199,838)
(200,839)(201,840)(202,846)(203,844)(204,845)(205,842)(206,843)(207,841)
(208,856)(209,857)(210,858)(211,864)(212,862)(213,863)(214,860)(215,861)
(216,859)(217,469)(218,470)(219,471)(220,477)(221,475)(222,476)(223,473)
(224,474)(225,472)(226,460)(227,461)(228,462)(229,468)(230,466)(231,467)
(232,464)(233,465)(234,463)(235,478)(236,479)(237,480)(238,486)(239,484)
(240,485)(241,482)(242,483)(243,481)(244,442)(245,443)(246,444)(247,450)
(248,448)(249,449)(250,446)(251,447)(252,445)(253,433)(254,434)(255,435)
(256,441)(257,439)(258,440)(259,437)(260,438)(261,436)(262,451)(263,452)
(264,453)(265,459)(266,457)(267,458)(268,455)(269,456)(270,454)(271,523)
(272,524)(273,525)(274,531)(275,529)(276,530)(277,527)(278,528)(279,526)
(280,514)(281,515)(282,516)(283,522)(284,520)(285,521)(286,518)(287,519)
(288,517)(289,532)(290,533)(291,534)(292,540)(293,538)(294,539)(295,536)
(296,537)(297,535)(298,496)(299,497)(300,498)(301,504)(302,502)(303,503)
(304,500)(305,501)(306,499)(307,487)(308,488)(309,489)(310,495)(311,493)
(312,494)(313,491)(314,492)(315,490)(316,505)(317,506)(318,507)(319,513)
(320,511)(321,512)(322,509)(323,510)(324,508)(325,577)(326,578)(327,579)
(328,585)(329,583)(330,584)(331,581)(332,582)(333,580)(334,568)(335,569)
(336,570)(337,576)(338,574)(339,575)(340,572)(341,573)(342,571)(343,586)
(344,587)(345,588)(346,594)(347,592)(348,593)(349,590)(350,591)(351,589)
(352,550)(353,551)(354,552)(355,558)(356,556)(357,557)(358,554)(359,555)
(360,553)(361,541)(362,542)(363,543)(364,549)(365,547)(366,548)(367,545)
(368,546)(369,544)(370,559)(371,560)(372,561)(373,567)(374,565)(375,566)
(376,563)(377,564)(378,562)(379,631)(380,632)(381,633)(382,639)(383,637)
(384,638)(385,635)(386,636)(387,634)(388,622)(389,623)(390,624)(391,630)
(392,628)(393,629)(394,626)(395,627)(396,625)(397,640)(398,641)(399,642)
(400,648)(401,646)(402,647)(403,644)(404,645)(405,643)(406,604)(407,605)
(408,606)(409,612)(410,610)(411,611)(412,608)(413,609)(414,607)(415,595)
(416,596)(417,597)(418,603)(419,601)(420,602)(421,599)(422,600)(423,598)
(424,613)(425,614)(426,615)(427,621)(428,619)(429,620)(430,617)(431,618)
(432,616);
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)(433,487)(434,494)(435,492)(436,493)(437,491)(438,489)(439,490)
(440,488)(441,495)(442,496)(443,503)(444,501)(445,502)(446,500)(447,498)
(448,499)(449,497)(450,504)(451,505)(452,512)(453,510)(454,511)(455,509)
(456,507)(457,508)(458,506)(459,513)(460,514)(461,521)(462,519)(463,520)
(464,518)(465,516)(466,517)(467,515)(468,522)(469,523)(470,530)(471,528)
(472,529)(473,527)(474,525)(475,526)(476,524)(477,531)(478,532)(479,539)
(480,537)(481,538)(482,536)(483,534)(484,535)(485,533)(486,540)(541,595)
(542,602)(543,600)(544,601)(545,599)(546,597)(547,598)(548,596)(549,603)
(550,604)(551,611)(552,609)(553,610)(554,608)(555,606)(556,607)(557,605)
(558,612)(559,613)(560,620)(561,618)(562,619)(563,617)(564,615)(565,616)
(566,614)(567,621)(568,622)(569,629)(570,627)(571,628)(572,626)(573,624)
(574,625)(575,623)(576,630)(577,631)(578,638)(579,636)(580,637)(581,635)
(582,633)(583,634)(584,632)(585,639)(586,640)(587,647)(588,645)(589,646)
(590,644)(591,642)(592,643)(593,641)(594,648)(649,703)(650,710)(651,708)
(652,709)(653,707)(654,705)(655,706)(656,704)(657,711)(658,712)(659,719)
(660,717)(661,718)(662,716)(663,714)(664,715)(665,713)(666,720)(667,721)
(668,728)(669,726)(670,727)(671,725)(672,723)(673,724)(674,722)(675,729)
(676,730)(677,737)(678,735)(679,736)(680,734)(681,732)(682,733)(683,731)
(684,738)(685,739)(686,746)(687,744)(688,745)(689,743)(690,741)(691,742)
(692,740)(693,747)(694,748)(695,755)(696,753)(697,754)(698,752)(699,750)
(700,751)(701,749)(702,756)(757,811)(758,818)(759,816)(760,817)(761,815)
(762,813)(763,814)(764,812)(765,819)(766,820)(767,827)(768,825)(769,826)
(770,824)(771,822)(772,823)(773,821)(774,828)(775,829)(776,836)(777,834)
(778,835)(779,833)(780,831)(781,832)(782,830)(783,837)(784,838)(785,845)
(786,843)(787,844)(788,842)(789,840)(790,841)(791,839)(792,846)(793,847)
(794,854)(795,852)(796,853)(797,851)(798,849)(799,850)(800,848)(801,855)
(802,856)(803,863)(804,861)(805,862)(806,860)(807,858)(808,859)(809,857)
(810,864);
s3 := Sym(864)!( 1,164)( 2,163)( 3,165)( 4,170)( 5,169)( 6,171)( 7,167)
( 8,166)( 9,168)( 10,173)( 11,172)( 12,174)( 13,179)( 14,178)( 15,180)
( 16,176)( 17,175)( 18,177)( 19,182)( 20,181)( 21,183)( 22,188)( 23,187)
( 24,189)( 25,185)( 26,184)( 27,186)( 28,191)( 29,190)( 30,192)( 31,197)
( 32,196)( 33,198)( 34,194)( 35,193)( 36,195)( 37,200)( 38,199)( 39,201)
( 40,206)( 41,205)( 42,207)( 43,203)( 44,202)( 45,204)( 46,209)( 47,208)
( 48,210)( 49,215)( 50,214)( 51,216)( 52,212)( 53,211)( 54,213)( 55,110)
( 56,109)( 57,111)( 58,116)( 59,115)( 60,117)( 61,113)( 62,112)( 63,114)
( 64,119)( 65,118)( 66,120)( 67,125)( 68,124)( 69,126)( 70,122)( 71,121)
( 72,123)( 73,128)( 74,127)( 75,129)( 76,134)( 77,133)( 78,135)( 79,131)
( 80,130)( 81,132)( 82,137)( 83,136)( 84,138)( 85,143)( 86,142)( 87,144)
( 88,140)( 89,139)( 90,141)( 91,146)( 92,145)( 93,147)( 94,152)( 95,151)
( 96,153)( 97,149)( 98,148)( 99,150)(100,155)(101,154)(102,156)(103,161)
(104,160)(105,162)(106,158)(107,157)(108,159)(217,380)(218,379)(219,381)
(220,386)(221,385)(222,387)(223,383)(224,382)(225,384)(226,389)(227,388)
(228,390)(229,395)(230,394)(231,396)(232,392)(233,391)(234,393)(235,398)
(236,397)(237,399)(238,404)(239,403)(240,405)(241,401)(242,400)(243,402)
(244,407)(245,406)(246,408)(247,413)(248,412)(249,414)(250,410)(251,409)
(252,411)(253,416)(254,415)(255,417)(256,422)(257,421)(258,423)(259,419)
(260,418)(261,420)(262,425)(263,424)(264,426)(265,431)(266,430)(267,432)
(268,428)(269,427)(270,429)(271,326)(272,325)(273,327)(274,332)(275,331)
(276,333)(277,329)(278,328)(279,330)(280,335)(281,334)(282,336)(283,341)
(284,340)(285,342)(286,338)(287,337)(288,339)(289,344)(290,343)(291,345)
(292,350)(293,349)(294,351)(295,347)(296,346)(297,348)(298,353)(299,352)
(300,354)(301,359)(302,358)(303,360)(304,356)(305,355)(306,357)(307,362)
(308,361)(309,363)(310,368)(311,367)(312,369)(313,365)(314,364)(315,366)
(316,371)(317,370)(318,372)(319,377)(320,376)(321,378)(322,374)(323,373)
(324,375)(433,596)(434,595)(435,597)(436,602)(437,601)(438,603)(439,599)
(440,598)(441,600)(442,605)(443,604)(444,606)(445,611)(446,610)(447,612)
(448,608)(449,607)(450,609)(451,614)(452,613)(453,615)(454,620)(455,619)
(456,621)(457,617)(458,616)(459,618)(460,623)(461,622)(462,624)(463,629)
(464,628)(465,630)(466,626)(467,625)(468,627)(469,632)(470,631)(471,633)
(472,638)(473,637)(474,639)(475,635)(476,634)(477,636)(478,641)(479,640)
(480,642)(481,647)(482,646)(483,648)(484,644)(485,643)(486,645)(487,542)
(488,541)(489,543)(490,548)(491,547)(492,549)(493,545)(494,544)(495,546)
(496,551)(497,550)(498,552)(499,557)(500,556)(501,558)(502,554)(503,553)
(504,555)(505,560)(506,559)(507,561)(508,566)(509,565)(510,567)(511,563)
(512,562)(513,564)(514,569)(515,568)(516,570)(517,575)(518,574)(519,576)
(520,572)(521,571)(522,573)(523,578)(524,577)(525,579)(526,584)(527,583)
(528,585)(529,581)(530,580)(531,582)(532,587)(533,586)(534,588)(535,593)
(536,592)(537,594)(538,590)(539,589)(540,591)(649,812)(650,811)(651,813)
(652,818)(653,817)(654,819)(655,815)(656,814)(657,816)(658,821)(659,820)
(660,822)(661,827)(662,826)(663,828)(664,824)(665,823)(666,825)(667,830)
(668,829)(669,831)(670,836)(671,835)(672,837)(673,833)(674,832)(675,834)
(676,839)(677,838)(678,840)(679,845)(680,844)(681,846)(682,842)(683,841)
(684,843)(685,848)(686,847)(687,849)(688,854)(689,853)(690,855)(691,851)
(692,850)(693,852)(694,857)(695,856)(696,858)(697,863)(698,862)(699,864)
(700,860)(701,859)(702,861)(703,758)(704,757)(705,759)(706,764)(707,763)
(708,765)(709,761)(710,760)(711,762)(712,767)(713,766)(714,768)(715,773)
(716,772)(717,774)(718,770)(719,769)(720,771)(721,776)(722,775)(723,777)
(724,782)(725,781)(726,783)(727,779)(728,778)(729,780)(730,785)(731,784)
(732,786)(733,791)(734,790)(735,792)(736,788)(737,787)(738,789)(739,794)
(740,793)(741,795)(742,800)(743,799)(744,801)(745,797)(746,796)(747,798)
(748,803)(749,802)(750,804)(751,809)(752,808)(753,810)(754,806)(755,805)
(756,807);
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,
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