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Polytope of Type {4,10,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,20}*1600c
if this polytope has a name.
Group : SmallGroup(1600,8626)
Rank : 4
Schlafli Type : {4,10,20}
Number of vertices, edges, etc : 4, 20, 100, 20
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,10,10}*800b, {2,10,20}*800c
   4-fold quotients : {2,10,10}*400c
   5-fold quotients : {4,10,4}*320
   8-fold quotients : {2,5,10}*200
   10-fold quotients : {2,10,4}*160, {4,10,2}*160
   20-fold quotients : {2,10,2}*80
   25-fold quotients : {4,2,4}*64
   40-fold quotients : {2,5,2}*40
   50-fold quotients : {2,2,4}*32, {4,2,2}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,201)(  2,202)(  3,203)(  4,204)(  5,205)(  6,206)(  7,207)(  8,208)
(  9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)( 16,216)
( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)( 24,224)
( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)( 32,232)
( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)( 40,240)
( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)( 48,248)
( 49,249)( 50,250)( 51,251)( 52,252)( 53,253)( 54,254)( 55,255)( 56,256)
( 57,257)( 58,258)( 59,259)( 60,260)( 61,261)( 62,262)( 63,263)( 64,264)
( 65,265)( 66,266)( 67,267)( 68,268)( 69,269)( 70,270)( 71,271)( 72,272)
( 73,273)( 74,274)( 75,275)( 76,276)( 77,277)( 78,278)( 79,279)( 80,280)
( 81,281)( 82,282)( 83,283)( 84,284)( 85,285)( 86,286)( 87,287)( 88,288)
( 89,289)( 90,290)( 91,291)( 92,292)( 93,293)( 94,294)( 95,295)( 96,296)
( 97,297)( 98,298)( 99,299)(100,300)(101,351)(102,352)(103,353)(104,354)
(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)(112,362)
(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)(120,370)
(121,371)(122,372)(123,373)(124,374)(125,375)(126,376)(127,377)(128,378)
(129,379)(130,380)(131,381)(132,382)(133,383)(134,384)(135,385)(136,386)
(137,387)(138,388)(139,389)(140,390)(141,391)(142,392)(143,393)(144,394)
(145,395)(146,396)(147,397)(148,398)(149,399)(150,400)(151,301)(152,302)
(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)(160,310)
(161,311)(162,312)(163,313)(164,314)(165,315)(166,316)(167,317)(168,318)
(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,325)(176,326)
(177,327)(178,328)(179,329)(180,330)(181,331)(182,332)(183,333)(184,334)
(185,335)(186,336)(187,337)(188,338)(189,339)(190,340)(191,341)(192,342)
(193,343)(194,344)(195,345)(196,346)(197,347)(198,348)(199,349)(200,350)
(401,601)(402,602)(403,603)(404,604)(405,605)(406,606)(407,607)(408,608)
(409,609)(410,610)(411,611)(412,612)(413,613)(414,614)(415,615)(416,616)
(417,617)(418,618)(419,619)(420,620)(421,621)(422,622)(423,623)(424,624)
(425,625)(426,626)(427,627)(428,628)(429,629)(430,630)(431,631)(432,632)
(433,633)(434,634)(435,635)(436,636)(437,637)(438,638)(439,639)(440,640)
(441,641)(442,642)(443,643)(444,644)(445,645)(446,646)(447,647)(448,648)
(449,649)(450,650)(451,651)(452,652)(453,653)(454,654)(455,655)(456,656)
(457,657)(458,658)(459,659)(460,660)(461,661)(462,662)(463,663)(464,664)
(465,665)(466,666)(467,667)(468,668)(469,669)(470,670)(471,671)(472,672)
(473,673)(474,674)(475,675)(476,676)(477,677)(478,678)(479,679)(480,680)
(481,681)(482,682)(483,683)(484,684)(485,685)(486,686)(487,687)(488,688)
(489,689)(490,690)(491,691)(492,692)(493,693)(494,694)(495,695)(496,696)
(497,697)(498,698)(499,699)(500,700)(501,751)(502,752)(503,753)(504,754)
(505,755)(506,756)(507,757)(508,758)(509,759)(510,760)(511,761)(512,762)
(513,763)(514,764)(515,765)(516,766)(517,767)(518,768)(519,769)(520,770)
(521,771)(522,772)(523,773)(524,774)(525,775)(526,776)(527,777)(528,778)
(529,779)(530,780)(531,781)(532,782)(533,783)(534,784)(535,785)(536,786)
(537,787)(538,788)(539,789)(540,790)(541,791)(542,792)(543,793)(544,794)
(545,795)(546,796)(547,797)(548,798)(549,799)(550,800)(551,701)(552,702)
(553,703)(554,704)(555,705)(556,706)(557,707)(558,708)(559,709)(560,710)
(561,711)(562,712)(563,713)(564,714)(565,715)(566,716)(567,717)(568,718)
(569,719)(570,720)(571,721)(572,722)(573,723)(574,724)(575,725)(576,726)
(577,727)(578,728)(579,729)(580,730)(581,731)(582,732)(583,733)(584,734)
(585,735)(586,736)(587,737)(588,738)(589,739)(590,740)(591,741)(592,742)
(593,743)(594,744)(595,745)(596,746)(597,747)(598,748)(599,749)(600,750);;
s1 := (  1,501)(  2,505)(  3,504)(  4,503)(  5,502)(  6,521)(  7,525)(  8,524)
(  9,523)( 10,522)( 11,516)( 12,520)( 13,519)( 14,518)( 15,517)( 16,511)
( 17,515)( 18,514)( 19,513)( 20,512)( 21,506)( 22,510)( 23,509)( 24,508)
( 25,507)( 26,526)( 27,530)( 28,529)( 29,528)( 30,527)( 31,546)( 32,550)
( 33,549)( 34,548)( 35,547)( 36,541)( 37,545)( 38,544)( 39,543)( 40,542)
( 41,536)( 42,540)( 43,539)( 44,538)( 45,537)( 46,531)( 47,535)( 48,534)
( 49,533)( 50,532)( 51,551)( 52,555)( 53,554)( 54,553)( 55,552)( 56,571)
( 57,575)( 58,574)( 59,573)( 60,572)( 61,566)( 62,570)( 63,569)( 64,568)
( 65,567)( 66,561)( 67,565)( 68,564)( 69,563)( 70,562)( 71,556)( 72,560)
( 73,559)( 74,558)( 75,557)( 76,576)( 77,580)( 78,579)( 79,578)( 80,577)
( 81,596)( 82,600)( 83,599)( 84,598)( 85,597)( 86,591)( 87,595)( 88,594)
( 89,593)( 90,592)( 91,586)( 92,590)( 93,589)( 94,588)( 95,587)( 96,581)
( 97,585)( 98,584)( 99,583)(100,582)(101,401)(102,405)(103,404)(104,403)
(105,402)(106,421)(107,425)(108,424)(109,423)(110,422)(111,416)(112,420)
(113,419)(114,418)(115,417)(116,411)(117,415)(118,414)(119,413)(120,412)
(121,406)(122,410)(123,409)(124,408)(125,407)(126,426)(127,430)(128,429)
(129,428)(130,427)(131,446)(132,450)(133,449)(134,448)(135,447)(136,441)
(137,445)(138,444)(139,443)(140,442)(141,436)(142,440)(143,439)(144,438)
(145,437)(146,431)(147,435)(148,434)(149,433)(150,432)(151,451)(152,455)
(153,454)(154,453)(155,452)(156,471)(157,475)(158,474)(159,473)(160,472)
(161,466)(162,470)(163,469)(164,468)(165,467)(166,461)(167,465)(168,464)
(169,463)(170,462)(171,456)(172,460)(173,459)(174,458)(175,457)(176,476)
(177,480)(178,479)(179,478)(180,477)(181,496)(182,500)(183,499)(184,498)
(185,497)(186,491)(187,495)(188,494)(189,493)(190,492)(191,486)(192,490)
(193,489)(194,488)(195,487)(196,481)(197,485)(198,484)(199,483)(200,482)
(201,701)(202,705)(203,704)(204,703)(205,702)(206,721)(207,725)(208,724)
(209,723)(210,722)(211,716)(212,720)(213,719)(214,718)(215,717)(216,711)
(217,715)(218,714)(219,713)(220,712)(221,706)(222,710)(223,709)(224,708)
(225,707)(226,726)(227,730)(228,729)(229,728)(230,727)(231,746)(232,750)
(233,749)(234,748)(235,747)(236,741)(237,745)(238,744)(239,743)(240,742)
(241,736)(242,740)(243,739)(244,738)(245,737)(246,731)(247,735)(248,734)
(249,733)(250,732)(251,751)(252,755)(253,754)(254,753)(255,752)(256,771)
(257,775)(258,774)(259,773)(260,772)(261,766)(262,770)(263,769)(264,768)
(265,767)(266,761)(267,765)(268,764)(269,763)(270,762)(271,756)(272,760)
(273,759)(274,758)(275,757)(276,776)(277,780)(278,779)(279,778)(280,777)
(281,796)(282,800)(283,799)(284,798)(285,797)(286,791)(287,795)(288,794)
(289,793)(290,792)(291,786)(292,790)(293,789)(294,788)(295,787)(296,781)
(297,785)(298,784)(299,783)(300,782)(301,601)(302,605)(303,604)(304,603)
(305,602)(306,621)(307,625)(308,624)(309,623)(310,622)(311,616)(312,620)
(313,619)(314,618)(315,617)(316,611)(317,615)(318,614)(319,613)(320,612)
(321,606)(322,610)(323,609)(324,608)(325,607)(326,626)(327,630)(328,629)
(329,628)(330,627)(331,646)(332,650)(333,649)(334,648)(335,647)(336,641)
(337,645)(338,644)(339,643)(340,642)(341,636)(342,640)(343,639)(344,638)
(345,637)(346,631)(347,635)(348,634)(349,633)(350,632)(351,651)(352,655)
(353,654)(354,653)(355,652)(356,671)(357,675)(358,674)(359,673)(360,672)
(361,666)(362,670)(363,669)(364,668)(365,667)(366,661)(367,665)(368,664)
(369,663)(370,662)(371,656)(372,660)(373,659)(374,658)(375,657)(376,676)
(377,680)(378,679)(379,678)(380,677)(381,696)(382,700)(383,699)(384,698)
(385,697)(386,691)(387,695)(388,694)(389,693)(390,692)(391,686)(392,690)
(393,689)(394,688)(395,687)(396,681)(397,685)(398,684)(399,683)(400,682);;
s2 := (  1,407)(  2,406)(  3,410)(  4,409)(  5,408)(  6,402)(  7,401)(  8,405)
(  9,404)( 10,403)( 11,422)( 12,421)( 13,425)( 14,424)( 15,423)( 16,417)
( 17,416)( 18,420)( 19,419)( 20,418)( 21,412)( 22,411)( 23,415)( 24,414)
( 25,413)( 26,432)( 27,431)( 28,435)( 29,434)( 30,433)( 31,427)( 32,426)
( 33,430)( 34,429)( 35,428)( 36,447)( 37,446)( 38,450)( 39,449)( 40,448)
( 41,442)( 42,441)( 43,445)( 44,444)( 45,443)( 46,437)( 47,436)( 48,440)
( 49,439)( 50,438)( 51,457)( 52,456)( 53,460)( 54,459)( 55,458)( 56,452)
( 57,451)( 58,455)( 59,454)( 60,453)( 61,472)( 62,471)( 63,475)( 64,474)
( 65,473)( 66,467)( 67,466)( 68,470)( 69,469)( 70,468)( 71,462)( 72,461)
( 73,465)( 74,464)( 75,463)( 76,482)( 77,481)( 78,485)( 79,484)( 80,483)
( 81,477)( 82,476)( 83,480)( 84,479)( 85,478)( 86,497)( 87,496)( 88,500)
( 89,499)( 90,498)( 91,492)( 92,491)( 93,495)( 94,494)( 95,493)( 96,487)
( 97,486)( 98,490)( 99,489)(100,488)(101,507)(102,506)(103,510)(104,509)
(105,508)(106,502)(107,501)(108,505)(109,504)(110,503)(111,522)(112,521)
(113,525)(114,524)(115,523)(116,517)(117,516)(118,520)(119,519)(120,518)
(121,512)(122,511)(123,515)(124,514)(125,513)(126,532)(127,531)(128,535)
(129,534)(130,533)(131,527)(132,526)(133,530)(134,529)(135,528)(136,547)
(137,546)(138,550)(139,549)(140,548)(141,542)(142,541)(143,545)(144,544)
(145,543)(146,537)(147,536)(148,540)(149,539)(150,538)(151,557)(152,556)
(153,560)(154,559)(155,558)(156,552)(157,551)(158,555)(159,554)(160,553)
(161,572)(162,571)(163,575)(164,574)(165,573)(166,567)(167,566)(168,570)
(169,569)(170,568)(171,562)(172,561)(173,565)(174,564)(175,563)(176,582)
(177,581)(178,585)(179,584)(180,583)(181,577)(182,576)(183,580)(184,579)
(185,578)(186,597)(187,596)(188,600)(189,599)(190,598)(191,592)(192,591)
(193,595)(194,594)(195,593)(196,587)(197,586)(198,590)(199,589)(200,588)
(201,607)(202,606)(203,610)(204,609)(205,608)(206,602)(207,601)(208,605)
(209,604)(210,603)(211,622)(212,621)(213,625)(214,624)(215,623)(216,617)
(217,616)(218,620)(219,619)(220,618)(221,612)(222,611)(223,615)(224,614)
(225,613)(226,632)(227,631)(228,635)(229,634)(230,633)(231,627)(232,626)
(233,630)(234,629)(235,628)(236,647)(237,646)(238,650)(239,649)(240,648)
(241,642)(242,641)(243,645)(244,644)(245,643)(246,637)(247,636)(248,640)
(249,639)(250,638)(251,657)(252,656)(253,660)(254,659)(255,658)(256,652)
(257,651)(258,655)(259,654)(260,653)(261,672)(262,671)(263,675)(264,674)
(265,673)(266,667)(267,666)(268,670)(269,669)(270,668)(271,662)(272,661)
(273,665)(274,664)(275,663)(276,682)(277,681)(278,685)(279,684)(280,683)
(281,677)(282,676)(283,680)(284,679)(285,678)(286,697)(287,696)(288,700)
(289,699)(290,698)(291,692)(292,691)(293,695)(294,694)(295,693)(296,687)
(297,686)(298,690)(299,689)(300,688)(301,707)(302,706)(303,710)(304,709)
(305,708)(306,702)(307,701)(308,705)(309,704)(310,703)(311,722)(312,721)
(313,725)(314,724)(315,723)(316,717)(317,716)(318,720)(319,719)(320,718)
(321,712)(322,711)(323,715)(324,714)(325,713)(326,732)(327,731)(328,735)
(329,734)(330,733)(331,727)(332,726)(333,730)(334,729)(335,728)(336,747)
(337,746)(338,750)(339,749)(340,748)(341,742)(342,741)(343,745)(344,744)
(345,743)(346,737)(347,736)(348,740)(349,739)(350,738)(351,757)(352,756)
(353,760)(354,759)(355,758)(356,752)(357,751)(358,755)(359,754)(360,753)
(361,772)(362,771)(363,775)(364,774)(365,773)(366,767)(367,766)(368,770)
(369,769)(370,768)(371,762)(372,761)(373,765)(374,764)(375,763)(376,782)
(377,781)(378,785)(379,784)(380,783)(381,777)(382,776)(383,780)(384,779)
(385,778)(386,797)(387,796)(388,800)(389,799)(390,798)(391,792)(392,791)
(393,795)(394,794)(395,793)(396,787)(397,786)(398,790)(399,789)(400,788);;
s3 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(101,126)(102,127)(103,128)(104,129)(105,130)(106,146)(107,147)(108,148)
(109,149)(110,150)(111,141)(112,142)(113,143)(114,144)(115,145)(116,136)
(117,137)(118,138)(119,139)(120,140)(121,131)(122,132)(123,133)(124,134)
(125,135)(151,176)(152,177)(153,178)(154,179)(155,180)(156,196)(157,197)
(158,198)(159,199)(160,200)(161,191)(162,192)(163,193)(164,194)(165,195)
(166,186)(167,187)(168,188)(169,189)(170,190)(171,181)(172,182)(173,183)
(174,184)(175,185)(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)
(212,217)(213,218)(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)
(235,250)(236,241)(237,242)(238,243)(239,244)(240,245)(256,271)(257,272)
(258,273)(259,274)(260,275)(261,266)(262,267)(263,268)(264,269)(265,270)
(281,296)(282,297)(283,298)(284,299)(285,300)(286,291)(287,292)(288,293)
(289,294)(290,295)(301,326)(302,327)(303,328)(304,329)(305,330)(306,346)
(307,347)(308,348)(309,349)(310,350)(311,341)(312,342)(313,343)(314,344)
(315,345)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)(322,332)
(323,333)(324,334)(325,335)(351,376)(352,377)(353,378)(354,379)(355,380)
(356,396)(357,397)(358,398)(359,399)(360,400)(361,391)(362,392)(363,393)
(364,394)(365,395)(366,386)(367,387)(368,388)(369,389)(370,390)(371,381)
(372,382)(373,383)(374,384)(375,385)(401,426)(402,427)(403,428)(404,429)
(405,430)(406,446)(407,447)(408,448)(409,449)(410,450)(411,441)(412,442)
(413,443)(414,444)(415,445)(416,436)(417,437)(418,438)(419,439)(420,440)
(421,431)(422,432)(423,433)(424,434)(425,435)(451,476)(452,477)(453,478)
(454,479)(455,480)(456,496)(457,497)(458,498)(459,499)(460,500)(461,491)
(462,492)(463,493)(464,494)(465,495)(466,486)(467,487)(468,488)(469,489)
(470,490)(471,481)(472,482)(473,483)(474,484)(475,485)(506,521)(507,522)
(508,523)(509,524)(510,525)(511,516)(512,517)(513,518)(514,519)(515,520)
(531,546)(532,547)(533,548)(534,549)(535,550)(536,541)(537,542)(538,543)
(539,544)(540,545)(556,571)(557,572)(558,573)(559,574)(560,575)(561,566)
(562,567)(563,568)(564,569)(565,570)(581,596)(582,597)(583,598)(584,599)
(585,600)(586,591)(587,592)(588,593)(589,594)(590,595)(601,626)(602,627)
(603,628)(604,629)(605,630)(606,646)(607,647)(608,648)(609,649)(610,650)
(611,641)(612,642)(613,643)(614,644)(615,645)(616,636)(617,637)(618,638)
(619,639)(620,640)(621,631)(622,632)(623,633)(624,634)(625,635)(651,676)
(652,677)(653,678)(654,679)(655,680)(656,696)(657,697)(658,698)(659,699)
(660,700)(661,691)(662,692)(663,693)(664,694)(665,695)(666,686)(667,687)
(668,688)(669,689)(670,690)(671,681)(672,682)(673,683)(674,684)(675,685)
(706,721)(707,722)(708,723)(709,724)(710,725)(711,716)(712,717)(713,718)
(714,719)(715,720)(731,746)(732,747)(733,748)(734,749)(735,750)(736,741)
(737,742)(738,743)(739,744)(740,745)(756,771)(757,772)(758,773)(759,774)
(760,775)(761,766)(762,767)(763,768)(764,769)(765,770)(781,796)(782,797)
(783,798)(784,799)(785,800)(786,791)(787,792)(788,793)(789,794)(790,795);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*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(800)!(  1,201)(  2,202)(  3,203)(  4,204)(  5,205)(  6,206)(  7,207)
(  8,208)(  9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)
( 16,216)( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)
( 24,224)( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)
( 32,232)( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)
( 40,240)( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)
( 48,248)( 49,249)( 50,250)( 51,251)( 52,252)( 53,253)( 54,254)( 55,255)
( 56,256)( 57,257)( 58,258)( 59,259)( 60,260)( 61,261)( 62,262)( 63,263)
( 64,264)( 65,265)( 66,266)( 67,267)( 68,268)( 69,269)( 70,270)( 71,271)
( 72,272)( 73,273)( 74,274)( 75,275)( 76,276)( 77,277)( 78,278)( 79,279)
( 80,280)( 81,281)( 82,282)( 83,283)( 84,284)( 85,285)( 86,286)( 87,287)
( 88,288)( 89,289)( 90,290)( 91,291)( 92,292)( 93,293)( 94,294)( 95,295)
( 96,296)( 97,297)( 98,298)( 99,299)(100,300)(101,351)(102,352)(103,353)
(104,354)(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)
(112,362)(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)
(120,370)(121,371)(122,372)(123,373)(124,374)(125,375)(126,376)(127,377)
(128,378)(129,379)(130,380)(131,381)(132,382)(133,383)(134,384)(135,385)
(136,386)(137,387)(138,388)(139,389)(140,390)(141,391)(142,392)(143,393)
(144,394)(145,395)(146,396)(147,397)(148,398)(149,399)(150,400)(151,301)
(152,302)(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)
(160,310)(161,311)(162,312)(163,313)(164,314)(165,315)(166,316)(167,317)
(168,318)(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,325)
(176,326)(177,327)(178,328)(179,329)(180,330)(181,331)(182,332)(183,333)
(184,334)(185,335)(186,336)(187,337)(188,338)(189,339)(190,340)(191,341)
(192,342)(193,343)(194,344)(195,345)(196,346)(197,347)(198,348)(199,349)
(200,350)(401,601)(402,602)(403,603)(404,604)(405,605)(406,606)(407,607)
(408,608)(409,609)(410,610)(411,611)(412,612)(413,613)(414,614)(415,615)
(416,616)(417,617)(418,618)(419,619)(420,620)(421,621)(422,622)(423,623)
(424,624)(425,625)(426,626)(427,627)(428,628)(429,629)(430,630)(431,631)
(432,632)(433,633)(434,634)(435,635)(436,636)(437,637)(438,638)(439,639)
(440,640)(441,641)(442,642)(443,643)(444,644)(445,645)(446,646)(447,647)
(448,648)(449,649)(450,650)(451,651)(452,652)(453,653)(454,654)(455,655)
(456,656)(457,657)(458,658)(459,659)(460,660)(461,661)(462,662)(463,663)
(464,664)(465,665)(466,666)(467,667)(468,668)(469,669)(470,670)(471,671)
(472,672)(473,673)(474,674)(475,675)(476,676)(477,677)(478,678)(479,679)
(480,680)(481,681)(482,682)(483,683)(484,684)(485,685)(486,686)(487,687)
(488,688)(489,689)(490,690)(491,691)(492,692)(493,693)(494,694)(495,695)
(496,696)(497,697)(498,698)(499,699)(500,700)(501,751)(502,752)(503,753)
(504,754)(505,755)(506,756)(507,757)(508,758)(509,759)(510,760)(511,761)
(512,762)(513,763)(514,764)(515,765)(516,766)(517,767)(518,768)(519,769)
(520,770)(521,771)(522,772)(523,773)(524,774)(525,775)(526,776)(527,777)
(528,778)(529,779)(530,780)(531,781)(532,782)(533,783)(534,784)(535,785)
(536,786)(537,787)(538,788)(539,789)(540,790)(541,791)(542,792)(543,793)
(544,794)(545,795)(546,796)(547,797)(548,798)(549,799)(550,800)(551,701)
(552,702)(553,703)(554,704)(555,705)(556,706)(557,707)(558,708)(559,709)
(560,710)(561,711)(562,712)(563,713)(564,714)(565,715)(566,716)(567,717)
(568,718)(569,719)(570,720)(571,721)(572,722)(573,723)(574,724)(575,725)
(576,726)(577,727)(578,728)(579,729)(580,730)(581,731)(582,732)(583,733)
(584,734)(585,735)(586,736)(587,737)(588,738)(589,739)(590,740)(591,741)
(592,742)(593,743)(594,744)(595,745)(596,746)(597,747)(598,748)(599,749)
(600,750);
s1 := Sym(800)!(  1,501)(  2,505)(  3,504)(  4,503)(  5,502)(  6,521)(  7,525)
(  8,524)(  9,523)( 10,522)( 11,516)( 12,520)( 13,519)( 14,518)( 15,517)
( 16,511)( 17,515)( 18,514)( 19,513)( 20,512)( 21,506)( 22,510)( 23,509)
( 24,508)( 25,507)( 26,526)( 27,530)( 28,529)( 29,528)( 30,527)( 31,546)
( 32,550)( 33,549)( 34,548)( 35,547)( 36,541)( 37,545)( 38,544)( 39,543)
( 40,542)( 41,536)( 42,540)( 43,539)( 44,538)( 45,537)( 46,531)( 47,535)
( 48,534)( 49,533)( 50,532)( 51,551)( 52,555)( 53,554)( 54,553)( 55,552)
( 56,571)( 57,575)( 58,574)( 59,573)( 60,572)( 61,566)( 62,570)( 63,569)
( 64,568)( 65,567)( 66,561)( 67,565)( 68,564)( 69,563)( 70,562)( 71,556)
( 72,560)( 73,559)( 74,558)( 75,557)( 76,576)( 77,580)( 78,579)( 79,578)
( 80,577)( 81,596)( 82,600)( 83,599)( 84,598)( 85,597)( 86,591)( 87,595)
( 88,594)( 89,593)( 90,592)( 91,586)( 92,590)( 93,589)( 94,588)( 95,587)
( 96,581)( 97,585)( 98,584)( 99,583)(100,582)(101,401)(102,405)(103,404)
(104,403)(105,402)(106,421)(107,425)(108,424)(109,423)(110,422)(111,416)
(112,420)(113,419)(114,418)(115,417)(116,411)(117,415)(118,414)(119,413)
(120,412)(121,406)(122,410)(123,409)(124,408)(125,407)(126,426)(127,430)
(128,429)(129,428)(130,427)(131,446)(132,450)(133,449)(134,448)(135,447)
(136,441)(137,445)(138,444)(139,443)(140,442)(141,436)(142,440)(143,439)
(144,438)(145,437)(146,431)(147,435)(148,434)(149,433)(150,432)(151,451)
(152,455)(153,454)(154,453)(155,452)(156,471)(157,475)(158,474)(159,473)
(160,472)(161,466)(162,470)(163,469)(164,468)(165,467)(166,461)(167,465)
(168,464)(169,463)(170,462)(171,456)(172,460)(173,459)(174,458)(175,457)
(176,476)(177,480)(178,479)(179,478)(180,477)(181,496)(182,500)(183,499)
(184,498)(185,497)(186,491)(187,495)(188,494)(189,493)(190,492)(191,486)
(192,490)(193,489)(194,488)(195,487)(196,481)(197,485)(198,484)(199,483)
(200,482)(201,701)(202,705)(203,704)(204,703)(205,702)(206,721)(207,725)
(208,724)(209,723)(210,722)(211,716)(212,720)(213,719)(214,718)(215,717)
(216,711)(217,715)(218,714)(219,713)(220,712)(221,706)(222,710)(223,709)
(224,708)(225,707)(226,726)(227,730)(228,729)(229,728)(230,727)(231,746)
(232,750)(233,749)(234,748)(235,747)(236,741)(237,745)(238,744)(239,743)
(240,742)(241,736)(242,740)(243,739)(244,738)(245,737)(246,731)(247,735)
(248,734)(249,733)(250,732)(251,751)(252,755)(253,754)(254,753)(255,752)
(256,771)(257,775)(258,774)(259,773)(260,772)(261,766)(262,770)(263,769)
(264,768)(265,767)(266,761)(267,765)(268,764)(269,763)(270,762)(271,756)
(272,760)(273,759)(274,758)(275,757)(276,776)(277,780)(278,779)(279,778)
(280,777)(281,796)(282,800)(283,799)(284,798)(285,797)(286,791)(287,795)
(288,794)(289,793)(290,792)(291,786)(292,790)(293,789)(294,788)(295,787)
(296,781)(297,785)(298,784)(299,783)(300,782)(301,601)(302,605)(303,604)
(304,603)(305,602)(306,621)(307,625)(308,624)(309,623)(310,622)(311,616)
(312,620)(313,619)(314,618)(315,617)(316,611)(317,615)(318,614)(319,613)
(320,612)(321,606)(322,610)(323,609)(324,608)(325,607)(326,626)(327,630)
(328,629)(329,628)(330,627)(331,646)(332,650)(333,649)(334,648)(335,647)
(336,641)(337,645)(338,644)(339,643)(340,642)(341,636)(342,640)(343,639)
(344,638)(345,637)(346,631)(347,635)(348,634)(349,633)(350,632)(351,651)
(352,655)(353,654)(354,653)(355,652)(356,671)(357,675)(358,674)(359,673)
(360,672)(361,666)(362,670)(363,669)(364,668)(365,667)(366,661)(367,665)
(368,664)(369,663)(370,662)(371,656)(372,660)(373,659)(374,658)(375,657)
(376,676)(377,680)(378,679)(379,678)(380,677)(381,696)(382,700)(383,699)
(384,698)(385,697)(386,691)(387,695)(388,694)(389,693)(390,692)(391,686)
(392,690)(393,689)(394,688)(395,687)(396,681)(397,685)(398,684)(399,683)
(400,682);
s2 := Sym(800)!(  1,407)(  2,406)(  3,410)(  4,409)(  5,408)(  6,402)(  7,401)
(  8,405)(  9,404)( 10,403)( 11,422)( 12,421)( 13,425)( 14,424)( 15,423)
( 16,417)( 17,416)( 18,420)( 19,419)( 20,418)( 21,412)( 22,411)( 23,415)
( 24,414)( 25,413)( 26,432)( 27,431)( 28,435)( 29,434)( 30,433)( 31,427)
( 32,426)( 33,430)( 34,429)( 35,428)( 36,447)( 37,446)( 38,450)( 39,449)
( 40,448)( 41,442)( 42,441)( 43,445)( 44,444)( 45,443)( 46,437)( 47,436)
( 48,440)( 49,439)( 50,438)( 51,457)( 52,456)( 53,460)( 54,459)( 55,458)
( 56,452)( 57,451)( 58,455)( 59,454)( 60,453)( 61,472)( 62,471)( 63,475)
( 64,474)( 65,473)( 66,467)( 67,466)( 68,470)( 69,469)( 70,468)( 71,462)
( 72,461)( 73,465)( 74,464)( 75,463)( 76,482)( 77,481)( 78,485)( 79,484)
( 80,483)( 81,477)( 82,476)( 83,480)( 84,479)( 85,478)( 86,497)( 87,496)
( 88,500)( 89,499)( 90,498)( 91,492)( 92,491)( 93,495)( 94,494)( 95,493)
( 96,487)( 97,486)( 98,490)( 99,489)(100,488)(101,507)(102,506)(103,510)
(104,509)(105,508)(106,502)(107,501)(108,505)(109,504)(110,503)(111,522)
(112,521)(113,525)(114,524)(115,523)(116,517)(117,516)(118,520)(119,519)
(120,518)(121,512)(122,511)(123,515)(124,514)(125,513)(126,532)(127,531)
(128,535)(129,534)(130,533)(131,527)(132,526)(133,530)(134,529)(135,528)
(136,547)(137,546)(138,550)(139,549)(140,548)(141,542)(142,541)(143,545)
(144,544)(145,543)(146,537)(147,536)(148,540)(149,539)(150,538)(151,557)
(152,556)(153,560)(154,559)(155,558)(156,552)(157,551)(158,555)(159,554)
(160,553)(161,572)(162,571)(163,575)(164,574)(165,573)(166,567)(167,566)
(168,570)(169,569)(170,568)(171,562)(172,561)(173,565)(174,564)(175,563)
(176,582)(177,581)(178,585)(179,584)(180,583)(181,577)(182,576)(183,580)
(184,579)(185,578)(186,597)(187,596)(188,600)(189,599)(190,598)(191,592)
(192,591)(193,595)(194,594)(195,593)(196,587)(197,586)(198,590)(199,589)
(200,588)(201,607)(202,606)(203,610)(204,609)(205,608)(206,602)(207,601)
(208,605)(209,604)(210,603)(211,622)(212,621)(213,625)(214,624)(215,623)
(216,617)(217,616)(218,620)(219,619)(220,618)(221,612)(222,611)(223,615)
(224,614)(225,613)(226,632)(227,631)(228,635)(229,634)(230,633)(231,627)
(232,626)(233,630)(234,629)(235,628)(236,647)(237,646)(238,650)(239,649)
(240,648)(241,642)(242,641)(243,645)(244,644)(245,643)(246,637)(247,636)
(248,640)(249,639)(250,638)(251,657)(252,656)(253,660)(254,659)(255,658)
(256,652)(257,651)(258,655)(259,654)(260,653)(261,672)(262,671)(263,675)
(264,674)(265,673)(266,667)(267,666)(268,670)(269,669)(270,668)(271,662)
(272,661)(273,665)(274,664)(275,663)(276,682)(277,681)(278,685)(279,684)
(280,683)(281,677)(282,676)(283,680)(284,679)(285,678)(286,697)(287,696)
(288,700)(289,699)(290,698)(291,692)(292,691)(293,695)(294,694)(295,693)
(296,687)(297,686)(298,690)(299,689)(300,688)(301,707)(302,706)(303,710)
(304,709)(305,708)(306,702)(307,701)(308,705)(309,704)(310,703)(311,722)
(312,721)(313,725)(314,724)(315,723)(316,717)(317,716)(318,720)(319,719)
(320,718)(321,712)(322,711)(323,715)(324,714)(325,713)(326,732)(327,731)
(328,735)(329,734)(330,733)(331,727)(332,726)(333,730)(334,729)(335,728)
(336,747)(337,746)(338,750)(339,749)(340,748)(341,742)(342,741)(343,745)
(344,744)(345,743)(346,737)(347,736)(348,740)(349,739)(350,738)(351,757)
(352,756)(353,760)(354,759)(355,758)(356,752)(357,751)(358,755)(359,754)
(360,753)(361,772)(362,771)(363,775)(364,774)(365,773)(366,767)(367,766)
(368,770)(369,769)(370,768)(371,762)(372,761)(373,765)(374,764)(375,763)
(376,782)(377,781)(378,785)(379,784)(380,783)(381,777)(382,776)(383,780)
(384,779)(385,778)(386,797)(387,796)(388,800)(389,799)(390,798)(391,792)
(392,791)(393,795)(394,794)(395,793)(396,787)(397,786)(398,790)(399,789)
(400,788);
s3 := Sym(800)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(101,126)(102,127)(103,128)(104,129)(105,130)(106,146)(107,147)
(108,148)(109,149)(110,150)(111,141)(112,142)(113,143)(114,144)(115,145)
(116,136)(117,137)(118,138)(119,139)(120,140)(121,131)(122,132)(123,133)
(124,134)(125,135)(151,176)(152,177)(153,178)(154,179)(155,180)(156,196)
(157,197)(158,198)(159,199)(160,200)(161,191)(162,192)(163,193)(164,194)
(165,195)(166,186)(167,187)(168,188)(169,189)(170,190)(171,181)(172,182)
(173,183)(174,184)(175,185)(206,221)(207,222)(208,223)(209,224)(210,225)
(211,216)(212,217)(213,218)(214,219)(215,220)(231,246)(232,247)(233,248)
(234,249)(235,250)(236,241)(237,242)(238,243)(239,244)(240,245)(256,271)
(257,272)(258,273)(259,274)(260,275)(261,266)(262,267)(263,268)(264,269)
(265,270)(281,296)(282,297)(283,298)(284,299)(285,300)(286,291)(287,292)
(288,293)(289,294)(290,295)(301,326)(302,327)(303,328)(304,329)(305,330)
(306,346)(307,347)(308,348)(309,349)(310,350)(311,341)(312,342)(313,343)
(314,344)(315,345)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)
(322,332)(323,333)(324,334)(325,335)(351,376)(352,377)(353,378)(354,379)
(355,380)(356,396)(357,397)(358,398)(359,399)(360,400)(361,391)(362,392)
(363,393)(364,394)(365,395)(366,386)(367,387)(368,388)(369,389)(370,390)
(371,381)(372,382)(373,383)(374,384)(375,385)(401,426)(402,427)(403,428)
(404,429)(405,430)(406,446)(407,447)(408,448)(409,449)(410,450)(411,441)
(412,442)(413,443)(414,444)(415,445)(416,436)(417,437)(418,438)(419,439)
(420,440)(421,431)(422,432)(423,433)(424,434)(425,435)(451,476)(452,477)
(453,478)(454,479)(455,480)(456,496)(457,497)(458,498)(459,499)(460,500)
(461,491)(462,492)(463,493)(464,494)(465,495)(466,486)(467,487)(468,488)
(469,489)(470,490)(471,481)(472,482)(473,483)(474,484)(475,485)(506,521)
(507,522)(508,523)(509,524)(510,525)(511,516)(512,517)(513,518)(514,519)
(515,520)(531,546)(532,547)(533,548)(534,549)(535,550)(536,541)(537,542)
(538,543)(539,544)(540,545)(556,571)(557,572)(558,573)(559,574)(560,575)
(561,566)(562,567)(563,568)(564,569)(565,570)(581,596)(582,597)(583,598)
(584,599)(585,600)(586,591)(587,592)(588,593)(589,594)(590,595)(601,626)
(602,627)(603,628)(604,629)(605,630)(606,646)(607,647)(608,648)(609,649)
(610,650)(611,641)(612,642)(613,643)(614,644)(615,645)(616,636)(617,637)
(618,638)(619,639)(620,640)(621,631)(622,632)(623,633)(624,634)(625,635)
(651,676)(652,677)(653,678)(654,679)(655,680)(656,696)(657,697)(658,698)
(659,699)(660,700)(661,691)(662,692)(663,693)(664,694)(665,695)(666,686)
(667,687)(668,688)(669,689)(670,690)(671,681)(672,682)(673,683)(674,684)
(675,685)(706,721)(707,722)(708,723)(709,724)(710,725)(711,716)(712,717)
(713,718)(714,719)(715,720)(731,746)(732,747)(733,748)(734,749)(735,750)
(736,741)(737,742)(738,743)(739,744)(740,745)(756,771)(757,772)(758,773)
(759,774)(760,775)(761,766)(762,767)(763,768)(764,769)(765,770)(781,796)
(782,797)(783,798)(784,799)(785,800)(786,791)(787,792)(788,793)(789,794)
(790,795);
poly := sub<Sym(800)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*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