Polytope of Type {225,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {225,4}*1800
if this polytope has a name.
Group : SmallGroup(1800,41)
Rank : 3
Schlafli Type : {225,4}
Number of vertices, edges, etc : 225, 450, 4
Order of s₀s₁s₂ : 225
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   Self-Petrie
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) :
   3-fold quotients : {75,4}*600
   5-fold quotients : {45,4}*360
   15-fold quotients : {15,4}*120
   25-fold quotients : {9,4}*72
   75-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)
( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)
( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)
( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 61,257)( 62,258)( 63,260)
( 64,259)( 65,253)( 66,254)( 67,256)( 68,255)( 69,249)( 70,250)( 71,252)
( 72,251)( 73,245)( 74,246)( 75,248)( 76,247)( 77,241)( 78,242)( 79,244)
( 80,243)( 81,297)( 82,298)( 83,300)( 84,299)( 85,293)( 86,294)( 87,296)
( 88,295)( 89,289)( 90,290)( 91,292)( 92,291)( 93,285)( 94,286)( 95,288)
( 96,287)( 97,281)( 98,282)( 99,284)(100,283)(101,277)(102,278)(103,280)
(104,279)(105,273)(106,274)(107,276)(108,275)(109,269)(110,270)(111,272)
(112,271)(113,265)(114,266)(115,268)(116,267)(117,261)(118,262)(119,264)
(120,263)(121,197)(122,198)(123,200)(124,199)(125,193)(126,194)(127,196)
(128,195)(129,189)(130,190)(131,192)(132,191)(133,185)(134,186)(135,188)
(136,187)(137,181)(138,182)(139,184)(140,183)(141,237)(142,238)(143,240)
(144,239)(145,233)(146,234)(147,236)(148,235)(149,229)(150,230)(151,232)
(152,231)(153,225)(154,226)(155,228)(156,227)(157,221)(158,222)(159,224)
(160,223)(161,217)(162,218)(163,220)(164,219)(165,213)(166,214)(167,216)
(168,215)(169,209)(170,210)(171,212)(172,211)(173,205)(174,206)(175,208)
(176,207)(177,201)(178,202)(179,204)(180,203)(301,641)(302,642)(303,644)
(304,643)(305,657)(306,658)(307,660)(308,659)(309,653)(310,654)(311,656)
(312,655)(313,649)(314,650)(315,652)(316,651)(317,645)(318,646)(319,648)
(320,647)(321,621)(322,622)(323,624)(324,623)(325,637)(326,638)(327,640)
(328,639)(329,633)(330,634)(331,636)(332,635)(333,629)(334,630)(335,632)
(336,631)(337,625)(338,626)(339,628)(340,627)(341,601)(342,602)(343,604)
(344,603)(345,617)(346,618)(347,620)(348,619)(349,613)(350,614)(351,616)
(352,615)(353,609)(354,610)(355,612)(356,611)(357,605)(358,606)(359,608)
(360,607)(361,897)(362,898)(363,900)(364,899)(365,893)(366,894)(367,896)
(368,895)(369,889)(370,890)(371,892)(372,891)(373,885)(374,886)(375,888)
(376,887)(377,881)(378,882)(379,884)(380,883)(381,877)(382,878)(383,880)
(384,879)(385,873)(386,874)(387,876)(388,875)(389,869)(390,870)(391,872)
(392,871)(393,865)(394,866)(395,868)(396,867)(397,861)(398,862)(399,864)
(400,863)(401,857)(402,858)(403,860)(404,859)(405,853)(406,854)(407,856)
(408,855)(409,849)(410,850)(411,852)(412,851)(413,845)(414,846)(415,848)
(416,847)(417,841)(418,842)(419,844)(420,843)(421,837)(422,838)(423,840)
(424,839)(425,833)(426,834)(427,836)(428,835)(429,829)(430,830)(431,832)
(432,831)(433,825)(434,826)(435,828)(436,827)(437,821)(438,822)(439,824)
(440,823)(441,817)(442,818)(443,820)(444,819)(445,813)(446,814)(447,816)
(448,815)(449,809)(450,810)(451,812)(452,811)(453,805)(454,806)(455,808)
(456,807)(457,801)(458,802)(459,804)(460,803)(461,797)(462,798)(463,800)
(464,799)(465,793)(466,794)(467,796)(468,795)(469,789)(470,790)(471,792)
(472,791)(473,785)(474,786)(475,788)(476,787)(477,781)(478,782)(479,784)
(480,783)(481,777)(482,778)(483,780)(484,779)(485,773)(486,774)(487,776)
(488,775)(489,769)(490,770)(491,772)(492,771)(493,765)(494,766)(495,768)
(496,767)(497,761)(498,762)(499,764)(500,763)(501,757)(502,758)(503,760)
(504,759)(505,753)(506,754)(507,756)(508,755)(509,749)(510,750)(511,752)
(512,751)(513,745)(514,746)(515,748)(516,747)(517,741)(518,742)(519,744)
(520,743)(521,737)(522,738)(523,740)(524,739)(525,733)(526,734)(527,736)
(528,735)(529,729)(530,730)(531,732)(532,731)(533,725)(534,726)(535,728)
(536,727)(537,721)(538,722)(539,724)(540,723)(541,717)(542,718)(543,720)
(544,719)(545,713)(546,714)(547,716)(548,715)(549,709)(550,710)(551,712)
(552,711)(553,705)(554,706)(555,708)(556,707)(557,701)(558,702)(559,704)
(560,703)(561,697)(562,698)(563,700)(564,699)(565,693)(566,694)(567,696)
(568,695)(569,689)(570,690)(571,692)(572,691)(573,685)(574,686)(575,688)
(576,687)(577,681)(578,682)(579,684)(580,683)(581,677)(582,678)(583,680)
(584,679)(585,673)(586,674)(587,676)(588,675)(589,669)(590,670)(591,672)
(592,671)(593,665)(594,666)(595,668)(596,667)(597,661)(598,662)(599,664)
(600,663);;
s1 := (  1,361)(  2,364)(  3,363)(  4,362)(  5,377)(  6,380)(  7,379)(  8,378)
(  9,373)( 10,376)( 11,375)( 12,374)( 13,369)( 14,372)( 15,371)( 16,370)
( 17,365)( 18,368)( 19,367)( 20,366)( 21,401)( 22,404)( 23,403)( 24,402)
( 25,417)( 26,420)( 27,419)( 28,418)( 29,413)( 30,416)( 31,415)( 32,414)
( 33,409)( 34,412)( 35,411)( 36,410)( 37,405)( 38,408)( 39,407)( 40,406)
( 41,381)( 42,384)( 43,383)( 44,382)( 45,397)( 46,400)( 47,399)( 48,398)
( 49,393)( 50,396)( 51,395)( 52,394)( 53,389)( 54,392)( 55,391)( 56,390)
( 57,385)( 58,388)( 59,387)( 60,386)( 61,301)( 62,304)( 63,303)( 64,302)
( 65,317)( 66,320)( 67,319)( 68,318)( 69,313)( 70,316)( 71,315)( 72,314)
( 73,309)( 74,312)( 75,311)( 76,310)( 77,305)( 78,308)( 79,307)( 80,306)
( 81,341)( 82,344)( 83,343)( 84,342)( 85,357)( 86,360)( 87,359)( 88,358)
( 89,353)( 90,356)( 91,355)( 92,354)( 93,349)( 94,352)( 95,351)( 96,350)
( 97,345)( 98,348)( 99,347)(100,346)(101,321)(102,324)(103,323)(104,322)
(105,337)(106,340)(107,339)(108,338)(109,333)(110,336)(111,335)(112,334)
(113,329)(114,332)(115,331)(116,330)(117,325)(118,328)(119,327)(120,326)
(121,557)(122,560)(123,559)(124,558)(125,553)(126,556)(127,555)(128,554)
(129,549)(130,552)(131,551)(132,550)(133,545)(134,548)(135,547)(136,546)
(137,541)(138,544)(139,543)(140,542)(141,597)(142,600)(143,599)(144,598)
(145,593)(146,596)(147,595)(148,594)(149,589)(150,592)(151,591)(152,590)
(153,585)(154,588)(155,587)(156,586)(157,581)(158,584)(159,583)(160,582)
(161,577)(162,580)(163,579)(164,578)(165,573)(166,576)(167,575)(168,574)
(169,569)(170,572)(171,571)(172,570)(173,565)(174,568)(175,567)(176,566)
(177,561)(178,564)(179,563)(180,562)(181,497)(182,500)(183,499)(184,498)
(185,493)(186,496)(187,495)(188,494)(189,489)(190,492)(191,491)(192,490)
(193,485)(194,488)(195,487)(196,486)(197,481)(198,484)(199,483)(200,482)
(201,537)(202,540)(203,539)(204,538)(205,533)(206,536)(207,535)(208,534)
(209,529)(210,532)(211,531)(212,530)(213,525)(214,528)(215,527)(216,526)
(217,521)(218,524)(219,523)(220,522)(221,517)(222,520)(223,519)(224,518)
(225,513)(226,516)(227,515)(228,514)(229,509)(230,512)(231,511)(232,510)
(233,505)(234,508)(235,507)(236,506)(237,501)(238,504)(239,503)(240,502)
(241,437)(242,440)(243,439)(244,438)(245,433)(246,436)(247,435)(248,434)
(249,429)(250,432)(251,431)(252,430)(253,425)(254,428)(255,427)(256,426)
(257,421)(258,424)(259,423)(260,422)(261,477)(262,480)(263,479)(264,478)
(265,473)(266,476)(267,475)(268,474)(269,469)(270,472)(271,471)(272,470)
(273,465)(274,468)(275,467)(276,466)(277,461)(278,464)(279,463)(280,462)
(281,457)(282,460)(283,459)(284,458)(285,453)(286,456)(287,455)(288,454)
(289,449)(290,452)(291,451)(292,450)(293,445)(294,448)(295,447)(296,446)
(297,441)(298,444)(299,443)(300,442)(601,701)(602,704)(603,703)(604,702)
(605,717)(606,720)(607,719)(608,718)(609,713)(610,716)(611,715)(612,714)
(613,709)(614,712)(615,711)(616,710)(617,705)(618,708)(619,707)(620,706)
(621,681)(622,684)(623,683)(624,682)(625,697)(626,700)(627,699)(628,698)
(629,693)(630,696)(631,695)(632,694)(633,689)(634,692)(635,691)(636,690)
(637,685)(638,688)(639,687)(640,686)(641,661)(642,664)(643,663)(644,662)
(645,677)(646,680)(647,679)(648,678)(649,673)(650,676)(651,675)(652,674)
(653,669)(654,672)(655,671)(656,670)(657,665)(658,668)(659,667)(660,666)
(721,897)(722,900)(723,899)(724,898)(725,893)(726,896)(727,895)(728,894)
(729,889)(730,892)(731,891)(732,890)(733,885)(734,888)(735,887)(736,886)
(737,881)(738,884)(739,883)(740,882)(741,877)(742,880)(743,879)(744,878)
(745,873)(746,876)(747,875)(748,874)(749,869)(750,872)(751,871)(752,870)
(753,865)(754,868)(755,867)(756,866)(757,861)(758,864)(759,863)(760,862)
(761,857)(762,860)(763,859)(764,858)(765,853)(766,856)(767,855)(768,854)
(769,849)(770,852)(771,851)(772,850)(773,845)(774,848)(775,847)(776,846)
(777,841)(778,844)(779,843)(780,842)(781,837)(782,840)(783,839)(784,838)
(785,833)(786,836)(787,835)(788,834)(789,829)(790,832)(791,831)(792,830)
(793,825)(794,828)(795,827)(796,826)(797,821)(798,824)(799,823)(800,822)
(801,817)(802,820)(803,819)(804,818)(805,813)(806,816)(807,815)(808,814)
(810,812);;
s2 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)
(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)
(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)
(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)
(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)
(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)
(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)
(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)
(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)
(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)
(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)
(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)
(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)
(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)
(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)
(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)
(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)
(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)
(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)
(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)
(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)
(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)
(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)
(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)(847,848)
(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)(863,864)
(865,866)(867,868)(869,870)(871,872)(873,874)(875,876)(877,878)(879,880)
(881,882)(883,884)(885,886)(887,888)(889,890)(891,892)(893,894)(895,896)
(897,898)(899,900);;
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, 
s2*s1*s0*s2*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*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*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*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(900)!(  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)
( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)
( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 61,257)( 62,258)
( 63,260)( 64,259)( 65,253)( 66,254)( 67,256)( 68,255)( 69,249)( 70,250)
( 71,252)( 72,251)( 73,245)( 74,246)( 75,248)( 76,247)( 77,241)( 78,242)
( 79,244)( 80,243)( 81,297)( 82,298)( 83,300)( 84,299)( 85,293)( 86,294)
( 87,296)( 88,295)( 89,289)( 90,290)( 91,292)( 92,291)( 93,285)( 94,286)
( 95,288)( 96,287)( 97,281)( 98,282)( 99,284)(100,283)(101,277)(102,278)
(103,280)(104,279)(105,273)(106,274)(107,276)(108,275)(109,269)(110,270)
(111,272)(112,271)(113,265)(114,266)(115,268)(116,267)(117,261)(118,262)
(119,264)(120,263)(121,197)(122,198)(123,200)(124,199)(125,193)(126,194)
(127,196)(128,195)(129,189)(130,190)(131,192)(132,191)(133,185)(134,186)
(135,188)(136,187)(137,181)(138,182)(139,184)(140,183)(141,237)(142,238)
(143,240)(144,239)(145,233)(146,234)(147,236)(148,235)(149,229)(150,230)
(151,232)(152,231)(153,225)(154,226)(155,228)(156,227)(157,221)(158,222)
(159,224)(160,223)(161,217)(162,218)(163,220)(164,219)(165,213)(166,214)
(167,216)(168,215)(169,209)(170,210)(171,212)(172,211)(173,205)(174,206)
(175,208)(176,207)(177,201)(178,202)(179,204)(180,203)(301,641)(302,642)
(303,644)(304,643)(305,657)(306,658)(307,660)(308,659)(309,653)(310,654)
(311,656)(312,655)(313,649)(314,650)(315,652)(316,651)(317,645)(318,646)
(319,648)(320,647)(321,621)(322,622)(323,624)(324,623)(325,637)(326,638)
(327,640)(328,639)(329,633)(330,634)(331,636)(332,635)(333,629)(334,630)
(335,632)(336,631)(337,625)(338,626)(339,628)(340,627)(341,601)(342,602)
(343,604)(344,603)(345,617)(346,618)(347,620)(348,619)(349,613)(350,614)
(351,616)(352,615)(353,609)(354,610)(355,612)(356,611)(357,605)(358,606)
(359,608)(360,607)(361,897)(362,898)(363,900)(364,899)(365,893)(366,894)
(367,896)(368,895)(369,889)(370,890)(371,892)(372,891)(373,885)(374,886)
(375,888)(376,887)(377,881)(378,882)(379,884)(380,883)(381,877)(382,878)
(383,880)(384,879)(385,873)(386,874)(387,876)(388,875)(389,869)(390,870)
(391,872)(392,871)(393,865)(394,866)(395,868)(396,867)(397,861)(398,862)
(399,864)(400,863)(401,857)(402,858)(403,860)(404,859)(405,853)(406,854)
(407,856)(408,855)(409,849)(410,850)(411,852)(412,851)(413,845)(414,846)
(415,848)(416,847)(417,841)(418,842)(419,844)(420,843)(421,837)(422,838)
(423,840)(424,839)(425,833)(426,834)(427,836)(428,835)(429,829)(430,830)
(431,832)(432,831)(433,825)(434,826)(435,828)(436,827)(437,821)(438,822)
(439,824)(440,823)(441,817)(442,818)(443,820)(444,819)(445,813)(446,814)
(447,816)(448,815)(449,809)(450,810)(451,812)(452,811)(453,805)(454,806)
(455,808)(456,807)(457,801)(458,802)(459,804)(460,803)(461,797)(462,798)
(463,800)(464,799)(465,793)(466,794)(467,796)(468,795)(469,789)(470,790)
(471,792)(472,791)(473,785)(474,786)(475,788)(476,787)(477,781)(478,782)
(479,784)(480,783)(481,777)(482,778)(483,780)(484,779)(485,773)(486,774)
(487,776)(488,775)(489,769)(490,770)(491,772)(492,771)(493,765)(494,766)
(495,768)(496,767)(497,761)(498,762)(499,764)(500,763)(501,757)(502,758)
(503,760)(504,759)(505,753)(506,754)(507,756)(508,755)(509,749)(510,750)
(511,752)(512,751)(513,745)(514,746)(515,748)(516,747)(517,741)(518,742)
(519,744)(520,743)(521,737)(522,738)(523,740)(524,739)(525,733)(526,734)
(527,736)(528,735)(529,729)(530,730)(531,732)(532,731)(533,725)(534,726)
(535,728)(536,727)(537,721)(538,722)(539,724)(540,723)(541,717)(542,718)
(543,720)(544,719)(545,713)(546,714)(547,716)(548,715)(549,709)(550,710)
(551,712)(552,711)(553,705)(554,706)(555,708)(556,707)(557,701)(558,702)
(559,704)(560,703)(561,697)(562,698)(563,700)(564,699)(565,693)(566,694)
(567,696)(568,695)(569,689)(570,690)(571,692)(572,691)(573,685)(574,686)
(575,688)(576,687)(577,681)(578,682)(579,684)(580,683)(581,677)(582,678)
(583,680)(584,679)(585,673)(586,674)(587,676)(588,675)(589,669)(590,670)
(591,672)(592,671)(593,665)(594,666)(595,668)(596,667)(597,661)(598,662)
(599,664)(600,663);
s1 := Sym(900)!(  1,361)(  2,364)(  3,363)(  4,362)(  5,377)(  6,380)(  7,379)
(  8,378)(  9,373)( 10,376)( 11,375)( 12,374)( 13,369)( 14,372)( 15,371)
( 16,370)( 17,365)( 18,368)( 19,367)( 20,366)( 21,401)( 22,404)( 23,403)
( 24,402)( 25,417)( 26,420)( 27,419)( 28,418)( 29,413)( 30,416)( 31,415)
( 32,414)( 33,409)( 34,412)( 35,411)( 36,410)( 37,405)( 38,408)( 39,407)
( 40,406)( 41,381)( 42,384)( 43,383)( 44,382)( 45,397)( 46,400)( 47,399)
( 48,398)( 49,393)( 50,396)( 51,395)( 52,394)( 53,389)( 54,392)( 55,391)
( 56,390)( 57,385)( 58,388)( 59,387)( 60,386)( 61,301)( 62,304)( 63,303)
( 64,302)( 65,317)( 66,320)( 67,319)( 68,318)( 69,313)( 70,316)( 71,315)
( 72,314)( 73,309)( 74,312)( 75,311)( 76,310)( 77,305)( 78,308)( 79,307)
( 80,306)( 81,341)( 82,344)( 83,343)( 84,342)( 85,357)( 86,360)( 87,359)
( 88,358)( 89,353)( 90,356)( 91,355)( 92,354)( 93,349)( 94,352)( 95,351)
( 96,350)( 97,345)( 98,348)( 99,347)(100,346)(101,321)(102,324)(103,323)
(104,322)(105,337)(106,340)(107,339)(108,338)(109,333)(110,336)(111,335)
(112,334)(113,329)(114,332)(115,331)(116,330)(117,325)(118,328)(119,327)
(120,326)(121,557)(122,560)(123,559)(124,558)(125,553)(126,556)(127,555)
(128,554)(129,549)(130,552)(131,551)(132,550)(133,545)(134,548)(135,547)
(136,546)(137,541)(138,544)(139,543)(140,542)(141,597)(142,600)(143,599)
(144,598)(145,593)(146,596)(147,595)(148,594)(149,589)(150,592)(151,591)
(152,590)(153,585)(154,588)(155,587)(156,586)(157,581)(158,584)(159,583)
(160,582)(161,577)(162,580)(163,579)(164,578)(165,573)(166,576)(167,575)
(168,574)(169,569)(170,572)(171,571)(172,570)(173,565)(174,568)(175,567)
(176,566)(177,561)(178,564)(179,563)(180,562)(181,497)(182,500)(183,499)
(184,498)(185,493)(186,496)(187,495)(188,494)(189,489)(190,492)(191,491)
(192,490)(193,485)(194,488)(195,487)(196,486)(197,481)(198,484)(199,483)
(200,482)(201,537)(202,540)(203,539)(204,538)(205,533)(206,536)(207,535)
(208,534)(209,529)(210,532)(211,531)(212,530)(213,525)(214,528)(215,527)
(216,526)(217,521)(218,524)(219,523)(220,522)(221,517)(222,520)(223,519)
(224,518)(225,513)(226,516)(227,515)(228,514)(229,509)(230,512)(231,511)
(232,510)(233,505)(234,508)(235,507)(236,506)(237,501)(238,504)(239,503)
(240,502)(241,437)(242,440)(243,439)(244,438)(245,433)(246,436)(247,435)
(248,434)(249,429)(250,432)(251,431)(252,430)(253,425)(254,428)(255,427)
(256,426)(257,421)(258,424)(259,423)(260,422)(261,477)(262,480)(263,479)
(264,478)(265,473)(266,476)(267,475)(268,474)(269,469)(270,472)(271,471)
(272,470)(273,465)(274,468)(275,467)(276,466)(277,461)(278,464)(279,463)
(280,462)(281,457)(282,460)(283,459)(284,458)(285,453)(286,456)(287,455)
(288,454)(289,449)(290,452)(291,451)(292,450)(293,445)(294,448)(295,447)
(296,446)(297,441)(298,444)(299,443)(300,442)(601,701)(602,704)(603,703)
(604,702)(605,717)(606,720)(607,719)(608,718)(609,713)(610,716)(611,715)
(612,714)(613,709)(614,712)(615,711)(616,710)(617,705)(618,708)(619,707)
(620,706)(621,681)(622,684)(623,683)(624,682)(625,697)(626,700)(627,699)
(628,698)(629,693)(630,696)(631,695)(632,694)(633,689)(634,692)(635,691)
(636,690)(637,685)(638,688)(639,687)(640,686)(641,661)(642,664)(643,663)
(644,662)(645,677)(646,680)(647,679)(648,678)(649,673)(650,676)(651,675)
(652,674)(653,669)(654,672)(655,671)(656,670)(657,665)(658,668)(659,667)
(660,666)(721,897)(722,900)(723,899)(724,898)(725,893)(726,896)(727,895)
(728,894)(729,889)(730,892)(731,891)(732,890)(733,885)(734,888)(735,887)
(736,886)(737,881)(738,884)(739,883)(740,882)(741,877)(742,880)(743,879)
(744,878)(745,873)(746,876)(747,875)(748,874)(749,869)(750,872)(751,871)
(752,870)(753,865)(754,868)(755,867)(756,866)(757,861)(758,864)(759,863)
(760,862)(761,857)(762,860)(763,859)(764,858)(765,853)(766,856)(767,855)
(768,854)(769,849)(770,852)(771,851)(772,850)(773,845)(774,848)(775,847)
(776,846)(777,841)(778,844)(779,843)(780,842)(781,837)(782,840)(783,839)
(784,838)(785,833)(786,836)(787,835)(788,834)(789,829)(790,832)(791,831)
(792,830)(793,825)(794,828)(795,827)(796,826)(797,821)(798,824)(799,823)
(800,822)(801,817)(802,820)(803,819)(804,818)(805,813)(806,816)(807,815)
(808,814)(810,812);
s2 := Sym(900)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)
(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)
(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)
(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)
(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)
(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)
(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)
(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)
(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)
(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)
(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)
(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)
(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)
(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)
(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)
(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)
(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)
(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)
(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)
(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)
(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)
(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)
(831,832)(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)
(847,848)(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)
(863,864)(865,866)(867,868)(869,870)(871,872)(873,874)(875,876)(877,878)
(879,880)(881,882)(883,884)(885,886)(887,888)(889,890)(891,892)(893,894)
(895,896)(897,898)(899,900);
poly := sub<Sym(900)|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, 
s2*s1*s0*s2*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*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*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*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