Polytope of Type {4,216}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,216}*1728d
if this polytope has a name.
Group : SmallGroup(1728,2203)
Rank : 3
Schlafli Type : {4,216}
Number of vertices, edges, etc : 4, 432, 216
Order of s0s1s2 : 216
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-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 : {4,108}*864b
3-fold quotients : {4,72}*576d
4-fold quotients : {4,54}*432b
6-fold quotients : {4,36}*288b
8-fold quotients : {4,27}*216
9-fold quotients : {4,24}*192d
12-fold quotients : {4,18}*144b
18-fold quotients : {4,12}*96b
24-fold quotients : {4,9}*72
36-fold quotients : {4,6}*48c
72-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,111)( 2,112)( 3,109)( 4,110)( 5,115)( 6,116)( 7,113)( 8,114)
( 9,119)( 10,120)( 11,117)( 12,118)( 13,123)( 14,124)( 15,121)( 16,122)
( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)( 23,129)( 24,130)
( 25,135)( 26,136)( 27,133)( 28,134)( 29,139)( 30,140)( 31,137)( 32,138)
( 33,143)( 34,144)( 35,141)( 36,142)( 37,147)( 38,148)( 39,145)( 40,146)
( 41,151)( 42,152)( 43,149)( 44,150)( 45,155)( 46,156)( 47,153)( 48,154)
( 49,159)( 50,160)( 51,157)( 52,158)( 53,163)( 54,164)( 55,161)( 56,162)
( 57,167)( 58,168)( 59,165)( 60,166)( 61,171)( 62,172)( 63,169)( 64,170)
( 65,175)( 66,176)( 67,173)( 68,174)( 69,179)( 70,180)( 71,177)( 72,178)
( 73,183)( 74,184)( 75,181)( 76,182)( 77,187)( 78,188)( 79,185)( 80,186)
( 81,191)( 82,192)( 83,189)( 84,190)( 85,195)( 86,196)( 87,193)( 88,194)
( 89,199)( 90,200)( 91,197)( 92,198)( 93,203)( 94,204)( 95,201)( 96,202)
( 97,207)( 98,208)( 99,205)(100,206)(101,211)(102,212)(103,209)(104,210)
(105,215)(106,216)(107,213)(108,214)(217,327)(218,328)(219,325)(220,326)
(221,331)(222,332)(223,329)(224,330)(225,335)(226,336)(227,333)(228,334)
(229,339)(230,340)(231,337)(232,338)(233,343)(234,344)(235,341)(236,342)
(237,347)(238,348)(239,345)(240,346)(241,351)(242,352)(243,349)(244,350)
(245,355)(246,356)(247,353)(248,354)(249,359)(250,360)(251,357)(252,358)
(253,363)(254,364)(255,361)(256,362)(257,367)(258,368)(259,365)(260,366)
(261,371)(262,372)(263,369)(264,370)(265,375)(266,376)(267,373)(268,374)
(269,379)(270,380)(271,377)(272,378)(273,383)(274,384)(275,381)(276,382)
(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)(283,389)(284,390)
(285,395)(286,396)(287,393)(288,394)(289,399)(290,400)(291,397)(292,398)
(293,403)(294,404)(295,401)(296,402)(297,407)(298,408)(299,405)(300,406)
(301,411)(302,412)(303,409)(304,410)(305,415)(306,416)(307,413)(308,414)
(309,419)(310,420)(311,417)(312,418)(313,423)(314,424)(315,421)(316,422)
(317,427)(318,428)(319,425)(320,426)(321,431)(322,432)(323,429)(324,430)
(433,543)(434,544)(435,541)(436,542)(437,547)(438,548)(439,545)(440,546)
(441,551)(442,552)(443,549)(444,550)(445,555)(446,556)(447,553)(448,554)
(449,559)(450,560)(451,557)(452,558)(453,563)(454,564)(455,561)(456,562)
(457,567)(458,568)(459,565)(460,566)(461,571)(462,572)(463,569)(464,570)
(465,575)(466,576)(467,573)(468,574)(469,579)(470,580)(471,577)(472,578)
(473,583)(474,584)(475,581)(476,582)(477,587)(478,588)(479,585)(480,586)
(481,591)(482,592)(483,589)(484,590)(485,595)(486,596)(487,593)(488,594)
(489,599)(490,600)(491,597)(492,598)(493,603)(494,604)(495,601)(496,602)
(497,607)(498,608)(499,605)(500,606)(501,611)(502,612)(503,609)(504,610)
(505,615)(506,616)(507,613)(508,614)(509,619)(510,620)(511,617)(512,618)
(513,623)(514,624)(515,621)(516,622)(517,627)(518,628)(519,625)(520,626)
(521,631)(522,632)(523,629)(524,630)(525,635)(526,636)(527,633)(528,634)
(529,639)(530,640)(531,637)(532,638)(533,643)(534,644)(535,641)(536,642)
(537,647)(538,648)(539,645)(540,646)(649,759)(650,760)(651,757)(652,758)
(653,763)(654,764)(655,761)(656,762)(657,767)(658,768)(659,765)(660,766)
(661,771)(662,772)(663,769)(664,770)(665,775)(666,776)(667,773)(668,774)
(669,779)(670,780)(671,777)(672,778)(673,783)(674,784)(675,781)(676,782)
(677,787)(678,788)(679,785)(680,786)(681,791)(682,792)(683,789)(684,790)
(685,795)(686,796)(687,793)(688,794)(689,799)(690,800)(691,797)(692,798)
(693,803)(694,804)(695,801)(696,802)(697,807)(698,808)(699,805)(700,806)
(701,811)(702,812)(703,809)(704,810)(705,815)(706,816)(707,813)(708,814)
(709,819)(710,820)(711,817)(712,818)(713,823)(714,824)(715,821)(716,822)
(717,827)(718,828)(719,825)(720,826)(721,831)(722,832)(723,829)(724,830)
(725,835)(726,836)(727,833)(728,834)(729,839)(730,840)(731,837)(732,838)
(733,843)(734,844)(735,841)(736,842)(737,847)(738,848)(739,845)(740,846)
(741,851)(742,852)(743,849)(744,850)(745,855)(746,856)(747,853)(748,854)
(749,859)(750,860)(751,857)(752,858)(753,863)(754,864)(755,861)(756,862);;
s1 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)
( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)
( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)
( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)
( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)(114,118)
(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)(146,214)
(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)(154,206)
(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)
(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)(170,190)
(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)(178,182)
(179,184)(180,183)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)
(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,357)(230,358)
(231,360)(232,359)(233,353)(234,354)(235,356)(236,355)(237,349)(238,350)
(239,352)(240,351)(241,345)(242,346)(243,348)(244,347)(245,341)(246,342)
(247,344)(248,343)(249,337)(250,338)(251,340)(252,339)(253,429)(254,430)
(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)(261,421)(262,422)
(263,424)(264,423)(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)
(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)
(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)
(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)
(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)
(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)
(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)
(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(433,649)(434,650)
(435,652)(436,651)(437,657)(438,658)(439,660)(440,659)(441,653)(442,654)
(443,656)(444,655)(445,681)(446,682)(447,684)(448,683)(449,677)(450,678)
(451,680)(452,679)(453,673)(454,674)(455,676)(456,675)(457,669)(458,670)
(459,672)(460,671)(461,665)(462,666)(463,668)(464,667)(465,661)(466,662)
(467,664)(468,663)(469,753)(470,754)(471,756)(472,755)(473,749)(474,750)
(475,752)(476,751)(477,745)(478,746)(479,748)(480,747)(481,741)(482,742)
(483,744)(484,743)(485,737)(486,738)(487,740)(488,739)(489,733)(490,734)
(491,736)(492,735)(493,729)(494,730)(495,732)(496,731)(497,725)(498,726)
(499,728)(500,727)(501,721)(502,722)(503,724)(504,723)(505,717)(506,718)
(507,720)(508,719)(509,713)(510,714)(511,716)(512,715)(513,709)(514,710)
(515,712)(516,711)(517,705)(518,706)(519,708)(520,707)(521,701)(522,702)
(523,704)(524,703)(525,697)(526,698)(527,700)(528,699)(529,693)(530,694)
(531,696)(532,695)(533,689)(534,690)(535,692)(536,691)(537,685)(538,686)
(539,688)(540,687)(541,757)(542,758)(543,760)(544,759)(545,765)(546,766)
(547,768)(548,767)(549,761)(550,762)(551,764)(552,763)(553,789)(554,790)
(555,792)(556,791)(557,785)(558,786)(559,788)(560,787)(561,781)(562,782)
(563,784)(564,783)(565,777)(566,778)(567,780)(568,779)(569,773)(570,774)
(571,776)(572,775)(573,769)(574,770)(575,772)(576,771)(577,861)(578,862)
(579,864)(580,863)(581,857)(582,858)(583,860)(584,859)(585,853)(586,854)
(587,856)(588,855)(589,849)(590,850)(591,852)(592,851)(593,845)(594,846)
(595,848)(596,847)(597,841)(598,842)(599,844)(600,843)(601,837)(602,838)
(603,840)(604,839)(605,833)(606,834)(607,836)(608,835)(609,829)(610,830)
(611,832)(612,831)(613,825)(614,826)(615,828)(616,827)(617,821)(618,822)
(619,824)(620,823)(621,817)(622,818)(623,820)(624,819)(625,813)(626,814)
(627,816)(628,815)(629,809)(630,810)(631,812)(632,811)(633,805)(634,806)
(635,808)(636,807)(637,801)(638,802)(639,804)(640,803)(641,797)(642,798)
(643,800)(644,799)(645,793)(646,794)(647,796)(648,795);;
s2 := ( 1,469)( 2,472)( 3,471)( 4,470)( 5,477)( 6,480)( 7,479)( 8,478)
( 9,473)( 10,476)( 11,475)( 12,474)( 13,501)( 14,504)( 15,503)( 16,502)
( 17,497)( 18,500)( 19,499)( 20,498)( 21,493)( 22,496)( 23,495)( 24,494)
( 25,489)( 26,492)( 27,491)( 28,490)( 29,485)( 30,488)( 31,487)( 32,486)
( 33,481)( 34,484)( 35,483)( 36,482)( 37,433)( 38,436)( 39,435)( 40,434)
( 41,441)( 42,444)( 43,443)( 44,442)( 45,437)( 46,440)( 47,439)( 48,438)
( 49,465)( 50,468)( 51,467)( 52,466)( 53,461)( 54,464)( 55,463)( 56,462)
( 57,457)( 58,460)( 59,459)( 60,458)( 61,453)( 62,456)( 63,455)( 64,454)
( 65,449)( 66,452)( 67,451)( 68,450)( 69,445)( 70,448)( 71,447)( 72,446)
( 73,537)( 74,540)( 75,539)( 76,538)( 77,533)( 78,536)( 79,535)( 80,534)
( 81,529)( 82,532)( 83,531)( 84,530)( 85,525)( 86,528)( 87,527)( 88,526)
( 89,521)( 90,524)( 91,523)( 92,522)( 93,517)( 94,520)( 95,519)( 96,518)
( 97,513)( 98,516)( 99,515)(100,514)(101,509)(102,512)(103,511)(104,510)
(105,505)(106,508)(107,507)(108,506)(109,577)(110,580)(111,579)(112,578)
(113,585)(114,588)(115,587)(116,586)(117,581)(118,584)(119,583)(120,582)
(121,609)(122,612)(123,611)(124,610)(125,605)(126,608)(127,607)(128,606)
(129,601)(130,604)(131,603)(132,602)(133,597)(134,600)(135,599)(136,598)
(137,593)(138,596)(139,595)(140,594)(141,589)(142,592)(143,591)(144,590)
(145,541)(146,544)(147,543)(148,542)(149,549)(150,552)(151,551)(152,550)
(153,545)(154,548)(155,547)(156,546)(157,573)(158,576)(159,575)(160,574)
(161,569)(162,572)(163,571)(164,570)(165,565)(166,568)(167,567)(168,566)
(169,561)(170,564)(171,563)(172,562)(173,557)(174,560)(175,559)(176,558)
(177,553)(178,556)(179,555)(180,554)(181,645)(182,648)(183,647)(184,646)
(185,641)(186,644)(187,643)(188,642)(189,637)(190,640)(191,639)(192,638)
(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)(200,630)
(201,625)(202,628)(203,627)(204,626)(205,621)(206,624)(207,623)(208,622)
(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)(216,614)
(217,793)(218,796)(219,795)(220,794)(221,801)(222,804)(223,803)(224,802)
(225,797)(226,800)(227,799)(228,798)(229,825)(230,828)(231,827)(232,826)
(233,821)(234,824)(235,823)(236,822)(237,817)(238,820)(239,819)(240,818)
(241,813)(242,816)(243,815)(244,814)(245,809)(246,812)(247,811)(248,810)
(249,805)(250,808)(251,807)(252,806)(253,757)(254,760)(255,759)(256,758)
(257,765)(258,768)(259,767)(260,766)(261,761)(262,764)(263,763)(264,762)
(265,789)(266,792)(267,791)(268,790)(269,785)(270,788)(271,787)(272,786)
(273,781)(274,784)(275,783)(276,782)(277,777)(278,780)(279,779)(280,778)
(281,773)(282,776)(283,775)(284,774)(285,769)(286,772)(287,771)(288,770)
(289,861)(290,864)(291,863)(292,862)(293,857)(294,860)(295,859)(296,858)
(297,853)(298,856)(299,855)(300,854)(301,849)(302,852)(303,851)(304,850)
(305,845)(306,848)(307,847)(308,846)(309,841)(310,844)(311,843)(312,842)
(313,837)(314,840)(315,839)(316,838)(317,833)(318,836)(319,835)(320,834)
(321,829)(322,832)(323,831)(324,830)(325,685)(326,688)(327,687)(328,686)
(329,693)(330,696)(331,695)(332,694)(333,689)(334,692)(335,691)(336,690)
(337,717)(338,720)(339,719)(340,718)(341,713)(342,716)(343,715)(344,714)
(345,709)(346,712)(347,711)(348,710)(349,705)(350,708)(351,707)(352,706)
(353,701)(354,704)(355,703)(356,702)(357,697)(358,700)(359,699)(360,698)
(361,649)(362,652)(363,651)(364,650)(365,657)(366,660)(367,659)(368,658)
(369,653)(370,656)(371,655)(372,654)(373,681)(374,684)(375,683)(376,682)
(377,677)(378,680)(379,679)(380,678)(381,673)(382,676)(383,675)(384,674)
(385,669)(386,672)(387,671)(388,670)(389,665)(390,668)(391,667)(392,666)
(393,661)(394,664)(395,663)(396,662)(397,753)(398,756)(399,755)(400,754)
(401,749)(402,752)(403,751)(404,750)(405,745)(406,748)(407,747)(408,746)
(409,741)(410,744)(411,743)(412,742)(413,737)(414,740)(415,739)(416,738)
(417,733)(418,736)(419,735)(420,734)(421,729)(422,732)(423,731)(424,730)
(425,725)(426,728)(427,727)(428,726)(429,721)(430,724)(431,723)(432,722);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*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*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*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*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*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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,111)( 2,112)( 3,109)( 4,110)( 5,115)( 6,116)( 7,113)
( 8,114)( 9,119)( 10,120)( 11,117)( 12,118)( 13,123)( 14,124)( 15,121)
( 16,122)( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)( 23,129)
( 24,130)( 25,135)( 26,136)( 27,133)( 28,134)( 29,139)( 30,140)( 31,137)
( 32,138)( 33,143)( 34,144)( 35,141)( 36,142)( 37,147)( 38,148)( 39,145)
( 40,146)( 41,151)( 42,152)( 43,149)( 44,150)( 45,155)( 46,156)( 47,153)
( 48,154)( 49,159)( 50,160)( 51,157)( 52,158)( 53,163)( 54,164)( 55,161)
( 56,162)( 57,167)( 58,168)( 59,165)( 60,166)( 61,171)( 62,172)( 63,169)
( 64,170)( 65,175)( 66,176)( 67,173)( 68,174)( 69,179)( 70,180)( 71,177)
( 72,178)( 73,183)( 74,184)( 75,181)( 76,182)( 77,187)( 78,188)( 79,185)
( 80,186)( 81,191)( 82,192)( 83,189)( 84,190)( 85,195)( 86,196)( 87,193)
( 88,194)( 89,199)( 90,200)( 91,197)( 92,198)( 93,203)( 94,204)( 95,201)
( 96,202)( 97,207)( 98,208)( 99,205)(100,206)(101,211)(102,212)(103,209)
(104,210)(105,215)(106,216)(107,213)(108,214)(217,327)(218,328)(219,325)
(220,326)(221,331)(222,332)(223,329)(224,330)(225,335)(226,336)(227,333)
(228,334)(229,339)(230,340)(231,337)(232,338)(233,343)(234,344)(235,341)
(236,342)(237,347)(238,348)(239,345)(240,346)(241,351)(242,352)(243,349)
(244,350)(245,355)(246,356)(247,353)(248,354)(249,359)(250,360)(251,357)
(252,358)(253,363)(254,364)(255,361)(256,362)(257,367)(258,368)(259,365)
(260,366)(261,371)(262,372)(263,369)(264,370)(265,375)(266,376)(267,373)
(268,374)(269,379)(270,380)(271,377)(272,378)(273,383)(274,384)(275,381)
(276,382)(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)(283,389)
(284,390)(285,395)(286,396)(287,393)(288,394)(289,399)(290,400)(291,397)
(292,398)(293,403)(294,404)(295,401)(296,402)(297,407)(298,408)(299,405)
(300,406)(301,411)(302,412)(303,409)(304,410)(305,415)(306,416)(307,413)
(308,414)(309,419)(310,420)(311,417)(312,418)(313,423)(314,424)(315,421)
(316,422)(317,427)(318,428)(319,425)(320,426)(321,431)(322,432)(323,429)
(324,430)(433,543)(434,544)(435,541)(436,542)(437,547)(438,548)(439,545)
(440,546)(441,551)(442,552)(443,549)(444,550)(445,555)(446,556)(447,553)
(448,554)(449,559)(450,560)(451,557)(452,558)(453,563)(454,564)(455,561)
(456,562)(457,567)(458,568)(459,565)(460,566)(461,571)(462,572)(463,569)
(464,570)(465,575)(466,576)(467,573)(468,574)(469,579)(470,580)(471,577)
(472,578)(473,583)(474,584)(475,581)(476,582)(477,587)(478,588)(479,585)
(480,586)(481,591)(482,592)(483,589)(484,590)(485,595)(486,596)(487,593)
(488,594)(489,599)(490,600)(491,597)(492,598)(493,603)(494,604)(495,601)
(496,602)(497,607)(498,608)(499,605)(500,606)(501,611)(502,612)(503,609)
(504,610)(505,615)(506,616)(507,613)(508,614)(509,619)(510,620)(511,617)
(512,618)(513,623)(514,624)(515,621)(516,622)(517,627)(518,628)(519,625)
(520,626)(521,631)(522,632)(523,629)(524,630)(525,635)(526,636)(527,633)
(528,634)(529,639)(530,640)(531,637)(532,638)(533,643)(534,644)(535,641)
(536,642)(537,647)(538,648)(539,645)(540,646)(649,759)(650,760)(651,757)
(652,758)(653,763)(654,764)(655,761)(656,762)(657,767)(658,768)(659,765)
(660,766)(661,771)(662,772)(663,769)(664,770)(665,775)(666,776)(667,773)
(668,774)(669,779)(670,780)(671,777)(672,778)(673,783)(674,784)(675,781)
(676,782)(677,787)(678,788)(679,785)(680,786)(681,791)(682,792)(683,789)
(684,790)(685,795)(686,796)(687,793)(688,794)(689,799)(690,800)(691,797)
(692,798)(693,803)(694,804)(695,801)(696,802)(697,807)(698,808)(699,805)
(700,806)(701,811)(702,812)(703,809)(704,810)(705,815)(706,816)(707,813)
(708,814)(709,819)(710,820)(711,817)(712,818)(713,823)(714,824)(715,821)
(716,822)(717,827)(718,828)(719,825)(720,826)(721,831)(722,832)(723,829)
(724,830)(725,835)(726,836)(727,833)(728,834)(729,839)(730,840)(731,837)
(732,838)(733,843)(734,844)(735,841)(736,842)(737,847)(738,848)(739,845)
(740,846)(741,851)(742,852)(743,849)(744,850)(745,855)(746,856)(747,853)
(748,854)(749,859)(750,860)(751,857)(752,858)(753,863)(754,864)(755,861)
(756,862);
s1 := Sym(864)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)
( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)
( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)
( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)
(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)
(146,214)(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)
(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)
(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)
(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)
(178,182)(179,184)(180,183)(217,325)(218,326)(219,328)(220,327)(221,333)
(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,357)
(230,358)(231,360)(232,359)(233,353)(234,354)(235,356)(236,355)(237,349)
(238,350)(239,352)(240,351)(241,345)(242,346)(243,348)(244,347)(245,341)
(246,342)(247,344)(248,343)(249,337)(250,338)(251,340)(252,339)(253,429)
(254,430)(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)(261,421)
(262,422)(263,424)(264,423)(265,417)(266,418)(267,420)(268,419)(269,413)
(270,414)(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)
(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)
(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)
(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)
(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)
(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)
(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(433,649)
(434,650)(435,652)(436,651)(437,657)(438,658)(439,660)(440,659)(441,653)
(442,654)(443,656)(444,655)(445,681)(446,682)(447,684)(448,683)(449,677)
(450,678)(451,680)(452,679)(453,673)(454,674)(455,676)(456,675)(457,669)
(458,670)(459,672)(460,671)(461,665)(462,666)(463,668)(464,667)(465,661)
(466,662)(467,664)(468,663)(469,753)(470,754)(471,756)(472,755)(473,749)
(474,750)(475,752)(476,751)(477,745)(478,746)(479,748)(480,747)(481,741)
(482,742)(483,744)(484,743)(485,737)(486,738)(487,740)(488,739)(489,733)
(490,734)(491,736)(492,735)(493,729)(494,730)(495,732)(496,731)(497,725)
(498,726)(499,728)(500,727)(501,721)(502,722)(503,724)(504,723)(505,717)
(506,718)(507,720)(508,719)(509,713)(510,714)(511,716)(512,715)(513,709)
(514,710)(515,712)(516,711)(517,705)(518,706)(519,708)(520,707)(521,701)
(522,702)(523,704)(524,703)(525,697)(526,698)(527,700)(528,699)(529,693)
(530,694)(531,696)(532,695)(533,689)(534,690)(535,692)(536,691)(537,685)
(538,686)(539,688)(540,687)(541,757)(542,758)(543,760)(544,759)(545,765)
(546,766)(547,768)(548,767)(549,761)(550,762)(551,764)(552,763)(553,789)
(554,790)(555,792)(556,791)(557,785)(558,786)(559,788)(560,787)(561,781)
(562,782)(563,784)(564,783)(565,777)(566,778)(567,780)(568,779)(569,773)
(570,774)(571,776)(572,775)(573,769)(574,770)(575,772)(576,771)(577,861)
(578,862)(579,864)(580,863)(581,857)(582,858)(583,860)(584,859)(585,853)
(586,854)(587,856)(588,855)(589,849)(590,850)(591,852)(592,851)(593,845)
(594,846)(595,848)(596,847)(597,841)(598,842)(599,844)(600,843)(601,837)
(602,838)(603,840)(604,839)(605,833)(606,834)(607,836)(608,835)(609,829)
(610,830)(611,832)(612,831)(613,825)(614,826)(615,828)(616,827)(617,821)
(618,822)(619,824)(620,823)(621,817)(622,818)(623,820)(624,819)(625,813)
(626,814)(627,816)(628,815)(629,809)(630,810)(631,812)(632,811)(633,805)
(634,806)(635,808)(636,807)(637,801)(638,802)(639,804)(640,803)(641,797)
(642,798)(643,800)(644,799)(645,793)(646,794)(647,796)(648,795);
s2 := Sym(864)!( 1,469)( 2,472)( 3,471)( 4,470)( 5,477)( 6,480)( 7,479)
( 8,478)( 9,473)( 10,476)( 11,475)( 12,474)( 13,501)( 14,504)( 15,503)
( 16,502)( 17,497)( 18,500)( 19,499)( 20,498)( 21,493)( 22,496)( 23,495)
( 24,494)( 25,489)( 26,492)( 27,491)( 28,490)( 29,485)( 30,488)( 31,487)
( 32,486)( 33,481)( 34,484)( 35,483)( 36,482)( 37,433)( 38,436)( 39,435)
( 40,434)( 41,441)( 42,444)( 43,443)( 44,442)( 45,437)( 46,440)( 47,439)
( 48,438)( 49,465)( 50,468)( 51,467)( 52,466)( 53,461)( 54,464)( 55,463)
( 56,462)( 57,457)( 58,460)( 59,459)( 60,458)( 61,453)( 62,456)( 63,455)
( 64,454)( 65,449)( 66,452)( 67,451)( 68,450)( 69,445)( 70,448)( 71,447)
( 72,446)( 73,537)( 74,540)( 75,539)( 76,538)( 77,533)( 78,536)( 79,535)
( 80,534)( 81,529)( 82,532)( 83,531)( 84,530)( 85,525)( 86,528)( 87,527)
( 88,526)( 89,521)( 90,524)( 91,523)( 92,522)( 93,517)( 94,520)( 95,519)
( 96,518)( 97,513)( 98,516)( 99,515)(100,514)(101,509)(102,512)(103,511)
(104,510)(105,505)(106,508)(107,507)(108,506)(109,577)(110,580)(111,579)
(112,578)(113,585)(114,588)(115,587)(116,586)(117,581)(118,584)(119,583)
(120,582)(121,609)(122,612)(123,611)(124,610)(125,605)(126,608)(127,607)
(128,606)(129,601)(130,604)(131,603)(132,602)(133,597)(134,600)(135,599)
(136,598)(137,593)(138,596)(139,595)(140,594)(141,589)(142,592)(143,591)
(144,590)(145,541)(146,544)(147,543)(148,542)(149,549)(150,552)(151,551)
(152,550)(153,545)(154,548)(155,547)(156,546)(157,573)(158,576)(159,575)
(160,574)(161,569)(162,572)(163,571)(164,570)(165,565)(166,568)(167,567)
(168,566)(169,561)(170,564)(171,563)(172,562)(173,557)(174,560)(175,559)
(176,558)(177,553)(178,556)(179,555)(180,554)(181,645)(182,648)(183,647)
(184,646)(185,641)(186,644)(187,643)(188,642)(189,637)(190,640)(191,639)
(192,638)(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)
(200,630)(201,625)(202,628)(203,627)(204,626)(205,621)(206,624)(207,623)
(208,622)(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)
(216,614)(217,793)(218,796)(219,795)(220,794)(221,801)(222,804)(223,803)
(224,802)(225,797)(226,800)(227,799)(228,798)(229,825)(230,828)(231,827)
(232,826)(233,821)(234,824)(235,823)(236,822)(237,817)(238,820)(239,819)
(240,818)(241,813)(242,816)(243,815)(244,814)(245,809)(246,812)(247,811)
(248,810)(249,805)(250,808)(251,807)(252,806)(253,757)(254,760)(255,759)
(256,758)(257,765)(258,768)(259,767)(260,766)(261,761)(262,764)(263,763)
(264,762)(265,789)(266,792)(267,791)(268,790)(269,785)(270,788)(271,787)
(272,786)(273,781)(274,784)(275,783)(276,782)(277,777)(278,780)(279,779)
(280,778)(281,773)(282,776)(283,775)(284,774)(285,769)(286,772)(287,771)
(288,770)(289,861)(290,864)(291,863)(292,862)(293,857)(294,860)(295,859)
(296,858)(297,853)(298,856)(299,855)(300,854)(301,849)(302,852)(303,851)
(304,850)(305,845)(306,848)(307,847)(308,846)(309,841)(310,844)(311,843)
(312,842)(313,837)(314,840)(315,839)(316,838)(317,833)(318,836)(319,835)
(320,834)(321,829)(322,832)(323,831)(324,830)(325,685)(326,688)(327,687)
(328,686)(329,693)(330,696)(331,695)(332,694)(333,689)(334,692)(335,691)
(336,690)(337,717)(338,720)(339,719)(340,718)(341,713)(342,716)(343,715)
(344,714)(345,709)(346,712)(347,711)(348,710)(349,705)(350,708)(351,707)
(352,706)(353,701)(354,704)(355,703)(356,702)(357,697)(358,700)(359,699)
(360,698)(361,649)(362,652)(363,651)(364,650)(365,657)(366,660)(367,659)
(368,658)(369,653)(370,656)(371,655)(372,654)(373,681)(374,684)(375,683)
(376,682)(377,677)(378,680)(379,679)(380,678)(381,673)(382,676)(383,675)
(384,674)(385,669)(386,672)(387,671)(388,670)(389,665)(390,668)(391,667)
(392,666)(393,661)(394,664)(395,663)(396,662)(397,753)(398,756)(399,755)
(400,754)(401,749)(402,752)(403,751)(404,750)(405,745)(406,748)(407,747)
(408,746)(409,741)(410,744)(411,743)(412,742)(413,737)(414,740)(415,739)
(416,738)(417,733)(418,736)(419,735)(420,734)(421,729)(422,732)(423,731)
(424,730)(425,725)(426,728)(427,727)(428,726)(429,721)(430,724)(431,723)
(432,722);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*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*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*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*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*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*s1*s2*s1*s2 >;
References : None.
to this polytope