Polytope of Type {16,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,6,3}*1728b
if this polytope has a name.
Group : SmallGroup(1728,31412)
Rank : 4
Schlafli Type : {16,6,3}
Number of vertices, edges, etc : 48, 144, 27, 3
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 6
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 : {8,6,3}*864b
4-fold quotients : {4,6,3}*432b
9-fold quotients : {16,2,3}*192
18-fold quotients : {8,2,3}*96
36-fold quotients : {4,2,3}*48
72-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)( 21, 24)
( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)( 47, 53)
( 48, 51)( 49, 52)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)( 60, 84)
( 61, 85)( 62, 83)( 63, 90)( 64, 91)( 65, 98)( 66, 96)( 67, 97)( 68, 95)
( 69, 93)( 70, 94)( 71, 92)( 72, 99)( 73,100)( 74,107)( 75,105)( 76,106)
( 77,104)( 78,102)( 79,103)( 80,101)( 81,108)(109,163)(110,170)(111,168)
(112,169)(113,167)(114,165)(115,166)(116,164)(117,171)(118,172)(119,179)
(120,177)(121,178)(122,176)(123,174)(124,175)(125,173)(126,180)(127,181)
(128,188)(129,186)(130,187)(131,185)(132,183)(133,184)(134,182)(135,189)
(136,190)(137,197)(138,195)(139,196)(140,194)(141,192)(142,193)(143,191)
(144,198)(145,199)(146,206)(147,204)(148,205)(149,203)(150,201)(151,202)
(152,200)(153,207)(154,208)(155,215)(156,213)(157,214)(158,212)(159,210)
(160,211)(161,209)(162,216)(217,298)(218,305)(219,303)(220,304)(221,302)
(222,300)(223,301)(224,299)(225,306)(226,307)(227,314)(228,312)(229,313)
(230,311)(231,309)(232,310)(233,308)(234,315)(235,316)(236,323)(237,321)
(238,322)(239,320)(240,318)(241,319)(242,317)(243,324)(244,271)(245,278)
(246,276)(247,277)(248,275)(249,273)(250,274)(251,272)(252,279)(253,280)
(254,287)(255,285)(256,286)(257,284)(258,282)(259,283)(260,281)(261,288)
(262,289)(263,296)(264,294)(265,295)(266,293)(267,291)(268,292)(269,290)
(270,297)(326,332)(327,330)(328,331)(335,341)(336,339)(337,340)(344,350)
(345,348)(346,349)(353,359)(354,357)(355,358)(362,368)(363,366)(364,367)
(371,377)(372,375)(373,376)(379,406)(380,413)(381,411)(382,412)(383,410)
(384,408)(385,409)(386,407)(387,414)(388,415)(389,422)(390,420)(391,421)
(392,419)(393,417)(394,418)(395,416)(396,423)(397,424)(398,431)(399,429)
(400,430)(401,428)(402,426)(403,427)(404,425)(405,432)(433,541)(434,548)
(435,546)(436,547)(437,545)(438,543)(439,544)(440,542)(441,549)(442,550)
(443,557)(444,555)(445,556)(446,554)(447,552)(448,553)(449,551)(450,558)
(451,559)(452,566)(453,564)(454,565)(455,563)(456,561)(457,562)(458,560)
(459,567)(460,568)(461,575)(462,573)(463,574)(464,572)(465,570)(466,571)
(467,569)(468,576)(469,577)(470,584)(471,582)(472,583)(473,581)(474,579)
(475,580)(476,578)(477,585)(478,586)(479,593)(480,591)(481,592)(482,590)
(483,588)(484,589)(485,587)(486,594)(487,622)(488,629)(489,627)(490,628)
(491,626)(492,624)(493,625)(494,623)(495,630)(496,631)(497,638)(498,636)
(499,637)(500,635)(501,633)(502,634)(503,632)(504,639)(505,640)(506,647)
(507,645)(508,646)(509,644)(510,642)(511,643)(512,641)(513,648)(514,595)
(515,602)(516,600)(517,601)(518,599)(519,597)(520,598)(521,596)(522,603)
(523,604)(524,611)(525,609)(526,610)(527,608)(528,606)(529,607)(530,605)
(531,612)(532,613)(533,620)(534,618)(535,619)(536,617)(537,615)(538,616)
(539,614)(540,621)(649,838)(650,845)(651,843)(652,844)(653,842)(654,840)
(655,841)(656,839)(657,846)(658,847)(659,854)(660,852)(661,853)(662,851)
(663,849)(664,850)(665,848)(666,855)(667,856)(668,863)(669,861)(670,862)
(671,860)(672,858)(673,859)(674,857)(675,864)(676,811)(677,818)(678,816)
(679,817)(680,815)(681,813)(682,814)(683,812)(684,819)(685,820)(686,827)
(687,825)(688,826)(689,824)(690,822)(691,823)(692,821)(693,828)(694,829)
(695,836)(696,834)(697,835)(698,833)(699,831)(700,832)(701,830)(702,837)
(703,784)(704,791)(705,789)(706,790)(707,788)(708,786)(709,787)(710,785)
(711,792)(712,793)(713,800)(714,798)(715,799)(716,797)(717,795)(718,796)
(719,794)(720,801)(721,802)(722,809)(723,807)(724,808)(725,806)(726,804)
(727,805)(728,803)(729,810)(730,757)(731,764)(732,762)(733,763)(734,761)
(735,759)(736,760)(737,758)(738,765)(739,766)(740,773)(741,771)(742,772)
(743,770)(744,768)(745,769)(746,767)(747,774)(748,775)(749,782)(750,780)
(751,781)(752,779)(753,777)(754,778)(755,776)(756,783);;
s1 := ( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)( 8,438)
( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)( 16,446)
( 17,447)( 18,445)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)( 24,458)
( 25,455)( 26,456)( 27,454)( 28,460)( 29,461)( 30,462)( 31,468)( 32,466)
( 33,467)( 34,464)( 35,465)( 36,463)( 37,469)( 38,470)( 39,471)( 40,477)
( 41,475)( 42,476)( 43,473)( 44,474)( 45,472)( 46,478)( 47,479)( 48,480)
( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,514)( 56,515)
( 57,516)( 58,522)( 59,520)( 60,521)( 61,518)( 62,519)( 63,517)( 64,523)
( 65,524)( 66,525)( 67,531)( 68,529)( 69,530)( 70,527)( 71,528)( 72,526)
( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)( 80,537)
( 81,535)( 82,487)( 83,488)( 84,489)( 85,495)( 86,493)( 87,494)( 88,491)
( 89,492)( 90,490)( 91,496)( 92,497)( 93,498)( 94,504)( 95,502)( 96,503)
( 97,500)( 98,501)( 99,499)(100,505)(101,506)(102,507)(103,513)(104,511)
(105,512)(106,509)(107,510)(108,508)(109,595)(110,596)(111,597)(112,603)
(113,601)(114,602)(115,599)(116,600)(117,598)(118,604)(119,605)(120,606)
(121,612)(122,610)(123,611)(124,608)(125,609)(126,607)(127,613)(128,614)
(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)(136,622)
(137,623)(138,624)(139,630)(140,628)(141,629)(142,626)(143,627)(144,625)
(145,631)(146,632)(147,633)(148,639)(149,637)(150,638)(151,635)(152,636)
(153,634)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)
(161,645)(162,643)(163,541)(164,542)(165,543)(166,549)(167,547)(168,548)
(169,545)(170,546)(171,544)(172,550)(173,551)(174,552)(175,558)(176,556)
(177,557)(178,554)(179,555)(180,553)(181,559)(182,560)(183,561)(184,567)
(185,565)(186,566)(187,563)(188,564)(189,562)(190,568)(191,569)(192,570)
(193,576)(194,574)(195,575)(196,572)(197,573)(198,571)(199,577)(200,578)
(201,579)(202,585)(203,583)(204,584)(205,581)(206,582)(207,580)(208,586)
(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)(216,589)
(217,730)(218,731)(219,732)(220,738)(221,736)(222,737)(223,734)(224,735)
(225,733)(226,739)(227,740)(228,741)(229,747)(230,745)(231,746)(232,743)
(233,744)(234,742)(235,748)(236,749)(237,750)(238,756)(239,754)(240,755)
(241,752)(242,753)(243,751)(244,703)(245,704)(246,705)(247,711)(248,709)
(249,710)(250,707)(251,708)(252,706)(253,712)(254,713)(255,714)(256,720)
(257,718)(258,719)(259,716)(260,717)(261,715)(262,721)(263,722)(264,723)
(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,676)(272,677)
(273,678)(274,684)(275,682)(276,683)(277,680)(278,681)(279,679)(280,685)
(281,686)(282,687)(283,693)(284,691)(285,692)(286,689)(287,690)(288,688)
(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)(296,699)
(297,697)(298,649)(299,650)(300,651)(301,657)(302,655)(303,656)(304,653)
(305,654)(306,652)(307,658)(308,659)(309,660)(310,666)(311,664)(312,665)
(313,662)(314,663)(315,661)(316,667)(317,668)(318,669)(319,675)(320,673)
(321,674)(322,671)(323,672)(324,670)(325,757)(326,758)(327,759)(328,765)
(329,763)(330,764)(331,761)(332,762)(333,760)(334,766)(335,767)(336,768)
(337,774)(338,772)(339,773)(340,770)(341,771)(342,769)(343,775)(344,776)
(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)(352,784)
(353,785)(354,786)(355,792)(356,790)(357,791)(358,788)(359,789)(360,787)
(361,793)(362,794)(363,795)(364,801)(365,799)(366,800)(367,797)(368,798)
(369,796)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)(376,806)
(377,807)(378,805)(379,838)(380,839)(381,840)(382,846)(383,844)(384,845)
(385,842)(386,843)(387,841)(388,847)(389,848)(390,849)(391,855)(392,853)
(393,854)(394,851)(395,852)(396,850)(397,856)(398,857)(399,858)(400,864)
(401,862)(402,863)(403,860)(404,861)(405,859)(406,811)(407,812)(408,813)
(409,819)(410,817)(411,818)(412,815)(413,816)(414,814)(415,820)(416,821)
(417,822)(418,828)(419,826)(420,827)(421,824)(422,825)(423,823)(424,829)
(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)(432,832);;
s2 := ( 1,329)( 2,328)( 3,330)( 4,326)( 5,325)( 6,327)( 7,332)( 8,331)
( 9,333)( 10,347)( 11,346)( 12,348)( 13,344)( 14,343)( 15,345)( 16,350)
( 17,349)( 18,351)( 19,338)( 20,337)( 21,339)( 22,335)( 23,334)( 24,336)
( 25,341)( 26,340)( 27,342)( 28,356)( 29,355)( 30,357)( 31,353)( 32,352)
( 33,354)( 34,359)( 35,358)( 36,360)( 37,374)( 38,373)( 39,375)( 40,371)
( 41,370)( 42,372)( 43,377)( 44,376)( 45,378)( 46,365)( 47,364)( 48,366)
( 49,362)( 50,361)( 51,363)( 52,368)( 53,367)( 54,369)( 55,383)( 56,382)
( 57,384)( 58,380)( 59,379)( 60,381)( 61,386)( 62,385)( 63,387)( 64,401)
( 65,400)( 66,402)( 67,398)( 68,397)( 69,399)( 70,404)( 71,403)( 72,405)
( 73,392)( 74,391)( 75,393)( 76,389)( 77,388)( 78,390)( 79,395)( 80,394)
( 81,396)( 82,410)( 83,409)( 84,411)( 85,407)( 86,406)( 87,408)( 88,413)
( 89,412)( 90,414)( 91,428)( 92,427)( 93,429)( 94,425)( 95,424)( 96,426)
( 97,431)( 98,430)( 99,432)(100,419)(101,418)(102,420)(103,416)(104,415)
(105,417)(106,422)(107,421)(108,423)(109,302)(110,301)(111,303)(112,299)
(113,298)(114,300)(115,305)(116,304)(117,306)(118,320)(119,319)(120,321)
(121,317)(122,316)(123,318)(124,323)(125,322)(126,324)(127,311)(128,310)
(129,312)(130,308)(131,307)(132,309)(133,314)(134,313)(135,315)(136,275)
(137,274)(138,276)(139,272)(140,271)(141,273)(142,278)(143,277)(144,279)
(145,293)(146,292)(147,294)(148,290)(149,289)(150,291)(151,296)(152,295)
(153,297)(154,284)(155,283)(156,285)(157,281)(158,280)(159,282)(160,287)
(161,286)(162,288)(163,221)(164,220)(165,222)(166,218)(167,217)(168,219)
(169,224)(170,223)(171,225)(172,239)(173,238)(174,240)(175,236)(176,235)
(177,237)(178,242)(179,241)(180,243)(181,230)(182,229)(183,231)(184,227)
(185,226)(186,228)(187,233)(188,232)(189,234)(190,248)(191,247)(192,249)
(193,245)(194,244)(195,246)(196,251)(197,250)(198,252)(199,266)(200,265)
(201,267)(202,263)(203,262)(204,264)(205,269)(206,268)(207,270)(208,257)
(209,256)(210,258)(211,254)(212,253)(213,255)(214,260)(215,259)(216,261)
(433,761)(434,760)(435,762)(436,758)(437,757)(438,759)(439,764)(440,763)
(441,765)(442,779)(443,778)(444,780)(445,776)(446,775)(447,777)(448,782)
(449,781)(450,783)(451,770)(452,769)(453,771)(454,767)(455,766)(456,768)
(457,773)(458,772)(459,774)(460,788)(461,787)(462,789)(463,785)(464,784)
(465,786)(466,791)(467,790)(468,792)(469,806)(470,805)(471,807)(472,803)
(473,802)(474,804)(475,809)(476,808)(477,810)(478,797)(479,796)(480,798)
(481,794)(482,793)(483,795)(484,800)(485,799)(486,801)(487,815)(488,814)
(489,816)(490,812)(491,811)(492,813)(493,818)(494,817)(495,819)(496,833)
(497,832)(498,834)(499,830)(500,829)(501,831)(502,836)(503,835)(504,837)
(505,824)(506,823)(507,825)(508,821)(509,820)(510,822)(511,827)(512,826)
(513,828)(514,842)(515,841)(516,843)(517,839)(518,838)(519,840)(520,845)
(521,844)(522,846)(523,860)(524,859)(525,861)(526,857)(527,856)(528,858)
(529,863)(530,862)(531,864)(532,851)(533,850)(534,852)(535,848)(536,847)
(537,849)(538,854)(539,853)(540,855)(541,734)(542,733)(543,735)(544,731)
(545,730)(546,732)(547,737)(548,736)(549,738)(550,752)(551,751)(552,753)
(553,749)(554,748)(555,750)(556,755)(557,754)(558,756)(559,743)(560,742)
(561,744)(562,740)(563,739)(564,741)(565,746)(566,745)(567,747)(568,707)
(569,706)(570,708)(571,704)(572,703)(573,705)(574,710)(575,709)(576,711)
(577,725)(578,724)(579,726)(580,722)(581,721)(582,723)(583,728)(584,727)
(585,729)(586,716)(587,715)(588,717)(589,713)(590,712)(591,714)(592,719)
(593,718)(594,720)(595,653)(596,652)(597,654)(598,650)(599,649)(600,651)
(601,656)(602,655)(603,657)(604,671)(605,670)(606,672)(607,668)(608,667)
(609,669)(610,674)(611,673)(612,675)(613,662)(614,661)(615,663)(616,659)
(617,658)(618,660)(619,665)(620,664)(621,666)(622,680)(623,679)(624,681)
(625,677)(626,676)(627,678)(628,683)(629,682)(630,684)(631,698)(632,697)
(633,699)(634,695)(635,694)(636,696)(637,701)(638,700)(639,702)(640,689)
(641,688)(642,690)(643,686)(644,685)(645,687)(646,692)(647,691)(648,693);;
s3 := ( 1,334)( 2,336)( 3,335)( 4,340)( 5,342)( 6,341)( 7,337)( 8,339)
( 9,338)( 10,325)( 11,327)( 12,326)( 13,331)( 14,333)( 15,332)( 16,328)
( 17,330)( 18,329)( 19,343)( 20,345)( 21,344)( 22,349)( 23,351)( 24,350)
( 25,346)( 26,348)( 27,347)( 28,361)( 29,363)( 30,362)( 31,367)( 32,369)
( 33,368)( 34,364)( 35,366)( 36,365)( 37,352)( 38,354)( 39,353)( 40,358)
( 41,360)( 42,359)( 43,355)( 44,357)( 45,356)( 46,370)( 47,372)( 48,371)
( 49,376)( 50,378)( 51,377)( 52,373)( 53,375)( 54,374)( 55,388)( 56,390)
( 57,389)( 58,394)( 59,396)( 60,395)( 61,391)( 62,393)( 63,392)( 64,379)
( 65,381)( 66,380)( 67,385)( 68,387)( 69,386)( 70,382)( 71,384)( 72,383)
( 73,397)( 74,399)( 75,398)( 76,403)( 77,405)( 78,404)( 79,400)( 80,402)
( 81,401)( 82,415)( 83,417)( 84,416)( 85,421)( 86,423)( 87,422)( 88,418)
( 89,420)( 90,419)( 91,406)( 92,408)( 93,407)( 94,412)( 95,414)( 96,413)
( 97,409)( 98,411)( 99,410)(100,424)(101,426)(102,425)(103,430)(104,432)
(105,431)(106,427)(107,429)(108,428)(109,307)(110,309)(111,308)(112,313)
(113,315)(114,314)(115,310)(116,312)(117,311)(118,298)(119,300)(120,299)
(121,304)(122,306)(123,305)(124,301)(125,303)(126,302)(127,316)(128,318)
(129,317)(130,322)(131,324)(132,323)(133,319)(134,321)(135,320)(136,280)
(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)(144,284)
(145,271)(146,273)(147,272)(148,277)(149,279)(150,278)(151,274)(152,276)
(153,275)(154,289)(155,291)(156,290)(157,295)(158,297)(159,296)(160,292)
(161,294)(162,293)(163,226)(164,228)(165,227)(166,232)(167,234)(168,233)
(169,229)(170,231)(171,230)(172,217)(173,219)(174,218)(175,223)(176,225)
(177,224)(178,220)(179,222)(180,221)(181,235)(182,237)(183,236)(184,241)
(185,243)(186,242)(187,238)(188,240)(189,239)(190,253)(191,255)(192,254)
(193,259)(194,261)(195,260)(196,256)(197,258)(198,257)(199,244)(200,246)
(201,245)(202,250)(203,252)(204,251)(205,247)(206,249)(207,248)(208,262)
(209,264)(210,263)(211,268)(212,270)(213,269)(214,265)(215,267)(216,266)
(433,766)(434,768)(435,767)(436,772)(437,774)(438,773)(439,769)(440,771)
(441,770)(442,757)(443,759)(444,758)(445,763)(446,765)(447,764)(448,760)
(449,762)(450,761)(451,775)(452,777)(453,776)(454,781)(455,783)(456,782)
(457,778)(458,780)(459,779)(460,793)(461,795)(462,794)(463,799)(464,801)
(465,800)(466,796)(467,798)(468,797)(469,784)(470,786)(471,785)(472,790)
(473,792)(474,791)(475,787)(476,789)(477,788)(478,802)(479,804)(480,803)
(481,808)(482,810)(483,809)(484,805)(485,807)(486,806)(487,820)(488,822)
(489,821)(490,826)(491,828)(492,827)(493,823)(494,825)(495,824)(496,811)
(497,813)(498,812)(499,817)(500,819)(501,818)(502,814)(503,816)(504,815)
(505,829)(506,831)(507,830)(508,835)(509,837)(510,836)(511,832)(512,834)
(513,833)(514,847)(515,849)(516,848)(517,853)(518,855)(519,854)(520,850)
(521,852)(522,851)(523,838)(524,840)(525,839)(526,844)(527,846)(528,845)
(529,841)(530,843)(531,842)(532,856)(533,858)(534,857)(535,862)(536,864)
(537,863)(538,859)(539,861)(540,860)(541,739)(542,741)(543,740)(544,745)
(545,747)(546,746)(547,742)(548,744)(549,743)(550,730)(551,732)(552,731)
(553,736)(554,738)(555,737)(556,733)(557,735)(558,734)(559,748)(560,750)
(561,749)(562,754)(563,756)(564,755)(565,751)(566,753)(567,752)(568,712)
(569,714)(570,713)(571,718)(572,720)(573,719)(574,715)(575,717)(576,716)
(577,703)(578,705)(579,704)(580,709)(581,711)(582,710)(583,706)(584,708)
(585,707)(586,721)(587,723)(588,722)(589,727)(590,729)(591,728)(592,724)
(593,726)(594,725)(595,658)(596,660)(597,659)(598,664)(599,666)(600,665)
(601,661)(602,663)(603,662)(604,649)(605,651)(606,650)(607,655)(608,657)
(609,656)(610,652)(611,654)(612,653)(613,667)(614,669)(615,668)(616,673)
(617,675)(618,674)(619,670)(620,672)(621,671)(622,685)(623,687)(624,686)
(625,691)(626,693)(627,692)(628,688)(629,690)(630,689)(631,676)(632,678)
(633,677)(634,682)(635,684)(636,683)(637,679)(638,681)(639,680)(640,694)
(641,696)(642,695)(643,700)(644,702)(645,701)(646,697)(647,699)(648,698);;
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, s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)
( 21, 24)( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)
( 47, 53)( 48, 51)( 49, 52)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)
( 60, 84)( 61, 85)( 62, 83)( 63, 90)( 64, 91)( 65, 98)( 66, 96)( 67, 97)
( 68, 95)( 69, 93)( 70, 94)( 71, 92)( 72, 99)( 73,100)( 74,107)( 75,105)
( 76,106)( 77,104)( 78,102)( 79,103)( 80,101)( 81,108)(109,163)(110,170)
(111,168)(112,169)(113,167)(114,165)(115,166)(116,164)(117,171)(118,172)
(119,179)(120,177)(121,178)(122,176)(123,174)(124,175)(125,173)(126,180)
(127,181)(128,188)(129,186)(130,187)(131,185)(132,183)(133,184)(134,182)
(135,189)(136,190)(137,197)(138,195)(139,196)(140,194)(141,192)(142,193)
(143,191)(144,198)(145,199)(146,206)(147,204)(148,205)(149,203)(150,201)
(151,202)(152,200)(153,207)(154,208)(155,215)(156,213)(157,214)(158,212)
(159,210)(160,211)(161,209)(162,216)(217,298)(218,305)(219,303)(220,304)
(221,302)(222,300)(223,301)(224,299)(225,306)(226,307)(227,314)(228,312)
(229,313)(230,311)(231,309)(232,310)(233,308)(234,315)(235,316)(236,323)
(237,321)(238,322)(239,320)(240,318)(241,319)(242,317)(243,324)(244,271)
(245,278)(246,276)(247,277)(248,275)(249,273)(250,274)(251,272)(252,279)
(253,280)(254,287)(255,285)(256,286)(257,284)(258,282)(259,283)(260,281)
(261,288)(262,289)(263,296)(264,294)(265,295)(266,293)(267,291)(268,292)
(269,290)(270,297)(326,332)(327,330)(328,331)(335,341)(336,339)(337,340)
(344,350)(345,348)(346,349)(353,359)(354,357)(355,358)(362,368)(363,366)
(364,367)(371,377)(372,375)(373,376)(379,406)(380,413)(381,411)(382,412)
(383,410)(384,408)(385,409)(386,407)(387,414)(388,415)(389,422)(390,420)
(391,421)(392,419)(393,417)(394,418)(395,416)(396,423)(397,424)(398,431)
(399,429)(400,430)(401,428)(402,426)(403,427)(404,425)(405,432)(433,541)
(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)(440,542)(441,549)
(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)(448,553)(449,551)
(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)(456,561)(457,562)
(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)(464,572)(465,570)
(466,571)(467,569)(468,576)(469,577)(470,584)(471,582)(472,583)(473,581)
(474,579)(475,580)(476,578)(477,585)(478,586)(479,593)(480,591)(481,592)
(482,590)(483,588)(484,589)(485,587)(486,594)(487,622)(488,629)(489,627)
(490,628)(491,626)(492,624)(493,625)(494,623)(495,630)(496,631)(497,638)
(498,636)(499,637)(500,635)(501,633)(502,634)(503,632)(504,639)(505,640)
(506,647)(507,645)(508,646)(509,644)(510,642)(511,643)(512,641)(513,648)
(514,595)(515,602)(516,600)(517,601)(518,599)(519,597)(520,598)(521,596)
(522,603)(523,604)(524,611)(525,609)(526,610)(527,608)(528,606)(529,607)
(530,605)(531,612)(532,613)(533,620)(534,618)(535,619)(536,617)(537,615)
(538,616)(539,614)(540,621)(649,838)(650,845)(651,843)(652,844)(653,842)
(654,840)(655,841)(656,839)(657,846)(658,847)(659,854)(660,852)(661,853)
(662,851)(663,849)(664,850)(665,848)(666,855)(667,856)(668,863)(669,861)
(670,862)(671,860)(672,858)(673,859)(674,857)(675,864)(676,811)(677,818)
(678,816)(679,817)(680,815)(681,813)(682,814)(683,812)(684,819)(685,820)
(686,827)(687,825)(688,826)(689,824)(690,822)(691,823)(692,821)(693,828)
(694,829)(695,836)(696,834)(697,835)(698,833)(699,831)(700,832)(701,830)
(702,837)(703,784)(704,791)(705,789)(706,790)(707,788)(708,786)(709,787)
(710,785)(711,792)(712,793)(713,800)(714,798)(715,799)(716,797)(717,795)
(718,796)(719,794)(720,801)(721,802)(722,809)(723,807)(724,808)(725,806)
(726,804)(727,805)(728,803)(729,810)(730,757)(731,764)(732,762)(733,763)
(734,761)(735,759)(736,760)(737,758)(738,765)(739,766)(740,773)(741,771)
(742,772)(743,770)(744,768)(745,769)(746,767)(747,774)(748,775)(749,782)
(750,780)(751,781)(752,779)(753,777)(754,778)(755,776)(756,783);
s1 := Sym(864)!( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)
( 8,438)( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)
( 16,446)( 17,447)( 18,445)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)
( 24,458)( 25,455)( 26,456)( 27,454)( 28,460)( 29,461)( 30,462)( 31,468)
( 32,466)( 33,467)( 34,464)( 35,465)( 36,463)( 37,469)( 38,470)( 39,471)
( 40,477)( 41,475)( 42,476)( 43,473)( 44,474)( 45,472)( 46,478)( 47,479)
( 48,480)( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,514)
( 56,515)( 57,516)( 58,522)( 59,520)( 60,521)( 61,518)( 62,519)( 63,517)
( 64,523)( 65,524)( 66,525)( 67,531)( 68,529)( 69,530)( 70,527)( 71,528)
( 72,526)( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)
( 80,537)( 81,535)( 82,487)( 83,488)( 84,489)( 85,495)( 86,493)( 87,494)
( 88,491)( 89,492)( 90,490)( 91,496)( 92,497)( 93,498)( 94,504)( 95,502)
( 96,503)( 97,500)( 98,501)( 99,499)(100,505)(101,506)(102,507)(103,513)
(104,511)(105,512)(106,509)(107,510)(108,508)(109,595)(110,596)(111,597)
(112,603)(113,601)(114,602)(115,599)(116,600)(117,598)(118,604)(119,605)
(120,606)(121,612)(122,610)(123,611)(124,608)(125,609)(126,607)(127,613)
(128,614)(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)
(136,622)(137,623)(138,624)(139,630)(140,628)(141,629)(142,626)(143,627)
(144,625)(145,631)(146,632)(147,633)(148,639)(149,637)(150,638)(151,635)
(152,636)(153,634)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)
(160,644)(161,645)(162,643)(163,541)(164,542)(165,543)(166,549)(167,547)
(168,548)(169,545)(170,546)(171,544)(172,550)(173,551)(174,552)(175,558)
(176,556)(177,557)(178,554)(179,555)(180,553)(181,559)(182,560)(183,561)
(184,567)(185,565)(186,566)(187,563)(188,564)(189,562)(190,568)(191,569)
(192,570)(193,576)(194,574)(195,575)(196,572)(197,573)(198,571)(199,577)
(200,578)(201,579)(202,585)(203,583)(204,584)(205,581)(206,582)(207,580)
(208,586)(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)
(216,589)(217,730)(218,731)(219,732)(220,738)(221,736)(222,737)(223,734)
(224,735)(225,733)(226,739)(227,740)(228,741)(229,747)(230,745)(231,746)
(232,743)(233,744)(234,742)(235,748)(236,749)(237,750)(238,756)(239,754)
(240,755)(241,752)(242,753)(243,751)(244,703)(245,704)(246,705)(247,711)
(248,709)(249,710)(250,707)(251,708)(252,706)(253,712)(254,713)(255,714)
(256,720)(257,718)(258,719)(259,716)(260,717)(261,715)(262,721)(263,722)
(264,723)(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,676)
(272,677)(273,678)(274,684)(275,682)(276,683)(277,680)(278,681)(279,679)
(280,685)(281,686)(282,687)(283,693)(284,691)(285,692)(286,689)(287,690)
(288,688)(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)
(296,699)(297,697)(298,649)(299,650)(300,651)(301,657)(302,655)(303,656)
(304,653)(305,654)(306,652)(307,658)(308,659)(309,660)(310,666)(311,664)
(312,665)(313,662)(314,663)(315,661)(316,667)(317,668)(318,669)(319,675)
(320,673)(321,674)(322,671)(323,672)(324,670)(325,757)(326,758)(327,759)
(328,765)(329,763)(330,764)(331,761)(332,762)(333,760)(334,766)(335,767)
(336,768)(337,774)(338,772)(339,773)(340,770)(341,771)(342,769)(343,775)
(344,776)(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)
(352,784)(353,785)(354,786)(355,792)(356,790)(357,791)(358,788)(359,789)
(360,787)(361,793)(362,794)(363,795)(364,801)(365,799)(366,800)(367,797)
(368,798)(369,796)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)
(376,806)(377,807)(378,805)(379,838)(380,839)(381,840)(382,846)(383,844)
(384,845)(385,842)(386,843)(387,841)(388,847)(389,848)(390,849)(391,855)
(392,853)(393,854)(394,851)(395,852)(396,850)(397,856)(398,857)(399,858)
(400,864)(401,862)(402,863)(403,860)(404,861)(405,859)(406,811)(407,812)
(408,813)(409,819)(410,817)(411,818)(412,815)(413,816)(414,814)(415,820)
(416,821)(417,822)(418,828)(419,826)(420,827)(421,824)(422,825)(423,823)
(424,829)(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)
(432,832);
s2 := Sym(864)!( 1,329)( 2,328)( 3,330)( 4,326)( 5,325)( 6,327)( 7,332)
( 8,331)( 9,333)( 10,347)( 11,346)( 12,348)( 13,344)( 14,343)( 15,345)
( 16,350)( 17,349)( 18,351)( 19,338)( 20,337)( 21,339)( 22,335)( 23,334)
( 24,336)( 25,341)( 26,340)( 27,342)( 28,356)( 29,355)( 30,357)( 31,353)
( 32,352)( 33,354)( 34,359)( 35,358)( 36,360)( 37,374)( 38,373)( 39,375)
( 40,371)( 41,370)( 42,372)( 43,377)( 44,376)( 45,378)( 46,365)( 47,364)
( 48,366)( 49,362)( 50,361)( 51,363)( 52,368)( 53,367)( 54,369)( 55,383)
( 56,382)( 57,384)( 58,380)( 59,379)( 60,381)( 61,386)( 62,385)( 63,387)
( 64,401)( 65,400)( 66,402)( 67,398)( 68,397)( 69,399)( 70,404)( 71,403)
( 72,405)( 73,392)( 74,391)( 75,393)( 76,389)( 77,388)( 78,390)( 79,395)
( 80,394)( 81,396)( 82,410)( 83,409)( 84,411)( 85,407)( 86,406)( 87,408)
( 88,413)( 89,412)( 90,414)( 91,428)( 92,427)( 93,429)( 94,425)( 95,424)
( 96,426)( 97,431)( 98,430)( 99,432)(100,419)(101,418)(102,420)(103,416)
(104,415)(105,417)(106,422)(107,421)(108,423)(109,302)(110,301)(111,303)
(112,299)(113,298)(114,300)(115,305)(116,304)(117,306)(118,320)(119,319)
(120,321)(121,317)(122,316)(123,318)(124,323)(125,322)(126,324)(127,311)
(128,310)(129,312)(130,308)(131,307)(132,309)(133,314)(134,313)(135,315)
(136,275)(137,274)(138,276)(139,272)(140,271)(141,273)(142,278)(143,277)
(144,279)(145,293)(146,292)(147,294)(148,290)(149,289)(150,291)(151,296)
(152,295)(153,297)(154,284)(155,283)(156,285)(157,281)(158,280)(159,282)
(160,287)(161,286)(162,288)(163,221)(164,220)(165,222)(166,218)(167,217)
(168,219)(169,224)(170,223)(171,225)(172,239)(173,238)(174,240)(175,236)
(176,235)(177,237)(178,242)(179,241)(180,243)(181,230)(182,229)(183,231)
(184,227)(185,226)(186,228)(187,233)(188,232)(189,234)(190,248)(191,247)
(192,249)(193,245)(194,244)(195,246)(196,251)(197,250)(198,252)(199,266)
(200,265)(201,267)(202,263)(203,262)(204,264)(205,269)(206,268)(207,270)
(208,257)(209,256)(210,258)(211,254)(212,253)(213,255)(214,260)(215,259)
(216,261)(433,761)(434,760)(435,762)(436,758)(437,757)(438,759)(439,764)
(440,763)(441,765)(442,779)(443,778)(444,780)(445,776)(446,775)(447,777)
(448,782)(449,781)(450,783)(451,770)(452,769)(453,771)(454,767)(455,766)
(456,768)(457,773)(458,772)(459,774)(460,788)(461,787)(462,789)(463,785)
(464,784)(465,786)(466,791)(467,790)(468,792)(469,806)(470,805)(471,807)
(472,803)(473,802)(474,804)(475,809)(476,808)(477,810)(478,797)(479,796)
(480,798)(481,794)(482,793)(483,795)(484,800)(485,799)(486,801)(487,815)
(488,814)(489,816)(490,812)(491,811)(492,813)(493,818)(494,817)(495,819)
(496,833)(497,832)(498,834)(499,830)(500,829)(501,831)(502,836)(503,835)
(504,837)(505,824)(506,823)(507,825)(508,821)(509,820)(510,822)(511,827)
(512,826)(513,828)(514,842)(515,841)(516,843)(517,839)(518,838)(519,840)
(520,845)(521,844)(522,846)(523,860)(524,859)(525,861)(526,857)(527,856)
(528,858)(529,863)(530,862)(531,864)(532,851)(533,850)(534,852)(535,848)
(536,847)(537,849)(538,854)(539,853)(540,855)(541,734)(542,733)(543,735)
(544,731)(545,730)(546,732)(547,737)(548,736)(549,738)(550,752)(551,751)
(552,753)(553,749)(554,748)(555,750)(556,755)(557,754)(558,756)(559,743)
(560,742)(561,744)(562,740)(563,739)(564,741)(565,746)(566,745)(567,747)
(568,707)(569,706)(570,708)(571,704)(572,703)(573,705)(574,710)(575,709)
(576,711)(577,725)(578,724)(579,726)(580,722)(581,721)(582,723)(583,728)
(584,727)(585,729)(586,716)(587,715)(588,717)(589,713)(590,712)(591,714)
(592,719)(593,718)(594,720)(595,653)(596,652)(597,654)(598,650)(599,649)
(600,651)(601,656)(602,655)(603,657)(604,671)(605,670)(606,672)(607,668)
(608,667)(609,669)(610,674)(611,673)(612,675)(613,662)(614,661)(615,663)
(616,659)(617,658)(618,660)(619,665)(620,664)(621,666)(622,680)(623,679)
(624,681)(625,677)(626,676)(627,678)(628,683)(629,682)(630,684)(631,698)
(632,697)(633,699)(634,695)(635,694)(636,696)(637,701)(638,700)(639,702)
(640,689)(641,688)(642,690)(643,686)(644,685)(645,687)(646,692)(647,691)
(648,693);
s3 := Sym(864)!( 1,334)( 2,336)( 3,335)( 4,340)( 5,342)( 6,341)( 7,337)
( 8,339)( 9,338)( 10,325)( 11,327)( 12,326)( 13,331)( 14,333)( 15,332)
( 16,328)( 17,330)( 18,329)( 19,343)( 20,345)( 21,344)( 22,349)( 23,351)
( 24,350)( 25,346)( 26,348)( 27,347)( 28,361)( 29,363)( 30,362)( 31,367)
( 32,369)( 33,368)( 34,364)( 35,366)( 36,365)( 37,352)( 38,354)( 39,353)
( 40,358)( 41,360)( 42,359)( 43,355)( 44,357)( 45,356)( 46,370)( 47,372)
( 48,371)( 49,376)( 50,378)( 51,377)( 52,373)( 53,375)( 54,374)( 55,388)
( 56,390)( 57,389)( 58,394)( 59,396)( 60,395)( 61,391)( 62,393)( 63,392)
( 64,379)( 65,381)( 66,380)( 67,385)( 68,387)( 69,386)( 70,382)( 71,384)
( 72,383)( 73,397)( 74,399)( 75,398)( 76,403)( 77,405)( 78,404)( 79,400)
( 80,402)( 81,401)( 82,415)( 83,417)( 84,416)( 85,421)( 86,423)( 87,422)
( 88,418)( 89,420)( 90,419)( 91,406)( 92,408)( 93,407)( 94,412)( 95,414)
( 96,413)( 97,409)( 98,411)( 99,410)(100,424)(101,426)(102,425)(103,430)
(104,432)(105,431)(106,427)(107,429)(108,428)(109,307)(110,309)(111,308)
(112,313)(113,315)(114,314)(115,310)(116,312)(117,311)(118,298)(119,300)
(120,299)(121,304)(122,306)(123,305)(124,301)(125,303)(126,302)(127,316)
(128,318)(129,317)(130,322)(131,324)(132,323)(133,319)(134,321)(135,320)
(136,280)(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)
(144,284)(145,271)(146,273)(147,272)(148,277)(149,279)(150,278)(151,274)
(152,276)(153,275)(154,289)(155,291)(156,290)(157,295)(158,297)(159,296)
(160,292)(161,294)(162,293)(163,226)(164,228)(165,227)(166,232)(167,234)
(168,233)(169,229)(170,231)(171,230)(172,217)(173,219)(174,218)(175,223)
(176,225)(177,224)(178,220)(179,222)(180,221)(181,235)(182,237)(183,236)
(184,241)(185,243)(186,242)(187,238)(188,240)(189,239)(190,253)(191,255)
(192,254)(193,259)(194,261)(195,260)(196,256)(197,258)(198,257)(199,244)
(200,246)(201,245)(202,250)(203,252)(204,251)(205,247)(206,249)(207,248)
(208,262)(209,264)(210,263)(211,268)(212,270)(213,269)(214,265)(215,267)
(216,266)(433,766)(434,768)(435,767)(436,772)(437,774)(438,773)(439,769)
(440,771)(441,770)(442,757)(443,759)(444,758)(445,763)(446,765)(447,764)
(448,760)(449,762)(450,761)(451,775)(452,777)(453,776)(454,781)(455,783)
(456,782)(457,778)(458,780)(459,779)(460,793)(461,795)(462,794)(463,799)
(464,801)(465,800)(466,796)(467,798)(468,797)(469,784)(470,786)(471,785)
(472,790)(473,792)(474,791)(475,787)(476,789)(477,788)(478,802)(479,804)
(480,803)(481,808)(482,810)(483,809)(484,805)(485,807)(486,806)(487,820)
(488,822)(489,821)(490,826)(491,828)(492,827)(493,823)(494,825)(495,824)
(496,811)(497,813)(498,812)(499,817)(500,819)(501,818)(502,814)(503,816)
(504,815)(505,829)(506,831)(507,830)(508,835)(509,837)(510,836)(511,832)
(512,834)(513,833)(514,847)(515,849)(516,848)(517,853)(518,855)(519,854)
(520,850)(521,852)(522,851)(523,838)(524,840)(525,839)(526,844)(527,846)
(528,845)(529,841)(530,843)(531,842)(532,856)(533,858)(534,857)(535,862)
(536,864)(537,863)(538,859)(539,861)(540,860)(541,739)(542,741)(543,740)
(544,745)(545,747)(546,746)(547,742)(548,744)(549,743)(550,730)(551,732)
(552,731)(553,736)(554,738)(555,737)(556,733)(557,735)(558,734)(559,748)
(560,750)(561,749)(562,754)(563,756)(564,755)(565,751)(566,753)(567,752)
(568,712)(569,714)(570,713)(571,718)(572,720)(573,719)(574,715)(575,717)
(576,716)(577,703)(578,705)(579,704)(580,709)(581,711)(582,710)(583,706)
(584,708)(585,707)(586,721)(587,723)(588,722)(589,727)(590,729)(591,728)
(592,724)(593,726)(594,725)(595,658)(596,660)(597,659)(598,664)(599,666)
(600,665)(601,661)(602,663)(603,662)(604,649)(605,651)(606,650)(607,655)
(608,657)(609,656)(610,652)(611,654)(612,653)(613,667)(614,669)(615,668)
(616,673)(617,675)(618,674)(619,670)(620,672)(621,671)(622,685)(623,687)
(624,686)(625,691)(626,693)(627,692)(628,688)(629,690)(630,689)(631,676)
(632,678)(633,677)(634,682)(635,684)(636,683)(637,679)(638,681)(639,680)
(640,694)(641,696)(642,695)(643,700)(644,702)(645,701)(646,697)(647,699)
(648,698);
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,
s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope