Polytope of Type {6,3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3,12}*1728
if this polytope has a name.
Group : SmallGroup(1728,46303)
Rank : 4
Schlafli Type : {6,3,12}
Number of vertices, edges, etc : 6, 36, 72, 48
Order of s0s1s2s3 : 24
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 : {6,3,6}*864a
3-fold quotients : {2,3,12}*576
6-fold quotients : {2,3,6}*288
8-fold quotients : {6,3,6}*216
9-fold quotients : {2,3,12}*192
18-fold quotients : {2,3,6}*96
24-fold quotients : {2,3,6}*72, {6,3,2}*72
36-fold quotients : {2,3,3}*48
72-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)( 32, 56)
( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 61)( 38, 62)( 39, 63)( 40, 64)
( 41, 65)( 42, 66)( 43, 67)( 44, 68)( 45, 69)( 46, 70)( 47, 71)( 48, 72)
( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)
(105,129)(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)
(113,137)(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)
(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)
(177,201)(178,202)(179,203)(180,204)(181,205)(182,206)(183,207)(184,208)
(185,209)(186,210)(187,211)(188,212)(189,213)(190,214)(191,215)(192,216)
(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)
(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)(256,280)
(257,281)(258,282)(259,283)(260,284)(261,285)(262,286)(263,287)(264,288)
(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)(320,344)
(321,345)(322,346)(323,347)(324,348)(325,349)(326,350)(327,351)(328,352)
(329,353)(330,354)(331,355)(332,356)(333,357)(334,358)(335,359)(336,360)
(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)(392,416)
(393,417)(394,418)(395,419)(396,420)(397,421)(398,422)(399,423)(400,424)
(401,425)(402,426)(403,427)(404,428)(405,429)(406,430)(407,431)(408,432)
(457,481)(458,482)(459,483)(460,484)(461,485)(462,486)(463,487)(464,488)
(465,489)(466,490)(467,491)(468,492)(469,493)(470,494)(471,495)(472,496)
(473,497)(474,498)(475,499)(476,500)(477,501)(478,502)(479,503)(480,504)
(529,553)(530,554)(531,555)(532,556)(533,557)(534,558)(535,559)(536,560)
(537,561)(538,562)(539,563)(540,564)(541,565)(542,566)(543,567)(544,568)
(545,569)(546,570)(547,571)(548,572)(549,573)(550,574)(551,575)(552,576)
(601,625)(602,626)(603,627)(604,628)(605,629)(606,630)(607,631)(608,632)
(609,633)(610,634)(611,635)(612,636)(613,637)(614,638)(615,639)(616,640)
(617,641)(618,642)(619,643)(620,644)(621,645)(622,646)(623,647)(624,648)
(673,697)(674,698)(675,699)(676,700)(677,701)(678,702)(679,703)(680,704)
(681,705)(682,706)(683,707)(684,708)(685,709)(686,710)(687,711)(688,712)
(689,713)(690,714)(691,715)(692,716)(693,717)(694,718)(695,719)(696,720)
(745,769)(746,770)(747,771)(748,772)(749,773)(750,774)(751,775)(752,776)
(753,777)(754,778)(755,779)(756,780)(757,781)(758,782)(759,783)(760,784)
(761,785)(762,786)(763,787)(764,788)(765,789)(766,790)(767,791)(768,792)
(817,841)(818,842)(819,843)(820,844)(821,845)(822,846)(823,847)(824,848)
(825,849)(826,850)(827,851)(828,852)(829,853)(830,854)(831,855)(832,856)
(833,857)(834,858)(835,859)(836,860)(837,861)(838,862)(839,863)(840,864);;
s1 := ( 1,673)( 2,674)( 3,676)( 4,675)( 5,679)( 6,680)( 7,677)( 8,678)
( 9,689)( 10,690)( 11,692)( 12,691)( 13,695)( 14,696)( 15,693)( 16,694)
( 17,681)( 18,682)( 19,684)( 20,683)( 21,687)( 22,688)( 23,685)( 24,686)
( 25,649)( 26,650)( 27,652)( 28,651)( 29,655)( 30,656)( 31,653)( 32,654)
( 33,665)( 34,666)( 35,668)( 36,667)( 37,671)( 38,672)( 39,669)( 40,670)
( 41,657)( 42,658)( 43,660)( 44,659)( 45,663)( 46,664)( 47,661)( 48,662)
( 49,697)( 50,698)( 51,700)( 52,699)( 53,703)( 54,704)( 55,701)( 56,702)
( 57,713)( 58,714)( 59,716)( 60,715)( 61,719)( 62,720)( 63,717)( 64,718)
( 65,705)( 66,706)( 67,708)( 68,707)( 69,711)( 70,712)( 71,709)( 72,710)
( 73,817)( 74,818)( 75,820)( 76,819)( 77,823)( 78,824)( 79,821)( 80,822)
( 81,833)( 82,834)( 83,836)( 84,835)( 85,839)( 86,840)( 87,837)( 88,838)
( 89,825)( 90,826)( 91,828)( 92,827)( 93,831)( 94,832)( 95,829)( 96,830)
( 97,793)( 98,794)( 99,796)(100,795)(101,799)(102,800)(103,797)(104,798)
(105,809)(106,810)(107,812)(108,811)(109,815)(110,816)(111,813)(112,814)
(113,801)(114,802)(115,804)(116,803)(117,807)(118,808)(119,805)(120,806)
(121,841)(122,842)(123,844)(124,843)(125,847)(126,848)(127,845)(128,846)
(129,857)(130,858)(131,860)(132,859)(133,863)(134,864)(135,861)(136,862)
(137,849)(138,850)(139,852)(140,851)(141,855)(142,856)(143,853)(144,854)
(145,745)(146,746)(147,748)(148,747)(149,751)(150,752)(151,749)(152,750)
(153,761)(154,762)(155,764)(156,763)(157,767)(158,768)(159,765)(160,766)
(161,753)(162,754)(163,756)(164,755)(165,759)(166,760)(167,757)(168,758)
(169,721)(170,722)(171,724)(172,723)(173,727)(174,728)(175,725)(176,726)
(177,737)(178,738)(179,740)(180,739)(181,743)(182,744)(183,741)(184,742)
(185,729)(186,730)(187,732)(188,731)(189,735)(190,736)(191,733)(192,734)
(193,769)(194,770)(195,772)(196,771)(197,775)(198,776)(199,773)(200,774)
(201,785)(202,786)(203,788)(204,787)(205,791)(206,792)(207,789)(208,790)
(209,777)(210,778)(211,780)(212,779)(213,783)(214,784)(215,781)(216,782)
(217,458)(218,457)(219,459)(220,460)(221,464)(222,463)(223,462)(224,461)
(225,474)(226,473)(227,475)(228,476)(229,480)(230,479)(231,478)(232,477)
(233,466)(234,465)(235,467)(236,468)(237,472)(238,471)(239,470)(240,469)
(241,434)(242,433)(243,435)(244,436)(245,440)(246,439)(247,438)(248,437)
(249,450)(250,449)(251,451)(252,452)(253,456)(254,455)(255,454)(256,453)
(257,442)(258,441)(259,443)(260,444)(261,448)(262,447)(263,446)(264,445)
(265,482)(266,481)(267,483)(268,484)(269,488)(270,487)(271,486)(272,485)
(273,498)(274,497)(275,499)(276,500)(277,504)(278,503)(279,502)(280,501)
(281,490)(282,489)(283,491)(284,492)(285,496)(286,495)(287,494)(288,493)
(289,602)(290,601)(291,603)(292,604)(293,608)(294,607)(295,606)(296,605)
(297,618)(298,617)(299,619)(300,620)(301,624)(302,623)(303,622)(304,621)
(305,610)(306,609)(307,611)(308,612)(309,616)(310,615)(311,614)(312,613)
(313,578)(314,577)(315,579)(316,580)(317,584)(318,583)(319,582)(320,581)
(321,594)(322,593)(323,595)(324,596)(325,600)(326,599)(327,598)(328,597)
(329,586)(330,585)(331,587)(332,588)(333,592)(334,591)(335,590)(336,589)
(337,626)(338,625)(339,627)(340,628)(341,632)(342,631)(343,630)(344,629)
(345,642)(346,641)(347,643)(348,644)(349,648)(350,647)(351,646)(352,645)
(353,634)(354,633)(355,635)(356,636)(357,640)(358,639)(359,638)(360,637)
(361,530)(362,529)(363,531)(364,532)(365,536)(366,535)(367,534)(368,533)
(369,546)(370,545)(371,547)(372,548)(373,552)(374,551)(375,550)(376,549)
(377,538)(378,537)(379,539)(380,540)(381,544)(382,543)(383,542)(384,541)
(385,506)(386,505)(387,507)(388,508)(389,512)(390,511)(391,510)(392,509)
(393,522)(394,521)(395,523)(396,524)(397,528)(398,527)(399,526)(400,525)
(401,514)(402,513)(403,515)(404,516)(405,520)(406,519)(407,518)(408,517)
(409,554)(410,553)(411,555)(412,556)(413,560)(414,559)(415,558)(416,557)
(417,570)(418,569)(419,571)(420,572)(421,576)(422,575)(423,574)(424,573)
(425,562)(426,561)(427,563)(428,564)(429,568)(430,567)(431,566)(432,565);;
s2 := ( 1,729)( 2,730)( 3,735)( 4,736)( 5,734)( 6,733)( 7,731)( 8,732)
( 9,721)( 10,722)( 11,727)( 12,728)( 13,726)( 14,725)( 15,723)( 16,724)
( 17,737)( 18,738)( 19,743)( 20,744)( 21,742)( 22,741)( 23,739)( 24,740)
( 25,777)( 26,778)( 27,783)( 28,784)( 29,782)( 30,781)( 31,779)( 32,780)
( 33,769)( 34,770)( 35,775)( 36,776)( 37,774)( 38,773)( 39,771)( 40,772)
( 41,785)( 42,786)( 43,791)( 44,792)( 45,790)( 46,789)( 47,787)( 48,788)
( 49,753)( 50,754)( 51,759)( 52,760)( 53,758)( 54,757)( 55,755)( 56,756)
( 57,745)( 58,746)( 59,751)( 60,752)( 61,750)( 62,749)( 63,747)( 64,748)
( 65,761)( 66,762)( 67,767)( 68,768)( 69,766)( 70,765)( 71,763)( 72,764)
( 73,657)( 74,658)( 75,663)( 76,664)( 77,662)( 78,661)( 79,659)( 80,660)
( 81,649)( 82,650)( 83,655)( 84,656)( 85,654)( 86,653)( 87,651)( 88,652)
( 89,665)( 90,666)( 91,671)( 92,672)( 93,670)( 94,669)( 95,667)( 96,668)
( 97,705)( 98,706)( 99,711)(100,712)(101,710)(102,709)(103,707)(104,708)
(105,697)(106,698)(107,703)(108,704)(109,702)(110,701)(111,699)(112,700)
(113,713)(114,714)(115,719)(116,720)(117,718)(118,717)(119,715)(120,716)
(121,681)(122,682)(123,687)(124,688)(125,686)(126,685)(127,683)(128,684)
(129,673)(130,674)(131,679)(132,680)(133,678)(134,677)(135,675)(136,676)
(137,689)(138,690)(139,695)(140,696)(141,694)(142,693)(143,691)(144,692)
(145,801)(146,802)(147,807)(148,808)(149,806)(150,805)(151,803)(152,804)
(153,793)(154,794)(155,799)(156,800)(157,798)(158,797)(159,795)(160,796)
(161,809)(162,810)(163,815)(164,816)(165,814)(166,813)(167,811)(168,812)
(169,849)(170,850)(171,855)(172,856)(173,854)(174,853)(175,851)(176,852)
(177,841)(178,842)(179,847)(180,848)(181,846)(182,845)(183,843)(184,844)
(185,857)(186,858)(187,863)(188,864)(189,862)(190,861)(191,859)(192,860)
(193,825)(194,826)(195,831)(196,832)(197,830)(198,829)(199,827)(200,828)
(201,817)(202,818)(203,823)(204,824)(205,822)(206,821)(207,819)(208,820)
(209,833)(210,834)(211,839)(212,840)(213,838)(214,837)(215,835)(216,836)
(217,514)(218,513)(219,520)(220,519)(221,517)(222,518)(223,516)(224,515)
(225,506)(226,505)(227,512)(228,511)(229,509)(230,510)(231,508)(232,507)
(233,522)(234,521)(235,528)(236,527)(237,525)(238,526)(239,524)(240,523)
(241,562)(242,561)(243,568)(244,567)(245,565)(246,566)(247,564)(248,563)
(249,554)(250,553)(251,560)(252,559)(253,557)(254,558)(255,556)(256,555)
(257,570)(258,569)(259,576)(260,575)(261,573)(262,574)(263,572)(264,571)
(265,538)(266,537)(267,544)(268,543)(269,541)(270,542)(271,540)(272,539)
(273,530)(274,529)(275,536)(276,535)(277,533)(278,534)(279,532)(280,531)
(281,546)(282,545)(283,552)(284,551)(285,549)(286,550)(287,548)(288,547)
(289,442)(290,441)(291,448)(292,447)(293,445)(294,446)(295,444)(296,443)
(297,434)(298,433)(299,440)(300,439)(301,437)(302,438)(303,436)(304,435)
(305,450)(306,449)(307,456)(308,455)(309,453)(310,454)(311,452)(312,451)
(313,490)(314,489)(315,496)(316,495)(317,493)(318,494)(319,492)(320,491)
(321,482)(322,481)(323,488)(324,487)(325,485)(326,486)(327,484)(328,483)
(329,498)(330,497)(331,504)(332,503)(333,501)(334,502)(335,500)(336,499)
(337,466)(338,465)(339,472)(340,471)(341,469)(342,470)(343,468)(344,467)
(345,458)(346,457)(347,464)(348,463)(349,461)(350,462)(351,460)(352,459)
(353,474)(354,473)(355,480)(356,479)(357,477)(358,478)(359,476)(360,475)
(361,586)(362,585)(363,592)(364,591)(365,589)(366,590)(367,588)(368,587)
(369,578)(370,577)(371,584)(372,583)(373,581)(374,582)(375,580)(376,579)
(377,594)(378,593)(379,600)(380,599)(381,597)(382,598)(383,596)(384,595)
(385,634)(386,633)(387,640)(388,639)(389,637)(390,638)(391,636)(392,635)
(393,626)(394,625)(395,632)(396,631)(397,629)(398,630)(399,628)(400,627)
(401,642)(402,641)(403,648)(404,647)(405,645)(406,646)(407,644)(408,643)
(409,610)(410,609)(411,616)(412,615)(413,613)(414,614)(415,612)(416,611)
(417,602)(418,601)(419,608)(420,607)(421,605)(422,606)(423,604)(424,603)
(425,618)(426,617)(427,624)(428,623)(429,621)(430,622)(431,620)(432,619);;
s3 := ( 1,219)( 2,220)( 3,217)( 4,218)( 5,222)( 6,221)( 7,223)( 8,224)
( 9,227)( 10,228)( 11,225)( 12,226)( 13,230)( 14,229)( 15,231)( 16,232)
( 17,235)( 18,236)( 19,233)( 20,234)( 21,238)( 22,237)( 23,239)( 24,240)
( 25,243)( 26,244)( 27,241)( 28,242)( 29,246)( 30,245)( 31,247)( 32,248)
( 33,251)( 34,252)( 35,249)( 36,250)( 37,254)( 38,253)( 39,255)( 40,256)
( 41,259)( 42,260)( 43,257)( 44,258)( 45,262)( 46,261)( 47,263)( 48,264)
( 49,267)( 50,268)( 51,265)( 52,266)( 53,270)( 54,269)( 55,271)( 56,272)
( 57,275)( 58,276)( 59,273)( 60,274)( 61,278)( 62,277)( 63,279)( 64,280)
( 65,283)( 66,284)( 67,281)( 68,282)( 69,286)( 70,285)( 71,287)( 72,288)
( 73,363)( 74,364)( 75,361)( 76,362)( 77,366)( 78,365)( 79,367)( 80,368)
( 81,371)( 82,372)( 83,369)( 84,370)( 85,374)( 86,373)( 87,375)( 88,376)
( 89,379)( 90,380)( 91,377)( 92,378)( 93,382)( 94,381)( 95,383)( 96,384)
( 97,387)( 98,388)( 99,385)(100,386)(101,390)(102,389)(103,391)(104,392)
(105,395)(106,396)(107,393)(108,394)(109,398)(110,397)(111,399)(112,400)
(113,403)(114,404)(115,401)(116,402)(117,406)(118,405)(119,407)(120,408)
(121,411)(122,412)(123,409)(124,410)(125,414)(126,413)(127,415)(128,416)
(129,419)(130,420)(131,417)(132,418)(133,422)(134,421)(135,423)(136,424)
(137,427)(138,428)(139,425)(140,426)(141,430)(142,429)(143,431)(144,432)
(145,291)(146,292)(147,289)(148,290)(149,294)(150,293)(151,295)(152,296)
(153,299)(154,300)(155,297)(156,298)(157,302)(158,301)(159,303)(160,304)
(161,307)(162,308)(163,305)(164,306)(165,310)(166,309)(167,311)(168,312)
(169,315)(170,316)(171,313)(172,314)(173,318)(174,317)(175,319)(176,320)
(177,323)(178,324)(179,321)(180,322)(181,326)(182,325)(183,327)(184,328)
(185,331)(186,332)(187,329)(188,330)(189,334)(190,333)(191,335)(192,336)
(193,339)(194,340)(195,337)(196,338)(197,342)(198,341)(199,343)(200,344)
(201,347)(202,348)(203,345)(204,346)(205,350)(206,349)(207,351)(208,352)
(209,355)(210,356)(211,353)(212,354)(213,358)(214,357)(215,359)(216,360)
(433,651)(434,652)(435,649)(436,650)(437,654)(438,653)(439,655)(440,656)
(441,659)(442,660)(443,657)(444,658)(445,662)(446,661)(447,663)(448,664)
(449,667)(450,668)(451,665)(452,666)(453,670)(454,669)(455,671)(456,672)
(457,675)(458,676)(459,673)(460,674)(461,678)(462,677)(463,679)(464,680)
(465,683)(466,684)(467,681)(468,682)(469,686)(470,685)(471,687)(472,688)
(473,691)(474,692)(475,689)(476,690)(477,694)(478,693)(479,695)(480,696)
(481,699)(482,700)(483,697)(484,698)(485,702)(486,701)(487,703)(488,704)
(489,707)(490,708)(491,705)(492,706)(493,710)(494,709)(495,711)(496,712)
(497,715)(498,716)(499,713)(500,714)(501,718)(502,717)(503,719)(504,720)
(505,795)(506,796)(507,793)(508,794)(509,798)(510,797)(511,799)(512,800)
(513,803)(514,804)(515,801)(516,802)(517,806)(518,805)(519,807)(520,808)
(521,811)(522,812)(523,809)(524,810)(525,814)(526,813)(527,815)(528,816)
(529,819)(530,820)(531,817)(532,818)(533,822)(534,821)(535,823)(536,824)
(537,827)(538,828)(539,825)(540,826)(541,830)(542,829)(543,831)(544,832)
(545,835)(546,836)(547,833)(548,834)(549,838)(550,837)(551,839)(552,840)
(553,843)(554,844)(555,841)(556,842)(557,846)(558,845)(559,847)(560,848)
(561,851)(562,852)(563,849)(564,850)(565,854)(566,853)(567,855)(568,856)
(569,859)(570,860)(571,857)(572,858)(573,862)(574,861)(575,863)(576,864)
(577,723)(578,724)(579,721)(580,722)(581,726)(582,725)(583,727)(584,728)
(585,731)(586,732)(587,729)(588,730)(589,734)(590,733)(591,735)(592,736)
(593,739)(594,740)(595,737)(596,738)(597,742)(598,741)(599,743)(600,744)
(601,747)(602,748)(603,745)(604,746)(605,750)(606,749)(607,751)(608,752)
(609,755)(610,756)(611,753)(612,754)(613,758)(614,757)(615,759)(616,760)
(617,763)(618,764)(619,761)(620,762)(621,766)(622,765)(623,767)(624,768)
(625,771)(626,772)(627,769)(628,770)(629,774)(630,773)(631,775)(632,776)
(633,779)(634,780)(635,777)(636,778)(637,782)(638,781)(639,783)(640,784)
(641,787)(642,788)(643,785)(644,786)(645,790)(646,789)(647,791)(648,792);;
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,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)
( 32, 56)( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 61)( 38, 62)( 39, 63)
( 40, 64)( 41, 65)( 42, 66)( 43, 67)( 44, 68)( 45, 69)( 46, 70)( 47, 71)
( 48, 72)( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)
(104,128)(105,129)(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)
(112,136)(113,137)(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)
(120,144)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)
(176,200)(177,201)(178,202)(179,203)(180,204)(181,205)(182,206)(183,207)
(184,208)(185,209)(186,210)(187,211)(188,212)(189,213)(190,214)(191,215)
(192,216)(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)
(248,272)(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)
(256,280)(257,281)(258,282)(259,283)(260,284)(261,285)(262,286)(263,287)
(264,288)(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)
(320,344)(321,345)(322,346)(323,347)(324,348)(325,349)(326,350)(327,351)
(328,352)(329,353)(330,354)(331,355)(332,356)(333,357)(334,358)(335,359)
(336,360)(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)
(392,416)(393,417)(394,418)(395,419)(396,420)(397,421)(398,422)(399,423)
(400,424)(401,425)(402,426)(403,427)(404,428)(405,429)(406,430)(407,431)
(408,432)(457,481)(458,482)(459,483)(460,484)(461,485)(462,486)(463,487)
(464,488)(465,489)(466,490)(467,491)(468,492)(469,493)(470,494)(471,495)
(472,496)(473,497)(474,498)(475,499)(476,500)(477,501)(478,502)(479,503)
(480,504)(529,553)(530,554)(531,555)(532,556)(533,557)(534,558)(535,559)
(536,560)(537,561)(538,562)(539,563)(540,564)(541,565)(542,566)(543,567)
(544,568)(545,569)(546,570)(547,571)(548,572)(549,573)(550,574)(551,575)
(552,576)(601,625)(602,626)(603,627)(604,628)(605,629)(606,630)(607,631)
(608,632)(609,633)(610,634)(611,635)(612,636)(613,637)(614,638)(615,639)
(616,640)(617,641)(618,642)(619,643)(620,644)(621,645)(622,646)(623,647)
(624,648)(673,697)(674,698)(675,699)(676,700)(677,701)(678,702)(679,703)
(680,704)(681,705)(682,706)(683,707)(684,708)(685,709)(686,710)(687,711)
(688,712)(689,713)(690,714)(691,715)(692,716)(693,717)(694,718)(695,719)
(696,720)(745,769)(746,770)(747,771)(748,772)(749,773)(750,774)(751,775)
(752,776)(753,777)(754,778)(755,779)(756,780)(757,781)(758,782)(759,783)
(760,784)(761,785)(762,786)(763,787)(764,788)(765,789)(766,790)(767,791)
(768,792)(817,841)(818,842)(819,843)(820,844)(821,845)(822,846)(823,847)
(824,848)(825,849)(826,850)(827,851)(828,852)(829,853)(830,854)(831,855)
(832,856)(833,857)(834,858)(835,859)(836,860)(837,861)(838,862)(839,863)
(840,864);
s1 := Sym(864)!( 1,673)( 2,674)( 3,676)( 4,675)( 5,679)( 6,680)( 7,677)
( 8,678)( 9,689)( 10,690)( 11,692)( 12,691)( 13,695)( 14,696)( 15,693)
( 16,694)( 17,681)( 18,682)( 19,684)( 20,683)( 21,687)( 22,688)( 23,685)
( 24,686)( 25,649)( 26,650)( 27,652)( 28,651)( 29,655)( 30,656)( 31,653)
( 32,654)( 33,665)( 34,666)( 35,668)( 36,667)( 37,671)( 38,672)( 39,669)
( 40,670)( 41,657)( 42,658)( 43,660)( 44,659)( 45,663)( 46,664)( 47,661)
( 48,662)( 49,697)( 50,698)( 51,700)( 52,699)( 53,703)( 54,704)( 55,701)
( 56,702)( 57,713)( 58,714)( 59,716)( 60,715)( 61,719)( 62,720)( 63,717)
( 64,718)( 65,705)( 66,706)( 67,708)( 68,707)( 69,711)( 70,712)( 71,709)
( 72,710)( 73,817)( 74,818)( 75,820)( 76,819)( 77,823)( 78,824)( 79,821)
( 80,822)( 81,833)( 82,834)( 83,836)( 84,835)( 85,839)( 86,840)( 87,837)
( 88,838)( 89,825)( 90,826)( 91,828)( 92,827)( 93,831)( 94,832)( 95,829)
( 96,830)( 97,793)( 98,794)( 99,796)(100,795)(101,799)(102,800)(103,797)
(104,798)(105,809)(106,810)(107,812)(108,811)(109,815)(110,816)(111,813)
(112,814)(113,801)(114,802)(115,804)(116,803)(117,807)(118,808)(119,805)
(120,806)(121,841)(122,842)(123,844)(124,843)(125,847)(126,848)(127,845)
(128,846)(129,857)(130,858)(131,860)(132,859)(133,863)(134,864)(135,861)
(136,862)(137,849)(138,850)(139,852)(140,851)(141,855)(142,856)(143,853)
(144,854)(145,745)(146,746)(147,748)(148,747)(149,751)(150,752)(151,749)
(152,750)(153,761)(154,762)(155,764)(156,763)(157,767)(158,768)(159,765)
(160,766)(161,753)(162,754)(163,756)(164,755)(165,759)(166,760)(167,757)
(168,758)(169,721)(170,722)(171,724)(172,723)(173,727)(174,728)(175,725)
(176,726)(177,737)(178,738)(179,740)(180,739)(181,743)(182,744)(183,741)
(184,742)(185,729)(186,730)(187,732)(188,731)(189,735)(190,736)(191,733)
(192,734)(193,769)(194,770)(195,772)(196,771)(197,775)(198,776)(199,773)
(200,774)(201,785)(202,786)(203,788)(204,787)(205,791)(206,792)(207,789)
(208,790)(209,777)(210,778)(211,780)(212,779)(213,783)(214,784)(215,781)
(216,782)(217,458)(218,457)(219,459)(220,460)(221,464)(222,463)(223,462)
(224,461)(225,474)(226,473)(227,475)(228,476)(229,480)(230,479)(231,478)
(232,477)(233,466)(234,465)(235,467)(236,468)(237,472)(238,471)(239,470)
(240,469)(241,434)(242,433)(243,435)(244,436)(245,440)(246,439)(247,438)
(248,437)(249,450)(250,449)(251,451)(252,452)(253,456)(254,455)(255,454)
(256,453)(257,442)(258,441)(259,443)(260,444)(261,448)(262,447)(263,446)
(264,445)(265,482)(266,481)(267,483)(268,484)(269,488)(270,487)(271,486)
(272,485)(273,498)(274,497)(275,499)(276,500)(277,504)(278,503)(279,502)
(280,501)(281,490)(282,489)(283,491)(284,492)(285,496)(286,495)(287,494)
(288,493)(289,602)(290,601)(291,603)(292,604)(293,608)(294,607)(295,606)
(296,605)(297,618)(298,617)(299,619)(300,620)(301,624)(302,623)(303,622)
(304,621)(305,610)(306,609)(307,611)(308,612)(309,616)(310,615)(311,614)
(312,613)(313,578)(314,577)(315,579)(316,580)(317,584)(318,583)(319,582)
(320,581)(321,594)(322,593)(323,595)(324,596)(325,600)(326,599)(327,598)
(328,597)(329,586)(330,585)(331,587)(332,588)(333,592)(334,591)(335,590)
(336,589)(337,626)(338,625)(339,627)(340,628)(341,632)(342,631)(343,630)
(344,629)(345,642)(346,641)(347,643)(348,644)(349,648)(350,647)(351,646)
(352,645)(353,634)(354,633)(355,635)(356,636)(357,640)(358,639)(359,638)
(360,637)(361,530)(362,529)(363,531)(364,532)(365,536)(366,535)(367,534)
(368,533)(369,546)(370,545)(371,547)(372,548)(373,552)(374,551)(375,550)
(376,549)(377,538)(378,537)(379,539)(380,540)(381,544)(382,543)(383,542)
(384,541)(385,506)(386,505)(387,507)(388,508)(389,512)(390,511)(391,510)
(392,509)(393,522)(394,521)(395,523)(396,524)(397,528)(398,527)(399,526)
(400,525)(401,514)(402,513)(403,515)(404,516)(405,520)(406,519)(407,518)
(408,517)(409,554)(410,553)(411,555)(412,556)(413,560)(414,559)(415,558)
(416,557)(417,570)(418,569)(419,571)(420,572)(421,576)(422,575)(423,574)
(424,573)(425,562)(426,561)(427,563)(428,564)(429,568)(430,567)(431,566)
(432,565);
s2 := Sym(864)!( 1,729)( 2,730)( 3,735)( 4,736)( 5,734)( 6,733)( 7,731)
( 8,732)( 9,721)( 10,722)( 11,727)( 12,728)( 13,726)( 14,725)( 15,723)
( 16,724)( 17,737)( 18,738)( 19,743)( 20,744)( 21,742)( 22,741)( 23,739)
( 24,740)( 25,777)( 26,778)( 27,783)( 28,784)( 29,782)( 30,781)( 31,779)
( 32,780)( 33,769)( 34,770)( 35,775)( 36,776)( 37,774)( 38,773)( 39,771)
( 40,772)( 41,785)( 42,786)( 43,791)( 44,792)( 45,790)( 46,789)( 47,787)
( 48,788)( 49,753)( 50,754)( 51,759)( 52,760)( 53,758)( 54,757)( 55,755)
( 56,756)( 57,745)( 58,746)( 59,751)( 60,752)( 61,750)( 62,749)( 63,747)
( 64,748)( 65,761)( 66,762)( 67,767)( 68,768)( 69,766)( 70,765)( 71,763)
( 72,764)( 73,657)( 74,658)( 75,663)( 76,664)( 77,662)( 78,661)( 79,659)
( 80,660)( 81,649)( 82,650)( 83,655)( 84,656)( 85,654)( 86,653)( 87,651)
( 88,652)( 89,665)( 90,666)( 91,671)( 92,672)( 93,670)( 94,669)( 95,667)
( 96,668)( 97,705)( 98,706)( 99,711)(100,712)(101,710)(102,709)(103,707)
(104,708)(105,697)(106,698)(107,703)(108,704)(109,702)(110,701)(111,699)
(112,700)(113,713)(114,714)(115,719)(116,720)(117,718)(118,717)(119,715)
(120,716)(121,681)(122,682)(123,687)(124,688)(125,686)(126,685)(127,683)
(128,684)(129,673)(130,674)(131,679)(132,680)(133,678)(134,677)(135,675)
(136,676)(137,689)(138,690)(139,695)(140,696)(141,694)(142,693)(143,691)
(144,692)(145,801)(146,802)(147,807)(148,808)(149,806)(150,805)(151,803)
(152,804)(153,793)(154,794)(155,799)(156,800)(157,798)(158,797)(159,795)
(160,796)(161,809)(162,810)(163,815)(164,816)(165,814)(166,813)(167,811)
(168,812)(169,849)(170,850)(171,855)(172,856)(173,854)(174,853)(175,851)
(176,852)(177,841)(178,842)(179,847)(180,848)(181,846)(182,845)(183,843)
(184,844)(185,857)(186,858)(187,863)(188,864)(189,862)(190,861)(191,859)
(192,860)(193,825)(194,826)(195,831)(196,832)(197,830)(198,829)(199,827)
(200,828)(201,817)(202,818)(203,823)(204,824)(205,822)(206,821)(207,819)
(208,820)(209,833)(210,834)(211,839)(212,840)(213,838)(214,837)(215,835)
(216,836)(217,514)(218,513)(219,520)(220,519)(221,517)(222,518)(223,516)
(224,515)(225,506)(226,505)(227,512)(228,511)(229,509)(230,510)(231,508)
(232,507)(233,522)(234,521)(235,528)(236,527)(237,525)(238,526)(239,524)
(240,523)(241,562)(242,561)(243,568)(244,567)(245,565)(246,566)(247,564)
(248,563)(249,554)(250,553)(251,560)(252,559)(253,557)(254,558)(255,556)
(256,555)(257,570)(258,569)(259,576)(260,575)(261,573)(262,574)(263,572)
(264,571)(265,538)(266,537)(267,544)(268,543)(269,541)(270,542)(271,540)
(272,539)(273,530)(274,529)(275,536)(276,535)(277,533)(278,534)(279,532)
(280,531)(281,546)(282,545)(283,552)(284,551)(285,549)(286,550)(287,548)
(288,547)(289,442)(290,441)(291,448)(292,447)(293,445)(294,446)(295,444)
(296,443)(297,434)(298,433)(299,440)(300,439)(301,437)(302,438)(303,436)
(304,435)(305,450)(306,449)(307,456)(308,455)(309,453)(310,454)(311,452)
(312,451)(313,490)(314,489)(315,496)(316,495)(317,493)(318,494)(319,492)
(320,491)(321,482)(322,481)(323,488)(324,487)(325,485)(326,486)(327,484)
(328,483)(329,498)(330,497)(331,504)(332,503)(333,501)(334,502)(335,500)
(336,499)(337,466)(338,465)(339,472)(340,471)(341,469)(342,470)(343,468)
(344,467)(345,458)(346,457)(347,464)(348,463)(349,461)(350,462)(351,460)
(352,459)(353,474)(354,473)(355,480)(356,479)(357,477)(358,478)(359,476)
(360,475)(361,586)(362,585)(363,592)(364,591)(365,589)(366,590)(367,588)
(368,587)(369,578)(370,577)(371,584)(372,583)(373,581)(374,582)(375,580)
(376,579)(377,594)(378,593)(379,600)(380,599)(381,597)(382,598)(383,596)
(384,595)(385,634)(386,633)(387,640)(388,639)(389,637)(390,638)(391,636)
(392,635)(393,626)(394,625)(395,632)(396,631)(397,629)(398,630)(399,628)
(400,627)(401,642)(402,641)(403,648)(404,647)(405,645)(406,646)(407,644)
(408,643)(409,610)(410,609)(411,616)(412,615)(413,613)(414,614)(415,612)
(416,611)(417,602)(418,601)(419,608)(420,607)(421,605)(422,606)(423,604)
(424,603)(425,618)(426,617)(427,624)(428,623)(429,621)(430,622)(431,620)
(432,619);
s3 := Sym(864)!( 1,219)( 2,220)( 3,217)( 4,218)( 5,222)( 6,221)( 7,223)
( 8,224)( 9,227)( 10,228)( 11,225)( 12,226)( 13,230)( 14,229)( 15,231)
( 16,232)( 17,235)( 18,236)( 19,233)( 20,234)( 21,238)( 22,237)( 23,239)
( 24,240)( 25,243)( 26,244)( 27,241)( 28,242)( 29,246)( 30,245)( 31,247)
( 32,248)( 33,251)( 34,252)( 35,249)( 36,250)( 37,254)( 38,253)( 39,255)
( 40,256)( 41,259)( 42,260)( 43,257)( 44,258)( 45,262)( 46,261)( 47,263)
( 48,264)( 49,267)( 50,268)( 51,265)( 52,266)( 53,270)( 54,269)( 55,271)
( 56,272)( 57,275)( 58,276)( 59,273)( 60,274)( 61,278)( 62,277)( 63,279)
( 64,280)( 65,283)( 66,284)( 67,281)( 68,282)( 69,286)( 70,285)( 71,287)
( 72,288)( 73,363)( 74,364)( 75,361)( 76,362)( 77,366)( 78,365)( 79,367)
( 80,368)( 81,371)( 82,372)( 83,369)( 84,370)( 85,374)( 86,373)( 87,375)
( 88,376)( 89,379)( 90,380)( 91,377)( 92,378)( 93,382)( 94,381)( 95,383)
( 96,384)( 97,387)( 98,388)( 99,385)(100,386)(101,390)(102,389)(103,391)
(104,392)(105,395)(106,396)(107,393)(108,394)(109,398)(110,397)(111,399)
(112,400)(113,403)(114,404)(115,401)(116,402)(117,406)(118,405)(119,407)
(120,408)(121,411)(122,412)(123,409)(124,410)(125,414)(126,413)(127,415)
(128,416)(129,419)(130,420)(131,417)(132,418)(133,422)(134,421)(135,423)
(136,424)(137,427)(138,428)(139,425)(140,426)(141,430)(142,429)(143,431)
(144,432)(145,291)(146,292)(147,289)(148,290)(149,294)(150,293)(151,295)
(152,296)(153,299)(154,300)(155,297)(156,298)(157,302)(158,301)(159,303)
(160,304)(161,307)(162,308)(163,305)(164,306)(165,310)(166,309)(167,311)
(168,312)(169,315)(170,316)(171,313)(172,314)(173,318)(174,317)(175,319)
(176,320)(177,323)(178,324)(179,321)(180,322)(181,326)(182,325)(183,327)
(184,328)(185,331)(186,332)(187,329)(188,330)(189,334)(190,333)(191,335)
(192,336)(193,339)(194,340)(195,337)(196,338)(197,342)(198,341)(199,343)
(200,344)(201,347)(202,348)(203,345)(204,346)(205,350)(206,349)(207,351)
(208,352)(209,355)(210,356)(211,353)(212,354)(213,358)(214,357)(215,359)
(216,360)(433,651)(434,652)(435,649)(436,650)(437,654)(438,653)(439,655)
(440,656)(441,659)(442,660)(443,657)(444,658)(445,662)(446,661)(447,663)
(448,664)(449,667)(450,668)(451,665)(452,666)(453,670)(454,669)(455,671)
(456,672)(457,675)(458,676)(459,673)(460,674)(461,678)(462,677)(463,679)
(464,680)(465,683)(466,684)(467,681)(468,682)(469,686)(470,685)(471,687)
(472,688)(473,691)(474,692)(475,689)(476,690)(477,694)(478,693)(479,695)
(480,696)(481,699)(482,700)(483,697)(484,698)(485,702)(486,701)(487,703)
(488,704)(489,707)(490,708)(491,705)(492,706)(493,710)(494,709)(495,711)
(496,712)(497,715)(498,716)(499,713)(500,714)(501,718)(502,717)(503,719)
(504,720)(505,795)(506,796)(507,793)(508,794)(509,798)(510,797)(511,799)
(512,800)(513,803)(514,804)(515,801)(516,802)(517,806)(518,805)(519,807)
(520,808)(521,811)(522,812)(523,809)(524,810)(525,814)(526,813)(527,815)
(528,816)(529,819)(530,820)(531,817)(532,818)(533,822)(534,821)(535,823)
(536,824)(537,827)(538,828)(539,825)(540,826)(541,830)(542,829)(543,831)
(544,832)(545,835)(546,836)(547,833)(548,834)(549,838)(550,837)(551,839)
(552,840)(553,843)(554,844)(555,841)(556,842)(557,846)(558,845)(559,847)
(560,848)(561,851)(562,852)(563,849)(564,850)(565,854)(566,853)(567,855)
(568,856)(569,859)(570,860)(571,857)(572,858)(573,862)(574,861)(575,863)
(576,864)(577,723)(578,724)(579,721)(580,722)(581,726)(582,725)(583,727)
(584,728)(585,731)(586,732)(587,729)(588,730)(589,734)(590,733)(591,735)
(592,736)(593,739)(594,740)(595,737)(596,738)(597,742)(598,741)(599,743)
(600,744)(601,747)(602,748)(603,745)(604,746)(605,750)(606,749)(607,751)
(608,752)(609,755)(610,756)(611,753)(612,754)(613,758)(614,757)(615,759)
(616,760)(617,763)(618,764)(619,761)(620,762)(621,766)(622,765)(623,767)
(624,768)(625,771)(626,772)(627,769)(628,770)(629,774)(630,773)(631,775)
(632,776)(633,779)(634,780)(635,777)(636,778)(637,782)(638,781)(639,783)
(640,784)(641,787)(642,788)(643,785)(644,786)(645,790)(646,789)(647,791)
(648,792);
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 >;
References : None.
to this polytope