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