Polytope of Type {20,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8}*1600b
if this polytope has a name.
Group : SmallGroup(1600,6743)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 100, 400, 40
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {20,4}*800
   4-fold quotients : {10,4}*400
   8-fold quotients : {10,4}*200
   25-fold quotients : {4,8}*64b
   50-fold quotients : {4,4}*32
   100-fold quotients : {2,4}*16, {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
to this polytope