Polytope of Type {4,50,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,50,4}*1600
Also Known As : {{4,50|2},{50,4|2}}. if this polytope has another name.
Group : SmallGroup(1600,1266)
Rank : 4
Schlafli Type : {4,50,4}
Number of vertices, edges, etc : 4, 100, 100, 4
Order of s0s1s2s3 : 100
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Self-Dual
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 : {2,50,4}*800, {4,50,2}*800
4-fold quotients : {2,50,2}*400
5-fold quotients : {4,10,4}*320
8-fold quotients : {2,25,2}*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 := ( 1,401)( 2,402)( 3,403)( 4,404)( 5,405)( 6,406)( 7,407)( 8,408)
( 9,409)( 10,410)( 11,411)( 12,412)( 13,413)( 14,414)( 15,415)( 16,416)
( 17,417)( 18,418)( 19,419)( 20,420)( 21,421)( 22,422)( 23,423)( 24,424)
( 25,425)( 26,426)( 27,427)( 28,428)( 29,429)( 30,430)( 31,431)( 32,432)
( 33,433)( 34,434)( 35,435)( 36,436)( 37,437)( 38,438)( 39,439)( 40,440)
( 41,441)( 42,442)( 43,443)( 44,444)( 45,445)( 46,446)( 47,447)( 48,448)
( 49,449)( 50,450)( 51,451)( 52,452)( 53,453)( 54,454)( 55,455)( 56,456)
( 57,457)( 58,458)( 59,459)( 60,460)( 61,461)( 62,462)( 63,463)( 64,464)
( 65,465)( 66,466)( 67,467)( 68,468)( 69,469)( 70,470)( 71,471)( 72,472)
( 73,473)( 74,474)( 75,475)( 76,476)( 77,477)( 78,478)( 79,479)( 80,480)
( 81,481)( 82,482)( 83,483)( 84,484)( 85,485)( 86,486)( 87,487)( 88,488)
( 89,489)( 90,490)( 91,491)( 92,492)( 93,493)( 94,494)( 95,495)( 96,496)
( 97,497)( 98,498)( 99,499)(100,500)(101,526)(102,527)(103,528)(104,529)
(105,530)(106,531)(107,532)(108,533)(109,534)(110,535)(111,536)(112,537)
(113,538)(114,539)(115,540)(116,541)(117,542)(118,543)(119,544)(120,545)
(121,546)(122,547)(123,548)(124,549)(125,550)(126,501)(127,502)(128,503)
(129,504)(130,505)(131,506)(132,507)(133,508)(134,509)(135,510)(136,511)
(137,512)(138,513)(139,514)(140,515)(141,516)(142,517)(143,518)(144,519)
(145,520)(146,521)(147,522)(148,523)(149,524)(150,525)(151,576)(152,577)
(153,578)(154,579)(155,580)(156,581)(157,582)(158,583)(159,584)(160,585)
(161,586)(162,587)(163,588)(164,589)(165,590)(166,591)(167,592)(168,593)
(169,594)(170,595)(171,596)(172,597)(173,598)(174,599)(175,600)(176,551)
(177,552)(178,553)(179,554)(180,555)(181,556)(182,557)(183,558)(184,559)
(185,560)(186,561)(187,562)(188,563)(189,564)(190,565)(191,566)(192,567)
(193,568)(194,569)(195,570)(196,571)(197,572)(198,573)(199,574)(200,575)
(201,601)(202,602)(203,603)(204,604)(205,605)(206,606)(207,607)(208,608)
(209,609)(210,610)(211,611)(212,612)(213,613)(214,614)(215,615)(216,616)
(217,617)(218,618)(219,619)(220,620)(221,621)(222,622)(223,623)(224,624)
(225,625)(226,626)(227,627)(228,628)(229,629)(230,630)(231,631)(232,632)
(233,633)(234,634)(235,635)(236,636)(237,637)(238,638)(239,639)(240,640)
(241,641)(242,642)(243,643)(244,644)(245,645)(246,646)(247,647)(248,648)
(249,649)(250,650)(251,651)(252,652)(253,653)(254,654)(255,655)(256,656)
(257,657)(258,658)(259,659)(260,660)(261,661)(262,662)(263,663)(264,664)
(265,665)(266,666)(267,667)(268,668)(269,669)(270,670)(271,671)(272,672)
(273,673)(274,674)(275,675)(276,676)(277,677)(278,678)(279,679)(280,680)
(281,681)(282,682)(283,683)(284,684)(285,685)(286,686)(287,687)(288,688)
(289,689)(290,690)(291,691)(292,692)(293,693)(294,694)(295,695)(296,696)
(297,697)(298,698)(299,699)(300,700)(301,726)(302,727)(303,728)(304,729)
(305,730)(306,731)(307,732)(308,733)(309,734)(310,735)(311,736)(312,737)
(313,738)(314,739)(315,740)(316,741)(317,742)(318,743)(319,744)(320,745)
(321,746)(322,747)(323,748)(324,749)(325,750)(326,701)(327,702)(328,703)
(329,704)(330,705)(331,706)(332,707)(333,708)(334,709)(335,710)(336,711)
(337,712)(338,713)(339,714)(340,715)(341,716)(342,717)(343,718)(344,719)
(345,720)(346,721)(347,722)(348,723)(349,724)(350,725)(351,776)(352,777)
(353,778)(354,779)(355,780)(356,781)(357,782)(358,783)(359,784)(360,785)
(361,786)(362,787)(363,788)(364,789)(365,790)(366,791)(367,792)(368,793)
(369,794)(370,795)(371,796)(372,797)(373,798)(374,799)(375,800)(376,751)
(377,752)(378,753)(379,754)(380,755)(381,756)(382,757)(383,758)(384,759)
(385,760)(386,761)(387,762)(388,763)(389,764)(390,765)(391,766)(392,767)
(393,768)(394,769)(395,770)(396,771)(397,772)(398,773)(399,774)(400,775);;
s1 := ( 2, 5)( 3, 4)( 6, 25)( 7, 24)( 8, 23)( 9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)( 32, 49)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)
( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)( 82, 99)
( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)( 90, 91)
(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)
(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)(132,149)
(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141)
(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)
(162,169)(163,168)(164,167)(165,166)(177,180)(178,179)(181,200)(182,199)
(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192)(190,191)
(202,205)(203,204)(206,225)(207,224)(208,223)(209,222)(210,221)(211,220)
(212,219)(213,218)(214,217)(215,216)(227,230)(228,229)(231,250)(232,249)
(233,248)(234,247)(235,246)(236,245)(237,244)(238,243)(239,242)(240,241)
(252,255)(253,254)(256,275)(257,274)(258,273)(259,272)(260,271)(261,270)
(262,269)(263,268)(264,267)(265,266)(277,280)(278,279)(281,300)(282,299)
(283,298)(284,297)(285,296)(286,295)(287,294)(288,293)(289,292)(290,291)
(302,305)(303,304)(306,325)(307,324)(308,323)(309,322)(310,321)(311,320)
(312,319)(313,318)(314,317)(315,316)(327,330)(328,329)(331,350)(332,349)
(333,348)(334,347)(335,346)(336,345)(337,344)(338,343)(339,342)(340,341)
(352,355)(353,354)(356,375)(357,374)(358,373)(359,372)(360,371)(361,370)
(362,369)(363,368)(364,367)(365,366)(377,380)(378,379)(381,400)(382,399)
(383,398)(384,397)(385,396)(386,395)(387,394)(388,393)(389,392)(390,391)
(401,426)(402,430)(403,429)(404,428)(405,427)(406,450)(407,449)(408,448)
(409,447)(410,446)(411,445)(412,444)(413,443)(414,442)(415,441)(416,440)
(417,439)(418,438)(419,437)(420,436)(421,435)(422,434)(423,433)(424,432)
(425,431)(451,476)(452,480)(453,479)(454,478)(455,477)(456,500)(457,499)
(458,498)(459,497)(460,496)(461,495)(462,494)(463,493)(464,492)(465,491)
(466,490)(467,489)(468,488)(469,487)(470,486)(471,485)(472,484)(473,483)
(474,482)(475,481)(501,526)(502,530)(503,529)(504,528)(505,527)(506,550)
(507,549)(508,548)(509,547)(510,546)(511,545)(512,544)(513,543)(514,542)
(515,541)(516,540)(517,539)(518,538)(519,537)(520,536)(521,535)(522,534)
(523,533)(524,532)(525,531)(551,576)(552,580)(553,579)(554,578)(555,577)
(556,600)(557,599)(558,598)(559,597)(560,596)(561,595)(562,594)(563,593)
(564,592)(565,591)(566,590)(567,589)(568,588)(569,587)(570,586)(571,585)
(572,584)(573,583)(574,582)(575,581)(601,626)(602,630)(603,629)(604,628)
(605,627)(606,650)(607,649)(608,648)(609,647)(610,646)(611,645)(612,644)
(613,643)(614,642)(615,641)(616,640)(617,639)(618,638)(619,637)(620,636)
(621,635)(622,634)(623,633)(624,632)(625,631)(651,676)(652,680)(653,679)
(654,678)(655,677)(656,700)(657,699)(658,698)(659,697)(660,696)(661,695)
(662,694)(663,693)(664,692)(665,691)(666,690)(667,689)(668,688)(669,687)
(670,686)(671,685)(672,684)(673,683)(674,682)(675,681)(701,726)(702,730)
(703,729)(704,728)(705,727)(706,750)(707,749)(708,748)(709,747)(710,746)
(711,745)(712,744)(713,743)(714,742)(715,741)(716,740)(717,739)(718,738)
(719,737)(720,736)(721,735)(722,734)(723,733)(724,732)(725,731)(751,776)
(752,780)(753,779)(754,778)(755,777)(756,800)(757,799)(758,798)(759,797)
(760,796)(761,795)(762,794)(763,793)(764,792)(765,791)(766,790)(767,789)
(768,788)(769,787)(770,786)(771,785)(772,784)(773,783)(774,782)(775,781);;
s2 := ( 1,106)( 2,110)( 3,109)( 4,108)( 5,107)( 6,101)( 7,105)( 8,104)
( 9,103)( 10,102)( 11,125)( 12,124)( 13,123)( 14,122)( 15,121)( 16,120)
( 17,119)( 18,118)( 19,117)( 20,116)( 21,115)( 22,114)( 23,113)( 24,112)
( 25,111)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)( 32,130)
( 33,129)( 34,128)( 35,127)( 36,150)( 37,149)( 38,148)( 39,147)( 40,146)
( 41,145)( 42,144)( 43,143)( 44,142)( 45,141)( 46,140)( 47,139)( 48,138)
( 49,137)( 50,136)( 51,156)( 52,160)( 53,159)( 54,158)( 55,157)( 56,151)
( 57,155)( 58,154)( 59,153)( 60,152)( 61,175)( 62,174)( 63,173)( 64,172)
( 65,171)( 66,170)( 67,169)( 68,168)( 69,167)( 70,166)( 71,165)( 72,164)
( 73,163)( 74,162)( 75,161)( 76,181)( 77,185)( 78,184)( 79,183)( 80,182)
( 81,176)( 82,180)( 83,179)( 84,178)( 85,177)( 86,200)( 87,199)( 88,198)
( 89,197)( 90,196)( 91,195)( 92,194)( 93,193)( 94,192)( 95,191)( 96,190)
( 97,189)( 98,188)( 99,187)(100,186)(201,306)(202,310)(203,309)(204,308)
(205,307)(206,301)(207,305)(208,304)(209,303)(210,302)(211,325)(212,324)
(213,323)(214,322)(215,321)(216,320)(217,319)(218,318)(219,317)(220,316)
(221,315)(222,314)(223,313)(224,312)(225,311)(226,331)(227,335)(228,334)
(229,333)(230,332)(231,326)(232,330)(233,329)(234,328)(235,327)(236,350)
(237,349)(238,348)(239,347)(240,346)(241,345)(242,344)(243,343)(244,342)
(245,341)(246,340)(247,339)(248,338)(249,337)(250,336)(251,356)(252,360)
(253,359)(254,358)(255,357)(256,351)(257,355)(258,354)(259,353)(260,352)
(261,375)(262,374)(263,373)(264,372)(265,371)(266,370)(267,369)(268,368)
(269,367)(270,366)(271,365)(272,364)(273,363)(274,362)(275,361)(276,381)
(277,385)(278,384)(279,383)(280,382)(281,376)(282,380)(283,379)(284,378)
(285,377)(286,400)(287,399)(288,398)(289,397)(290,396)(291,395)(292,394)
(293,393)(294,392)(295,391)(296,390)(297,389)(298,388)(299,387)(300,386)
(401,531)(402,535)(403,534)(404,533)(405,532)(406,526)(407,530)(408,529)
(409,528)(410,527)(411,550)(412,549)(413,548)(414,547)(415,546)(416,545)
(417,544)(418,543)(419,542)(420,541)(421,540)(422,539)(423,538)(424,537)
(425,536)(426,506)(427,510)(428,509)(429,508)(430,507)(431,501)(432,505)
(433,504)(434,503)(435,502)(436,525)(437,524)(438,523)(439,522)(440,521)
(441,520)(442,519)(443,518)(444,517)(445,516)(446,515)(447,514)(448,513)
(449,512)(450,511)(451,581)(452,585)(453,584)(454,583)(455,582)(456,576)
(457,580)(458,579)(459,578)(460,577)(461,600)(462,599)(463,598)(464,597)
(465,596)(466,595)(467,594)(468,593)(469,592)(470,591)(471,590)(472,589)
(473,588)(474,587)(475,586)(476,556)(477,560)(478,559)(479,558)(480,557)
(481,551)(482,555)(483,554)(484,553)(485,552)(486,575)(487,574)(488,573)
(489,572)(490,571)(491,570)(492,569)(493,568)(494,567)(495,566)(496,565)
(497,564)(498,563)(499,562)(500,561)(601,731)(602,735)(603,734)(604,733)
(605,732)(606,726)(607,730)(608,729)(609,728)(610,727)(611,750)(612,749)
(613,748)(614,747)(615,746)(616,745)(617,744)(618,743)(619,742)(620,741)
(621,740)(622,739)(623,738)(624,737)(625,736)(626,706)(627,710)(628,709)
(629,708)(630,707)(631,701)(632,705)(633,704)(634,703)(635,702)(636,725)
(637,724)(638,723)(639,722)(640,721)(641,720)(642,719)(643,718)(644,717)
(645,716)(646,715)(647,714)(648,713)(649,712)(650,711)(651,781)(652,785)
(653,784)(654,783)(655,782)(656,776)(657,780)(658,779)(659,778)(660,777)
(661,800)(662,799)(663,798)(664,797)(665,796)(666,795)(667,794)(668,793)
(669,792)(670,791)(671,790)(672,789)(673,788)(674,787)(675,786)(676,756)
(677,760)(678,759)(679,758)(680,757)(681,751)(682,755)(683,754)(684,753)
(685,752)(686,775)(687,774)(688,773)(689,772)(690,771)(691,770)(692,769)
(693,768)(694,767)(695,766)(696,765)(697,764)(698,763)(699,762)(700,761);;
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*s0*s1*s0*s1*s0*s1,
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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)!( 1,401)( 2,402)( 3,403)( 4,404)( 5,405)( 6,406)( 7,407)
( 8,408)( 9,409)( 10,410)( 11,411)( 12,412)( 13,413)( 14,414)( 15,415)
( 16,416)( 17,417)( 18,418)( 19,419)( 20,420)( 21,421)( 22,422)( 23,423)
( 24,424)( 25,425)( 26,426)( 27,427)( 28,428)( 29,429)( 30,430)( 31,431)
( 32,432)( 33,433)( 34,434)( 35,435)( 36,436)( 37,437)( 38,438)( 39,439)
( 40,440)( 41,441)( 42,442)( 43,443)( 44,444)( 45,445)( 46,446)( 47,447)
( 48,448)( 49,449)( 50,450)( 51,451)( 52,452)( 53,453)( 54,454)( 55,455)
( 56,456)( 57,457)( 58,458)( 59,459)( 60,460)( 61,461)( 62,462)( 63,463)
( 64,464)( 65,465)( 66,466)( 67,467)( 68,468)( 69,469)( 70,470)( 71,471)
( 72,472)( 73,473)( 74,474)( 75,475)( 76,476)( 77,477)( 78,478)( 79,479)
( 80,480)( 81,481)( 82,482)( 83,483)( 84,484)( 85,485)( 86,486)( 87,487)
( 88,488)( 89,489)( 90,490)( 91,491)( 92,492)( 93,493)( 94,494)( 95,495)
( 96,496)( 97,497)( 98,498)( 99,499)(100,500)(101,526)(102,527)(103,528)
(104,529)(105,530)(106,531)(107,532)(108,533)(109,534)(110,535)(111,536)
(112,537)(113,538)(114,539)(115,540)(116,541)(117,542)(118,543)(119,544)
(120,545)(121,546)(122,547)(123,548)(124,549)(125,550)(126,501)(127,502)
(128,503)(129,504)(130,505)(131,506)(132,507)(133,508)(134,509)(135,510)
(136,511)(137,512)(138,513)(139,514)(140,515)(141,516)(142,517)(143,518)
(144,519)(145,520)(146,521)(147,522)(148,523)(149,524)(150,525)(151,576)
(152,577)(153,578)(154,579)(155,580)(156,581)(157,582)(158,583)(159,584)
(160,585)(161,586)(162,587)(163,588)(164,589)(165,590)(166,591)(167,592)
(168,593)(169,594)(170,595)(171,596)(172,597)(173,598)(174,599)(175,600)
(176,551)(177,552)(178,553)(179,554)(180,555)(181,556)(182,557)(183,558)
(184,559)(185,560)(186,561)(187,562)(188,563)(189,564)(190,565)(191,566)
(192,567)(193,568)(194,569)(195,570)(196,571)(197,572)(198,573)(199,574)
(200,575)(201,601)(202,602)(203,603)(204,604)(205,605)(206,606)(207,607)
(208,608)(209,609)(210,610)(211,611)(212,612)(213,613)(214,614)(215,615)
(216,616)(217,617)(218,618)(219,619)(220,620)(221,621)(222,622)(223,623)
(224,624)(225,625)(226,626)(227,627)(228,628)(229,629)(230,630)(231,631)
(232,632)(233,633)(234,634)(235,635)(236,636)(237,637)(238,638)(239,639)
(240,640)(241,641)(242,642)(243,643)(244,644)(245,645)(246,646)(247,647)
(248,648)(249,649)(250,650)(251,651)(252,652)(253,653)(254,654)(255,655)
(256,656)(257,657)(258,658)(259,659)(260,660)(261,661)(262,662)(263,663)
(264,664)(265,665)(266,666)(267,667)(268,668)(269,669)(270,670)(271,671)
(272,672)(273,673)(274,674)(275,675)(276,676)(277,677)(278,678)(279,679)
(280,680)(281,681)(282,682)(283,683)(284,684)(285,685)(286,686)(287,687)
(288,688)(289,689)(290,690)(291,691)(292,692)(293,693)(294,694)(295,695)
(296,696)(297,697)(298,698)(299,699)(300,700)(301,726)(302,727)(303,728)
(304,729)(305,730)(306,731)(307,732)(308,733)(309,734)(310,735)(311,736)
(312,737)(313,738)(314,739)(315,740)(316,741)(317,742)(318,743)(319,744)
(320,745)(321,746)(322,747)(323,748)(324,749)(325,750)(326,701)(327,702)
(328,703)(329,704)(330,705)(331,706)(332,707)(333,708)(334,709)(335,710)
(336,711)(337,712)(338,713)(339,714)(340,715)(341,716)(342,717)(343,718)
(344,719)(345,720)(346,721)(347,722)(348,723)(349,724)(350,725)(351,776)
(352,777)(353,778)(354,779)(355,780)(356,781)(357,782)(358,783)(359,784)
(360,785)(361,786)(362,787)(363,788)(364,789)(365,790)(366,791)(367,792)
(368,793)(369,794)(370,795)(371,796)(372,797)(373,798)(374,799)(375,800)
(376,751)(377,752)(378,753)(379,754)(380,755)(381,756)(382,757)(383,758)
(384,759)(385,760)(386,761)(387,762)(388,763)(389,764)(390,765)(391,766)
(392,767)(393,768)(394,769)(395,770)(396,771)(397,772)(398,773)(399,774)
(400,775);
s1 := Sym(800)!( 2, 5)( 3, 4)( 6, 25)( 7, 24)( 8, 23)( 9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)
( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)
( 82, 99)( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)
( 90, 91)(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)
(111,120)(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)
(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)
(140,141)(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)(160,171)
(161,170)(162,169)(163,168)(164,167)(165,166)(177,180)(178,179)(181,200)
(182,199)(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192)
(190,191)(202,205)(203,204)(206,225)(207,224)(208,223)(209,222)(210,221)
(211,220)(212,219)(213,218)(214,217)(215,216)(227,230)(228,229)(231,250)
(232,249)(233,248)(234,247)(235,246)(236,245)(237,244)(238,243)(239,242)
(240,241)(252,255)(253,254)(256,275)(257,274)(258,273)(259,272)(260,271)
(261,270)(262,269)(263,268)(264,267)(265,266)(277,280)(278,279)(281,300)
(282,299)(283,298)(284,297)(285,296)(286,295)(287,294)(288,293)(289,292)
(290,291)(302,305)(303,304)(306,325)(307,324)(308,323)(309,322)(310,321)
(311,320)(312,319)(313,318)(314,317)(315,316)(327,330)(328,329)(331,350)
(332,349)(333,348)(334,347)(335,346)(336,345)(337,344)(338,343)(339,342)
(340,341)(352,355)(353,354)(356,375)(357,374)(358,373)(359,372)(360,371)
(361,370)(362,369)(363,368)(364,367)(365,366)(377,380)(378,379)(381,400)
(382,399)(383,398)(384,397)(385,396)(386,395)(387,394)(388,393)(389,392)
(390,391)(401,426)(402,430)(403,429)(404,428)(405,427)(406,450)(407,449)
(408,448)(409,447)(410,446)(411,445)(412,444)(413,443)(414,442)(415,441)
(416,440)(417,439)(418,438)(419,437)(420,436)(421,435)(422,434)(423,433)
(424,432)(425,431)(451,476)(452,480)(453,479)(454,478)(455,477)(456,500)
(457,499)(458,498)(459,497)(460,496)(461,495)(462,494)(463,493)(464,492)
(465,491)(466,490)(467,489)(468,488)(469,487)(470,486)(471,485)(472,484)
(473,483)(474,482)(475,481)(501,526)(502,530)(503,529)(504,528)(505,527)
(506,550)(507,549)(508,548)(509,547)(510,546)(511,545)(512,544)(513,543)
(514,542)(515,541)(516,540)(517,539)(518,538)(519,537)(520,536)(521,535)
(522,534)(523,533)(524,532)(525,531)(551,576)(552,580)(553,579)(554,578)
(555,577)(556,600)(557,599)(558,598)(559,597)(560,596)(561,595)(562,594)
(563,593)(564,592)(565,591)(566,590)(567,589)(568,588)(569,587)(570,586)
(571,585)(572,584)(573,583)(574,582)(575,581)(601,626)(602,630)(603,629)
(604,628)(605,627)(606,650)(607,649)(608,648)(609,647)(610,646)(611,645)
(612,644)(613,643)(614,642)(615,641)(616,640)(617,639)(618,638)(619,637)
(620,636)(621,635)(622,634)(623,633)(624,632)(625,631)(651,676)(652,680)
(653,679)(654,678)(655,677)(656,700)(657,699)(658,698)(659,697)(660,696)
(661,695)(662,694)(663,693)(664,692)(665,691)(666,690)(667,689)(668,688)
(669,687)(670,686)(671,685)(672,684)(673,683)(674,682)(675,681)(701,726)
(702,730)(703,729)(704,728)(705,727)(706,750)(707,749)(708,748)(709,747)
(710,746)(711,745)(712,744)(713,743)(714,742)(715,741)(716,740)(717,739)
(718,738)(719,737)(720,736)(721,735)(722,734)(723,733)(724,732)(725,731)
(751,776)(752,780)(753,779)(754,778)(755,777)(756,800)(757,799)(758,798)
(759,797)(760,796)(761,795)(762,794)(763,793)(764,792)(765,791)(766,790)
(767,789)(768,788)(769,787)(770,786)(771,785)(772,784)(773,783)(774,782)
(775,781);
s2 := Sym(800)!( 1,106)( 2,110)( 3,109)( 4,108)( 5,107)( 6,101)( 7,105)
( 8,104)( 9,103)( 10,102)( 11,125)( 12,124)( 13,123)( 14,122)( 15,121)
( 16,120)( 17,119)( 18,118)( 19,117)( 20,116)( 21,115)( 22,114)( 23,113)
( 24,112)( 25,111)( 26,131)( 27,135)( 28,134)( 29,133)( 30,132)( 31,126)
( 32,130)( 33,129)( 34,128)( 35,127)( 36,150)( 37,149)( 38,148)( 39,147)
( 40,146)( 41,145)( 42,144)( 43,143)( 44,142)( 45,141)( 46,140)( 47,139)
( 48,138)( 49,137)( 50,136)( 51,156)( 52,160)( 53,159)( 54,158)( 55,157)
( 56,151)( 57,155)( 58,154)( 59,153)( 60,152)( 61,175)( 62,174)( 63,173)
( 64,172)( 65,171)( 66,170)( 67,169)( 68,168)( 69,167)( 70,166)( 71,165)
( 72,164)( 73,163)( 74,162)( 75,161)( 76,181)( 77,185)( 78,184)( 79,183)
( 80,182)( 81,176)( 82,180)( 83,179)( 84,178)( 85,177)( 86,200)( 87,199)
( 88,198)( 89,197)( 90,196)( 91,195)( 92,194)( 93,193)( 94,192)( 95,191)
( 96,190)( 97,189)( 98,188)( 99,187)(100,186)(201,306)(202,310)(203,309)
(204,308)(205,307)(206,301)(207,305)(208,304)(209,303)(210,302)(211,325)
(212,324)(213,323)(214,322)(215,321)(216,320)(217,319)(218,318)(219,317)
(220,316)(221,315)(222,314)(223,313)(224,312)(225,311)(226,331)(227,335)
(228,334)(229,333)(230,332)(231,326)(232,330)(233,329)(234,328)(235,327)
(236,350)(237,349)(238,348)(239,347)(240,346)(241,345)(242,344)(243,343)
(244,342)(245,341)(246,340)(247,339)(248,338)(249,337)(250,336)(251,356)
(252,360)(253,359)(254,358)(255,357)(256,351)(257,355)(258,354)(259,353)
(260,352)(261,375)(262,374)(263,373)(264,372)(265,371)(266,370)(267,369)
(268,368)(269,367)(270,366)(271,365)(272,364)(273,363)(274,362)(275,361)
(276,381)(277,385)(278,384)(279,383)(280,382)(281,376)(282,380)(283,379)
(284,378)(285,377)(286,400)(287,399)(288,398)(289,397)(290,396)(291,395)
(292,394)(293,393)(294,392)(295,391)(296,390)(297,389)(298,388)(299,387)
(300,386)(401,531)(402,535)(403,534)(404,533)(405,532)(406,526)(407,530)
(408,529)(409,528)(410,527)(411,550)(412,549)(413,548)(414,547)(415,546)
(416,545)(417,544)(418,543)(419,542)(420,541)(421,540)(422,539)(423,538)
(424,537)(425,536)(426,506)(427,510)(428,509)(429,508)(430,507)(431,501)
(432,505)(433,504)(434,503)(435,502)(436,525)(437,524)(438,523)(439,522)
(440,521)(441,520)(442,519)(443,518)(444,517)(445,516)(446,515)(447,514)
(448,513)(449,512)(450,511)(451,581)(452,585)(453,584)(454,583)(455,582)
(456,576)(457,580)(458,579)(459,578)(460,577)(461,600)(462,599)(463,598)
(464,597)(465,596)(466,595)(467,594)(468,593)(469,592)(470,591)(471,590)
(472,589)(473,588)(474,587)(475,586)(476,556)(477,560)(478,559)(479,558)
(480,557)(481,551)(482,555)(483,554)(484,553)(485,552)(486,575)(487,574)
(488,573)(489,572)(490,571)(491,570)(492,569)(493,568)(494,567)(495,566)
(496,565)(497,564)(498,563)(499,562)(500,561)(601,731)(602,735)(603,734)
(604,733)(605,732)(606,726)(607,730)(608,729)(609,728)(610,727)(611,750)
(612,749)(613,748)(614,747)(615,746)(616,745)(617,744)(618,743)(619,742)
(620,741)(621,740)(622,739)(623,738)(624,737)(625,736)(626,706)(627,710)
(628,709)(629,708)(630,707)(631,701)(632,705)(633,704)(634,703)(635,702)
(636,725)(637,724)(638,723)(639,722)(640,721)(641,720)(642,719)(643,718)
(644,717)(645,716)(646,715)(647,714)(648,713)(649,712)(650,711)(651,781)
(652,785)(653,784)(654,783)(655,782)(656,776)(657,780)(658,779)(659,778)
(660,777)(661,800)(662,799)(663,798)(664,797)(665,796)(666,795)(667,794)
(668,793)(669,792)(670,791)(671,790)(672,789)(673,788)(674,787)(675,786)
(676,756)(677,760)(678,759)(679,758)(680,757)(681,751)(682,755)(683,754)
(684,753)(685,752)(686,775)(687,774)(688,773)(689,772)(690,771)(691,770)
(692,769)(693,768)(694,767)(695,766)(696,765)(697,764)(698,763)(699,762)
(700,761);
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*s0*s1*s0*s1*s0*s1, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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