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Polytope of Type {12,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,18,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,17257)
Rank : 4
Schlafli Type : {12,18,4}
Number of vertices, edges, etc : 12, 108, 36, 4
Order of s0s1s2s3 : 36
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 : {6,18,4}*864b, {12,18,2}*864b
   3-fold quotients : {4,18,4}*576a, {12,6,4}*576c
   4-fold quotients : {6,18,2}*432b
   6-fold quotients : {2,18,4}*288a, {4,18,2}*288a, {6,6,4}*288b, {12,6,2}*288c
   8-fold quotients : {6,9,2}*216
   9-fold quotients : {4,6,4}*192a
   12-fold quotients : {2,18,2}*144, {6,6,2}*144b
   18-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   24-fold quotients : {2,9,2}*72, {6,3,2}*72
   27-fold quotients : {4,2,4}*64
   36-fold quotients : {2,6,2}*48
   54-fold quotients : {2,2,4}*32, {4,2,2}*32
   72-fold quotients : {2,3,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 10, 19)( 11, 20)( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)
( 18, 27)( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)
( 44, 53)( 45, 54)( 64, 73)( 65, 74)( 66, 75)( 67, 76)( 68, 77)( 69, 78)
( 70, 79)( 71, 80)( 72, 81)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)
( 96,105)( 97,106)( 98,107)( 99,108)(109,136)(110,137)(111,138)(112,139)
(113,140)(114,141)(115,142)(116,143)(117,144)(118,154)(119,155)(120,156)
(121,157)(122,158)(123,159)(124,160)(125,161)(126,162)(127,145)(128,146)
(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(163,190)
(164,191)(165,192)(166,193)(167,194)(168,195)(169,196)(170,197)(171,198)
(172,208)(173,209)(174,210)(175,211)(176,212)(177,213)(178,214)(179,215)
(180,216)(181,199)(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)
(188,206)(189,207)(226,235)(227,236)(228,237)(229,238)(230,239)(231,240)
(232,241)(233,242)(234,243)(253,262)(254,263)(255,264)(256,265)(257,266)
(258,267)(259,268)(260,269)(261,270)(280,289)(281,290)(282,291)(283,292)
(284,293)(285,294)(286,295)(287,296)(288,297)(307,316)(308,317)(309,318)
(310,319)(311,320)(312,321)(313,322)(314,323)(315,324)(325,352)(326,353)
(327,354)(328,355)(329,356)(330,357)(331,358)(332,359)(333,360)(334,370)
(335,371)(336,372)(337,373)(338,374)(339,375)(340,376)(341,377)(342,378)
(343,361)(344,362)(345,363)(346,364)(347,365)(348,366)(349,367)(350,368)
(351,369)(379,406)(380,407)(381,408)(382,409)(383,410)(384,411)(385,412)
(386,413)(387,414)(388,424)(389,425)(390,426)(391,427)(392,428)(393,429)
(394,430)(395,431)(396,432)(397,415)(398,416)(399,417)(400,418)(401,419)
(402,420)(403,421)(404,422)(405,423)(433,460)(434,461)(435,462)(436,463)
(437,464)(438,465)(439,466)(440,467)(441,468)(442,478)(443,479)(444,480)
(445,481)(446,482)(447,483)(448,484)(449,485)(450,486)(451,469)(452,470)
(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)(487,514)
(488,515)(489,516)(490,517)(491,518)(492,519)(493,520)(494,521)(495,522)
(496,532)(497,533)(498,534)(499,535)(500,536)(501,537)(502,538)(503,539)
(504,540)(505,523)(506,524)(507,525)(508,526)(509,527)(510,528)(511,529)
(512,530)(513,531)(550,559)(551,560)(552,561)(553,562)(554,563)(555,564)
(556,565)(557,566)(558,567)(577,586)(578,587)(579,588)(580,589)(581,590)
(582,591)(583,592)(584,593)(585,594)(604,613)(605,614)(606,615)(607,616)
(608,617)(609,618)(610,619)(611,620)(612,621)(631,640)(632,641)(633,642)
(634,643)(635,644)(636,645)(637,646)(638,647)(639,648)(649,676)(650,677)
(651,678)(652,679)(653,680)(654,681)(655,682)(656,683)(657,684)(658,694)
(659,695)(660,696)(661,697)(662,698)(663,699)(664,700)(665,701)(666,702)
(667,685)(668,686)(669,687)(670,688)(671,689)(672,690)(673,691)(674,692)
(675,693)(703,730)(704,731)(705,732)(706,733)(707,734)(708,735)(709,736)
(710,737)(711,738)(712,748)(713,749)(714,750)(715,751)(716,752)(717,753)
(718,754)(719,755)(720,756)(721,739)(722,740)(723,741)(724,742)(725,743)
(726,744)(727,745)(728,746)(729,747)(766,775)(767,776)(768,777)(769,778)
(770,779)(771,780)(772,781)(773,782)(774,783)(793,802)(794,803)(795,804)
(796,805)(797,806)(798,807)(799,808)(800,809)(801,810)(820,829)(821,830)
(822,831)(823,832)(824,833)(825,834)(826,835)(827,836)(828,837)(847,856)
(848,857)(849,858)(850,859)(851,860)(852,861)(853,862)(854,863)(855,864);;
s1 := (  1,442)(  2,444)(  3,443)(  4,450)(  5,449)(  6,448)(  7,447)(  8,446)
(  9,445)( 10,433)( 11,435)( 12,434)( 13,441)( 14,440)( 15,439)( 16,438)
( 17,437)( 18,436)( 19,451)( 20,453)( 21,452)( 22,459)( 23,458)( 24,457)
( 25,456)( 26,455)( 27,454)( 28,469)( 29,471)( 30,470)( 31,477)( 32,476)
( 33,475)( 34,474)( 35,473)( 36,472)( 37,460)( 38,462)( 39,461)( 40,468)
( 41,467)( 42,466)( 43,465)( 44,464)( 45,463)( 46,478)( 47,480)( 48,479)
( 49,486)( 50,485)( 51,484)( 52,483)( 53,482)( 54,481)( 55,496)( 56,498)
( 57,497)( 58,504)( 59,503)( 60,502)( 61,501)( 62,500)( 63,499)( 64,487)
( 65,489)( 66,488)( 67,495)( 68,494)( 69,493)( 70,492)( 71,491)( 72,490)
( 73,505)( 74,507)( 75,506)( 76,513)( 77,512)( 78,511)( 79,510)( 80,509)
( 81,508)( 82,523)( 83,525)( 84,524)( 85,531)( 86,530)( 87,529)( 88,528)
( 89,527)( 90,526)( 91,514)( 92,516)( 93,515)( 94,522)( 95,521)( 96,520)
( 97,519)( 98,518)( 99,517)(100,532)(101,534)(102,533)(103,540)(104,539)
(105,538)(106,537)(107,536)(108,535)(109,550)(110,552)(111,551)(112,558)
(113,557)(114,556)(115,555)(116,554)(117,553)(118,541)(119,543)(120,542)
(121,549)(122,548)(123,547)(124,546)(125,545)(126,544)(127,559)(128,561)
(129,560)(130,567)(131,566)(132,565)(133,564)(134,563)(135,562)(136,577)
(137,579)(138,578)(139,585)(140,584)(141,583)(142,582)(143,581)(144,580)
(145,568)(146,570)(147,569)(148,576)(149,575)(150,574)(151,573)(152,572)
(153,571)(154,586)(155,588)(156,587)(157,594)(158,593)(159,592)(160,591)
(161,590)(162,589)(163,604)(164,606)(165,605)(166,612)(167,611)(168,610)
(169,609)(170,608)(171,607)(172,595)(173,597)(174,596)(175,603)(176,602)
(177,601)(178,600)(179,599)(180,598)(181,613)(182,615)(183,614)(184,621)
(185,620)(186,619)(187,618)(188,617)(189,616)(190,631)(191,633)(192,632)
(193,639)(194,638)(195,637)(196,636)(197,635)(198,634)(199,622)(200,624)
(201,623)(202,630)(203,629)(204,628)(205,627)(206,626)(207,625)(208,640)
(209,642)(210,641)(211,648)(212,647)(213,646)(214,645)(215,644)(216,643)
(217,658)(218,660)(219,659)(220,666)(221,665)(222,664)(223,663)(224,662)
(225,661)(226,649)(227,651)(228,650)(229,657)(230,656)(231,655)(232,654)
(233,653)(234,652)(235,667)(236,669)(237,668)(238,675)(239,674)(240,673)
(241,672)(242,671)(243,670)(244,685)(245,687)(246,686)(247,693)(248,692)
(249,691)(250,690)(251,689)(252,688)(253,676)(254,678)(255,677)(256,684)
(257,683)(258,682)(259,681)(260,680)(261,679)(262,694)(263,696)(264,695)
(265,702)(266,701)(267,700)(268,699)(269,698)(270,697)(271,712)(272,714)
(273,713)(274,720)(275,719)(276,718)(277,717)(278,716)(279,715)(280,703)
(281,705)(282,704)(283,711)(284,710)(285,709)(286,708)(287,707)(288,706)
(289,721)(290,723)(291,722)(292,729)(293,728)(294,727)(295,726)(296,725)
(297,724)(298,739)(299,741)(300,740)(301,747)(302,746)(303,745)(304,744)
(305,743)(306,742)(307,730)(308,732)(309,731)(310,738)(311,737)(312,736)
(313,735)(314,734)(315,733)(316,748)(317,750)(318,749)(319,756)(320,755)
(321,754)(322,753)(323,752)(324,751)(325,766)(326,768)(327,767)(328,774)
(329,773)(330,772)(331,771)(332,770)(333,769)(334,757)(335,759)(336,758)
(337,765)(338,764)(339,763)(340,762)(341,761)(342,760)(343,775)(344,777)
(345,776)(346,783)(347,782)(348,781)(349,780)(350,779)(351,778)(352,793)
(353,795)(354,794)(355,801)(356,800)(357,799)(358,798)(359,797)(360,796)
(361,784)(362,786)(363,785)(364,792)(365,791)(366,790)(367,789)(368,788)
(369,787)(370,802)(371,804)(372,803)(373,810)(374,809)(375,808)(376,807)
(377,806)(378,805)(379,820)(380,822)(381,821)(382,828)(383,827)(384,826)
(385,825)(386,824)(387,823)(388,811)(389,813)(390,812)(391,819)(392,818)
(393,817)(394,816)(395,815)(396,814)(397,829)(398,831)(399,830)(400,837)
(401,836)(402,835)(403,834)(404,833)(405,832)(406,847)(407,849)(408,848)
(409,855)(410,854)(411,853)(412,852)(413,851)(414,850)(415,838)(416,840)
(417,839)(418,846)(419,845)(420,844)(421,843)(422,842)(423,841)(424,856)
(425,858)(426,857)(427,864)(428,863)(429,862)(430,861)(431,860)(432,859);;
s2 := (  1,544)(  2,546)(  3,545)(  4,541)(  5,543)(  6,542)(  7,549)(  8,548)
(  9,547)( 10,562)( 11,564)( 12,563)( 13,559)( 14,561)( 15,560)( 16,567)
( 17,566)( 18,565)( 19,553)( 20,555)( 21,554)( 22,550)( 23,552)( 24,551)
( 25,558)( 26,557)( 27,556)( 28,571)( 29,573)( 30,572)( 31,568)( 32,570)
( 33,569)( 34,576)( 35,575)( 36,574)( 37,589)( 38,591)( 39,590)( 40,586)
( 41,588)( 42,587)( 43,594)( 44,593)( 45,592)( 46,580)( 47,582)( 48,581)
( 49,577)( 50,579)( 51,578)( 52,585)( 53,584)( 54,583)( 55,598)( 56,600)
( 57,599)( 58,595)( 59,597)( 60,596)( 61,603)( 62,602)( 63,601)( 64,616)
( 65,618)( 66,617)( 67,613)( 68,615)( 69,614)( 70,621)( 71,620)( 72,619)
( 73,607)( 74,609)( 75,608)( 76,604)( 77,606)( 78,605)( 79,612)( 80,611)
( 81,610)( 82,625)( 83,627)( 84,626)( 85,622)( 86,624)( 87,623)( 88,630)
( 89,629)( 90,628)( 91,643)( 92,645)( 93,644)( 94,640)( 95,642)( 96,641)
( 97,648)( 98,647)( 99,646)(100,634)(101,636)(102,635)(103,631)(104,633)
(105,632)(106,639)(107,638)(108,637)(109,436)(110,438)(111,437)(112,433)
(113,435)(114,434)(115,441)(116,440)(117,439)(118,454)(119,456)(120,455)
(121,451)(122,453)(123,452)(124,459)(125,458)(126,457)(127,445)(128,447)
(129,446)(130,442)(131,444)(132,443)(133,450)(134,449)(135,448)(136,463)
(137,465)(138,464)(139,460)(140,462)(141,461)(142,468)(143,467)(144,466)
(145,481)(146,483)(147,482)(148,478)(149,480)(150,479)(151,486)(152,485)
(153,484)(154,472)(155,474)(156,473)(157,469)(158,471)(159,470)(160,477)
(161,476)(162,475)(163,490)(164,492)(165,491)(166,487)(167,489)(168,488)
(169,495)(170,494)(171,493)(172,508)(173,510)(174,509)(175,505)(176,507)
(177,506)(178,513)(179,512)(180,511)(181,499)(182,501)(183,500)(184,496)
(185,498)(186,497)(187,504)(188,503)(189,502)(190,517)(191,519)(192,518)
(193,514)(194,516)(195,515)(196,522)(197,521)(198,520)(199,535)(200,537)
(201,536)(202,532)(203,534)(204,533)(205,540)(206,539)(207,538)(208,526)
(209,528)(210,527)(211,523)(212,525)(213,524)(214,531)(215,530)(216,529)
(217,760)(218,762)(219,761)(220,757)(221,759)(222,758)(223,765)(224,764)
(225,763)(226,778)(227,780)(228,779)(229,775)(230,777)(231,776)(232,783)
(233,782)(234,781)(235,769)(236,771)(237,770)(238,766)(239,768)(240,767)
(241,774)(242,773)(243,772)(244,787)(245,789)(246,788)(247,784)(248,786)
(249,785)(250,792)(251,791)(252,790)(253,805)(254,807)(255,806)(256,802)
(257,804)(258,803)(259,810)(260,809)(261,808)(262,796)(263,798)(264,797)
(265,793)(266,795)(267,794)(268,801)(269,800)(270,799)(271,814)(272,816)
(273,815)(274,811)(275,813)(276,812)(277,819)(278,818)(279,817)(280,832)
(281,834)(282,833)(283,829)(284,831)(285,830)(286,837)(287,836)(288,835)
(289,823)(290,825)(291,824)(292,820)(293,822)(294,821)(295,828)(296,827)
(297,826)(298,841)(299,843)(300,842)(301,838)(302,840)(303,839)(304,846)
(305,845)(306,844)(307,859)(308,861)(309,860)(310,856)(311,858)(312,857)
(313,864)(314,863)(315,862)(316,850)(317,852)(318,851)(319,847)(320,849)
(321,848)(322,855)(323,854)(324,853)(325,652)(326,654)(327,653)(328,649)
(329,651)(330,650)(331,657)(332,656)(333,655)(334,670)(335,672)(336,671)
(337,667)(338,669)(339,668)(340,675)(341,674)(342,673)(343,661)(344,663)
(345,662)(346,658)(347,660)(348,659)(349,666)(350,665)(351,664)(352,679)
(353,681)(354,680)(355,676)(356,678)(357,677)(358,684)(359,683)(360,682)
(361,697)(362,699)(363,698)(364,694)(365,696)(366,695)(367,702)(368,701)
(369,700)(370,688)(371,690)(372,689)(373,685)(374,687)(375,686)(376,693)
(377,692)(378,691)(379,706)(380,708)(381,707)(382,703)(383,705)(384,704)
(385,711)(386,710)(387,709)(388,724)(389,726)(390,725)(391,721)(392,723)
(393,722)(394,729)(395,728)(396,727)(397,715)(398,717)(399,716)(400,712)
(401,714)(402,713)(403,720)(404,719)(405,718)(406,733)(407,735)(408,734)
(409,730)(410,732)(411,731)(412,738)(413,737)(414,736)(415,751)(416,753)
(417,752)(418,748)(419,750)(420,749)(421,756)(422,755)(423,754)(424,742)
(425,744)(426,743)(427,739)(428,741)(429,740)(430,747)(431,746)(432,745);;
s3 := (  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)(  8,224)
(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)( 16,232)
( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)( 40,256)
( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,379)(110,380)(111,381)(112,382)
(113,383)(114,384)(115,385)(116,386)(117,387)(118,388)(119,389)(120,390)
(121,391)(122,392)(123,393)(124,394)(125,395)(126,396)(127,397)(128,398)
(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)
(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)(144,414)
(145,415)(146,416)(147,417)(148,418)(149,419)(150,420)(151,421)(152,422)
(153,423)(154,424)(155,425)(156,426)(157,427)(158,428)(159,429)(160,430)
(161,431)(162,432)(163,325)(164,326)(165,327)(166,328)(167,329)(168,330)
(169,331)(170,332)(171,333)(172,334)(173,335)(174,336)(175,337)(176,338)
(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,345)(184,346)
(185,347)(186,348)(187,349)(188,350)(189,351)(190,352)(191,353)(192,354)
(193,355)(194,356)(195,357)(196,358)(197,359)(198,360)(199,361)(200,362)
(201,363)(202,364)(203,365)(204,366)(205,367)(206,368)(207,369)(208,370)
(209,371)(210,372)(211,373)(212,374)(213,375)(214,376)(215,377)(216,378)
(433,649)(434,650)(435,651)(436,652)(437,653)(438,654)(439,655)(440,656)
(441,657)(442,658)(443,659)(444,660)(445,661)(446,662)(447,663)(448,664)
(449,665)(450,666)(451,667)(452,668)(453,669)(454,670)(455,671)(456,672)
(457,673)(458,674)(459,675)(460,676)(461,677)(462,678)(463,679)(464,680)
(465,681)(466,682)(467,683)(468,684)(469,685)(470,686)(471,687)(472,688)
(473,689)(474,690)(475,691)(476,692)(477,693)(478,694)(479,695)(480,696)
(481,697)(482,698)(483,699)(484,700)(485,701)(486,702)(487,703)(488,704)
(489,705)(490,706)(491,707)(492,708)(493,709)(494,710)(495,711)(496,712)
(497,713)(498,714)(499,715)(500,716)(501,717)(502,718)(503,719)(504,720)
(505,721)(506,722)(507,723)(508,724)(509,725)(510,726)(511,727)(512,728)
(513,729)(514,730)(515,731)(516,732)(517,733)(518,734)(519,735)(520,736)
(521,737)(522,738)(523,739)(524,740)(525,741)(526,742)(527,743)(528,744)
(529,745)(530,746)(531,747)(532,748)(533,749)(534,750)(535,751)(536,752)
(537,753)(538,754)(539,755)(540,756)(541,811)(542,812)(543,813)(544,814)
(545,815)(546,816)(547,817)(548,818)(549,819)(550,820)(551,821)(552,822)
(553,823)(554,824)(555,825)(556,826)(557,827)(558,828)(559,829)(560,830)
(561,831)(562,832)(563,833)(564,834)(565,835)(566,836)(567,837)(568,838)
(569,839)(570,840)(571,841)(572,842)(573,843)(574,844)(575,845)(576,846)
(577,847)(578,848)(579,849)(580,850)(581,851)(582,852)(583,853)(584,854)
(585,855)(586,856)(587,857)(588,858)(589,859)(590,860)(591,861)(592,862)
(593,863)(594,864)(595,757)(596,758)(597,759)(598,760)(599,761)(600,762)
(601,763)(602,764)(603,765)(604,766)(605,767)(606,768)(607,769)(608,770)
(609,771)(610,772)(611,773)(612,774)(613,775)(614,776)(615,777)(616,778)
(617,779)(618,780)(619,781)(620,782)(621,783)(622,784)(623,785)(624,786)
(625,787)(626,788)(627,789)(628,790)(629,791)(630,792)(631,793)(632,794)
(633,795)(634,796)(635,797)(636,798)(637,799)(638,800)(639,801)(640,802)
(641,803)(642,804)(643,805)(644,806)(645,807)(646,808)(647,809)(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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s0*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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(864)!( 10, 19)( 11, 20)( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)
( 17, 26)( 18, 27)( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)
( 43, 52)( 44, 53)( 45, 54)( 64, 73)( 65, 74)( 66, 75)( 67, 76)( 68, 77)
( 69, 78)( 70, 79)( 71, 80)( 72, 81)( 91,100)( 92,101)( 93,102)( 94,103)
( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(109,136)(110,137)(111,138)
(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,154)(119,155)
(120,156)(121,157)(122,158)(123,159)(124,160)(125,161)(126,162)(127,145)
(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)
(163,190)(164,191)(165,192)(166,193)(167,194)(168,195)(169,196)(170,197)
(171,198)(172,208)(173,209)(174,210)(175,211)(176,212)(177,213)(178,214)
(179,215)(180,216)(181,199)(182,200)(183,201)(184,202)(185,203)(186,204)
(187,205)(188,206)(189,207)(226,235)(227,236)(228,237)(229,238)(230,239)
(231,240)(232,241)(233,242)(234,243)(253,262)(254,263)(255,264)(256,265)
(257,266)(258,267)(259,268)(260,269)(261,270)(280,289)(281,290)(282,291)
(283,292)(284,293)(285,294)(286,295)(287,296)(288,297)(307,316)(308,317)
(309,318)(310,319)(311,320)(312,321)(313,322)(314,323)(315,324)(325,352)
(326,353)(327,354)(328,355)(329,356)(330,357)(331,358)(332,359)(333,360)
(334,370)(335,371)(336,372)(337,373)(338,374)(339,375)(340,376)(341,377)
(342,378)(343,361)(344,362)(345,363)(346,364)(347,365)(348,366)(349,367)
(350,368)(351,369)(379,406)(380,407)(381,408)(382,409)(383,410)(384,411)
(385,412)(386,413)(387,414)(388,424)(389,425)(390,426)(391,427)(392,428)
(393,429)(394,430)(395,431)(396,432)(397,415)(398,416)(399,417)(400,418)
(401,419)(402,420)(403,421)(404,422)(405,423)(433,460)(434,461)(435,462)
(436,463)(437,464)(438,465)(439,466)(440,467)(441,468)(442,478)(443,479)
(444,480)(445,481)(446,482)(447,483)(448,484)(449,485)(450,486)(451,469)
(452,470)(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)
(487,514)(488,515)(489,516)(490,517)(491,518)(492,519)(493,520)(494,521)
(495,522)(496,532)(497,533)(498,534)(499,535)(500,536)(501,537)(502,538)
(503,539)(504,540)(505,523)(506,524)(507,525)(508,526)(509,527)(510,528)
(511,529)(512,530)(513,531)(550,559)(551,560)(552,561)(553,562)(554,563)
(555,564)(556,565)(557,566)(558,567)(577,586)(578,587)(579,588)(580,589)
(581,590)(582,591)(583,592)(584,593)(585,594)(604,613)(605,614)(606,615)
(607,616)(608,617)(609,618)(610,619)(611,620)(612,621)(631,640)(632,641)
(633,642)(634,643)(635,644)(636,645)(637,646)(638,647)(639,648)(649,676)
(650,677)(651,678)(652,679)(653,680)(654,681)(655,682)(656,683)(657,684)
(658,694)(659,695)(660,696)(661,697)(662,698)(663,699)(664,700)(665,701)
(666,702)(667,685)(668,686)(669,687)(670,688)(671,689)(672,690)(673,691)
(674,692)(675,693)(703,730)(704,731)(705,732)(706,733)(707,734)(708,735)
(709,736)(710,737)(711,738)(712,748)(713,749)(714,750)(715,751)(716,752)
(717,753)(718,754)(719,755)(720,756)(721,739)(722,740)(723,741)(724,742)
(725,743)(726,744)(727,745)(728,746)(729,747)(766,775)(767,776)(768,777)
(769,778)(770,779)(771,780)(772,781)(773,782)(774,783)(793,802)(794,803)
(795,804)(796,805)(797,806)(798,807)(799,808)(800,809)(801,810)(820,829)
(821,830)(822,831)(823,832)(824,833)(825,834)(826,835)(827,836)(828,837)
(847,856)(848,857)(849,858)(850,859)(851,860)(852,861)(853,862)(854,863)
(855,864);
s1 := Sym(864)!(  1,442)(  2,444)(  3,443)(  4,450)(  5,449)(  6,448)(  7,447)
(  8,446)(  9,445)( 10,433)( 11,435)( 12,434)( 13,441)( 14,440)( 15,439)
( 16,438)( 17,437)( 18,436)( 19,451)( 20,453)( 21,452)( 22,459)( 23,458)
( 24,457)( 25,456)( 26,455)( 27,454)( 28,469)( 29,471)( 30,470)( 31,477)
( 32,476)( 33,475)( 34,474)( 35,473)( 36,472)( 37,460)( 38,462)( 39,461)
( 40,468)( 41,467)( 42,466)( 43,465)( 44,464)( 45,463)( 46,478)( 47,480)
( 48,479)( 49,486)( 50,485)( 51,484)( 52,483)( 53,482)( 54,481)( 55,496)
( 56,498)( 57,497)( 58,504)( 59,503)( 60,502)( 61,501)( 62,500)( 63,499)
( 64,487)( 65,489)( 66,488)( 67,495)( 68,494)( 69,493)( 70,492)( 71,491)
( 72,490)( 73,505)( 74,507)( 75,506)( 76,513)( 77,512)( 78,511)( 79,510)
( 80,509)( 81,508)( 82,523)( 83,525)( 84,524)( 85,531)( 86,530)( 87,529)
( 88,528)( 89,527)( 90,526)( 91,514)( 92,516)( 93,515)( 94,522)( 95,521)
( 96,520)( 97,519)( 98,518)( 99,517)(100,532)(101,534)(102,533)(103,540)
(104,539)(105,538)(106,537)(107,536)(108,535)(109,550)(110,552)(111,551)
(112,558)(113,557)(114,556)(115,555)(116,554)(117,553)(118,541)(119,543)
(120,542)(121,549)(122,548)(123,547)(124,546)(125,545)(126,544)(127,559)
(128,561)(129,560)(130,567)(131,566)(132,565)(133,564)(134,563)(135,562)
(136,577)(137,579)(138,578)(139,585)(140,584)(141,583)(142,582)(143,581)
(144,580)(145,568)(146,570)(147,569)(148,576)(149,575)(150,574)(151,573)
(152,572)(153,571)(154,586)(155,588)(156,587)(157,594)(158,593)(159,592)
(160,591)(161,590)(162,589)(163,604)(164,606)(165,605)(166,612)(167,611)
(168,610)(169,609)(170,608)(171,607)(172,595)(173,597)(174,596)(175,603)
(176,602)(177,601)(178,600)(179,599)(180,598)(181,613)(182,615)(183,614)
(184,621)(185,620)(186,619)(187,618)(188,617)(189,616)(190,631)(191,633)
(192,632)(193,639)(194,638)(195,637)(196,636)(197,635)(198,634)(199,622)
(200,624)(201,623)(202,630)(203,629)(204,628)(205,627)(206,626)(207,625)
(208,640)(209,642)(210,641)(211,648)(212,647)(213,646)(214,645)(215,644)
(216,643)(217,658)(218,660)(219,659)(220,666)(221,665)(222,664)(223,663)
(224,662)(225,661)(226,649)(227,651)(228,650)(229,657)(230,656)(231,655)
(232,654)(233,653)(234,652)(235,667)(236,669)(237,668)(238,675)(239,674)
(240,673)(241,672)(242,671)(243,670)(244,685)(245,687)(246,686)(247,693)
(248,692)(249,691)(250,690)(251,689)(252,688)(253,676)(254,678)(255,677)
(256,684)(257,683)(258,682)(259,681)(260,680)(261,679)(262,694)(263,696)
(264,695)(265,702)(266,701)(267,700)(268,699)(269,698)(270,697)(271,712)
(272,714)(273,713)(274,720)(275,719)(276,718)(277,717)(278,716)(279,715)
(280,703)(281,705)(282,704)(283,711)(284,710)(285,709)(286,708)(287,707)
(288,706)(289,721)(290,723)(291,722)(292,729)(293,728)(294,727)(295,726)
(296,725)(297,724)(298,739)(299,741)(300,740)(301,747)(302,746)(303,745)
(304,744)(305,743)(306,742)(307,730)(308,732)(309,731)(310,738)(311,737)
(312,736)(313,735)(314,734)(315,733)(316,748)(317,750)(318,749)(319,756)
(320,755)(321,754)(322,753)(323,752)(324,751)(325,766)(326,768)(327,767)
(328,774)(329,773)(330,772)(331,771)(332,770)(333,769)(334,757)(335,759)
(336,758)(337,765)(338,764)(339,763)(340,762)(341,761)(342,760)(343,775)
(344,777)(345,776)(346,783)(347,782)(348,781)(349,780)(350,779)(351,778)
(352,793)(353,795)(354,794)(355,801)(356,800)(357,799)(358,798)(359,797)
(360,796)(361,784)(362,786)(363,785)(364,792)(365,791)(366,790)(367,789)
(368,788)(369,787)(370,802)(371,804)(372,803)(373,810)(374,809)(375,808)
(376,807)(377,806)(378,805)(379,820)(380,822)(381,821)(382,828)(383,827)
(384,826)(385,825)(386,824)(387,823)(388,811)(389,813)(390,812)(391,819)
(392,818)(393,817)(394,816)(395,815)(396,814)(397,829)(398,831)(399,830)
(400,837)(401,836)(402,835)(403,834)(404,833)(405,832)(406,847)(407,849)
(408,848)(409,855)(410,854)(411,853)(412,852)(413,851)(414,850)(415,838)
(416,840)(417,839)(418,846)(419,845)(420,844)(421,843)(422,842)(423,841)
(424,856)(425,858)(426,857)(427,864)(428,863)(429,862)(430,861)(431,860)
(432,859);
s2 := Sym(864)!(  1,544)(  2,546)(  3,545)(  4,541)(  5,543)(  6,542)(  7,549)
(  8,548)(  9,547)( 10,562)( 11,564)( 12,563)( 13,559)( 14,561)( 15,560)
( 16,567)( 17,566)( 18,565)( 19,553)( 20,555)( 21,554)( 22,550)( 23,552)
( 24,551)( 25,558)( 26,557)( 27,556)( 28,571)( 29,573)( 30,572)( 31,568)
( 32,570)( 33,569)( 34,576)( 35,575)( 36,574)( 37,589)( 38,591)( 39,590)
( 40,586)( 41,588)( 42,587)( 43,594)( 44,593)( 45,592)( 46,580)( 47,582)
( 48,581)( 49,577)( 50,579)( 51,578)( 52,585)( 53,584)( 54,583)( 55,598)
( 56,600)( 57,599)( 58,595)( 59,597)( 60,596)( 61,603)( 62,602)( 63,601)
( 64,616)( 65,618)( 66,617)( 67,613)( 68,615)( 69,614)( 70,621)( 71,620)
( 72,619)( 73,607)( 74,609)( 75,608)( 76,604)( 77,606)( 78,605)( 79,612)
( 80,611)( 81,610)( 82,625)( 83,627)( 84,626)( 85,622)( 86,624)( 87,623)
( 88,630)( 89,629)( 90,628)( 91,643)( 92,645)( 93,644)( 94,640)( 95,642)
( 96,641)( 97,648)( 98,647)( 99,646)(100,634)(101,636)(102,635)(103,631)
(104,633)(105,632)(106,639)(107,638)(108,637)(109,436)(110,438)(111,437)
(112,433)(113,435)(114,434)(115,441)(116,440)(117,439)(118,454)(119,456)
(120,455)(121,451)(122,453)(123,452)(124,459)(125,458)(126,457)(127,445)
(128,447)(129,446)(130,442)(131,444)(132,443)(133,450)(134,449)(135,448)
(136,463)(137,465)(138,464)(139,460)(140,462)(141,461)(142,468)(143,467)
(144,466)(145,481)(146,483)(147,482)(148,478)(149,480)(150,479)(151,486)
(152,485)(153,484)(154,472)(155,474)(156,473)(157,469)(158,471)(159,470)
(160,477)(161,476)(162,475)(163,490)(164,492)(165,491)(166,487)(167,489)
(168,488)(169,495)(170,494)(171,493)(172,508)(173,510)(174,509)(175,505)
(176,507)(177,506)(178,513)(179,512)(180,511)(181,499)(182,501)(183,500)
(184,496)(185,498)(186,497)(187,504)(188,503)(189,502)(190,517)(191,519)
(192,518)(193,514)(194,516)(195,515)(196,522)(197,521)(198,520)(199,535)
(200,537)(201,536)(202,532)(203,534)(204,533)(205,540)(206,539)(207,538)
(208,526)(209,528)(210,527)(211,523)(212,525)(213,524)(214,531)(215,530)
(216,529)(217,760)(218,762)(219,761)(220,757)(221,759)(222,758)(223,765)
(224,764)(225,763)(226,778)(227,780)(228,779)(229,775)(230,777)(231,776)
(232,783)(233,782)(234,781)(235,769)(236,771)(237,770)(238,766)(239,768)
(240,767)(241,774)(242,773)(243,772)(244,787)(245,789)(246,788)(247,784)
(248,786)(249,785)(250,792)(251,791)(252,790)(253,805)(254,807)(255,806)
(256,802)(257,804)(258,803)(259,810)(260,809)(261,808)(262,796)(263,798)
(264,797)(265,793)(266,795)(267,794)(268,801)(269,800)(270,799)(271,814)
(272,816)(273,815)(274,811)(275,813)(276,812)(277,819)(278,818)(279,817)
(280,832)(281,834)(282,833)(283,829)(284,831)(285,830)(286,837)(287,836)
(288,835)(289,823)(290,825)(291,824)(292,820)(293,822)(294,821)(295,828)
(296,827)(297,826)(298,841)(299,843)(300,842)(301,838)(302,840)(303,839)
(304,846)(305,845)(306,844)(307,859)(308,861)(309,860)(310,856)(311,858)
(312,857)(313,864)(314,863)(315,862)(316,850)(317,852)(318,851)(319,847)
(320,849)(321,848)(322,855)(323,854)(324,853)(325,652)(326,654)(327,653)
(328,649)(329,651)(330,650)(331,657)(332,656)(333,655)(334,670)(335,672)
(336,671)(337,667)(338,669)(339,668)(340,675)(341,674)(342,673)(343,661)
(344,663)(345,662)(346,658)(347,660)(348,659)(349,666)(350,665)(351,664)
(352,679)(353,681)(354,680)(355,676)(356,678)(357,677)(358,684)(359,683)
(360,682)(361,697)(362,699)(363,698)(364,694)(365,696)(366,695)(367,702)
(368,701)(369,700)(370,688)(371,690)(372,689)(373,685)(374,687)(375,686)
(376,693)(377,692)(378,691)(379,706)(380,708)(381,707)(382,703)(383,705)
(384,704)(385,711)(386,710)(387,709)(388,724)(389,726)(390,725)(391,721)
(392,723)(393,722)(394,729)(395,728)(396,727)(397,715)(398,717)(399,716)
(400,712)(401,714)(402,713)(403,720)(404,719)(405,718)(406,733)(407,735)
(408,734)(409,730)(410,732)(411,731)(412,738)(413,737)(414,736)(415,751)
(416,753)(417,752)(418,748)(419,750)(420,749)(421,756)(422,755)(423,754)
(424,742)(425,744)(426,743)(427,739)(428,741)(429,740)(430,747)(431,746)
(432,745);
s3 := Sym(864)!(  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)
(  8,224)(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)
( 16,232)( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)
( 40,256)( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,379)(110,380)(111,381)
(112,382)(113,383)(114,384)(115,385)(116,386)(117,387)(118,388)(119,389)
(120,390)(121,391)(122,392)(123,393)(124,394)(125,395)(126,396)(127,397)
(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)
(136,406)(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)
(144,414)(145,415)(146,416)(147,417)(148,418)(149,419)(150,420)(151,421)
(152,422)(153,423)(154,424)(155,425)(156,426)(157,427)(158,428)(159,429)
(160,430)(161,431)(162,432)(163,325)(164,326)(165,327)(166,328)(167,329)
(168,330)(169,331)(170,332)(171,333)(172,334)(173,335)(174,336)(175,337)
(176,338)(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,345)
(184,346)(185,347)(186,348)(187,349)(188,350)(189,351)(190,352)(191,353)
(192,354)(193,355)(194,356)(195,357)(196,358)(197,359)(198,360)(199,361)
(200,362)(201,363)(202,364)(203,365)(204,366)(205,367)(206,368)(207,369)
(208,370)(209,371)(210,372)(211,373)(212,374)(213,375)(214,376)(215,377)
(216,378)(433,649)(434,650)(435,651)(436,652)(437,653)(438,654)(439,655)
(440,656)(441,657)(442,658)(443,659)(444,660)(445,661)(446,662)(447,663)
(448,664)(449,665)(450,666)(451,667)(452,668)(453,669)(454,670)(455,671)
(456,672)(457,673)(458,674)(459,675)(460,676)(461,677)(462,678)(463,679)
(464,680)(465,681)(466,682)(467,683)(468,684)(469,685)(470,686)(471,687)
(472,688)(473,689)(474,690)(475,691)(476,692)(477,693)(478,694)(479,695)
(480,696)(481,697)(482,698)(483,699)(484,700)(485,701)(486,702)(487,703)
(488,704)(489,705)(490,706)(491,707)(492,708)(493,709)(494,710)(495,711)
(496,712)(497,713)(498,714)(499,715)(500,716)(501,717)(502,718)(503,719)
(504,720)(505,721)(506,722)(507,723)(508,724)(509,725)(510,726)(511,727)
(512,728)(513,729)(514,730)(515,731)(516,732)(517,733)(518,734)(519,735)
(520,736)(521,737)(522,738)(523,739)(524,740)(525,741)(526,742)(527,743)
(528,744)(529,745)(530,746)(531,747)(532,748)(533,749)(534,750)(535,751)
(536,752)(537,753)(538,754)(539,755)(540,756)(541,811)(542,812)(543,813)
(544,814)(545,815)(546,816)(547,817)(548,818)(549,819)(550,820)(551,821)
(552,822)(553,823)(554,824)(555,825)(556,826)(557,827)(558,828)(559,829)
(560,830)(561,831)(562,832)(563,833)(564,834)(565,835)(566,836)(567,837)
(568,838)(569,839)(570,840)(571,841)(572,842)(573,843)(574,844)(575,845)
(576,846)(577,847)(578,848)(579,849)(580,850)(581,851)(582,852)(583,853)
(584,854)(585,855)(586,856)(587,857)(588,858)(589,859)(590,860)(591,861)
(592,862)(593,863)(594,864)(595,757)(596,758)(597,759)(598,760)(599,761)
(600,762)(601,763)(602,764)(603,765)(604,766)(605,767)(606,768)(607,769)
(608,770)(609,771)(610,772)(611,773)(612,774)(613,775)(614,776)(615,777)
(616,778)(617,779)(618,780)(619,781)(620,782)(621,783)(622,784)(623,785)
(624,786)(625,787)(626,788)(627,789)(628,790)(629,791)(630,792)(631,793)
(632,794)(633,795)(634,796)(635,797)(636,798)(637,799)(638,800)(639,801)
(640,802)(641,803)(642,804)(643,805)(644,806)(645,807)(646,808)(647,809)
(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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s0*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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope