Polytope of Type {12,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,12}*1728b
Also Known As : {{12,6|2},{6,12|2}}. if this polytope has another name.
Group : SmallGroup(1728,36990)
Rank : 4
Schlafli Type : {12,6,12}
Number of vertices, edges, etc : 12, 36, 36, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Self-Dual
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 : {6,6,12}*864b, {12,6,6}*864b
3-fold quotients : {12,2,12}*576, {4,6,12}*576a, {12,6,4}*576a
4-fold quotients : {6,6,6}*432b
6-fold quotients : {2,6,12}*288a, {6,2,12}*288, {12,2,6}*288, {12,6,2}*288a, {4,6,6}*288a, {6,6,4}*288a
9-fold quotients : {4,2,12}*192, {12,2,4}*192, {4,6,4}*192a
12-fold quotients : {3,2,12}*144, {12,2,3}*144, {2,6,6}*144a, {6,2,6}*144, {6,6,2}*144a
18-fold quotients : {2,2,12}*96, {12,2,2}*96, {2,6,4}*96a, {4,2,6}*96, {4,6,2}*96a, {6,2,4}*96
24-fold quotients : {3,2,6}*72, {6,2,3}*72
27-fold quotients : {4,2,4}*64
36-fold quotients : {3,2,4}*48, {4,2,3}*48, {2,2,6}*48, {2,6,2}*48, {6,2,2}*48
48-fold quotients : {3,2,3}*36
54-fold quotients : {2,2,4}*32, {4,2,2}*32
72-fold quotients : {2,2,3}*24, {2,3,2}*24, {3,2,2}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)
( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)
( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)
( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)(112,142)
(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)(120,147)
(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)(128,155)
(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)(163,190)
(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)(171,195)
(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)
(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)(187,211)
(188,212)(189,213)(220,223)(221,224)(222,225)(229,232)(230,233)(231,234)
(238,241)(239,242)(240,243)(247,250)(248,251)(249,252)(256,259)(257,260)
(258,261)(265,268)(266,269)(267,270)(274,277)(275,278)(276,279)(283,286)
(284,287)(285,288)(292,295)(293,296)(294,297)(301,304)(302,305)(303,306)
(310,313)(311,314)(312,315)(319,322)(320,323)(321,324)(325,352)(326,353)
(327,354)(328,358)(329,359)(330,360)(331,355)(332,356)(333,357)(334,361)
(335,362)(336,363)(337,367)(338,368)(339,369)(340,364)(341,365)(342,366)
(343,370)(344,371)(345,372)(346,376)(347,377)(348,378)(349,373)(350,374)
(351,375)(379,406)(380,407)(381,408)(382,412)(383,413)(384,414)(385,409)
(386,410)(387,411)(388,415)(389,416)(390,417)(391,421)(392,422)(393,423)
(394,418)(395,419)(396,420)(397,424)(398,425)(399,426)(400,430)(401,431)
(402,432)(403,427)(404,428)(405,429)(433,460)(434,461)(435,462)(436,466)
(437,467)(438,468)(439,463)(440,464)(441,465)(442,469)(443,470)(444,471)
(445,475)(446,476)(447,477)(448,472)(449,473)(450,474)(451,478)(452,479)
(453,480)(454,484)(455,485)(456,486)(457,481)(458,482)(459,483)(487,514)
(488,515)(489,516)(490,520)(491,521)(492,522)(493,517)(494,518)(495,519)
(496,523)(497,524)(498,525)(499,529)(500,530)(501,531)(502,526)(503,527)
(504,528)(505,532)(506,533)(507,534)(508,538)(509,539)(510,540)(511,535)
(512,536)(513,537)(544,547)(545,548)(546,549)(553,556)(554,557)(555,558)
(562,565)(563,566)(564,567)(571,574)(572,575)(573,576)(580,583)(581,584)
(582,585)(589,592)(590,593)(591,594)(598,601)(599,602)(600,603)(607,610)
(608,611)(609,612)(616,619)(617,620)(618,621)(625,628)(626,629)(627,630)
(634,637)(635,638)(636,639)(643,646)(644,647)(645,648)(649,676)(650,677)
(651,678)(652,682)(653,683)(654,684)(655,679)(656,680)(657,681)(658,685)
(659,686)(660,687)(661,691)(662,692)(663,693)(664,688)(665,689)(666,690)
(667,694)(668,695)(669,696)(670,700)(671,701)(672,702)(673,697)(674,698)
(675,699)(703,730)(704,731)(705,732)(706,736)(707,737)(708,738)(709,733)
(710,734)(711,735)(712,739)(713,740)(714,741)(715,745)(716,746)(717,747)
(718,742)(719,743)(720,744)(721,748)(722,749)(723,750)(724,754)(725,755)
(726,756)(727,751)(728,752)(729,753)(760,763)(761,764)(762,765)(769,772)
(770,773)(771,774)(778,781)(779,782)(780,783)(787,790)(788,791)(789,792)
(796,799)(797,800)(798,801)(805,808)(806,809)(807,810)(814,817)(815,818)
(816,819)(823,826)(824,827)(825,828)(832,835)(833,836)(834,837)(841,844)
(842,845)(843,846)(850,853)(851,854)(852,855)(859,862)(860,863)(861,864);;
s1 := ( 1,436)( 2,437)( 3,438)( 4,433)( 5,434)( 6,435)( 7,439)( 8,440)
( 9,441)( 10,454)( 11,455)( 12,456)( 13,451)( 14,452)( 15,453)( 16,457)
( 17,458)( 18,459)( 19,445)( 20,446)( 21,447)( 22,442)( 23,443)( 24,444)
( 25,448)( 26,449)( 27,450)( 28,463)( 29,464)( 30,465)( 31,460)( 32,461)
( 33,462)( 34,466)( 35,467)( 36,468)( 37,481)( 38,482)( 39,483)( 40,478)
( 41,479)( 42,480)( 43,484)( 44,485)( 45,486)( 46,472)( 47,473)( 48,474)
( 49,469)( 50,470)( 51,471)( 52,475)( 53,476)( 54,477)( 55,490)( 56,491)
( 57,492)( 58,487)( 59,488)( 60,489)( 61,493)( 62,494)( 63,495)( 64,508)
( 65,509)( 66,510)( 67,505)( 68,506)( 69,507)( 70,511)( 71,512)( 72,513)
( 73,499)( 74,500)( 75,501)( 76,496)( 77,497)( 78,498)( 79,502)( 80,503)
( 81,504)( 82,517)( 83,518)( 84,519)( 85,514)( 86,515)( 87,516)( 88,520)
( 89,521)( 90,522)( 91,535)( 92,536)( 93,537)( 94,532)( 95,533)( 96,534)
( 97,538)( 98,539)( 99,540)(100,526)(101,527)(102,528)(103,523)(104,524)
(105,525)(106,529)(107,530)(108,531)(109,571)(110,572)(111,573)(112,568)
(113,569)(114,570)(115,574)(116,575)(117,576)(118,589)(119,590)(120,591)
(121,586)(122,587)(123,588)(124,592)(125,593)(126,594)(127,580)(128,581)
(129,582)(130,577)(131,578)(132,579)(133,583)(134,584)(135,585)(136,544)
(137,545)(138,546)(139,541)(140,542)(141,543)(142,547)(143,548)(144,549)
(145,562)(146,563)(147,564)(148,559)(149,560)(150,561)(151,565)(152,566)
(153,567)(154,553)(155,554)(156,555)(157,550)(158,551)(159,552)(160,556)
(161,557)(162,558)(163,625)(164,626)(165,627)(166,622)(167,623)(168,624)
(169,628)(170,629)(171,630)(172,643)(173,644)(174,645)(175,640)(176,641)
(177,642)(178,646)(179,647)(180,648)(181,634)(182,635)(183,636)(184,631)
(185,632)(186,633)(187,637)(188,638)(189,639)(190,598)(191,599)(192,600)
(193,595)(194,596)(195,597)(196,601)(197,602)(198,603)(199,616)(200,617)
(201,618)(202,613)(203,614)(204,615)(205,619)(206,620)(207,621)(208,607)
(209,608)(210,609)(211,604)(212,605)(213,606)(214,610)(215,611)(216,612)
(217,652)(218,653)(219,654)(220,649)(221,650)(222,651)(223,655)(224,656)
(225,657)(226,670)(227,671)(228,672)(229,667)(230,668)(231,669)(232,673)
(233,674)(234,675)(235,661)(236,662)(237,663)(238,658)(239,659)(240,660)
(241,664)(242,665)(243,666)(244,679)(245,680)(246,681)(247,676)(248,677)
(249,678)(250,682)(251,683)(252,684)(253,697)(254,698)(255,699)(256,694)
(257,695)(258,696)(259,700)(260,701)(261,702)(262,688)(263,689)(264,690)
(265,685)(266,686)(267,687)(268,691)(269,692)(270,693)(271,706)(272,707)
(273,708)(274,703)(275,704)(276,705)(277,709)(278,710)(279,711)(280,724)
(281,725)(282,726)(283,721)(284,722)(285,723)(286,727)(287,728)(288,729)
(289,715)(290,716)(291,717)(292,712)(293,713)(294,714)(295,718)(296,719)
(297,720)(298,733)(299,734)(300,735)(301,730)(302,731)(303,732)(304,736)
(305,737)(306,738)(307,751)(308,752)(309,753)(310,748)(311,749)(312,750)
(313,754)(314,755)(315,756)(316,742)(317,743)(318,744)(319,739)(320,740)
(321,741)(322,745)(323,746)(324,747)(325,787)(326,788)(327,789)(328,784)
(329,785)(330,786)(331,790)(332,791)(333,792)(334,805)(335,806)(336,807)
(337,802)(338,803)(339,804)(340,808)(341,809)(342,810)(343,796)(344,797)
(345,798)(346,793)(347,794)(348,795)(349,799)(350,800)(351,801)(352,760)
(353,761)(354,762)(355,757)(356,758)(357,759)(358,763)(359,764)(360,765)
(361,778)(362,779)(363,780)(364,775)(365,776)(366,777)(367,781)(368,782)
(369,783)(370,769)(371,770)(372,771)(373,766)(374,767)(375,768)(376,772)
(377,773)(378,774)(379,841)(380,842)(381,843)(382,838)(383,839)(384,840)
(385,844)(386,845)(387,846)(388,859)(389,860)(390,861)(391,856)(392,857)
(393,858)(394,862)(395,863)(396,864)(397,850)(398,851)(399,852)(400,847)
(401,848)(402,849)(403,853)(404,854)(405,855)(406,814)(407,815)(408,816)
(409,811)(410,812)(411,813)(412,817)(413,818)(414,819)(415,832)(416,833)
(417,834)(418,829)(419,830)(420,831)(421,835)(422,836)(423,837)(424,823)
(425,824)(426,825)(427,820)(428,821)(429,822)(430,826)(431,827)(432,828);;
s2 := ( 1,766)( 2,768)( 3,767)( 4,769)( 5,771)( 6,770)( 7,772)( 8,774)
( 9,773)( 10,757)( 11,759)( 12,758)( 13,760)( 14,762)( 15,761)( 16,763)
( 17,765)( 18,764)( 19,775)( 20,777)( 21,776)( 22,778)( 23,780)( 24,779)
( 25,781)( 26,783)( 27,782)( 28,793)( 29,795)( 30,794)( 31,796)( 32,798)
( 33,797)( 34,799)( 35,801)( 36,800)( 37,784)( 38,786)( 39,785)( 40,787)
( 41,789)( 42,788)( 43,790)( 44,792)( 45,791)( 46,802)( 47,804)( 48,803)
( 49,805)( 50,807)( 51,806)( 52,808)( 53,810)( 54,809)( 55,820)( 56,822)
( 57,821)( 58,823)( 59,825)( 60,824)( 61,826)( 62,828)( 63,827)( 64,811)
( 65,813)( 66,812)( 67,814)( 68,816)( 69,815)( 70,817)( 71,819)( 72,818)
( 73,829)( 74,831)( 75,830)( 76,832)( 77,834)( 78,833)( 79,835)( 80,837)
( 81,836)( 82,847)( 83,849)( 84,848)( 85,850)( 86,852)( 87,851)( 88,853)
( 89,855)( 90,854)( 91,838)( 92,840)( 93,839)( 94,841)( 95,843)( 96,842)
( 97,844)( 98,846)( 99,845)(100,856)(101,858)(102,857)(103,859)(104,861)
(105,860)(106,862)(107,864)(108,863)(109,685)(110,687)(111,686)(112,688)
(113,690)(114,689)(115,691)(116,693)(117,692)(118,676)(119,678)(120,677)
(121,679)(122,681)(123,680)(124,682)(125,684)(126,683)(127,694)(128,696)
(129,695)(130,697)(131,699)(132,698)(133,700)(134,702)(135,701)(136,658)
(137,660)(138,659)(139,661)(140,663)(141,662)(142,664)(143,666)(144,665)
(145,649)(146,651)(147,650)(148,652)(149,654)(150,653)(151,655)(152,657)
(153,656)(154,667)(155,669)(156,668)(157,670)(158,672)(159,671)(160,673)
(161,675)(162,674)(163,739)(164,741)(165,740)(166,742)(167,744)(168,743)
(169,745)(170,747)(171,746)(172,730)(173,732)(174,731)(175,733)(176,735)
(177,734)(178,736)(179,738)(180,737)(181,748)(182,750)(183,749)(184,751)
(185,753)(186,752)(187,754)(188,756)(189,755)(190,712)(191,714)(192,713)
(193,715)(194,717)(195,716)(196,718)(197,720)(198,719)(199,703)(200,705)
(201,704)(202,706)(203,708)(204,707)(205,709)(206,711)(207,710)(208,721)
(209,723)(210,722)(211,724)(212,726)(213,725)(214,727)(215,729)(216,728)
(217,550)(218,552)(219,551)(220,553)(221,555)(222,554)(223,556)(224,558)
(225,557)(226,541)(227,543)(228,542)(229,544)(230,546)(231,545)(232,547)
(233,549)(234,548)(235,559)(236,561)(237,560)(238,562)(239,564)(240,563)
(241,565)(242,567)(243,566)(244,577)(245,579)(246,578)(247,580)(248,582)
(249,581)(250,583)(251,585)(252,584)(253,568)(254,570)(255,569)(256,571)
(257,573)(258,572)(259,574)(260,576)(261,575)(262,586)(263,588)(264,587)
(265,589)(266,591)(267,590)(268,592)(269,594)(270,593)(271,604)(272,606)
(273,605)(274,607)(275,609)(276,608)(277,610)(278,612)(279,611)(280,595)
(281,597)(282,596)(283,598)(284,600)(285,599)(286,601)(287,603)(288,602)
(289,613)(290,615)(291,614)(292,616)(293,618)(294,617)(295,619)(296,621)
(297,620)(298,631)(299,633)(300,632)(301,634)(302,636)(303,635)(304,637)
(305,639)(306,638)(307,622)(308,624)(309,623)(310,625)(311,627)(312,626)
(313,628)(314,630)(315,629)(316,640)(317,642)(318,641)(319,643)(320,645)
(321,644)(322,646)(323,648)(324,647)(325,469)(326,471)(327,470)(328,472)
(329,474)(330,473)(331,475)(332,477)(333,476)(334,460)(335,462)(336,461)
(337,463)(338,465)(339,464)(340,466)(341,468)(342,467)(343,478)(344,480)
(345,479)(346,481)(347,483)(348,482)(349,484)(350,486)(351,485)(352,442)
(353,444)(354,443)(355,445)(356,447)(357,446)(358,448)(359,450)(360,449)
(361,433)(362,435)(363,434)(364,436)(365,438)(366,437)(367,439)(368,441)
(369,440)(370,451)(371,453)(372,452)(373,454)(374,456)(375,455)(376,457)
(377,459)(378,458)(379,523)(380,525)(381,524)(382,526)(383,528)(384,527)
(385,529)(386,531)(387,530)(388,514)(389,516)(390,515)(391,517)(392,519)
(393,518)(394,520)(395,522)(396,521)(397,532)(398,534)(399,533)(400,535)
(401,537)(402,536)(403,538)(404,540)(405,539)(406,496)(407,498)(408,497)
(409,499)(410,501)(411,500)(412,502)(413,504)(414,503)(415,487)(416,489)
(417,488)(418,490)(419,492)(420,491)(421,493)(422,495)(423,494)(424,505)
(425,507)(426,506)(427,508)(428,510)(429,509)(430,511)(431,513)(432,512);;
s3 := ( 1,218)( 2,217)( 3,219)( 4,221)( 5,220)( 6,222)( 7,224)( 8,223)
( 9,225)( 10,227)( 11,226)( 12,228)( 13,230)( 14,229)( 15,231)( 16,233)
( 17,232)( 18,234)( 19,236)( 20,235)( 21,237)( 22,239)( 23,238)( 24,240)
( 25,242)( 26,241)( 27,243)( 28,245)( 29,244)( 30,246)( 31,248)( 32,247)
( 33,249)( 34,251)( 35,250)( 36,252)( 37,254)( 38,253)( 39,255)( 40,257)
( 41,256)( 42,258)( 43,260)( 44,259)( 45,261)( 46,263)( 47,262)( 48,264)
( 49,266)( 50,265)( 51,267)( 52,269)( 53,268)( 54,270)( 55,272)( 56,271)
( 57,273)( 58,275)( 59,274)( 60,276)( 61,278)( 62,277)( 63,279)( 64,281)
( 65,280)( 66,282)( 67,284)( 68,283)( 69,285)( 70,287)( 71,286)( 72,288)
( 73,290)( 74,289)( 75,291)( 76,293)( 77,292)( 78,294)( 79,296)( 80,295)
( 81,297)( 82,299)( 83,298)( 84,300)( 85,302)( 86,301)( 87,303)( 88,305)
( 89,304)( 90,306)( 91,308)( 92,307)( 93,309)( 94,311)( 95,310)( 96,312)
( 97,314)( 98,313)( 99,315)(100,317)(101,316)(102,318)(103,320)(104,319)
(105,321)(106,323)(107,322)(108,324)(109,380)(110,379)(111,381)(112,383)
(113,382)(114,384)(115,386)(116,385)(117,387)(118,389)(119,388)(120,390)
(121,392)(122,391)(123,393)(124,395)(125,394)(126,396)(127,398)(128,397)
(129,399)(130,401)(131,400)(132,402)(133,404)(134,403)(135,405)(136,407)
(137,406)(138,408)(139,410)(140,409)(141,411)(142,413)(143,412)(144,414)
(145,416)(146,415)(147,417)(148,419)(149,418)(150,420)(151,422)(152,421)
(153,423)(154,425)(155,424)(156,426)(157,428)(158,427)(159,429)(160,431)
(161,430)(162,432)(163,326)(164,325)(165,327)(166,329)(167,328)(168,330)
(169,332)(170,331)(171,333)(172,335)(173,334)(174,336)(175,338)(176,337)
(177,339)(178,341)(179,340)(180,342)(181,344)(182,343)(183,345)(184,347)
(185,346)(186,348)(187,350)(188,349)(189,351)(190,353)(191,352)(192,354)
(193,356)(194,355)(195,357)(196,359)(197,358)(198,360)(199,362)(200,361)
(201,363)(202,365)(203,364)(204,366)(205,368)(206,367)(207,369)(208,371)
(209,370)(210,372)(211,374)(212,373)(213,375)(214,377)(215,376)(216,378)
(433,650)(434,649)(435,651)(436,653)(437,652)(438,654)(439,656)(440,655)
(441,657)(442,659)(443,658)(444,660)(445,662)(446,661)(447,663)(448,665)
(449,664)(450,666)(451,668)(452,667)(453,669)(454,671)(455,670)(456,672)
(457,674)(458,673)(459,675)(460,677)(461,676)(462,678)(463,680)(464,679)
(465,681)(466,683)(467,682)(468,684)(469,686)(470,685)(471,687)(472,689)
(473,688)(474,690)(475,692)(476,691)(477,693)(478,695)(479,694)(480,696)
(481,698)(482,697)(483,699)(484,701)(485,700)(486,702)(487,704)(488,703)
(489,705)(490,707)(491,706)(492,708)(493,710)(494,709)(495,711)(496,713)
(497,712)(498,714)(499,716)(500,715)(501,717)(502,719)(503,718)(504,720)
(505,722)(506,721)(507,723)(508,725)(509,724)(510,726)(511,728)(512,727)
(513,729)(514,731)(515,730)(516,732)(517,734)(518,733)(519,735)(520,737)
(521,736)(522,738)(523,740)(524,739)(525,741)(526,743)(527,742)(528,744)
(529,746)(530,745)(531,747)(532,749)(533,748)(534,750)(535,752)(536,751)
(537,753)(538,755)(539,754)(540,756)(541,812)(542,811)(543,813)(544,815)
(545,814)(546,816)(547,818)(548,817)(549,819)(550,821)(551,820)(552,822)
(553,824)(554,823)(555,825)(556,827)(557,826)(558,828)(559,830)(560,829)
(561,831)(562,833)(563,832)(564,834)(565,836)(566,835)(567,837)(568,839)
(569,838)(570,840)(571,842)(572,841)(573,843)(574,845)(575,844)(576,846)
(577,848)(578,847)(579,849)(580,851)(581,850)(582,852)(583,854)(584,853)
(585,855)(586,857)(587,856)(588,858)(589,860)(590,859)(591,861)(592,863)
(593,862)(594,864)(595,758)(596,757)(597,759)(598,761)(599,760)(600,762)
(601,764)(602,763)(603,765)(604,767)(605,766)(606,768)(607,770)(608,769)
(609,771)(610,773)(611,772)(612,774)(613,776)(614,775)(615,777)(616,779)
(617,778)(618,780)(619,782)(620,781)(621,783)(622,785)(623,784)(624,786)
(625,788)(626,787)(627,789)(628,791)(629,790)(630,792)(631,794)(632,793)
(633,795)(634,797)(635,796)(636,798)(637,800)(638,799)(639,801)(640,803)
(641,802)(642,804)(643,806)(644,805)(645,807)(646,809)(647,808)(648,810);;
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*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)
( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)
( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)
( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)
( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)
(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)
(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)
(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)
(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)
(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)
(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)
(187,211)(188,212)(189,213)(220,223)(221,224)(222,225)(229,232)(230,233)
(231,234)(238,241)(239,242)(240,243)(247,250)(248,251)(249,252)(256,259)
(257,260)(258,261)(265,268)(266,269)(267,270)(274,277)(275,278)(276,279)
(283,286)(284,287)(285,288)(292,295)(293,296)(294,297)(301,304)(302,305)
(303,306)(310,313)(311,314)(312,315)(319,322)(320,323)(321,324)(325,352)
(326,353)(327,354)(328,358)(329,359)(330,360)(331,355)(332,356)(333,357)
(334,361)(335,362)(336,363)(337,367)(338,368)(339,369)(340,364)(341,365)
(342,366)(343,370)(344,371)(345,372)(346,376)(347,377)(348,378)(349,373)
(350,374)(351,375)(379,406)(380,407)(381,408)(382,412)(383,413)(384,414)
(385,409)(386,410)(387,411)(388,415)(389,416)(390,417)(391,421)(392,422)
(393,423)(394,418)(395,419)(396,420)(397,424)(398,425)(399,426)(400,430)
(401,431)(402,432)(403,427)(404,428)(405,429)(433,460)(434,461)(435,462)
(436,466)(437,467)(438,468)(439,463)(440,464)(441,465)(442,469)(443,470)
(444,471)(445,475)(446,476)(447,477)(448,472)(449,473)(450,474)(451,478)
(452,479)(453,480)(454,484)(455,485)(456,486)(457,481)(458,482)(459,483)
(487,514)(488,515)(489,516)(490,520)(491,521)(492,522)(493,517)(494,518)
(495,519)(496,523)(497,524)(498,525)(499,529)(500,530)(501,531)(502,526)
(503,527)(504,528)(505,532)(506,533)(507,534)(508,538)(509,539)(510,540)
(511,535)(512,536)(513,537)(544,547)(545,548)(546,549)(553,556)(554,557)
(555,558)(562,565)(563,566)(564,567)(571,574)(572,575)(573,576)(580,583)
(581,584)(582,585)(589,592)(590,593)(591,594)(598,601)(599,602)(600,603)
(607,610)(608,611)(609,612)(616,619)(617,620)(618,621)(625,628)(626,629)
(627,630)(634,637)(635,638)(636,639)(643,646)(644,647)(645,648)(649,676)
(650,677)(651,678)(652,682)(653,683)(654,684)(655,679)(656,680)(657,681)
(658,685)(659,686)(660,687)(661,691)(662,692)(663,693)(664,688)(665,689)
(666,690)(667,694)(668,695)(669,696)(670,700)(671,701)(672,702)(673,697)
(674,698)(675,699)(703,730)(704,731)(705,732)(706,736)(707,737)(708,738)
(709,733)(710,734)(711,735)(712,739)(713,740)(714,741)(715,745)(716,746)
(717,747)(718,742)(719,743)(720,744)(721,748)(722,749)(723,750)(724,754)
(725,755)(726,756)(727,751)(728,752)(729,753)(760,763)(761,764)(762,765)
(769,772)(770,773)(771,774)(778,781)(779,782)(780,783)(787,790)(788,791)
(789,792)(796,799)(797,800)(798,801)(805,808)(806,809)(807,810)(814,817)
(815,818)(816,819)(823,826)(824,827)(825,828)(832,835)(833,836)(834,837)
(841,844)(842,845)(843,846)(850,853)(851,854)(852,855)(859,862)(860,863)
(861,864);
s1 := Sym(864)!( 1,436)( 2,437)( 3,438)( 4,433)( 5,434)( 6,435)( 7,439)
( 8,440)( 9,441)( 10,454)( 11,455)( 12,456)( 13,451)( 14,452)( 15,453)
( 16,457)( 17,458)( 18,459)( 19,445)( 20,446)( 21,447)( 22,442)( 23,443)
( 24,444)( 25,448)( 26,449)( 27,450)( 28,463)( 29,464)( 30,465)( 31,460)
( 32,461)( 33,462)( 34,466)( 35,467)( 36,468)( 37,481)( 38,482)( 39,483)
( 40,478)( 41,479)( 42,480)( 43,484)( 44,485)( 45,486)( 46,472)( 47,473)
( 48,474)( 49,469)( 50,470)( 51,471)( 52,475)( 53,476)( 54,477)( 55,490)
( 56,491)( 57,492)( 58,487)( 59,488)( 60,489)( 61,493)( 62,494)( 63,495)
( 64,508)( 65,509)( 66,510)( 67,505)( 68,506)( 69,507)( 70,511)( 71,512)
( 72,513)( 73,499)( 74,500)( 75,501)( 76,496)( 77,497)( 78,498)( 79,502)
( 80,503)( 81,504)( 82,517)( 83,518)( 84,519)( 85,514)( 86,515)( 87,516)
( 88,520)( 89,521)( 90,522)( 91,535)( 92,536)( 93,537)( 94,532)( 95,533)
( 96,534)( 97,538)( 98,539)( 99,540)(100,526)(101,527)(102,528)(103,523)
(104,524)(105,525)(106,529)(107,530)(108,531)(109,571)(110,572)(111,573)
(112,568)(113,569)(114,570)(115,574)(116,575)(117,576)(118,589)(119,590)
(120,591)(121,586)(122,587)(123,588)(124,592)(125,593)(126,594)(127,580)
(128,581)(129,582)(130,577)(131,578)(132,579)(133,583)(134,584)(135,585)
(136,544)(137,545)(138,546)(139,541)(140,542)(141,543)(142,547)(143,548)
(144,549)(145,562)(146,563)(147,564)(148,559)(149,560)(150,561)(151,565)
(152,566)(153,567)(154,553)(155,554)(156,555)(157,550)(158,551)(159,552)
(160,556)(161,557)(162,558)(163,625)(164,626)(165,627)(166,622)(167,623)
(168,624)(169,628)(170,629)(171,630)(172,643)(173,644)(174,645)(175,640)
(176,641)(177,642)(178,646)(179,647)(180,648)(181,634)(182,635)(183,636)
(184,631)(185,632)(186,633)(187,637)(188,638)(189,639)(190,598)(191,599)
(192,600)(193,595)(194,596)(195,597)(196,601)(197,602)(198,603)(199,616)
(200,617)(201,618)(202,613)(203,614)(204,615)(205,619)(206,620)(207,621)
(208,607)(209,608)(210,609)(211,604)(212,605)(213,606)(214,610)(215,611)
(216,612)(217,652)(218,653)(219,654)(220,649)(221,650)(222,651)(223,655)
(224,656)(225,657)(226,670)(227,671)(228,672)(229,667)(230,668)(231,669)
(232,673)(233,674)(234,675)(235,661)(236,662)(237,663)(238,658)(239,659)
(240,660)(241,664)(242,665)(243,666)(244,679)(245,680)(246,681)(247,676)
(248,677)(249,678)(250,682)(251,683)(252,684)(253,697)(254,698)(255,699)
(256,694)(257,695)(258,696)(259,700)(260,701)(261,702)(262,688)(263,689)
(264,690)(265,685)(266,686)(267,687)(268,691)(269,692)(270,693)(271,706)
(272,707)(273,708)(274,703)(275,704)(276,705)(277,709)(278,710)(279,711)
(280,724)(281,725)(282,726)(283,721)(284,722)(285,723)(286,727)(287,728)
(288,729)(289,715)(290,716)(291,717)(292,712)(293,713)(294,714)(295,718)
(296,719)(297,720)(298,733)(299,734)(300,735)(301,730)(302,731)(303,732)
(304,736)(305,737)(306,738)(307,751)(308,752)(309,753)(310,748)(311,749)
(312,750)(313,754)(314,755)(315,756)(316,742)(317,743)(318,744)(319,739)
(320,740)(321,741)(322,745)(323,746)(324,747)(325,787)(326,788)(327,789)
(328,784)(329,785)(330,786)(331,790)(332,791)(333,792)(334,805)(335,806)
(336,807)(337,802)(338,803)(339,804)(340,808)(341,809)(342,810)(343,796)
(344,797)(345,798)(346,793)(347,794)(348,795)(349,799)(350,800)(351,801)
(352,760)(353,761)(354,762)(355,757)(356,758)(357,759)(358,763)(359,764)
(360,765)(361,778)(362,779)(363,780)(364,775)(365,776)(366,777)(367,781)
(368,782)(369,783)(370,769)(371,770)(372,771)(373,766)(374,767)(375,768)
(376,772)(377,773)(378,774)(379,841)(380,842)(381,843)(382,838)(383,839)
(384,840)(385,844)(386,845)(387,846)(388,859)(389,860)(390,861)(391,856)
(392,857)(393,858)(394,862)(395,863)(396,864)(397,850)(398,851)(399,852)
(400,847)(401,848)(402,849)(403,853)(404,854)(405,855)(406,814)(407,815)
(408,816)(409,811)(410,812)(411,813)(412,817)(413,818)(414,819)(415,832)
(416,833)(417,834)(418,829)(419,830)(420,831)(421,835)(422,836)(423,837)
(424,823)(425,824)(426,825)(427,820)(428,821)(429,822)(430,826)(431,827)
(432,828);
s2 := Sym(864)!( 1,766)( 2,768)( 3,767)( 4,769)( 5,771)( 6,770)( 7,772)
( 8,774)( 9,773)( 10,757)( 11,759)( 12,758)( 13,760)( 14,762)( 15,761)
( 16,763)( 17,765)( 18,764)( 19,775)( 20,777)( 21,776)( 22,778)( 23,780)
( 24,779)( 25,781)( 26,783)( 27,782)( 28,793)( 29,795)( 30,794)( 31,796)
( 32,798)( 33,797)( 34,799)( 35,801)( 36,800)( 37,784)( 38,786)( 39,785)
( 40,787)( 41,789)( 42,788)( 43,790)( 44,792)( 45,791)( 46,802)( 47,804)
( 48,803)( 49,805)( 50,807)( 51,806)( 52,808)( 53,810)( 54,809)( 55,820)
( 56,822)( 57,821)( 58,823)( 59,825)( 60,824)( 61,826)( 62,828)( 63,827)
( 64,811)( 65,813)( 66,812)( 67,814)( 68,816)( 69,815)( 70,817)( 71,819)
( 72,818)( 73,829)( 74,831)( 75,830)( 76,832)( 77,834)( 78,833)( 79,835)
( 80,837)( 81,836)( 82,847)( 83,849)( 84,848)( 85,850)( 86,852)( 87,851)
( 88,853)( 89,855)( 90,854)( 91,838)( 92,840)( 93,839)( 94,841)( 95,843)
( 96,842)( 97,844)( 98,846)( 99,845)(100,856)(101,858)(102,857)(103,859)
(104,861)(105,860)(106,862)(107,864)(108,863)(109,685)(110,687)(111,686)
(112,688)(113,690)(114,689)(115,691)(116,693)(117,692)(118,676)(119,678)
(120,677)(121,679)(122,681)(123,680)(124,682)(125,684)(126,683)(127,694)
(128,696)(129,695)(130,697)(131,699)(132,698)(133,700)(134,702)(135,701)
(136,658)(137,660)(138,659)(139,661)(140,663)(141,662)(142,664)(143,666)
(144,665)(145,649)(146,651)(147,650)(148,652)(149,654)(150,653)(151,655)
(152,657)(153,656)(154,667)(155,669)(156,668)(157,670)(158,672)(159,671)
(160,673)(161,675)(162,674)(163,739)(164,741)(165,740)(166,742)(167,744)
(168,743)(169,745)(170,747)(171,746)(172,730)(173,732)(174,731)(175,733)
(176,735)(177,734)(178,736)(179,738)(180,737)(181,748)(182,750)(183,749)
(184,751)(185,753)(186,752)(187,754)(188,756)(189,755)(190,712)(191,714)
(192,713)(193,715)(194,717)(195,716)(196,718)(197,720)(198,719)(199,703)
(200,705)(201,704)(202,706)(203,708)(204,707)(205,709)(206,711)(207,710)
(208,721)(209,723)(210,722)(211,724)(212,726)(213,725)(214,727)(215,729)
(216,728)(217,550)(218,552)(219,551)(220,553)(221,555)(222,554)(223,556)
(224,558)(225,557)(226,541)(227,543)(228,542)(229,544)(230,546)(231,545)
(232,547)(233,549)(234,548)(235,559)(236,561)(237,560)(238,562)(239,564)
(240,563)(241,565)(242,567)(243,566)(244,577)(245,579)(246,578)(247,580)
(248,582)(249,581)(250,583)(251,585)(252,584)(253,568)(254,570)(255,569)
(256,571)(257,573)(258,572)(259,574)(260,576)(261,575)(262,586)(263,588)
(264,587)(265,589)(266,591)(267,590)(268,592)(269,594)(270,593)(271,604)
(272,606)(273,605)(274,607)(275,609)(276,608)(277,610)(278,612)(279,611)
(280,595)(281,597)(282,596)(283,598)(284,600)(285,599)(286,601)(287,603)
(288,602)(289,613)(290,615)(291,614)(292,616)(293,618)(294,617)(295,619)
(296,621)(297,620)(298,631)(299,633)(300,632)(301,634)(302,636)(303,635)
(304,637)(305,639)(306,638)(307,622)(308,624)(309,623)(310,625)(311,627)
(312,626)(313,628)(314,630)(315,629)(316,640)(317,642)(318,641)(319,643)
(320,645)(321,644)(322,646)(323,648)(324,647)(325,469)(326,471)(327,470)
(328,472)(329,474)(330,473)(331,475)(332,477)(333,476)(334,460)(335,462)
(336,461)(337,463)(338,465)(339,464)(340,466)(341,468)(342,467)(343,478)
(344,480)(345,479)(346,481)(347,483)(348,482)(349,484)(350,486)(351,485)
(352,442)(353,444)(354,443)(355,445)(356,447)(357,446)(358,448)(359,450)
(360,449)(361,433)(362,435)(363,434)(364,436)(365,438)(366,437)(367,439)
(368,441)(369,440)(370,451)(371,453)(372,452)(373,454)(374,456)(375,455)
(376,457)(377,459)(378,458)(379,523)(380,525)(381,524)(382,526)(383,528)
(384,527)(385,529)(386,531)(387,530)(388,514)(389,516)(390,515)(391,517)
(392,519)(393,518)(394,520)(395,522)(396,521)(397,532)(398,534)(399,533)
(400,535)(401,537)(402,536)(403,538)(404,540)(405,539)(406,496)(407,498)
(408,497)(409,499)(410,501)(411,500)(412,502)(413,504)(414,503)(415,487)
(416,489)(417,488)(418,490)(419,492)(420,491)(421,493)(422,495)(423,494)
(424,505)(425,507)(426,506)(427,508)(428,510)(429,509)(430,511)(431,513)
(432,512);
s3 := Sym(864)!( 1,218)( 2,217)( 3,219)( 4,221)( 5,220)( 6,222)( 7,224)
( 8,223)( 9,225)( 10,227)( 11,226)( 12,228)( 13,230)( 14,229)( 15,231)
( 16,233)( 17,232)( 18,234)( 19,236)( 20,235)( 21,237)( 22,239)( 23,238)
( 24,240)( 25,242)( 26,241)( 27,243)( 28,245)( 29,244)( 30,246)( 31,248)
( 32,247)( 33,249)( 34,251)( 35,250)( 36,252)( 37,254)( 38,253)( 39,255)
( 40,257)( 41,256)( 42,258)( 43,260)( 44,259)( 45,261)( 46,263)( 47,262)
( 48,264)( 49,266)( 50,265)( 51,267)( 52,269)( 53,268)( 54,270)( 55,272)
( 56,271)( 57,273)( 58,275)( 59,274)( 60,276)( 61,278)( 62,277)( 63,279)
( 64,281)( 65,280)( 66,282)( 67,284)( 68,283)( 69,285)( 70,287)( 71,286)
( 72,288)( 73,290)( 74,289)( 75,291)( 76,293)( 77,292)( 78,294)( 79,296)
( 80,295)( 81,297)( 82,299)( 83,298)( 84,300)( 85,302)( 86,301)( 87,303)
( 88,305)( 89,304)( 90,306)( 91,308)( 92,307)( 93,309)( 94,311)( 95,310)
( 96,312)( 97,314)( 98,313)( 99,315)(100,317)(101,316)(102,318)(103,320)
(104,319)(105,321)(106,323)(107,322)(108,324)(109,380)(110,379)(111,381)
(112,383)(113,382)(114,384)(115,386)(116,385)(117,387)(118,389)(119,388)
(120,390)(121,392)(122,391)(123,393)(124,395)(125,394)(126,396)(127,398)
(128,397)(129,399)(130,401)(131,400)(132,402)(133,404)(134,403)(135,405)
(136,407)(137,406)(138,408)(139,410)(140,409)(141,411)(142,413)(143,412)
(144,414)(145,416)(146,415)(147,417)(148,419)(149,418)(150,420)(151,422)
(152,421)(153,423)(154,425)(155,424)(156,426)(157,428)(158,427)(159,429)
(160,431)(161,430)(162,432)(163,326)(164,325)(165,327)(166,329)(167,328)
(168,330)(169,332)(170,331)(171,333)(172,335)(173,334)(174,336)(175,338)
(176,337)(177,339)(178,341)(179,340)(180,342)(181,344)(182,343)(183,345)
(184,347)(185,346)(186,348)(187,350)(188,349)(189,351)(190,353)(191,352)
(192,354)(193,356)(194,355)(195,357)(196,359)(197,358)(198,360)(199,362)
(200,361)(201,363)(202,365)(203,364)(204,366)(205,368)(206,367)(207,369)
(208,371)(209,370)(210,372)(211,374)(212,373)(213,375)(214,377)(215,376)
(216,378)(433,650)(434,649)(435,651)(436,653)(437,652)(438,654)(439,656)
(440,655)(441,657)(442,659)(443,658)(444,660)(445,662)(446,661)(447,663)
(448,665)(449,664)(450,666)(451,668)(452,667)(453,669)(454,671)(455,670)
(456,672)(457,674)(458,673)(459,675)(460,677)(461,676)(462,678)(463,680)
(464,679)(465,681)(466,683)(467,682)(468,684)(469,686)(470,685)(471,687)
(472,689)(473,688)(474,690)(475,692)(476,691)(477,693)(478,695)(479,694)
(480,696)(481,698)(482,697)(483,699)(484,701)(485,700)(486,702)(487,704)
(488,703)(489,705)(490,707)(491,706)(492,708)(493,710)(494,709)(495,711)
(496,713)(497,712)(498,714)(499,716)(500,715)(501,717)(502,719)(503,718)
(504,720)(505,722)(506,721)(507,723)(508,725)(509,724)(510,726)(511,728)
(512,727)(513,729)(514,731)(515,730)(516,732)(517,734)(518,733)(519,735)
(520,737)(521,736)(522,738)(523,740)(524,739)(525,741)(526,743)(527,742)
(528,744)(529,746)(530,745)(531,747)(532,749)(533,748)(534,750)(535,752)
(536,751)(537,753)(538,755)(539,754)(540,756)(541,812)(542,811)(543,813)
(544,815)(545,814)(546,816)(547,818)(548,817)(549,819)(550,821)(551,820)
(552,822)(553,824)(554,823)(555,825)(556,827)(557,826)(558,828)(559,830)
(560,829)(561,831)(562,833)(563,832)(564,834)(565,836)(566,835)(567,837)
(568,839)(569,838)(570,840)(571,842)(572,841)(573,843)(574,845)(575,844)
(576,846)(577,848)(578,847)(579,849)(580,851)(581,850)(582,852)(583,854)
(584,853)(585,855)(586,857)(587,856)(588,858)(589,860)(590,859)(591,861)
(592,863)(593,862)(594,864)(595,758)(596,757)(597,759)(598,761)(599,760)
(600,762)(601,764)(602,763)(603,765)(604,767)(605,766)(606,768)(607,770)
(608,769)(609,771)(610,773)(611,772)(612,774)(613,776)(614,775)(615,777)
(616,779)(617,778)(618,780)(619,782)(620,781)(621,783)(622,785)(623,784)
(624,786)(625,788)(626,787)(627,789)(628,791)(629,790)(630,792)(631,794)
(632,793)(633,795)(634,797)(635,796)(636,798)(637,800)(638,799)(639,801)
(640,803)(641,802)(642,804)(643,806)(644,805)(645,807)(646,809)(647,808)
(648,810);
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*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope