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