Polytope of Type {6,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,16}*1728a
if this polytope has a name.
Group : SmallGroup(1728,12518)
Rank : 3
Schlafli Type : {6,16}
Number of vertices, edges, etc : 54, 432, 144
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {6,8}*864a
3-fold quotients : {6,16}*576
4-fold quotients : {6,4}*432a
6-fold quotients : {6,8}*288
8-fold quotients : {6,4}*216
12-fold quotients : {6,4}*144
24-fold quotients : {6,4}*72
27-fold quotients : {2,16}*64
54-fold quotients : {2,8}*32
108-fold quotients : {2,4}*16
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,325)( 2,326)( 3,327)( 4,333)( 5,331)( 6,332)( 7,329)( 8,330)
( 9,328)( 10,345)( 11,343)( 12,344)( 13,350)( 14,351)( 15,349)( 16,346)
( 17,347)( 18,348)( 19,335)( 20,336)( 21,334)( 22,340)( 23,341)( 24,342)
( 25,339)( 26,337)( 27,338)( 28,352)( 29,353)( 30,354)( 31,360)( 32,358)
( 33,359)( 34,356)( 35,357)( 36,355)( 37,372)( 38,370)( 39,371)( 40,377)
( 41,378)( 42,376)( 43,373)( 44,374)( 45,375)( 46,362)( 47,363)( 48,361)
( 49,367)( 50,368)( 51,369)( 52,366)( 53,364)( 54,365)( 55,379)( 56,380)
( 57,381)( 58,387)( 59,385)( 60,386)( 61,383)( 62,384)( 63,382)( 64,399)
( 65,397)( 66,398)( 67,404)( 68,405)( 69,403)( 70,400)( 71,401)( 72,402)
( 73,389)( 74,390)( 75,388)( 76,394)( 77,395)( 78,396)( 79,393)( 80,391)
( 81,392)( 82,406)( 83,407)( 84,408)( 85,414)( 86,412)( 87,413)( 88,410)
( 89,411)( 90,409)( 91,426)( 92,424)( 93,425)( 94,431)( 95,432)( 96,430)
( 97,427)( 98,428)( 99,429)(100,416)(101,417)(102,415)(103,421)(104,422)
(105,423)(106,420)(107,418)(108,419)(109,298)(110,299)(111,300)(112,306)
(113,304)(114,305)(115,302)(116,303)(117,301)(118,318)(119,316)(120,317)
(121,323)(122,324)(123,322)(124,319)(125,320)(126,321)(127,308)(128,309)
(129,307)(130,313)(131,314)(132,315)(133,312)(134,310)(135,311)(136,271)
(137,272)(138,273)(139,279)(140,277)(141,278)(142,275)(143,276)(144,274)
(145,291)(146,289)(147,290)(148,296)(149,297)(150,295)(151,292)(152,293)
(153,294)(154,281)(155,282)(156,280)(157,286)(158,287)(159,288)(160,285)
(161,283)(162,284)(163,217)(164,218)(165,219)(166,225)(167,223)(168,224)
(169,221)(170,222)(171,220)(172,237)(173,235)(174,236)(175,242)(176,243)
(177,241)(178,238)(179,239)(180,240)(181,227)(182,228)(183,226)(184,232)
(185,233)(186,234)(187,231)(188,229)(189,230)(190,244)(191,245)(192,246)
(193,252)(194,250)(195,251)(196,248)(197,249)(198,247)(199,264)(200,262)
(201,263)(202,269)(203,270)(204,268)(205,265)(206,266)(207,267)(208,254)
(209,255)(210,253)(211,259)(212,260)(213,261)(214,258)(215,256)(216,257)
(433,757)(434,758)(435,759)(436,765)(437,763)(438,764)(439,761)(440,762)
(441,760)(442,777)(443,775)(444,776)(445,782)(446,783)(447,781)(448,778)
(449,779)(450,780)(451,767)(452,768)(453,766)(454,772)(455,773)(456,774)
(457,771)(458,769)(459,770)(460,784)(461,785)(462,786)(463,792)(464,790)
(465,791)(466,788)(467,789)(468,787)(469,804)(470,802)(471,803)(472,809)
(473,810)(474,808)(475,805)(476,806)(477,807)(478,794)(479,795)(480,793)
(481,799)(482,800)(483,801)(484,798)(485,796)(486,797)(487,811)(488,812)
(489,813)(490,819)(491,817)(492,818)(493,815)(494,816)(495,814)(496,831)
(497,829)(498,830)(499,836)(500,837)(501,835)(502,832)(503,833)(504,834)
(505,821)(506,822)(507,820)(508,826)(509,827)(510,828)(511,825)(512,823)
(513,824)(514,838)(515,839)(516,840)(517,846)(518,844)(519,845)(520,842)
(521,843)(522,841)(523,858)(524,856)(525,857)(526,863)(527,864)(528,862)
(529,859)(530,860)(531,861)(532,848)(533,849)(534,847)(535,853)(536,854)
(537,855)(538,852)(539,850)(540,851)(541,730)(542,731)(543,732)(544,738)
(545,736)(546,737)(547,734)(548,735)(549,733)(550,750)(551,748)(552,749)
(553,755)(554,756)(555,754)(556,751)(557,752)(558,753)(559,740)(560,741)
(561,739)(562,745)(563,746)(564,747)(565,744)(566,742)(567,743)(568,703)
(569,704)(570,705)(571,711)(572,709)(573,710)(574,707)(575,708)(576,706)
(577,723)(578,721)(579,722)(580,728)(581,729)(582,727)(583,724)(584,725)
(585,726)(586,713)(587,714)(588,712)(589,718)(590,719)(591,720)(592,717)
(593,715)(594,716)(595,649)(596,650)(597,651)(598,657)(599,655)(600,656)
(601,653)(602,654)(603,652)(604,669)(605,667)(606,668)(607,674)(608,675)
(609,673)(610,670)(611,671)(612,672)(613,659)(614,660)(615,658)(616,664)
(617,665)(618,666)(619,663)(620,661)(621,662)(622,676)(623,677)(624,678)
(625,684)(626,682)(627,683)(628,680)(629,681)(630,679)(631,696)(632,694)
(633,695)(634,701)(635,702)(636,700)(637,697)(638,698)(639,699)(640,686)
(641,687)(642,685)(643,691)(644,692)(645,693)(646,690)(647,688)(648,689);;
s1 := ( 1, 10)( 2, 12)( 3, 11)( 4, 5)( 7, 26)( 8, 25)( 9, 27)( 13, 23)
( 14, 22)( 15, 24)( 16, 17)( 20, 21)( 28, 37)( 29, 39)( 30, 38)( 31, 32)
( 34, 53)( 35, 52)( 36, 54)( 40, 50)( 41, 49)( 42, 51)( 43, 44)( 47, 48)
( 55, 91)( 56, 93)( 57, 92)( 58, 86)( 59, 85)( 60, 87)( 61,107)( 62,106)
( 63,108)( 64, 82)( 65, 84)( 66, 83)( 67,104)( 68,103)( 69,105)( 70, 98)
( 71, 97)( 72, 99)( 73,100)( 74,102)( 75,101)( 76, 95)( 77, 94)( 78, 96)
( 79, 89)( 80, 88)( 81, 90)(109,172)(110,174)(111,173)(112,167)(113,166)
(114,168)(115,188)(116,187)(117,189)(118,163)(119,165)(120,164)(121,185)
(122,184)(123,186)(124,179)(125,178)(126,180)(127,181)(128,183)(129,182)
(130,176)(131,175)(132,177)(133,170)(134,169)(135,171)(136,199)(137,201)
(138,200)(139,194)(140,193)(141,195)(142,215)(143,214)(144,216)(145,190)
(146,192)(147,191)(148,212)(149,211)(150,213)(151,206)(152,205)(153,207)
(154,208)(155,210)(156,209)(157,203)(158,202)(159,204)(160,197)(161,196)
(162,198)(217,307)(218,309)(219,308)(220,302)(221,301)(222,303)(223,323)
(224,322)(225,324)(226,298)(227,300)(228,299)(229,320)(230,319)(231,321)
(232,314)(233,313)(234,315)(235,316)(236,318)(237,317)(238,311)(239,310)
(240,312)(241,305)(242,304)(243,306)(244,280)(245,282)(246,281)(247,275)
(248,274)(249,276)(250,296)(251,295)(252,297)(253,271)(254,273)(255,272)
(256,293)(257,292)(258,294)(259,287)(260,286)(261,288)(262,289)(263,291)
(264,290)(265,284)(266,283)(267,285)(268,278)(269,277)(270,279)(325,334)
(326,336)(327,335)(328,329)(331,350)(332,349)(333,351)(337,347)(338,346)
(339,348)(340,341)(344,345)(352,361)(353,363)(354,362)(355,356)(358,377)
(359,376)(360,378)(364,374)(365,373)(366,375)(367,368)(371,372)(379,415)
(380,417)(381,416)(382,410)(383,409)(384,411)(385,431)(386,430)(387,432)
(388,406)(389,408)(390,407)(391,428)(392,427)(393,429)(394,422)(395,421)
(396,423)(397,424)(398,426)(399,425)(400,419)(401,418)(402,420)(403,413)
(404,412)(405,414)(433,550)(434,552)(435,551)(436,545)(437,544)(438,546)
(439,566)(440,565)(441,567)(442,541)(443,543)(444,542)(445,563)(446,562)
(447,564)(448,557)(449,556)(450,558)(451,559)(452,561)(453,560)(454,554)
(455,553)(456,555)(457,548)(458,547)(459,549)(460,577)(461,579)(462,578)
(463,572)(464,571)(465,573)(466,593)(467,592)(468,594)(469,568)(470,570)
(471,569)(472,590)(473,589)(474,591)(475,584)(476,583)(477,585)(478,586)
(479,588)(480,587)(481,581)(482,580)(483,582)(484,575)(485,574)(486,576)
(487,631)(488,633)(489,632)(490,626)(491,625)(492,627)(493,647)(494,646)
(495,648)(496,622)(497,624)(498,623)(499,644)(500,643)(501,645)(502,638)
(503,637)(504,639)(505,640)(506,642)(507,641)(508,635)(509,634)(510,636)
(511,629)(512,628)(513,630)(514,604)(515,606)(516,605)(517,599)(518,598)
(519,600)(520,620)(521,619)(522,621)(523,595)(524,597)(525,596)(526,617)
(527,616)(528,618)(529,611)(530,610)(531,612)(532,613)(533,615)(534,614)
(535,608)(536,607)(537,609)(538,602)(539,601)(540,603)(649,847)(650,849)
(651,848)(652,842)(653,841)(654,843)(655,863)(656,862)(657,864)(658,838)
(659,840)(660,839)(661,860)(662,859)(663,861)(664,854)(665,853)(666,855)
(667,856)(668,858)(669,857)(670,851)(671,850)(672,852)(673,845)(674,844)
(675,846)(676,820)(677,822)(678,821)(679,815)(680,814)(681,816)(682,836)
(683,835)(684,837)(685,811)(686,813)(687,812)(688,833)(689,832)(690,834)
(691,827)(692,826)(693,828)(694,829)(695,831)(696,830)(697,824)(698,823)
(699,825)(700,818)(701,817)(702,819)(703,793)(704,795)(705,794)(706,788)
(707,787)(708,789)(709,809)(710,808)(711,810)(712,784)(713,786)(714,785)
(715,806)(716,805)(717,807)(718,800)(719,799)(720,801)(721,802)(722,804)
(723,803)(724,797)(725,796)(726,798)(727,791)(728,790)(729,792)(730,766)
(731,768)(732,767)(733,761)(734,760)(735,762)(736,782)(737,781)(738,783)
(739,757)(740,759)(741,758)(742,779)(743,778)(744,780)(745,773)(746,772)
(747,774)(748,775)(749,777)(750,776)(751,770)(752,769)(753,771)(754,764)
(755,763)(756,765);;
s2 := ( 1,433)( 2,435)( 3,434)( 4,437)( 5,436)( 6,438)( 7,441)( 8,440)
( 9,439)( 10,457)( 11,459)( 12,458)( 13,452)( 14,451)( 15,453)( 16,456)
( 17,455)( 18,454)( 19,446)( 20,445)( 21,447)( 22,450)( 23,449)( 24,448)
( 25,442)( 26,444)( 27,443)( 28,460)( 29,462)( 30,461)( 31,464)( 32,463)
( 33,465)( 34,468)( 35,467)( 36,466)( 37,484)( 38,486)( 39,485)( 40,479)
( 41,478)( 42,480)( 43,483)( 44,482)( 45,481)( 46,473)( 47,472)( 48,474)
( 49,477)( 50,476)( 51,475)( 52,469)( 53,471)( 54,470)( 55,514)( 56,516)
( 57,515)( 58,518)( 59,517)( 60,519)( 61,522)( 62,521)( 63,520)( 64,538)
( 65,540)( 66,539)( 67,533)( 68,532)( 69,534)( 70,537)( 71,536)( 72,535)
( 73,527)( 74,526)( 75,528)( 76,531)( 77,530)( 78,529)( 79,523)( 80,525)
( 81,524)( 82,487)( 83,489)( 84,488)( 85,491)( 86,490)( 87,492)( 88,495)
( 89,494)( 90,493)( 91,511)( 92,513)( 93,512)( 94,506)( 95,505)( 96,507)
( 97,510)( 98,509)( 99,508)(100,500)(101,499)(102,501)(103,504)(104,503)
(105,502)(106,496)(107,498)(108,497)(109,595)(110,597)(111,596)(112,599)
(113,598)(114,600)(115,603)(116,602)(117,601)(118,619)(119,621)(120,620)
(121,614)(122,613)(123,615)(124,618)(125,617)(126,616)(127,608)(128,607)
(129,609)(130,612)(131,611)(132,610)(133,604)(134,606)(135,605)(136,622)
(137,624)(138,623)(139,626)(140,625)(141,627)(142,630)(143,629)(144,628)
(145,646)(146,648)(147,647)(148,641)(149,640)(150,642)(151,645)(152,644)
(153,643)(154,635)(155,634)(156,636)(157,639)(158,638)(159,637)(160,631)
(161,633)(162,632)(163,541)(164,543)(165,542)(166,545)(167,544)(168,546)
(169,549)(170,548)(171,547)(172,565)(173,567)(174,566)(175,560)(176,559)
(177,561)(178,564)(179,563)(180,562)(181,554)(182,553)(183,555)(184,558)
(185,557)(186,556)(187,550)(188,552)(189,551)(190,568)(191,570)(192,569)
(193,572)(194,571)(195,573)(196,576)(197,575)(198,574)(199,592)(200,594)
(201,593)(202,587)(203,586)(204,588)(205,591)(206,590)(207,589)(208,581)
(209,580)(210,582)(211,585)(212,584)(213,583)(214,577)(215,579)(216,578)
(217,730)(218,732)(219,731)(220,734)(221,733)(222,735)(223,738)(224,737)
(225,736)(226,754)(227,756)(228,755)(229,749)(230,748)(231,750)(232,753)
(233,752)(234,751)(235,743)(236,742)(237,744)(238,747)(239,746)(240,745)
(241,739)(242,741)(243,740)(244,703)(245,705)(246,704)(247,707)(248,706)
(249,708)(250,711)(251,710)(252,709)(253,727)(254,729)(255,728)(256,722)
(257,721)(258,723)(259,726)(260,725)(261,724)(262,716)(263,715)(264,717)
(265,720)(266,719)(267,718)(268,712)(269,714)(270,713)(271,676)(272,678)
(273,677)(274,680)(275,679)(276,681)(277,684)(278,683)(279,682)(280,700)
(281,702)(282,701)(283,695)(284,694)(285,696)(286,699)(287,698)(288,697)
(289,689)(290,688)(291,690)(292,693)(293,692)(294,691)(295,685)(296,687)
(297,686)(298,649)(299,651)(300,650)(301,653)(302,652)(303,654)(304,657)
(305,656)(306,655)(307,673)(308,675)(309,674)(310,668)(311,667)(312,669)
(313,672)(314,671)(315,670)(316,662)(317,661)(318,663)(319,666)(320,665)
(321,664)(322,658)(323,660)(324,659)(325,757)(326,759)(327,758)(328,761)
(329,760)(330,762)(331,765)(332,764)(333,763)(334,781)(335,783)(336,782)
(337,776)(338,775)(339,777)(340,780)(341,779)(342,778)(343,770)(344,769)
(345,771)(346,774)(347,773)(348,772)(349,766)(350,768)(351,767)(352,784)
(353,786)(354,785)(355,788)(356,787)(357,789)(358,792)(359,791)(360,790)
(361,808)(362,810)(363,809)(364,803)(365,802)(366,804)(367,807)(368,806)
(369,805)(370,797)(371,796)(372,798)(373,801)(374,800)(375,799)(376,793)
(377,795)(378,794)(379,838)(380,840)(381,839)(382,842)(383,841)(384,843)
(385,846)(386,845)(387,844)(388,862)(389,864)(390,863)(391,857)(392,856)
(393,858)(394,861)(395,860)(396,859)(397,851)(398,850)(399,852)(400,855)
(401,854)(402,853)(403,847)(404,849)(405,848)(406,811)(407,813)(408,812)
(409,815)(410,814)(411,816)(412,819)(413,818)(414,817)(415,835)(416,837)
(417,836)(418,830)(419,829)(420,831)(421,834)(422,833)(423,832)(424,824)
(425,823)(426,825)(427,828)(428,827)(429,826)(430,820)(431,822)(432,821);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,325)( 2,326)( 3,327)( 4,333)( 5,331)( 6,332)( 7,329)
( 8,330)( 9,328)( 10,345)( 11,343)( 12,344)( 13,350)( 14,351)( 15,349)
( 16,346)( 17,347)( 18,348)( 19,335)( 20,336)( 21,334)( 22,340)( 23,341)
( 24,342)( 25,339)( 26,337)( 27,338)( 28,352)( 29,353)( 30,354)( 31,360)
( 32,358)( 33,359)( 34,356)( 35,357)( 36,355)( 37,372)( 38,370)( 39,371)
( 40,377)( 41,378)( 42,376)( 43,373)( 44,374)( 45,375)( 46,362)( 47,363)
( 48,361)( 49,367)( 50,368)( 51,369)( 52,366)( 53,364)( 54,365)( 55,379)
( 56,380)( 57,381)( 58,387)( 59,385)( 60,386)( 61,383)( 62,384)( 63,382)
( 64,399)( 65,397)( 66,398)( 67,404)( 68,405)( 69,403)( 70,400)( 71,401)
( 72,402)( 73,389)( 74,390)( 75,388)( 76,394)( 77,395)( 78,396)( 79,393)
( 80,391)( 81,392)( 82,406)( 83,407)( 84,408)( 85,414)( 86,412)( 87,413)
( 88,410)( 89,411)( 90,409)( 91,426)( 92,424)( 93,425)( 94,431)( 95,432)
( 96,430)( 97,427)( 98,428)( 99,429)(100,416)(101,417)(102,415)(103,421)
(104,422)(105,423)(106,420)(107,418)(108,419)(109,298)(110,299)(111,300)
(112,306)(113,304)(114,305)(115,302)(116,303)(117,301)(118,318)(119,316)
(120,317)(121,323)(122,324)(123,322)(124,319)(125,320)(126,321)(127,308)
(128,309)(129,307)(130,313)(131,314)(132,315)(133,312)(134,310)(135,311)
(136,271)(137,272)(138,273)(139,279)(140,277)(141,278)(142,275)(143,276)
(144,274)(145,291)(146,289)(147,290)(148,296)(149,297)(150,295)(151,292)
(152,293)(153,294)(154,281)(155,282)(156,280)(157,286)(158,287)(159,288)
(160,285)(161,283)(162,284)(163,217)(164,218)(165,219)(166,225)(167,223)
(168,224)(169,221)(170,222)(171,220)(172,237)(173,235)(174,236)(175,242)
(176,243)(177,241)(178,238)(179,239)(180,240)(181,227)(182,228)(183,226)
(184,232)(185,233)(186,234)(187,231)(188,229)(189,230)(190,244)(191,245)
(192,246)(193,252)(194,250)(195,251)(196,248)(197,249)(198,247)(199,264)
(200,262)(201,263)(202,269)(203,270)(204,268)(205,265)(206,266)(207,267)
(208,254)(209,255)(210,253)(211,259)(212,260)(213,261)(214,258)(215,256)
(216,257)(433,757)(434,758)(435,759)(436,765)(437,763)(438,764)(439,761)
(440,762)(441,760)(442,777)(443,775)(444,776)(445,782)(446,783)(447,781)
(448,778)(449,779)(450,780)(451,767)(452,768)(453,766)(454,772)(455,773)
(456,774)(457,771)(458,769)(459,770)(460,784)(461,785)(462,786)(463,792)
(464,790)(465,791)(466,788)(467,789)(468,787)(469,804)(470,802)(471,803)
(472,809)(473,810)(474,808)(475,805)(476,806)(477,807)(478,794)(479,795)
(480,793)(481,799)(482,800)(483,801)(484,798)(485,796)(486,797)(487,811)
(488,812)(489,813)(490,819)(491,817)(492,818)(493,815)(494,816)(495,814)
(496,831)(497,829)(498,830)(499,836)(500,837)(501,835)(502,832)(503,833)
(504,834)(505,821)(506,822)(507,820)(508,826)(509,827)(510,828)(511,825)
(512,823)(513,824)(514,838)(515,839)(516,840)(517,846)(518,844)(519,845)
(520,842)(521,843)(522,841)(523,858)(524,856)(525,857)(526,863)(527,864)
(528,862)(529,859)(530,860)(531,861)(532,848)(533,849)(534,847)(535,853)
(536,854)(537,855)(538,852)(539,850)(540,851)(541,730)(542,731)(543,732)
(544,738)(545,736)(546,737)(547,734)(548,735)(549,733)(550,750)(551,748)
(552,749)(553,755)(554,756)(555,754)(556,751)(557,752)(558,753)(559,740)
(560,741)(561,739)(562,745)(563,746)(564,747)(565,744)(566,742)(567,743)
(568,703)(569,704)(570,705)(571,711)(572,709)(573,710)(574,707)(575,708)
(576,706)(577,723)(578,721)(579,722)(580,728)(581,729)(582,727)(583,724)
(584,725)(585,726)(586,713)(587,714)(588,712)(589,718)(590,719)(591,720)
(592,717)(593,715)(594,716)(595,649)(596,650)(597,651)(598,657)(599,655)
(600,656)(601,653)(602,654)(603,652)(604,669)(605,667)(606,668)(607,674)
(608,675)(609,673)(610,670)(611,671)(612,672)(613,659)(614,660)(615,658)
(616,664)(617,665)(618,666)(619,663)(620,661)(621,662)(622,676)(623,677)
(624,678)(625,684)(626,682)(627,683)(628,680)(629,681)(630,679)(631,696)
(632,694)(633,695)(634,701)(635,702)(636,700)(637,697)(638,698)(639,699)
(640,686)(641,687)(642,685)(643,691)(644,692)(645,693)(646,690)(647,688)
(648,689);
s1 := Sym(864)!( 1, 10)( 2, 12)( 3, 11)( 4, 5)( 7, 26)( 8, 25)( 9, 27)
( 13, 23)( 14, 22)( 15, 24)( 16, 17)( 20, 21)( 28, 37)( 29, 39)( 30, 38)
( 31, 32)( 34, 53)( 35, 52)( 36, 54)( 40, 50)( 41, 49)( 42, 51)( 43, 44)
( 47, 48)( 55, 91)( 56, 93)( 57, 92)( 58, 86)( 59, 85)( 60, 87)( 61,107)
( 62,106)( 63,108)( 64, 82)( 65, 84)( 66, 83)( 67,104)( 68,103)( 69,105)
( 70, 98)( 71, 97)( 72, 99)( 73,100)( 74,102)( 75,101)( 76, 95)( 77, 94)
( 78, 96)( 79, 89)( 80, 88)( 81, 90)(109,172)(110,174)(111,173)(112,167)
(113,166)(114,168)(115,188)(116,187)(117,189)(118,163)(119,165)(120,164)
(121,185)(122,184)(123,186)(124,179)(125,178)(126,180)(127,181)(128,183)
(129,182)(130,176)(131,175)(132,177)(133,170)(134,169)(135,171)(136,199)
(137,201)(138,200)(139,194)(140,193)(141,195)(142,215)(143,214)(144,216)
(145,190)(146,192)(147,191)(148,212)(149,211)(150,213)(151,206)(152,205)
(153,207)(154,208)(155,210)(156,209)(157,203)(158,202)(159,204)(160,197)
(161,196)(162,198)(217,307)(218,309)(219,308)(220,302)(221,301)(222,303)
(223,323)(224,322)(225,324)(226,298)(227,300)(228,299)(229,320)(230,319)
(231,321)(232,314)(233,313)(234,315)(235,316)(236,318)(237,317)(238,311)
(239,310)(240,312)(241,305)(242,304)(243,306)(244,280)(245,282)(246,281)
(247,275)(248,274)(249,276)(250,296)(251,295)(252,297)(253,271)(254,273)
(255,272)(256,293)(257,292)(258,294)(259,287)(260,286)(261,288)(262,289)
(263,291)(264,290)(265,284)(266,283)(267,285)(268,278)(269,277)(270,279)
(325,334)(326,336)(327,335)(328,329)(331,350)(332,349)(333,351)(337,347)
(338,346)(339,348)(340,341)(344,345)(352,361)(353,363)(354,362)(355,356)
(358,377)(359,376)(360,378)(364,374)(365,373)(366,375)(367,368)(371,372)
(379,415)(380,417)(381,416)(382,410)(383,409)(384,411)(385,431)(386,430)
(387,432)(388,406)(389,408)(390,407)(391,428)(392,427)(393,429)(394,422)
(395,421)(396,423)(397,424)(398,426)(399,425)(400,419)(401,418)(402,420)
(403,413)(404,412)(405,414)(433,550)(434,552)(435,551)(436,545)(437,544)
(438,546)(439,566)(440,565)(441,567)(442,541)(443,543)(444,542)(445,563)
(446,562)(447,564)(448,557)(449,556)(450,558)(451,559)(452,561)(453,560)
(454,554)(455,553)(456,555)(457,548)(458,547)(459,549)(460,577)(461,579)
(462,578)(463,572)(464,571)(465,573)(466,593)(467,592)(468,594)(469,568)
(470,570)(471,569)(472,590)(473,589)(474,591)(475,584)(476,583)(477,585)
(478,586)(479,588)(480,587)(481,581)(482,580)(483,582)(484,575)(485,574)
(486,576)(487,631)(488,633)(489,632)(490,626)(491,625)(492,627)(493,647)
(494,646)(495,648)(496,622)(497,624)(498,623)(499,644)(500,643)(501,645)
(502,638)(503,637)(504,639)(505,640)(506,642)(507,641)(508,635)(509,634)
(510,636)(511,629)(512,628)(513,630)(514,604)(515,606)(516,605)(517,599)
(518,598)(519,600)(520,620)(521,619)(522,621)(523,595)(524,597)(525,596)
(526,617)(527,616)(528,618)(529,611)(530,610)(531,612)(532,613)(533,615)
(534,614)(535,608)(536,607)(537,609)(538,602)(539,601)(540,603)(649,847)
(650,849)(651,848)(652,842)(653,841)(654,843)(655,863)(656,862)(657,864)
(658,838)(659,840)(660,839)(661,860)(662,859)(663,861)(664,854)(665,853)
(666,855)(667,856)(668,858)(669,857)(670,851)(671,850)(672,852)(673,845)
(674,844)(675,846)(676,820)(677,822)(678,821)(679,815)(680,814)(681,816)
(682,836)(683,835)(684,837)(685,811)(686,813)(687,812)(688,833)(689,832)
(690,834)(691,827)(692,826)(693,828)(694,829)(695,831)(696,830)(697,824)
(698,823)(699,825)(700,818)(701,817)(702,819)(703,793)(704,795)(705,794)
(706,788)(707,787)(708,789)(709,809)(710,808)(711,810)(712,784)(713,786)
(714,785)(715,806)(716,805)(717,807)(718,800)(719,799)(720,801)(721,802)
(722,804)(723,803)(724,797)(725,796)(726,798)(727,791)(728,790)(729,792)
(730,766)(731,768)(732,767)(733,761)(734,760)(735,762)(736,782)(737,781)
(738,783)(739,757)(740,759)(741,758)(742,779)(743,778)(744,780)(745,773)
(746,772)(747,774)(748,775)(749,777)(750,776)(751,770)(752,769)(753,771)
(754,764)(755,763)(756,765);
s2 := Sym(864)!( 1,433)( 2,435)( 3,434)( 4,437)( 5,436)( 6,438)( 7,441)
( 8,440)( 9,439)( 10,457)( 11,459)( 12,458)( 13,452)( 14,451)( 15,453)
( 16,456)( 17,455)( 18,454)( 19,446)( 20,445)( 21,447)( 22,450)( 23,449)
( 24,448)( 25,442)( 26,444)( 27,443)( 28,460)( 29,462)( 30,461)( 31,464)
( 32,463)( 33,465)( 34,468)( 35,467)( 36,466)( 37,484)( 38,486)( 39,485)
( 40,479)( 41,478)( 42,480)( 43,483)( 44,482)( 45,481)( 46,473)( 47,472)
( 48,474)( 49,477)( 50,476)( 51,475)( 52,469)( 53,471)( 54,470)( 55,514)
( 56,516)( 57,515)( 58,518)( 59,517)( 60,519)( 61,522)( 62,521)( 63,520)
( 64,538)( 65,540)( 66,539)( 67,533)( 68,532)( 69,534)( 70,537)( 71,536)
( 72,535)( 73,527)( 74,526)( 75,528)( 76,531)( 77,530)( 78,529)( 79,523)
( 80,525)( 81,524)( 82,487)( 83,489)( 84,488)( 85,491)( 86,490)( 87,492)
( 88,495)( 89,494)( 90,493)( 91,511)( 92,513)( 93,512)( 94,506)( 95,505)
( 96,507)( 97,510)( 98,509)( 99,508)(100,500)(101,499)(102,501)(103,504)
(104,503)(105,502)(106,496)(107,498)(108,497)(109,595)(110,597)(111,596)
(112,599)(113,598)(114,600)(115,603)(116,602)(117,601)(118,619)(119,621)
(120,620)(121,614)(122,613)(123,615)(124,618)(125,617)(126,616)(127,608)
(128,607)(129,609)(130,612)(131,611)(132,610)(133,604)(134,606)(135,605)
(136,622)(137,624)(138,623)(139,626)(140,625)(141,627)(142,630)(143,629)
(144,628)(145,646)(146,648)(147,647)(148,641)(149,640)(150,642)(151,645)
(152,644)(153,643)(154,635)(155,634)(156,636)(157,639)(158,638)(159,637)
(160,631)(161,633)(162,632)(163,541)(164,543)(165,542)(166,545)(167,544)
(168,546)(169,549)(170,548)(171,547)(172,565)(173,567)(174,566)(175,560)
(176,559)(177,561)(178,564)(179,563)(180,562)(181,554)(182,553)(183,555)
(184,558)(185,557)(186,556)(187,550)(188,552)(189,551)(190,568)(191,570)
(192,569)(193,572)(194,571)(195,573)(196,576)(197,575)(198,574)(199,592)
(200,594)(201,593)(202,587)(203,586)(204,588)(205,591)(206,590)(207,589)
(208,581)(209,580)(210,582)(211,585)(212,584)(213,583)(214,577)(215,579)
(216,578)(217,730)(218,732)(219,731)(220,734)(221,733)(222,735)(223,738)
(224,737)(225,736)(226,754)(227,756)(228,755)(229,749)(230,748)(231,750)
(232,753)(233,752)(234,751)(235,743)(236,742)(237,744)(238,747)(239,746)
(240,745)(241,739)(242,741)(243,740)(244,703)(245,705)(246,704)(247,707)
(248,706)(249,708)(250,711)(251,710)(252,709)(253,727)(254,729)(255,728)
(256,722)(257,721)(258,723)(259,726)(260,725)(261,724)(262,716)(263,715)
(264,717)(265,720)(266,719)(267,718)(268,712)(269,714)(270,713)(271,676)
(272,678)(273,677)(274,680)(275,679)(276,681)(277,684)(278,683)(279,682)
(280,700)(281,702)(282,701)(283,695)(284,694)(285,696)(286,699)(287,698)
(288,697)(289,689)(290,688)(291,690)(292,693)(293,692)(294,691)(295,685)
(296,687)(297,686)(298,649)(299,651)(300,650)(301,653)(302,652)(303,654)
(304,657)(305,656)(306,655)(307,673)(308,675)(309,674)(310,668)(311,667)
(312,669)(313,672)(314,671)(315,670)(316,662)(317,661)(318,663)(319,666)
(320,665)(321,664)(322,658)(323,660)(324,659)(325,757)(326,759)(327,758)
(328,761)(329,760)(330,762)(331,765)(332,764)(333,763)(334,781)(335,783)
(336,782)(337,776)(338,775)(339,777)(340,780)(341,779)(342,778)(343,770)
(344,769)(345,771)(346,774)(347,773)(348,772)(349,766)(350,768)(351,767)
(352,784)(353,786)(354,785)(355,788)(356,787)(357,789)(358,792)(359,791)
(360,790)(361,808)(362,810)(363,809)(364,803)(365,802)(366,804)(367,807)
(368,806)(369,805)(370,797)(371,796)(372,798)(373,801)(374,800)(375,799)
(376,793)(377,795)(378,794)(379,838)(380,840)(381,839)(382,842)(383,841)
(384,843)(385,846)(386,845)(387,844)(388,862)(389,864)(390,863)(391,857)
(392,856)(393,858)(394,861)(395,860)(396,859)(397,851)(398,850)(399,852)
(400,855)(401,854)(402,853)(403,847)(404,849)(405,848)(406,811)(407,813)
(408,812)(409,815)(410,814)(411,816)(412,819)(413,818)(414,817)(415,835)
(416,837)(417,836)(418,830)(419,829)(420,831)(421,834)(422,833)(423,832)
(424,824)(425,823)(426,825)(427,828)(428,827)(429,826)(430,820)(431,822)
(432,821);
poly := sub<Sym(864)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*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 >;
References : None.
to this polytope