Polytope of Type {4,225}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,225}*1800
if this polytope has a name.
Group : SmallGroup(1800,41)
Rank : 3
Schlafli Type : {4,225}
Number of vertices, edges, etc : 4, 450, 225
Order of s₀s₁s₂ : 225
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) :
   3-fold quotients : {4,75}*600
   5-fold quotients : {4,45}*360
   15-fold quotients : {4,15}*120
   25-fold quotients : {4,9}*72
   75-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)(889,891)(890,892)(893,895)(894,896)
(897,899)(898,900);;
s1 := (  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);;
s2 := (  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);;
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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(900)!(  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)(889,891)(890,892)(893,895)
(894,896)(897,899)(898,900);
s1 := 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);
s2 := 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);
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, 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*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope