Polytope of Type {4,222}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,222}*1776b
if this polytope has a name.
Group : SmallGroup(1776,245)
Rank : 3
Schlafli Type : {4,222}
Number of vertices, edges, etc : 4, 444, 222
Order of s₀s₁s₂ : 222
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 : {4,111}*888
   37-fold quotients : {4,6}*48c
   74-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)
(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)
(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)
(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480)
(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)(494,496)
(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)(510,512)
(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)(526,528)
(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)(542,544)
(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)(558,560)
(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)(574,576)
(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)(590,592)
(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)(606,608)
(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)(622,624)
(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)(638,640)
(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)(654,656)
(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)(670,672)
(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)(686,688)
(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)(702,704)
(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)(718,720)
(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)(734,736)
(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)(750,752)
(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)(766,768)
(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)(782,784)
(785,787)(786,788)(789,791)(790,792)(793,795)(794,796)(797,799)(798,800)
(801,803)(802,804)(805,807)(806,808)(809,811)(810,812)(813,815)(814,816)
(817,819)(818,820)(821,823)(822,824)(825,827)(826,828)(829,831)(830,832)
(833,835)(834,836)(837,839)(838,840)(841,843)(842,844)(845,847)(846,848)
(849,851)(850,852)(853,855)(854,856)(857,859)(858,860)(861,863)(862,864)
(865,867)(866,868)(869,871)(870,872)(873,875)(874,876)(877,879)(878,880)
(881,883)(882,884)(885,887)(886,888);;
s1 := (  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);;
s2 := (  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);;
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*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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(888)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)
(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)
(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)
(478,480)(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)
(494,496)(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)
(510,512)(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)
(526,528)(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)
(542,544)(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)
(558,560)(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)
(574,576)(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)
(590,592)(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)
(606,608)(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)
(622,624)(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)
(638,640)(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)
(654,656)(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)
(670,672)(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)
(686,688)(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)
(702,704)(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)
(718,720)(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)
(734,736)(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)
(750,752)(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)
(766,768)(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)
(782,784)(785,787)(786,788)(789,791)(790,792)(793,795)(794,796)(797,799)
(798,800)(801,803)(802,804)(805,807)(806,808)(809,811)(810,812)(813,815)
(814,816)(817,819)(818,820)(821,823)(822,824)(825,827)(826,828)(829,831)
(830,832)(833,835)(834,836)(837,839)(838,840)(841,843)(842,844)(845,847)
(846,848)(849,851)(850,852)(853,855)(854,856)(857,859)(858,860)(861,863)
(862,864)(865,867)(866,868)(869,871)(870,872)(873,875)(874,876)(877,879)
(878,880)(881,883)(882,884)(885,887)(886,888);
s1 := 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);
s2 := 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);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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