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Polytope of Type {20,10,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10,4}*1600a
Also Known As : {{20,10|2},{10,4|2}}. if this polytope has another name.
Group : SmallGroup(1600,7600)
Rank : 4
Schlafli Type : {20,10,4}
Number of vertices, edges, etc : 20, 100, 20, 4
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 : {20,10,2}*800a, {10,10,4}*800a
   4-fold quotients : {10,10,2}*400a
   5-fold quotients : {20,2,4}*320, {4,10,4}*320
   10-fold quotients : {20,2,2}*160, {2,10,4}*160, {4,10,2}*160, {10,2,4}*160
   20-fold quotients : {5,2,4}*80, {2,10,2}*80, {10,2,2}*80
   25-fold quotients : {4,2,4}*64
   40-fold quotients : {2,5,2}*40, {5,2,2}*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 := (  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);;
s1 := (  1,406)(  2,410)(  3,409)(  4,408)(  5,407)(  6,401)(  7,405)(  8,404)
(  9,403)( 10,402)( 11,421)( 12,425)( 13,424)( 14,423)( 15,422)( 16,416)
( 17,420)( 18,419)( 19,418)( 20,417)( 21,411)( 22,415)( 23,414)( 24,413)
( 25,412)( 26,431)( 27,435)( 28,434)( 29,433)( 30,432)( 31,426)( 32,430)
( 33,429)( 34,428)( 35,427)( 36,446)( 37,450)( 38,449)( 39,448)( 40,447)
( 41,441)( 42,445)( 43,444)( 44,443)( 45,442)( 46,436)( 47,440)( 48,439)
( 49,438)( 50,437)( 51,456)( 52,460)( 53,459)( 54,458)( 55,457)( 56,451)
( 57,455)( 58,454)( 59,453)( 60,452)( 61,471)( 62,475)( 63,474)( 64,473)
( 65,472)( 66,466)( 67,470)( 68,469)( 69,468)( 70,467)( 71,461)( 72,465)
( 73,464)( 74,463)( 75,462)( 76,481)( 77,485)( 78,484)( 79,483)( 80,482)
( 81,476)( 82,480)( 83,479)( 84,478)( 85,477)( 86,496)( 87,500)( 88,499)
( 89,498)( 90,497)( 91,491)( 92,495)( 93,494)( 94,493)( 95,492)( 96,486)
( 97,490)( 98,489)( 99,488)(100,487)(101,531)(102,535)(103,534)(104,533)
(105,532)(106,526)(107,530)(108,529)(109,528)(110,527)(111,546)(112,550)
(113,549)(114,548)(115,547)(116,541)(117,545)(118,544)(119,543)(120,542)
(121,536)(122,540)(123,539)(124,538)(125,537)(126,506)(127,510)(128,509)
(129,508)(130,507)(131,501)(132,505)(133,504)(134,503)(135,502)(136,521)
(137,525)(138,524)(139,523)(140,522)(141,516)(142,520)(143,519)(144,518)
(145,517)(146,511)(147,515)(148,514)(149,513)(150,512)(151,581)(152,585)
(153,584)(154,583)(155,582)(156,576)(157,580)(158,579)(159,578)(160,577)
(161,596)(162,600)(163,599)(164,598)(165,597)(166,591)(167,595)(168,594)
(169,593)(170,592)(171,586)(172,590)(173,589)(174,588)(175,587)(176,556)
(177,560)(178,559)(179,558)(180,557)(181,551)(182,555)(183,554)(184,553)
(185,552)(186,571)(187,575)(188,574)(189,573)(190,572)(191,566)(192,570)
(193,569)(194,568)(195,567)(196,561)(197,565)(198,564)(199,563)(200,562)
(201,606)(202,610)(203,609)(204,608)(205,607)(206,601)(207,605)(208,604)
(209,603)(210,602)(211,621)(212,625)(213,624)(214,623)(215,622)(216,616)
(217,620)(218,619)(219,618)(220,617)(221,611)(222,615)(223,614)(224,613)
(225,612)(226,631)(227,635)(228,634)(229,633)(230,632)(231,626)(232,630)
(233,629)(234,628)(235,627)(236,646)(237,650)(238,649)(239,648)(240,647)
(241,641)(242,645)(243,644)(244,643)(245,642)(246,636)(247,640)(248,639)
(249,638)(250,637)(251,656)(252,660)(253,659)(254,658)(255,657)(256,651)
(257,655)(258,654)(259,653)(260,652)(261,671)(262,675)(263,674)(264,673)
(265,672)(266,666)(267,670)(268,669)(269,668)(270,667)(271,661)(272,665)
(273,664)(274,663)(275,662)(276,681)(277,685)(278,684)(279,683)(280,682)
(281,676)(282,680)(283,679)(284,678)(285,677)(286,696)(287,700)(288,699)
(289,698)(290,697)(291,691)(292,695)(293,694)(294,693)(295,692)(296,686)
(297,690)(298,689)(299,688)(300,687)(301,731)(302,735)(303,734)(304,733)
(305,732)(306,726)(307,730)(308,729)(309,728)(310,727)(311,746)(312,750)
(313,749)(314,748)(315,747)(316,741)(317,745)(318,744)(319,743)(320,742)
(321,736)(322,740)(323,739)(324,738)(325,737)(326,706)(327,710)(328,709)
(329,708)(330,707)(331,701)(332,705)(333,704)(334,703)(335,702)(336,721)
(337,725)(338,724)(339,723)(340,722)(341,716)(342,720)(343,719)(344,718)
(345,717)(346,711)(347,715)(348,714)(349,713)(350,712)(351,781)(352,785)
(353,784)(354,783)(355,782)(356,776)(357,780)(358,779)(359,778)(360,777)
(361,796)(362,800)(363,799)(364,798)(365,797)(366,791)(367,795)(368,794)
(369,793)(370,792)(371,786)(372,790)(373,789)(374,788)(375,787)(376,756)
(377,760)(378,759)(379,758)(380,757)(381,751)(382,755)(383,754)(384,753)
(385,752)(386,771)(387,775)(388,774)(389,773)(390,772)(391,766)(392,770)
(393,769)(394,768)(395,767)(396,761)(397,765)(398,764)(399,763)(400,762);;
s2 := (  1,502)(  2,501)(  3,505)(  4,504)(  5,503)(  6,507)(  7,506)(  8,510)
(  9,509)( 10,508)( 11,512)( 12,511)( 13,515)( 14,514)( 15,513)( 16,517)
( 17,516)( 18,520)( 19,519)( 20,518)( 21,522)( 22,521)( 23,525)( 24,524)
( 25,523)( 26,527)( 27,526)( 28,530)( 29,529)( 30,528)( 31,532)( 32,531)
( 33,535)( 34,534)( 35,533)( 36,537)( 37,536)( 38,540)( 39,539)( 40,538)
( 41,542)( 42,541)( 43,545)( 44,544)( 45,543)( 46,547)( 47,546)( 48,550)
( 49,549)( 50,548)( 51,552)( 52,551)( 53,555)( 54,554)( 55,553)( 56,557)
( 57,556)( 58,560)( 59,559)( 60,558)( 61,562)( 62,561)( 63,565)( 64,564)
( 65,563)( 66,567)( 67,566)( 68,570)( 69,569)( 70,568)( 71,572)( 72,571)
( 73,575)( 74,574)( 75,573)( 76,577)( 77,576)( 78,580)( 79,579)( 80,578)
( 81,582)( 82,581)( 83,585)( 84,584)( 85,583)( 86,587)( 87,586)( 88,590)
( 89,589)( 90,588)( 91,592)( 92,591)( 93,595)( 94,594)( 95,593)( 96,597)
( 97,596)( 98,600)( 99,599)(100,598)(101,427)(102,426)(103,430)(104,429)
(105,428)(106,432)(107,431)(108,435)(109,434)(110,433)(111,437)(112,436)
(113,440)(114,439)(115,438)(116,442)(117,441)(118,445)(119,444)(120,443)
(121,447)(122,446)(123,450)(124,449)(125,448)(126,402)(127,401)(128,405)
(129,404)(130,403)(131,407)(132,406)(133,410)(134,409)(135,408)(136,412)
(137,411)(138,415)(139,414)(140,413)(141,417)(142,416)(143,420)(144,419)
(145,418)(146,422)(147,421)(148,425)(149,424)(150,423)(151,477)(152,476)
(153,480)(154,479)(155,478)(156,482)(157,481)(158,485)(159,484)(160,483)
(161,487)(162,486)(163,490)(164,489)(165,488)(166,492)(167,491)(168,495)
(169,494)(170,493)(171,497)(172,496)(173,500)(174,499)(175,498)(176,452)
(177,451)(178,455)(179,454)(180,453)(181,457)(182,456)(183,460)(184,459)
(185,458)(186,462)(187,461)(188,465)(189,464)(190,463)(191,467)(192,466)
(193,470)(194,469)(195,468)(196,472)(197,471)(198,475)(199,474)(200,473)
(201,702)(202,701)(203,705)(204,704)(205,703)(206,707)(207,706)(208,710)
(209,709)(210,708)(211,712)(212,711)(213,715)(214,714)(215,713)(216,717)
(217,716)(218,720)(219,719)(220,718)(221,722)(222,721)(223,725)(224,724)
(225,723)(226,727)(227,726)(228,730)(229,729)(230,728)(231,732)(232,731)
(233,735)(234,734)(235,733)(236,737)(237,736)(238,740)(239,739)(240,738)
(241,742)(242,741)(243,745)(244,744)(245,743)(246,747)(247,746)(248,750)
(249,749)(250,748)(251,752)(252,751)(253,755)(254,754)(255,753)(256,757)
(257,756)(258,760)(259,759)(260,758)(261,762)(262,761)(263,765)(264,764)
(265,763)(266,767)(267,766)(268,770)(269,769)(270,768)(271,772)(272,771)
(273,775)(274,774)(275,773)(276,777)(277,776)(278,780)(279,779)(280,778)
(281,782)(282,781)(283,785)(284,784)(285,783)(286,787)(287,786)(288,790)
(289,789)(290,788)(291,792)(292,791)(293,795)(294,794)(295,793)(296,797)
(297,796)(298,800)(299,799)(300,798)(301,627)(302,626)(303,630)(304,629)
(305,628)(306,632)(307,631)(308,635)(309,634)(310,633)(311,637)(312,636)
(313,640)(314,639)(315,638)(316,642)(317,641)(318,645)(319,644)(320,643)
(321,647)(322,646)(323,650)(324,649)(325,648)(326,602)(327,601)(328,605)
(329,604)(330,603)(331,607)(332,606)(333,610)(334,609)(335,608)(336,612)
(337,611)(338,615)(339,614)(340,613)(341,617)(342,616)(343,620)(344,619)
(345,618)(346,622)(347,621)(348,625)(349,624)(350,623)(351,677)(352,676)
(353,680)(354,679)(355,678)(356,682)(357,681)(358,685)(359,684)(360,683)
(361,687)(362,686)(363,690)(364,689)(365,688)(366,692)(367,691)(368,695)
(369,694)(370,693)(371,697)(372,696)(373,700)(374,699)(375,698)(376,652)
(377,651)(378,655)(379,654)(380,653)(381,657)(382,656)(383,660)(384,659)
(385,658)(386,662)(387,661)(388,665)(389,664)(390,663)(391,667)(392,666)
(393,670)(394,669)(395,668)(396,672)(397,671)(398,675)(399,674)(400,673);;
s3 := (  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);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(800)!(  1,406)(  2,410)(  3,409)(  4,408)(  5,407)(  6,401)(  7,405)
(  8,404)(  9,403)( 10,402)( 11,421)( 12,425)( 13,424)( 14,423)( 15,422)
( 16,416)( 17,420)( 18,419)( 19,418)( 20,417)( 21,411)( 22,415)( 23,414)
( 24,413)( 25,412)( 26,431)( 27,435)( 28,434)( 29,433)( 30,432)( 31,426)
( 32,430)( 33,429)( 34,428)( 35,427)( 36,446)( 37,450)( 38,449)( 39,448)
( 40,447)( 41,441)( 42,445)( 43,444)( 44,443)( 45,442)( 46,436)( 47,440)
( 48,439)( 49,438)( 50,437)( 51,456)( 52,460)( 53,459)( 54,458)( 55,457)
( 56,451)( 57,455)( 58,454)( 59,453)( 60,452)( 61,471)( 62,475)( 63,474)
( 64,473)( 65,472)( 66,466)( 67,470)( 68,469)( 69,468)( 70,467)( 71,461)
( 72,465)( 73,464)( 74,463)( 75,462)( 76,481)( 77,485)( 78,484)( 79,483)
( 80,482)( 81,476)( 82,480)( 83,479)( 84,478)( 85,477)( 86,496)( 87,500)
( 88,499)( 89,498)( 90,497)( 91,491)( 92,495)( 93,494)( 94,493)( 95,492)
( 96,486)( 97,490)( 98,489)( 99,488)(100,487)(101,531)(102,535)(103,534)
(104,533)(105,532)(106,526)(107,530)(108,529)(109,528)(110,527)(111,546)
(112,550)(113,549)(114,548)(115,547)(116,541)(117,545)(118,544)(119,543)
(120,542)(121,536)(122,540)(123,539)(124,538)(125,537)(126,506)(127,510)
(128,509)(129,508)(130,507)(131,501)(132,505)(133,504)(134,503)(135,502)
(136,521)(137,525)(138,524)(139,523)(140,522)(141,516)(142,520)(143,519)
(144,518)(145,517)(146,511)(147,515)(148,514)(149,513)(150,512)(151,581)
(152,585)(153,584)(154,583)(155,582)(156,576)(157,580)(158,579)(159,578)
(160,577)(161,596)(162,600)(163,599)(164,598)(165,597)(166,591)(167,595)
(168,594)(169,593)(170,592)(171,586)(172,590)(173,589)(174,588)(175,587)
(176,556)(177,560)(178,559)(179,558)(180,557)(181,551)(182,555)(183,554)
(184,553)(185,552)(186,571)(187,575)(188,574)(189,573)(190,572)(191,566)
(192,570)(193,569)(194,568)(195,567)(196,561)(197,565)(198,564)(199,563)
(200,562)(201,606)(202,610)(203,609)(204,608)(205,607)(206,601)(207,605)
(208,604)(209,603)(210,602)(211,621)(212,625)(213,624)(214,623)(215,622)
(216,616)(217,620)(218,619)(219,618)(220,617)(221,611)(222,615)(223,614)
(224,613)(225,612)(226,631)(227,635)(228,634)(229,633)(230,632)(231,626)
(232,630)(233,629)(234,628)(235,627)(236,646)(237,650)(238,649)(239,648)
(240,647)(241,641)(242,645)(243,644)(244,643)(245,642)(246,636)(247,640)
(248,639)(249,638)(250,637)(251,656)(252,660)(253,659)(254,658)(255,657)
(256,651)(257,655)(258,654)(259,653)(260,652)(261,671)(262,675)(263,674)
(264,673)(265,672)(266,666)(267,670)(268,669)(269,668)(270,667)(271,661)
(272,665)(273,664)(274,663)(275,662)(276,681)(277,685)(278,684)(279,683)
(280,682)(281,676)(282,680)(283,679)(284,678)(285,677)(286,696)(287,700)
(288,699)(289,698)(290,697)(291,691)(292,695)(293,694)(294,693)(295,692)
(296,686)(297,690)(298,689)(299,688)(300,687)(301,731)(302,735)(303,734)
(304,733)(305,732)(306,726)(307,730)(308,729)(309,728)(310,727)(311,746)
(312,750)(313,749)(314,748)(315,747)(316,741)(317,745)(318,744)(319,743)
(320,742)(321,736)(322,740)(323,739)(324,738)(325,737)(326,706)(327,710)
(328,709)(329,708)(330,707)(331,701)(332,705)(333,704)(334,703)(335,702)
(336,721)(337,725)(338,724)(339,723)(340,722)(341,716)(342,720)(343,719)
(344,718)(345,717)(346,711)(347,715)(348,714)(349,713)(350,712)(351,781)
(352,785)(353,784)(354,783)(355,782)(356,776)(357,780)(358,779)(359,778)
(360,777)(361,796)(362,800)(363,799)(364,798)(365,797)(366,791)(367,795)
(368,794)(369,793)(370,792)(371,786)(372,790)(373,789)(374,788)(375,787)
(376,756)(377,760)(378,759)(379,758)(380,757)(381,751)(382,755)(383,754)
(384,753)(385,752)(386,771)(387,775)(388,774)(389,773)(390,772)(391,766)
(392,770)(393,769)(394,768)(395,767)(396,761)(397,765)(398,764)(399,763)
(400,762);
s2 := Sym(800)!(  1,502)(  2,501)(  3,505)(  4,504)(  5,503)(  6,507)(  7,506)
(  8,510)(  9,509)( 10,508)( 11,512)( 12,511)( 13,515)( 14,514)( 15,513)
( 16,517)( 17,516)( 18,520)( 19,519)( 20,518)( 21,522)( 22,521)( 23,525)
( 24,524)( 25,523)( 26,527)( 27,526)( 28,530)( 29,529)( 30,528)( 31,532)
( 32,531)( 33,535)( 34,534)( 35,533)( 36,537)( 37,536)( 38,540)( 39,539)
( 40,538)( 41,542)( 42,541)( 43,545)( 44,544)( 45,543)( 46,547)( 47,546)
( 48,550)( 49,549)( 50,548)( 51,552)( 52,551)( 53,555)( 54,554)( 55,553)
( 56,557)( 57,556)( 58,560)( 59,559)( 60,558)( 61,562)( 62,561)( 63,565)
( 64,564)( 65,563)( 66,567)( 67,566)( 68,570)( 69,569)( 70,568)( 71,572)
( 72,571)( 73,575)( 74,574)( 75,573)( 76,577)( 77,576)( 78,580)( 79,579)
( 80,578)( 81,582)( 82,581)( 83,585)( 84,584)( 85,583)( 86,587)( 87,586)
( 88,590)( 89,589)( 90,588)( 91,592)( 92,591)( 93,595)( 94,594)( 95,593)
( 96,597)( 97,596)( 98,600)( 99,599)(100,598)(101,427)(102,426)(103,430)
(104,429)(105,428)(106,432)(107,431)(108,435)(109,434)(110,433)(111,437)
(112,436)(113,440)(114,439)(115,438)(116,442)(117,441)(118,445)(119,444)
(120,443)(121,447)(122,446)(123,450)(124,449)(125,448)(126,402)(127,401)
(128,405)(129,404)(130,403)(131,407)(132,406)(133,410)(134,409)(135,408)
(136,412)(137,411)(138,415)(139,414)(140,413)(141,417)(142,416)(143,420)
(144,419)(145,418)(146,422)(147,421)(148,425)(149,424)(150,423)(151,477)
(152,476)(153,480)(154,479)(155,478)(156,482)(157,481)(158,485)(159,484)
(160,483)(161,487)(162,486)(163,490)(164,489)(165,488)(166,492)(167,491)
(168,495)(169,494)(170,493)(171,497)(172,496)(173,500)(174,499)(175,498)
(176,452)(177,451)(178,455)(179,454)(180,453)(181,457)(182,456)(183,460)
(184,459)(185,458)(186,462)(187,461)(188,465)(189,464)(190,463)(191,467)
(192,466)(193,470)(194,469)(195,468)(196,472)(197,471)(198,475)(199,474)
(200,473)(201,702)(202,701)(203,705)(204,704)(205,703)(206,707)(207,706)
(208,710)(209,709)(210,708)(211,712)(212,711)(213,715)(214,714)(215,713)
(216,717)(217,716)(218,720)(219,719)(220,718)(221,722)(222,721)(223,725)
(224,724)(225,723)(226,727)(227,726)(228,730)(229,729)(230,728)(231,732)
(232,731)(233,735)(234,734)(235,733)(236,737)(237,736)(238,740)(239,739)
(240,738)(241,742)(242,741)(243,745)(244,744)(245,743)(246,747)(247,746)
(248,750)(249,749)(250,748)(251,752)(252,751)(253,755)(254,754)(255,753)
(256,757)(257,756)(258,760)(259,759)(260,758)(261,762)(262,761)(263,765)
(264,764)(265,763)(266,767)(267,766)(268,770)(269,769)(270,768)(271,772)
(272,771)(273,775)(274,774)(275,773)(276,777)(277,776)(278,780)(279,779)
(280,778)(281,782)(282,781)(283,785)(284,784)(285,783)(286,787)(287,786)
(288,790)(289,789)(290,788)(291,792)(292,791)(293,795)(294,794)(295,793)
(296,797)(297,796)(298,800)(299,799)(300,798)(301,627)(302,626)(303,630)
(304,629)(305,628)(306,632)(307,631)(308,635)(309,634)(310,633)(311,637)
(312,636)(313,640)(314,639)(315,638)(316,642)(317,641)(318,645)(319,644)
(320,643)(321,647)(322,646)(323,650)(324,649)(325,648)(326,602)(327,601)
(328,605)(329,604)(330,603)(331,607)(332,606)(333,610)(334,609)(335,608)
(336,612)(337,611)(338,615)(339,614)(340,613)(341,617)(342,616)(343,620)
(344,619)(345,618)(346,622)(347,621)(348,625)(349,624)(350,623)(351,677)
(352,676)(353,680)(354,679)(355,678)(356,682)(357,681)(358,685)(359,684)
(360,683)(361,687)(362,686)(363,690)(364,689)(365,688)(366,692)(367,691)
(368,695)(369,694)(370,693)(371,697)(372,696)(373,700)(374,699)(375,698)
(376,652)(377,651)(378,655)(379,654)(380,653)(381,657)(382,656)(383,660)
(384,659)(385,658)(386,662)(387,661)(388,665)(389,664)(390,663)(391,667)
(392,666)(393,670)(394,669)(395,668)(396,672)(397,671)(398,675)(399,674)
(400,673);
s3 := 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);
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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*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 >; 
 
References : None.
to this polytope