Polytope of Type {222,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {222,4}*1776c
if this polytope has a name.
Group : SmallGroup(1776,245)
Rank : 3
Schlafli Type : {222,4}
Number of vertices, edges, etc : 222, 444, 4
Order of s0s1s2 : 111
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {111,4}*888
37-fold quotients : {6,4}*48b
74-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,145)( 6,146)( 7,148)( 8,147)( 9,141)( 10,142)( 11,144)
( 12,143)( 13,137)( 14,138)( 15,140)( 16,139)( 17,133)( 18,134)( 19,136)
( 20,135)( 21,129)( 22,130)( 23,132)( 24,131)( 25,125)( 26,126)( 27,128)
( 28,127)( 29,121)( 30,122)( 31,124)( 32,123)( 33,117)( 34,118)( 35,120)
( 36,119)( 37,113)( 38,114)( 39,116)( 40,115)( 41,109)( 42,110)( 43,112)
( 44,111)( 45,105)( 46,106)( 47,108)( 48,107)( 49,101)( 50,102)( 51,104)
( 52,103)( 53, 97)( 54, 98)( 55,100)( 56, 99)( 57, 93)( 58, 94)( 59, 96)
( 60, 95)( 61, 89)( 62, 90)( 63, 92)( 64, 91)( 65, 85)( 66, 86)( 67, 88)
( 68, 87)( 69, 81)( 70, 82)( 71, 84)( 72, 83)( 73, 77)( 74, 78)( 75, 80)
( 76, 79)(149,297)(150,298)(151,300)(152,299)(153,441)(154,442)(155,444)
(156,443)(157,437)(158,438)(159,440)(160,439)(161,433)(162,434)(163,436)
(164,435)(165,429)(166,430)(167,432)(168,431)(169,425)(170,426)(171,428)
(172,427)(173,421)(174,422)(175,424)(176,423)(177,417)(178,418)(179,420)
(180,419)(181,413)(182,414)(183,416)(184,415)(185,409)(186,410)(187,412)
(188,411)(189,405)(190,406)(191,408)(192,407)(193,401)(194,402)(195,404)
(196,403)(197,397)(198,398)(199,400)(200,399)(201,393)(202,394)(203,396)
(204,395)(205,389)(206,390)(207,392)(208,391)(209,385)(210,386)(211,388)
(212,387)(213,381)(214,382)(215,384)(216,383)(217,377)(218,378)(219,380)
(220,379)(221,373)(222,374)(223,376)(224,375)(225,369)(226,370)(227,372)
(228,371)(229,365)(230,366)(231,368)(232,367)(233,361)(234,362)(235,364)
(236,363)(237,357)(238,358)(239,360)(240,359)(241,353)(242,354)(243,356)
(244,355)(245,349)(246,350)(247,352)(248,351)(249,345)(250,346)(251,348)
(252,347)(253,341)(254,342)(255,344)(256,343)(257,337)(258,338)(259,340)
(260,339)(261,333)(262,334)(263,336)(264,335)(265,329)(266,330)(267,332)
(268,331)(269,325)(270,326)(271,328)(272,327)(273,321)(274,322)(275,324)
(276,323)(277,317)(278,318)(279,320)(280,319)(281,313)(282,314)(283,316)
(284,315)(285,309)(286,310)(287,312)(288,311)(289,305)(290,306)(291,308)
(292,307)(293,301)(294,302)(295,304)(296,303)(447,448)(449,589)(450,590)
(451,592)(452,591)(453,585)(454,586)(455,588)(456,587)(457,581)(458,582)
(459,584)(460,583)(461,577)(462,578)(463,580)(464,579)(465,573)(466,574)
(467,576)(468,575)(469,569)(470,570)(471,572)(472,571)(473,565)(474,566)
(475,568)(476,567)(477,561)(478,562)(479,564)(480,563)(481,557)(482,558)
(483,560)(484,559)(485,553)(486,554)(487,556)(488,555)(489,549)(490,550)
(491,552)(492,551)(493,545)(494,546)(495,548)(496,547)(497,541)(498,542)
(499,544)(500,543)(501,537)(502,538)(503,540)(504,539)(505,533)(506,534)
(507,536)(508,535)(509,529)(510,530)(511,532)(512,531)(513,525)(514,526)
(515,528)(516,527)(517,521)(518,522)(519,524)(520,523)(593,741)(594,742)
(595,744)(596,743)(597,885)(598,886)(599,888)(600,887)(601,881)(602,882)
(603,884)(604,883)(605,877)(606,878)(607,880)(608,879)(609,873)(610,874)
(611,876)(612,875)(613,869)(614,870)(615,872)(616,871)(617,865)(618,866)
(619,868)(620,867)(621,861)(622,862)(623,864)(624,863)(625,857)(626,858)
(627,860)(628,859)(629,853)(630,854)(631,856)(632,855)(633,849)(634,850)
(635,852)(636,851)(637,845)(638,846)(639,848)(640,847)(641,841)(642,842)
(643,844)(644,843)(645,837)(646,838)(647,840)(648,839)(649,833)(650,834)
(651,836)(652,835)(653,829)(654,830)(655,832)(656,831)(657,825)(658,826)
(659,828)(660,827)(661,821)(662,822)(663,824)(664,823)(665,817)(666,818)
(667,820)(668,819)(669,813)(670,814)(671,816)(672,815)(673,809)(674,810)
(675,812)(676,811)(677,805)(678,806)(679,808)(680,807)(681,801)(682,802)
(683,804)(684,803)(685,797)(686,798)(687,800)(688,799)(689,793)(690,794)
(691,796)(692,795)(693,789)(694,790)(695,792)(696,791)(697,785)(698,786)
(699,788)(700,787)(701,781)(702,782)(703,784)(704,783)(705,777)(706,778)
(707,780)(708,779)(709,773)(710,774)(711,776)(712,775)(713,769)(714,770)
(715,772)(716,771)(717,765)(718,766)(719,768)(720,767)(721,761)(722,762)
(723,764)(724,763)(725,757)(726,758)(727,760)(728,759)(729,753)(730,754)
(731,756)(732,755)(733,749)(734,750)(735,752)(736,751)(737,745)(738,746)
(739,748)(740,747);;
s1 := ( 1,597)( 2,600)( 3,599)( 4,598)( 5,593)( 6,596)( 7,595)( 8,594)
( 9,737)( 10,740)( 11,739)( 12,738)( 13,733)( 14,736)( 15,735)( 16,734)
( 17,729)( 18,732)( 19,731)( 20,730)( 21,725)( 22,728)( 23,727)( 24,726)
( 25,721)( 26,724)( 27,723)( 28,722)( 29,717)( 30,720)( 31,719)( 32,718)
( 33,713)( 34,716)( 35,715)( 36,714)( 37,709)( 38,712)( 39,711)( 40,710)
( 41,705)( 42,708)( 43,707)( 44,706)( 45,701)( 46,704)( 47,703)( 48,702)
( 49,697)( 50,700)( 51,699)( 52,698)( 53,693)( 54,696)( 55,695)( 56,694)
( 57,689)( 58,692)( 59,691)( 60,690)( 61,685)( 62,688)( 63,687)( 64,686)
( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)( 72,678)
( 73,673)( 74,676)( 75,675)( 76,674)( 77,669)( 78,672)( 79,671)( 80,670)
( 81,665)( 82,668)( 83,667)( 84,666)( 85,661)( 86,664)( 87,663)( 88,662)
( 89,657)( 90,660)( 91,659)( 92,658)( 93,653)( 94,656)( 95,655)( 96,654)
( 97,649)( 98,652)( 99,651)(100,650)(101,645)(102,648)(103,647)(104,646)
(105,641)(106,644)(107,643)(108,642)(109,637)(110,640)(111,639)(112,638)
(113,633)(114,636)(115,635)(116,634)(117,629)(118,632)(119,631)(120,630)
(121,625)(122,628)(123,627)(124,626)(125,621)(126,624)(127,623)(128,622)
(129,617)(130,620)(131,619)(132,618)(133,613)(134,616)(135,615)(136,614)
(137,609)(138,612)(139,611)(140,610)(141,605)(142,608)(143,607)(144,606)
(145,601)(146,604)(147,603)(148,602)(149,449)(150,452)(151,451)(152,450)
(153,445)(154,448)(155,447)(156,446)(157,589)(158,592)(159,591)(160,590)
(161,585)(162,588)(163,587)(164,586)(165,581)(166,584)(167,583)(168,582)
(169,577)(170,580)(171,579)(172,578)(173,573)(174,576)(175,575)(176,574)
(177,569)(178,572)(179,571)(180,570)(181,565)(182,568)(183,567)(184,566)
(185,561)(186,564)(187,563)(188,562)(189,557)(190,560)(191,559)(192,558)
(193,553)(194,556)(195,555)(196,554)(197,549)(198,552)(199,551)(200,550)
(201,545)(202,548)(203,547)(204,546)(205,541)(206,544)(207,543)(208,542)
(209,537)(210,540)(211,539)(212,538)(213,533)(214,536)(215,535)(216,534)
(217,529)(218,532)(219,531)(220,530)(221,525)(222,528)(223,527)(224,526)
(225,521)(226,524)(227,523)(228,522)(229,517)(230,520)(231,519)(232,518)
(233,513)(234,516)(235,515)(236,514)(237,509)(238,512)(239,511)(240,510)
(241,505)(242,508)(243,507)(244,506)(245,501)(246,504)(247,503)(248,502)
(249,497)(250,500)(251,499)(252,498)(253,493)(254,496)(255,495)(256,494)
(257,489)(258,492)(259,491)(260,490)(261,485)(262,488)(263,487)(264,486)
(265,481)(266,484)(267,483)(268,482)(269,477)(270,480)(271,479)(272,478)
(273,473)(274,476)(275,475)(276,474)(277,469)(278,472)(279,471)(280,470)
(281,465)(282,468)(283,467)(284,466)(285,461)(286,464)(287,463)(288,462)
(289,457)(290,460)(291,459)(292,458)(293,453)(294,456)(295,455)(296,454)
(297,745)(298,748)(299,747)(300,746)(301,741)(302,744)(303,743)(304,742)
(305,885)(306,888)(307,887)(308,886)(309,881)(310,884)(311,883)(312,882)
(313,877)(314,880)(315,879)(316,878)(317,873)(318,876)(319,875)(320,874)
(321,869)(322,872)(323,871)(324,870)(325,865)(326,868)(327,867)(328,866)
(329,861)(330,864)(331,863)(332,862)(333,857)(334,860)(335,859)(336,858)
(337,853)(338,856)(339,855)(340,854)(341,849)(342,852)(343,851)(344,850)
(345,845)(346,848)(347,847)(348,846)(349,841)(350,844)(351,843)(352,842)
(353,837)(354,840)(355,839)(356,838)(357,833)(358,836)(359,835)(360,834)
(361,829)(362,832)(363,831)(364,830)(365,825)(366,828)(367,827)(368,826)
(369,821)(370,824)(371,823)(372,822)(373,817)(374,820)(375,819)(376,818)
(377,813)(378,816)(379,815)(380,814)(381,809)(382,812)(383,811)(384,810)
(385,805)(386,808)(387,807)(388,806)(389,801)(390,804)(391,803)(392,802)
(393,797)(394,800)(395,799)(396,798)(397,793)(398,796)(399,795)(400,794)
(401,789)(402,792)(403,791)(404,790)(405,785)(406,788)(407,787)(408,786)
(409,781)(410,784)(411,783)(412,782)(413,777)(414,780)(415,779)(416,778)
(417,773)(418,776)(419,775)(420,774)(421,769)(422,772)(423,771)(424,770)
(425,765)(426,768)(427,767)(428,766)(429,761)(430,764)(431,763)(432,762)
(433,757)(434,760)(435,759)(436,758)(437,753)(438,756)(439,755)(440,754)
(441,749)(442,752)(443,751)(444,750);;
s2 := ( 1,446)( 2,445)( 3,448)( 4,447)( 5,450)( 6,449)( 7,452)( 8,451)
( 9,454)( 10,453)( 11,456)( 12,455)( 13,458)( 14,457)( 15,460)( 16,459)
( 17,462)( 18,461)( 19,464)( 20,463)( 21,466)( 22,465)( 23,468)( 24,467)
( 25,470)( 26,469)( 27,472)( 28,471)( 29,474)( 30,473)( 31,476)( 32,475)
( 33,478)( 34,477)( 35,480)( 36,479)( 37,482)( 38,481)( 39,484)( 40,483)
( 41,486)( 42,485)( 43,488)( 44,487)( 45,490)( 46,489)( 47,492)( 48,491)
( 49,494)( 50,493)( 51,496)( 52,495)( 53,498)( 54,497)( 55,500)( 56,499)
( 57,502)( 58,501)( 59,504)( 60,503)( 61,506)( 62,505)( 63,508)( 64,507)
( 65,510)( 66,509)( 67,512)( 68,511)( 69,514)( 70,513)( 71,516)( 72,515)
( 73,518)( 74,517)( 75,520)( 76,519)( 77,522)( 78,521)( 79,524)( 80,523)
( 81,526)( 82,525)( 83,528)( 84,527)( 85,530)( 86,529)( 87,532)( 88,531)
( 89,534)( 90,533)( 91,536)( 92,535)( 93,538)( 94,537)( 95,540)( 96,539)
( 97,542)( 98,541)( 99,544)(100,543)(101,546)(102,545)(103,548)(104,547)
(105,550)(106,549)(107,552)(108,551)(109,554)(110,553)(111,556)(112,555)
(113,558)(114,557)(115,560)(116,559)(117,562)(118,561)(119,564)(120,563)
(121,566)(122,565)(123,568)(124,567)(125,570)(126,569)(127,572)(128,571)
(129,574)(130,573)(131,576)(132,575)(133,578)(134,577)(135,580)(136,579)
(137,582)(138,581)(139,584)(140,583)(141,586)(142,585)(143,588)(144,587)
(145,590)(146,589)(147,592)(148,591)(149,594)(150,593)(151,596)(152,595)
(153,598)(154,597)(155,600)(156,599)(157,602)(158,601)(159,604)(160,603)
(161,606)(162,605)(163,608)(164,607)(165,610)(166,609)(167,612)(168,611)
(169,614)(170,613)(171,616)(172,615)(173,618)(174,617)(175,620)(176,619)
(177,622)(178,621)(179,624)(180,623)(181,626)(182,625)(183,628)(184,627)
(185,630)(186,629)(187,632)(188,631)(189,634)(190,633)(191,636)(192,635)
(193,638)(194,637)(195,640)(196,639)(197,642)(198,641)(199,644)(200,643)
(201,646)(202,645)(203,648)(204,647)(205,650)(206,649)(207,652)(208,651)
(209,654)(210,653)(211,656)(212,655)(213,658)(214,657)(215,660)(216,659)
(217,662)(218,661)(219,664)(220,663)(221,666)(222,665)(223,668)(224,667)
(225,670)(226,669)(227,672)(228,671)(229,674)(230,673)(231,676)(232,675)
(233,678)(234,677)(235,680)(236,679)(237,682)(238,681)(239,684)(240,683)
(241,686)(242,685)(243,688)(244,687)(245,690)(246,689)(247,692)(248,691)
(249,694)(250,693)(251,696)(252,695)(253,698)(254,697)(255,700)(256,699)
(257,702)(258,701)(259,704)(260,703)(261,706)(262,705)(263,708)(264,707)
(265,710)(266,709)(267,712)(268,711)(269,714)(270,713)(271,716)(272,715)
(273,718)(274,717)(275,720)(276,719)(277,722)(278,721)(279,724)(280,723)
(281,726)(282,725)(283,728)(284,727)(285,730)(286,729)(287,732)(288,731)
(289,734)(290,733)(291,736)(292,735)(293,738)(294,737)(295,740)(296,739)
(297,742)(298,741)(299,744)(300,743)(301,746)(302,745)(303,748)(304,747)
(305,750)(306,749)(307,752)(308,751)(309,754)(310,753)(311,756)(312,755)
(313,758)(314,757)(315,760)(316,759)(317,762)(318,761)(319,764)(320,763)
(321,766)(322,765)(323,768)(324,767)(325,770)(326,769)(327,772)(328,771)
(329,774)(330,773)(331,776)(332,775)(333,778)(334,777)(335,780)(336,779)
(337,782)(338,781)(339,784)(340,783)(341,786)(342,785)(343,788)(344,787)
(345,790)(346,789)(347,792)(348,791)(349,794)(350,793)(351,796)(352,795)
(353,798)(354,797)(355,800)(356,799)(357,802)(358,801)(359,804)(360,803)
(361,806)(362,805)(363,808)(364,807)(365,810)(366,809)(367,812)(368,811)
(369,814)(370,813)(371,816)(372,815)(373,818)(374,817)(375,820)(376,819)
(377,822)(378,821)(379,824)(380,823)(381,826)(382,825)(383,828)(384,827)
(385,830)(386,829)(387,832)(388,831)(389,834)(390,833)(391,836)(392,835)
(393,838)(394,837)(395,840)(396,839)(397,842)(398,841)(399,844)(400,843)
(401,846)(402,845)(403,848)(404,847)(405,850)(406,849)(407,852)(408,851)
(409,854)(410,853)(411,856)(412,855)(413,858)(414,857)(415,860)(416,859)
(417,862)(418,861)(419,864)(420,863)(421,866)(422,865)(423,868)(424,867)
(425,870)(426,869)(427,872)(428,871)(429,874)(430,873)(431,876)(432,875)
(433,878)(434,877)(435,880)(436,879)(437,882)(438,881)(439,884)(440,883)
(441,886)(442,885)(443,888)(444,887);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*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*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*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*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(888)!( 3, 4)( 5,145)( 6,146)( 7,148)( 8,147)( 9,141)( 10,142)
( 11,144)( 12,143)( 13,137)( 14,138)( 15,140)( 16,139)( 17,133)( 18,134)
( 19,136)( 20,135)( 21,129)( 22,130)( 23,132)( 24,131)( 25,125)( 26,126)
( 27,128)( 28,127)( 29,121)( 30,122)( 31,124)( 32,123)( 33,117)( 34,118)
( 35,120)( 36,119)( 37,113)( 38,114)( 39,116)( 40,115)( 41,109)( 42,110)
( 43,112)( 44,111)( 45,105)( 46,106)( 47,108)( 48,107)( 49,101)( 50,102)
( 51,104)( 52,103)( 53, 97)( 54, 98)( 55,100)( 56, 99)( 57, 93)( 58, 94)
( 59, 96)( 60, 95)( 61, 89)( 62, 90)( 63, 92)( 64, 91)( 65, 85)( 66, 86)
( 67, 88)( 68, 87)( 69, 81)( 70, 82)( 71, 84)( 72, 83)( 73, 77)( 74, 78)
( 75, 80)( 76, 79)(149,297)(150,298)(151,300)(152,299)(153,441)(154,442)
(155,444)(156,443)(157,437)(158,438)(159,440)(160,439)(161,433)(162,434)
(163,436)(164,435)(165,429)(166,430)(167,432)(168,431)(169,425)(170,426)
(171,428)(172,427)(173,421)(174,422)(175,424)(176,423)(177,417)(178,418)
(179,420)(180,419)(181,413)(182,414)(183,416)(184,415)(185,409)(186,410)
(187,412)(188,411)(189,405)(190,406)(191,408)(192,407)(193,401)(194,402)
(195,404)(196,403)(197,397)(198,398)(199,400)(200,399)(201,393)(202,394)
(203,396)(204,395)(205,389)(206,390)(207,392)(208,391)(209,385)(210,386)
(211,388)(212,387)(213,381)(214,382)(215,384)(216,383)(217,377)(218,378)
(219,380)(220,379)(221,373)(222,374)(223,376)(224,375)(225,369)(226,370)
(227,372)(228,371)(229,365)(230,366)(231,368)(232,367)(233,361)(234,362)
(235,364)(236,363)(237,357)(238,358)(239,360)(240,359)(241,353)(242,354)
(243,356)(244,355)(245,349)(246,350)(247,352)(248,351)(249,345)(250,346)
(251,348)(252,347)(253,341)(254,342)(255,344)(256,343)(257,337)(258,338)
(259,340)(260,339)(261,333)(262,334)(263,336)(264,335)(265,329)(266,330)
(267,332)(268,331)(269,325)(270,326)(271,328)(272,327)(273,321)(274,322)
(275,324)(276,323)(277,317)(278,318)(279,320)(280,319)(281,313)(282,314)
(283,316)(284,315)(285,309)(286,310)(287,312)(288,311)(289,305)(290,306)
(291,308)(292,307)(293,301)(294,302)(295,304)(296,303)(447,448)(449,589)
(450,590)(451,592)(452,591)(453,585)(454,586)(455,588)(456,587)(457,581)
(458,582)(459,584)(460,583)(461,577)(462,578)(463,580)(464,579)(465,573)
(466,574)(467,576)(468,575)(469,569)(470,570)(471,572)(472,571)(473,565)
(474,566)(475,568)(476,567)(477,561)(478,562)(479,564)(480,563)(481,557)
(482,558)(483,560)(484,559)(485,553)(486,554)(487,556)(488,555)(489,549)
(490,550)(491,552)(492,551)(493,545)(494,546)(495,548)(496,547)(497,541)
(498,542)(499,544)(500,543)(501,537)(502,538)(503,540)(504,539)(505,533)
(506,534)(507,536)(508,535)(509,529)(510,530)(511,532)(512,531)(513,525)
(514,526)(515,528)(516,527)(517,521)(518,522)(519,524)(520,523)(593,741)
(594,742)(595,744)(596,743)(597,885)(598,886)(599,888)(600,887)(601,881)
(602,882)(603,884)(604,883)(605,877)(606,878)(607,880)(608,879)(609,873)
(610,874)(611,876)(612,875)(613,869)(614,870)(615,872)(616,871)(617,865)
(618,866)(619,868)(620,867)(621,861)(622,862)(623,864)(624,863)(625,857)
(626,858)(627,860)(628,859)(629,853)(630,854)(631,856)(632,855)(633,849)
(634,850)(635,852)(636,851)(637,845)(638,846)(639,848)(640,847)(641,841)
(642,842)(643,844)(644,843)(645,837)(646,838)(647,840)(648,839)(649,833)
(650,834)(651,836)(652,835)(653,829)(654,830)(655,832)(656,831)(657,825)
(658,826)(659,828)(660,827)(661,821)(662,822)(663,824)(664,823)(665,817)
(666,818)(667,820)(668,819)(669,813)(670,814)(671,816)(672,815)(673,809)
(674,810)(675,812)(676,811)(677,805)(678,806)(679,808)(680,807)(681,801)
(682,802)(683,804)(684,803)(685,797)(686,798)(687,800)(688,799)(689,793)
(690,794)(691,796)(692,795)(693,789)(694,790)(695,792)(696,791)(697,785)
(698,786)(699,788)(700,787)(701,781)(702,782)(703,784)(704,783)(705,777)
(706,778)(707,780)(708,779)(709,773)(710,774)(711,776)(712,775)(713,769)
(714,770)(715,772)(716,771)(717,765)(718,766)(719,768)(720,767)(721,761)
(722,762)(723,764)(724,763)(725,757)(726,758)(727,760)(728,759)(729,753)
(730,754)(731,756)(732,755)(733,749)(734,750)(735,752)(736,751)(737,745)
(738,746)(739,748)(740,747);
s1 := Sym(888)!( 1,597)( 2,600)( 3,599)( 4,598)( 5,593)( 6,596)( 7,595)
( 8,594)( 9,737)( 10,740)( 11,739)( 12,738)( 13,733)( 14,736)( 15,735)
( 16,734)( 17,729)( 18,732)( 19,731)( 20,730)( 21,725)( 22,728)( 23,727)
( 24,726)( 25,721)( 26,724)( 27,723)( 28,722)( 29,717)( 30,720)( 31,719)
( 32,718)( 33,713)( 34,716)( 35,715)( 36,714)( 37,709)( 38,712)( 39,711)
( 40,710)( 41,705)( 42,708)( 43,707)( 44,706)( 45,701)( 46,704)( 47,703)
( 48,702)( 49,697)( 50,700)( 51,699)( 52,698)( 53,693)( 54,696)( 55,695)
( 56,694)( 57,689)( 58,692)( 59,691)( 60,690)( 61,685)( 62,688)( 63,687)
( 64,686)( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)
( 72,678)( 73,673)( 74,676)( 75,675)( 76,674)( 77,669)( 78,672)( 79,671)
( 80,670)( 81,665)( 82,668)( 83,667)( 84,666)( 85,661)( 86,664)( 87,663)
( 88,662)( 89,657)( 90,660)( 91,659)( 92,658)( 93,653)( 94,656)( 95,655)
( 96,654)( 97,649)( 98,652)( 99,651)(100,650)(101,645)(102,648)(103,647)
(104,646)(105,641)(106,644)(107,643)(108,642)(109,637)(110,640)(111,639)
(112,638)(113,633)(114,636)(115,635)(116,634)(117,629)(118,632)(119,631)
(120,630)(121,625)(122,628)(123,627)(124,626)(125,621)(126,624)(127,623)
(128,622)(129,617)(130,620)(131,619)(132,618)(133,613)(134,616)(135,615)
(136,614)(137,609)(138,612)(139,611)(140,610)(141,605)(142,608)(143,607)
(144,606)(145,601)(146,604)(147,603)(148,602)(149,449)(150,452)(151,451)
(152,450)(153,445)(154,448)(155,447)(156,446)(157,589)(158,592)(159,591)
(160,590)(161,585)(162,588)(163,587)(164,586)(165,581)(166,584)(167,583)
(168,582)(169,577)(170,580)(171,579)(172,578)(173,573)(174,576)(175,575)
(176,574)(177,569)(178,572)(179,571)(180,570)(181,565)(182,568)(183,567)
(184,566)(185,561)(186,564)(187,563)(188,562)(189,557)(190,560)(191,559)
(192,558)(193,553)(194,556)(195,555)(196,554)(197,549)(198,552)(199,551)
(200,550)(201,545)(202,548)(203,547)(204,546)(205,541)(206,544)(207,543)
(208,542)(209,537)(210,540)(211,539)(212,538)(213,533)(214,536)(215,535)
(216,534)(217,529)(218,532)(219,531)(220,530)(221,525)(222,528)(223,527)
(224,526)(225,521)(226,524)(227,523)(228,522)(229,517)(230,520)(231,519)
(232,518)(233,513)(234,516)(235,515)(236,514)(237,509)(238,512)(239,511)
(240,510)(241,505)(242,508)(243,507)(244,506)(245,501)(246,504)(247,503)
(248,502)(249,497)(250,500)(251,499)(252,498)(253,493)(254,496)(255,495)
(256,494)(257,489)(258,492)(259,491)(260,490)(261,485)(262,488)(263,487)
(264,486)(265,481)(266,484)(267,483)(268,482)(269,477)(270,480)(271,479)
(272,478)(273,473)(274,476)(275,475)(276,474)(277,469)(278,472)(279,471)
(280,470)(281,465)(282,468)(283,467)(284,466)(285,461)(286,464)(287,463)
(288,462)(289,457)(290,460)(291,459)(292,458)(293,453)(294,456)(295,455)
(296,454)(297,745)(298,748)(299,747)(300,746)(301,741)(302,744)(303,743)
(304,742)(305,885)(306,888)(307,887)(308,886)(309,881)(310,884)(311,883)
(312,882)(313,877)(314,880)(315,879)(316,878)(317,873)(318,876)(319,875)
(320,874)(321,869)(322,872)(323,871)(324,870)(325,865)(326,868)(327,867)
(328,866)(329,861)(330,864)(331,863)(332,862)(333,857)(334,860)(335,859)
(336,858)(337,853)(338,856)(339,855)(340,854)(341,849)(342,852)(343,851)
(344,850)(345,845)(346,848)(347,847)(348,846)(349,841)(350,844)(351,843)
(352,842)(353,837)(354,840)(355,839)(356,838)(357,833)(358,836)(359,835)
(360,834)(361,829)(362,832)(363,831)(364,830)(365,825)(366,828)(367,827)
(368,826)(369,821)(370,824)(371,823)(372,822)(373,817)(374,820)(375,819)
(376,818)(377,813)(378,816)(379,815)(380,814)(381,809)(382,812)(383,811)
(384,810)(385,805)(386,808)(387,807)(388,806)(389,801)(390,804)(391,803)
(392,802)(393,797)(394,800)(395,799)(396,798)(397,793)(398,796)(399,795)
(400,794)(401,789)(402,792)(403,791)(404,790)(405,785)(406,788)(407,787)
(408,786)(409,781)(410,784)(411,783)(412,782)(413,777)(414,780)(415,779)
(416,778)(417,773)(418,776)(419,775)(420,774)(421,769)(422,772)(423,771)
(424,770)(425,765)(426,768)(427,767)(428,766)(429,761)(430,764)(431,763)
(432,762)(433,757)(434,760)(435,759)(436,758)(437,753)(438,756)(439,755)
(440,754)(441,749)(442,752)(443,751)(444,750);
s2 := Sym(888)!( 1,446)( 2,445)( 3,448)( 4,447)( 5,450)( 6,449)( 7,452)
( 8,451)( 9,454)( 10,453)( 11,456)( 12,455)( 13,458)( 14,457)( 15,460)
( 16,459)( 17,462)( 18,461)( 19,464)( 20,463)( 21,466)( 22,465)( 23,468)
( 24,467)( 25,470)( 26,469)( 27,472)( 28,471)( 29,474)( 30,473)( 31,476)
( 32,475)( 33,478)( 34,477)( 35,480)( 36,479)( 37,482)( 38,481)( 39,484)
( 40,483)( 41,486)( 42,485)( 43,488)( 44,487)( 45,490)( 46,489)( 47,492)
( 48,491)( 49,494)( 50,493)( 51,496)( 52,495)( 53,498)( 54,497)( 55,500)
( 56,499)( 57,502)( 58,501)( 59,504)( 60,503)( 61,506)( 62,505)( 63,508)
( 64,507)( 65,510)( 66,509)( 67,512)( 68,511)( 69,514)( 70,513)( 71,516)
( 72,515)( 73,518)( 74,517)( 75,520)( 76,519)( 77,522)( 78,521)( 79,524)
( 80,523)( 81,526)( 82,525)( 83,528)( 84,527)( 85,530)( 86,529)( 87,532)
( 88,531)( 89,534)( 90,533)( 91,536)( 92,535)( 93,538)( 94,537)( 95,540)
( 96,539)( 97,542)( 98,541)( 99,544)(100,543)(101,546)(102,545)(103,548)
(104,547)(105,550)(106,549)(107,552)(108,551)(109,554)(110,553)(111,556)
(112,555)(113,558)(114,557)(115,560)(116,559)(117,562)(118,561)(119,564)
(120,563)(121,566)(122,565)(123,568)(124,567)(125,570)(126,569)(127,572)
(128,571)(129,574)(130,573)(131,576)(132,575)(133,578)(134,577)(135,580)
(136,579)(137,582)(138,581)(139,584)(140,583)(141,586)(142,585)(143,588)
(144,587)(145,590)(146,589)(147,592)(148,591)(149,594)(150,593)(151,596)
(152,595)(153,598)(154,597)(155,600)(156,599)(157,602)(158,601)(159,604)
(160,603)(161,606)(162,605)(163,608)(164,607)(165,610)(166,609)(167,612)
(168,611)(169,614)(170,613)(171,616)(172,615)(173,618)(174,617)(175,620)
(176,619)(177,622)(178,621)(179,624)(180,623)(181,626)(182,625)(183,628)
(184,627)(185,630)(186,629)(187,632)(188,631)(189,634)(190,633)(191,636)
(192,635)(193,638)(194,637)(195,640)(196,639)(197,642)(198,641)(199,644)
(200,643)(201,646)(202,645)(203,648)(204,647)(205,650)(206,649)(207,652)
(208,651)(209,654)(210,653)(211,656)(212,655)(213,658)(214,657)(215,660)
(216,659)(217,662)(218,661)(219,664)(220,663)(221,666)(222,665)(223,668)
(224,667)(225,670)(226,669)(227,672)(228,671)(229,674)(230,673)(231,676)
(232,675)(233,678)(234,677)(235,680)(236,679)(237,682)(238,681)(239,684)
(240,683)(241,686)(242,685)(243,688)(244,687)(245,690)(246,689)(247,692)
(248,691)(249,694)(250,693)(251,696)(252,695)(253,698)(254,697)(255,700)
(256,699)(257,702)(258,701)(259,704)(260,703)(261,706)(262,705)(263,708)
(264,707)(265,710)(266,709)(267,712)(268,711)(269,714)(270,713)(271,716)
(272,715)(273,718)(274,717)(275,720)(276,719)(277,722)(278,721)(279,724)
(280,723)(281,726)(282,725)(283,728)(284,727)(285,730)(286,729)(287,732)
(288,731)(289,734)(290,733)(291,736)(292,735)(293,738)(294,737)(295,740)
(296,739)(297,742)(298,741)(299,744)(300,743)(301,746)(302,745)(303,748)
(304,747)(305,750)(306,749)(307,752)(308,751)(309,754)(310,753)(311,756)
(312,755)(313,758)(314,757)(315,760)(316,759)(317,762)(318,761)(319,764)
(320,763)(321,766)(322,765)(323,768)(324,767)(325,770)(326,769)(327,772)
(328,771)(329,774)(330,773)(331,776)(332,775)(333,778)(334,777)(335,780)
(336,779)(337,782)(338,781)(339,784)(340,783)(341,786)(342,785)(343,788)
(344,787)(345,790)(346,789)(347,792)(348,791)(349,794)(350,793)(351,796)
(352,795)(353,798)(354,797)(355,800)(356,799)(357,802)(358,801)(359,804)
(360,803)(361,806)(362,805)(363,808)(364,807)(365,810)(366,809)(367,812)
(368,811)(369,814)(370,813)(371,816)(372,815)(373,818)(374,817)(375,820)
(376,819)(377,822)(378,821)(379,824)(380,823)(381,826)(382,825)(383,828)
(384,827)(385,830)(386,829)(387,832)(388,831)(389,834)(390,833)(391,836)
(392,835)(393,838)(394,837)(395,840)(396,839)(397,842)(398,841)(399,844)
(400,843)(401,846)(402,845)(403,848)(404,847)(405,850)(406,849)(407,852)
(408,851)(409,854)(410,853)(411,856)(412,855)(413,858)(414,857)(415,860)
(416,859)(417,862)(418,861)(419,864)(420,863)(421,866)(422,865)(423,868)
(424,867)(425,870)(426,869)(427,872)(428,871)(429,874)(430,873)(431,876)
(432,875)(433,878)(434,877)(435,880)(436,879)(437,882)(438,881)(439,884)
(440,883)(441,886)(442,885)(443,888)(444,887);
poly := sub<Sym(888)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*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*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*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*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