Polytope of Type {25,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {25,4}*1600
if this polytope has a name.
Group : SmallGroup(1600,5601)
Rank : 3
Schlafli Type : {25,4}
Number of vertices, edges, etc : 200, 400, 32
Order of s₀s₁s₂ : 50
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {25,4}*800
   5-fold quotients : {5,4}*320
   10-fold quotients : {5,4}*160
   16-fold quotients : {25,2}*100
   80-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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