Polytope of Type {52,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,4,4}*1664
Also Known As : {{52,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1664,7822)
Rank : 4
Schlafli Type : {52,4,4}
Number of vertices, edges, etc : 52, 104, 8, 4
Order of s0s1s2s3 : 52
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 : {52,4,2}*832, {52,2,4}*832, {26,4,4}*832
4-fold quotients : {52,2,2}*416, {26,2,4}*416, {26,4,2}*416
8-fold quotients : {13,2,4}*208, {26,2,2}*208
13-fold quotients : {4,4,4}*128
16-fold quotients : {13,2,2}*104
26-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
52-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
104-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,521)( 2,533)( 3,532)( 4,531)( 5,530)( 6,529)( 7,528)( 8,527)
( 9,526)( 10,525)( 11,524)( 12,523)( 13,522)( 14,534)( 15,546)( 16,545)
( 17,544)( 18,543)( 19,542)( 20,541)( 21,540)( 22,539)( 23,538)( 24,537)
( 25,536)( 26,535)( 27,547)( 28,559)( 29,558)( 30,557)( 31,556)( 32,555)
( 33,554)( 34,553)( 35,552)( 36,551)( 37,550)( 38,549)( 39,548)( 40,560)
( 41,572)( 42,571)( 43,570)( 44,569)( 45,568)( 46,567)( 47,566)( 48,565)
( 49,564)( 50,563)( 51,562)( 52,561)( 53,573)( 54,585)( 55,584)( 56,583)
( 57,582)( 58,581)( 59,580)( 60,579)( 61,578)( 62,577)( 63,576)( 64,575)
( 65,574)( 66,586)( 67,598)( 68,597)( 69,596)( 70,595)( 71,594)( 72,593)
( 73,592)( 74,591)( 75,590)( 76,589)( 77,588)( 78,587)( 79,599)( 80,611)
( 81,610)( 82,609)( 83,608)( 84,607)( 85,606)( 86,605)( 87,604)( 88,603)
( 89,602)( 90,601)( 91,600)( 92,612)( 93,624)( 94,623)( 95,622)( 96,621)
( 97,620)( 98,619)( 99,618)(100,617)(101,616)(102,615)(103,614)(104,613)
(105,417)(106,429)(107,428)(108,427)(109,426)(110,425)(111,424)(112,423)
(113,422)(114,421)(115,420)(116,419)(117,418)(118,430)(119,442)(120,441)
(121,440)(122,439)(123,438)(124,437)(125,436)(126,435)(127,434)(128,433)
(129,432)(130,431)(131,443)(132,455)(133,454)(134,453)(135,452)(136,451)
(137,450)(138,449)(139,448)(140,447)(141,446)(142,445)(143,444)(144,456)
(145,468)(146,467)(147,466)(148,465)(149,464)(150,463)(151,462)(152,461)
(153,460)(154,459)(155,458)(156,457)(157,469)(158,481)(159,480)(160,479)
(161,478)(162,477)(163,476)(164,475)(165,474)(166,473)(167,472)(168,471)
(169,470)(170,482)(171,494)(172,493)(173,492)(174,491)(175,490)(176,489)
(177,488)(178,487)(179,486)(180,485)(181,484)(182,483)(183,495)(184,507)
(185,506)(186,505)(187,504)(188,503)(189,502)(190,501)(191,500)(192,499)
(193,498)(194,497)(195,496)(196,508)(197,520)(198,519)(199,518)(200,517)
(201,516)(202,515)(203,514)(204,513)(205,512)(206,511)(207,510)(208,509)
(209,742)(210,754)(211,753)(212,752)(213,751)(214,750)(215,749)(216,748)
(217,747)(218,746)(219,745)(220,744)(221,743)(222,729)(223,741)(224,740)
(225,739)(226,738)(227,737)(228,736)(229,735)(230,734)(231,733)(232,732)
(233,731)(234,730)(235,768)(236,780)(237,779)(238,778)(239,777)(240,776)
(241,775)(242,774)(243,773)(244,772)(245,771)(246,770)(247,769)(248,755)
(249,767)(250,766)(251,765)(252,764)(253,763)(254,762)(255,761)(256,760)
(257,759)(258,758)(259,757)(260,756)(261,794)(262,806)(263,805)(264,804)
(265,803)(266,802)(267,801)(268,800)(269,799)(270,798)(271,797)(272,796)
(273,795)(274,781)(275,793)(276,792)(277,791)(278,790)(279,789)(280,788)
(281,787)(282,786)(283,785)(284,784)(285,783)(286,782)(287,820)(288,832)
(289,831)(290,830)(291,829)(292,828)(293,827)(294,826)(295,825)(296,824)
(297,823)(298,822)(299,821)(300,807)(301,819)(302,818)(303,817)(304,816)
(305,815)(306,814)(307,813)(308,812)(309,811)(310,810)(311,809)(312,808)
(313,638)(314,650)(315,649)(316,648)(317,647)(318,646)(319,645)(320,644)
(321,643)(322,642)(323,641)(324,640)(325,639)(326,625)(327,637)(328,636)
(329,635)(330,634)(331,633)(332,632)(333,631)(334,630)(335,629)(336,628)
(337,627)(338,626)(339,664)(340,676)(341,675)(342,674)(343,673)(344,672)
(345,671)(346,670)(347,669)(348,668)(349,667)(350,666)(351,665)(352,651)
(353,663)(354,662)(355,661)(356,660)(357,659)(358,658)(359,657)(360,656)
(361,655)(362,654)(363,653)(364,652)(365,690)(366,702)(367,701)(368,700)
(369,699)(370,698)(371,697)(372,696)(373,695)(374,694)(375,693)(376,692)
(377,691)(378,677)(379,689)(380,688)(381,687)(382,686)(383,685)(384,684)
(385,683)(386,682)(387,681)(388,680)(389,679)(390,678)(391,716)(392,728)
(393,727)(394,726)(395,725)(396,724)(397,723)(398,722)(399,721)(400,720)
(401,719)(402,718)(403,717)(404,703)(405,715)(406,714)(407,713)(408,712)
(409,711)(410,710)(411,709)(412,708)(413,707)(414,706)(415,705)(416,704);;
s1 := ( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)( 8,216)
( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)( 16,234)
( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)
( 25,225)( 26,224)( 27,236)( 28,235)( 29,247)( 30,246)( 31,245)( 32,244)
( 33,243)( 34,242)( 35,241)( 36,240)( 37,239)( 38,238)( 39,237)( 40,249)
( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)( 48,254)
( 49,253)( 50,252)( 51,251)( 52,250)( 53,262)( 54,261)( 55,273)( 56,272)
( 57,271)( 58,270)( 59,269)( 60,268)( 61,267)( 62,266)( 63,265)( 64,264)
( 65,263)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)( 72,282)
( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,288)( 80,287)
( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)( 88,292)
( 89,291)( 90,290)( 91,289)( 92,301)( 93,300)( 94,312)( 95,311)( 96,310)
( 97,309)( 98,308)( 99,307)(100,306)(101,305)(102,304)(103,303)(104,302)
(105,314)(106,313)(107,325)(108,324)(109,323)(110,322)(111,321)(112,320)
(113,319)(114,318)(115,317)(116,316)(117,315)(118,327)(119,326)(120,338)
(121,337)(122,336)(123,335)(124,334)(125,333)(126,332)(127,331)(128,330)
(129,329)(130,328)(131,340)(132,339)(133,351)(134,350)(135,349)(136,348)
(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)(144,353)
(145,352)(146,364)(147,363)(148,362)(149,361)(150,360)(151,359)(152,358)
(153,357)(154,356)(155,355)(156,354)(157,366)(158,365)(159,377)(160,376)
(161,375)(162,374)(163,373)(164,372)(165,371)(166,370)(167,369)(168,368)
(169,367)(170,379)(171,378)(172,390)(173,389)(174,388)(175,387)(176,386)
(177,385)(178,384)(179,383)(180,382)(181,381)(182,380)(183,392)(184,391)
(185,403)(186,402)(187,401)(188,400)(189,399)(190,398)(191,397)(192,396)
(193,395)(194,394)(195,393)(196,405)(197,404)(198,416)(199,415)(200,414)
(201,413)(202,412)(203,411)(204,410)(205,409)(206,408)(207,407)(208,406)
(417,626)(418,625)(419,637)(420,636)(421,635)(422,634)(423,633)(424,632)
(425,631)(426,630)(427,629)(428,628)(429,627)(430,639)(431,638)(432,650)
(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)(439,643)(440,642)
(441,641)(442,640)(443,652)(444,651)(445,663)(446,662)(447,661)(448,660)
(449,659)(450,658)(451,657)(452,656)(453,655)(454,654)(455,653)(456,665)
(457,664)(458,676)(459,675)(460,674)(461,673)(462,672)(463,671)(464,670)
(465,669)(466,668)(467,667)(468,666)(469,678)(470,677)(471,689)(472,688)
(473,687)(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)(480,680)
(481,679)(482,691)(483,690)(484,702)(485,701)(486,700)(487,699)(488,698)
(489,697)(490,696)(491,695)(492,694)(493,693)(494,692)(495,704)(496,703)
(497,715)(498,714)(499,713)(500,712)(501,711)(502,710)(503,709)(504,708)
(505,707)(506,706)(507,705)(508,717)(509,716)(510,728)(511,727)(512,726)
(513,725)(514,724)(515,723)(516,722)(517,721)(518,720)(519,719)(520,718)
(521,730)(522,729)(523,741)(524,740)(525,739)(526,738)(527,737)(528,736)
(529,735)(530,734)(531,733)(532,732)(533,731)(534,743)(535,742)(536,754)
(537,753)(538,752)(539,751)(540,750)(541,749)(542,748)(543,747)(544,746)
(545,745)(546,744)(547,756)(548,755)(549,767)(550,766)(551,765)(552,764)
(553,763)(554,762)(555,761)(556,760)(557,759)(558,758)(559,757)(560,769)
(561,768)(562,780)(563,779)(564,778)(565,777)(566,776)(567,775)(568,774)
(569,773)(570,772)(571,771)(572,770)(573,782)(574,781)(575,793)(576,792)
(577,791)(578,790)(579,789)(580,788)(581,787)(582,786)(583,785)(584,784)
(585,783)(586,795)(587,794)(588,806)(589,805)(590,804)(591,803)(592,802)
(593,801)(594,800)(595,799)(596,798)(597,797)(598,796)(599,808)(600,807)
(601,819)(602,818)(603,817)(604,816)(605,815)(606,814)(607,813)(608,812)
(609,811)(610,810)(611,809)(612,821)(613,820)(614,832)(615,831)(616,830)
(617,829)(618,828)(619,827)(620,826)(621,825)(622,824)(623,823)(624,822);;
s2 := (105,157)(106,158)(107,159)(108,160)(109,161)(110,162)(111,163)(112,164)
(113,165)(114,166)(115,167)(116,168)(117,169)(118,170)(119,171)(120,172)
(121,173)(122,174)(123,175)(124,176)(125,177)(126,178)(127,179)(128,180)
(129,181)(130,182)(131,183)(132,184)(133,185)(134,186)(135,187)(136,188)
(137,189)(138,190)(139,191)(140,192)(141,193)(142,194)(143,195)(144,196)
(145,197)(146,198)(147,199)(148,200)(149,201)(150,202)(151,203)(152,204)
(153,205)(154,206)(155,207)(156,208)(209,235)(210,236)(211,237)(212,238)
(213,239)(214,240)(215,241)(216,242)(217,243)(218,244)(219,245)(220,246)
(221,247)(222,248)(223,249)(224,250)(225,251)(226,252)(227,253)(228,254)
(229,255)(230,256)(231,257)(232,258)(233,259)(234,260)(261,287)(262,288)
(263,289)(264,290)(265,291)(266,292)(267,293)(268,294)(269,295)(270,296)
(271,297)(272,298)(273,299)(274,300)(275,301)(276,302)(277,303)(278,304)
(279,305)(280,306)(281,307)(282,308)(283,309)(284,310)(285,311)(286,312)
(313,391)(314,392)(315,393)(316,394)(317,395)(318,396)(319,397)(320,398)
(321,399)(322,400)(323,401)(324,402)(325,403)(326,404)(327,405)(328,406)
(329,407)(330,408)(331,409)(332,410)(333,411)(334,412)(335,413)(336,414)
(337,415)(338,416)(339,365)(340,366)(341,367)(342,368)(343,369)(344,370)
(345,371)(346,372)(347,373)(348,374)(349,375)(350,376)(351,377)(352,378)
(353,379)(354,380)(355,381)(356,382)(357,383)(358,384)(359,385)(360,386)
(361,387)(362,388)(363,389)(364,390)(417,469)(418,470)(419,471)(420,472)
(421,473)(422,474)(423,475)(424,476)(425,477)(426,478)(427,479)(428,480)
(429,481)(430,482)(431,483)(432,484)(433,485)(434,486)(435,487)(436,488)
(437,489)(438,490)(439,491)(440,492)(441,493)(442,494)(443,495)(444,496)
(445,497)(446,498)(447,499)(448,500)(449,501)(450,502)(451,503)(452,504)
(453,505)(454,506)(455,507)(456,508)(457,509)(458,510)(459,511)(460,512)
(461,513)(462,514)(463,515)(464,516)(465,517)(466,518)(467,519)(468,520)
(625,703)(626,704)(627,705)(628,706)(629,707)(630,708)(631,709)(632,710)
(633,711)(634,712)(635,713)(636,714)(637,715)(638,716)(639,717)(640,718)
(641,719)(642,720)(643,721)(644,722)(645,723)(646,724)(647,725)(648,726)
(649,727)(650,728)(651,677)(652,678)(653,679)(654,680)(655,681)(656,682)
(657,683)(658,684)(659,685)(660,686)(661,687)(662,688)(663,689)(664,690)
(665,691)(666,692)(667,693)(668,694)(669,695)(670,696)(671,697)(672,698)
(673,699)(674,700)(675,701)(676,702)(729,755)(730,756)(731,757)(732,758)
(733,759)(734,760)(735,761)(736,762)(737,763)(738,764)(739,765)(740,766)
(741,767)(742,768)(743,769)(744,770)(745,771)(746,772)(747,773)(748,774)
(749,775)(750,776)(751,777)(752,778)(753,779)(754,780)(781,807)(782,808)
(783,809)(784,810)(785,811)(786,812)(787,813)(788,814)(789,815)(790,816)
(791,817)(792,818)(793,819)(794,820)(795,821)(796,822)(797,823)(798,824)
(799,825)(800,826)(801,827)(802,828)(803,829)(804,830)(805,831)(806,832);;
s3 := ( 1,105)( 2,106)( 3,107)( 4,108)( 5,109)( 6,110)( 7,111)( 8,112)
( 9,113)( 10,114)( 11,115)( 12,116)( 13,117)( 14,118)( 15,119)( 16,120)
( 17,121)( 18,122)( 19,123)( 20,124)( 21,125)( 22,126)( 23,127)( 24,128)
( 25,129)( 26,130)( 27,131)( 28,132)( 29,133)( 30,134)( 31,135)( 32,136)
( 33,137)( 34,138)( 35,139)( 36,140)( 37,141)( 38,142)( 39,143)( 40,144)
( 41,145)( 42,146)( 43,147)( 44,148)( 45,149)( 46,150)( 47,151)( 48,152)
( 49,153)( 50,154)( 51,155)( 52,156)( 53,157)( 54,158)( 55,159)( 56,160)
( 57,161)( 58,162)( 59,163)( 60,164)( 61,165)( 62,166)( 63,167)( 64,168)
( 65,169)( 66,170)( 67,171)( 68,172)( 69,173)( 70,174)( 71,175)( 72,176)
( 73,177)( 74,178)( 75,179)( 76,180)( 77,181)( 78,182)( 79,183)( 80,184)
( 81,185)( 82,186)( 83,187)( 84,188)( 85,189)( 86,190)( 87,191)( 88,192)
( 89,193)( 90,194)( 91,195)( 92,196)( 93,197)( 94,198)( 95,199)( 96,200)
( 97,201)( 98,202)( 99,203)(100,204)(101,205)(102,206)(103,207)(104,208)
(209,313)(210,314)(211,315)(212,316)(213,317)(214,318)(215,319)(216,320)
(217,321)(218,322)(219,323)(220,324)(221,325)(222,326)(223,327)(224,328)
(225,329)(226,330)(227,331)(228,332)(229,333)(230,334)(231,335)(232,336)
(233,337)(234,338)(235,339)(236,340)(237,341)(238,342)(239,343)(240,344)
(241,345)(242,346)(243,347)(244,348)(245,349)(246,350)(247,351)(248,352)
(249,353)(250,354)(251,355)(252,356)(253,357)(254,358)(255,359)(256,360)
(257,361)(258,362)(259,363)(260,364)(261,365)(262,366)(263,367)(264,368)
(265,369)(266,370)(267,371)(268,372)(269,373)(270,374)(271,375)(272,376)
(273,377)(274,378)(275,379)(276,380)(277,381)(278,382)(279,383)(280,384)
(281,385)(282,386)(283,387)(284,388)(285,389)(286,390)(287,391)(288,392)
(289,393)(290,394)(291,395)(292,396)(293,397)(294,398)(295,399)(296,400)
(297,401)(298,402)(299,403)(300,404)(301,405)(302,406)(303,407)(304,408)
(305,409)(306,410)(307,411)(308,412)(309,413)(310,414)(311,415)(312,416)
(417,521)(418,522)(419,523)(420,524)(421,525)(422,526)(423,527)(424,528)
(425,529)(426,530)(427,531)(428,532)(429,533)(430,534)(431,535)(432,536)
(433,537)(434,538)(435,539)(436,540)(437,541)(438,542)(439,543)(440,544)
(441,545)(442,546)(443,547)(444,548)(445,549)(446,550)(447,551)(448,552)
(449,553)(450,554)(451,555)(452,556)(453,557)(454,558)(455,559)(456,560)
(457,561)(458,562)(459,563)(460,564)(461,565)(462,566)(463,567)(464,568)
(465,569)(466,570)(467,571)(468,572)(469,573)(470,574)(471,575)(472,576)
(473,577)(474,578)(475,579)(476,580)(477,581)(478,582)(479,583)(480,584)
(481,585)(482,586)(483,587)(484,588)(485,589)(486,590)(487,591)(488,592)
(489,593)(490,594)(491,595)(492,596)(493,597)(494,598)(495,599)(496,600)
(497,601)(498,602)(499,603)(500,604)(501,605)(502,606)(503,607)(504,608)
(505,609)(506,610)(507,611)(508,612)(509,613)(510,614)(511,615)(512,616)
(513,617)(514,618)(515,619)(516,620)(517,621)(518,622)(519,623)(520,624)
(625,729)(626,730)(627,731)(628,732)(629,733)(630,734)(631,735)(632,736)
(633,737)(634,738)(635,739)(636,740)(637,741)(638,742)(639,743)(640,744)
(641,745)(642,746)(643,747)(644,748)(645,749)(646,750)(647,751)(648,752)
(649,753)(650,754)(651,755)(652,756)(653,757)(654,758)(655,759)(656,760)
(657,761)(658,762)(659,763)(660,764)(661,765)(662,766)(663,767)(664,768)
(665,769)(666,770)(667,771)(668,772)(669,773)(670,774)(671,775)(672,776)
(673,777)(674,778)(675,779)(676,780)(677,781)(678,782)(679,783)(680,784)
(681,785)(682,786)(683,787)(684,788)(685,789)(686,790)(687,791)(688,792)
(689,793)(690,794)(691,795)(692,796)(693,797)(694,798)(695,799)(696,800)
(697,801)(698,802)(699,803)(700,804)(701,805)(702,806)(703,807)(704,808)
(705,809)(706,810)(707,811)(708,812)(709,813)(710,814)(711,815)(712,816)
(713,817)(714,818)(715,819)(716,820)(717,821)(718,822)(719,823)(720,824)
(721,825)(722,826)(723,827)(724,828)(725,829)(726,830)(727,831)(728,832);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(832)!( 1,521)( 2,533)( 3,532)( 4,531)( 5,530)( 6,529)( 7,528)
( 8,527)( 9,526)( 10,525)( 11,524)( 12,523)( 13,522)( 14,534)( 15,546)
( 16,545)( 17,544)( 18,543)( 19,542)( 20,541)( 21,540)( 22,539)( 23,538)
( 24,537)( 25,536)( 26,535)( 27,547)( 28,559)( 29,558)( 30,557)( 31,556)
( 32,555)( 33,554)( 34,553)( 35,552)( 36,551)( 37,550)( 38,549)( 39,548)
( 40,560)( 41,572)( 42,571)( 43,570)( 44,569)( 45,568)( 46,567)( 47,566)
( 48,565)( 49,564)( 50,563)( 51,562)( 52,561)( 53,573)( 54,585)( 55,584)
( 56,583)( 57,582)( 58,581)( 59,580)( 60,579)( 61,578)( 62,577)( 63,576)
( 64,575)( 65,574)( 66,586)( 67,598)( 68,597)( 69,596)( 70,595)( 71,594)
( 72,593)( 73,592)( 74,591)( 75,590)( 76,589)( 77,588)( 78,587)( 79,599)
( 80,611)( 81,610)( 82,609)( 83,608)( 84,607)( 85,606)( 86,605)( 87,604)
( 88,603)( 89,602)( 90,601)( 91,600)( 92,612)( 93,624)( 94,623)( 95,622)
( 96,621)( 97,620)( 98,619)( 99,618)(100,617)(101,616)(102,615)(103,614)
(104,613)(105,417)(106,429)(107,428)(108,427)(109,426)(110,425)(111,424)
(112,423)(113,422)(114,421)(115,420)(116,419)(117,418)(118,430)(119,442)
(120,441)(121,440)(122,439)(123,438)(124,437)(125,436)(126,435)(127,434)
(128,433)(129,432)(130,431)(131,443)(132,455)(133,454)(134,453)(135,452)
(136,451)(137,450)(138,449)(139,448)(140,447)(141,446)(142,445)(143,444)
(144,456)(145,468)(146,467)(147,466)(148,465)(149,464)(150,463)(151,462)
(152,461)(153,460)(154,459)(155,458)(156,457)(157,469)(158,481)(159,480)
(160,479)(161,478)(162,477)(163,476)(164,475)(165,474)(166,473)(167,472)
(168,471)(169,470)(170,482)(171,494)(172,493)(173,492)(174,491)(175,490)
(176,489)(177,488)(178,487)(179,486)(180,485)(181,484)(182,483)(183,495)
(184,507)(185,506)(186,505)(187,504)(188,503)(189,502)(190,501)(191,500)
(192,499)(193,498)(194,497)(195,496)(196,508)(197,520)(198,519)(199,518)
(200,517)(201,516)(202,515)(203,514)(204,513)(205,512)(206,511)(207,510)
(208,509)(209,742)(210,754)(211,753)(212,752)(213,751)(214,750)(215,749)
(216,748)(217,747)(218,746)(219,745)(220,744)(221,743)(222,729)(223,741)
(224,740)(225,739)(226,738)(227,737)(228,736)(229,735)(230,734)(231,733)
(232,732)(233,731)(234,730)(235,768)(236,780)(237,779)(238,778)(239,777)
(240,776)(241,775)(242,774)(243,773)(244,772)(245,771)(246,770)(247,769)
(248,755)(249,767)(250,766)(251,765)(252,764)(253,763)(254,762)(255,761)
(256,760)(257,759)(258,758)(259,757)(260,756)(261,794)(262,806)(263,805)
(264,804)(265,803)(266,802)(267,801)(268,800)(269,799)(270,798)(271,797)
(272,796)(273,795)(274,781)(275,793)(276,792)(277,791)(278,790)(279,789)
(280,788)(281,787)(282,786)(283,785)(284,784)(285,783)(286,782)(287,820)
(288,832)(289,831)(290,830)(291,829)(292,828)(293,827)(294,826)(295,825)
(296,824)(297,823)(298,822)(299,821)(300,807)(301,819)(302,818)(303,817)
(304,816)(305,815)(306,814)(307,813)(308,812)(309,811)(310,810)(311,809)
(312,808)(313,638)(314,650)(315,649)(316,648)(317,647)(318,646)(319,645)
(320,644)(321,643)(322,642)(323,641)(324,640)(325,639)(326,625)(327,637)
(328,636)(329,635)(330,634)(331,633)(332,632)(333,631)(334,630)(335,629)
(336,628)(337,627)(338,626)(339,664)(340,676)(341,675)(342,674)(343,673)
(344,672)(345,671)(346,670)(347,669)(348,668)(349,667)(350,666)(351,665)
(352,651)(353,663)(354,662)(355,661)(356,660)(357,659)(358,658)(359,657)
(360,656)(361,655)(362,654)(363,653)(364,652)(365,690)(366,702)(367,701)
(368,700)(369,699)(370,698)(371,697)(372,696)(373,695)(374,694)(375,693)
(376,692)(377,691)(378,677)(379,689)(380,688)(381,687)(382,686)(383,685)
(384,684)(385,683)(386,682)(387,681)(388,680)(389,679)(390,678)(391,716)
(392,728)(393,727)(394,726)(395,725)(396,724)(397,723)(398,722)(399,721)
(400,720)(401,719)(402,718)(403,717)(404,703)(405,715)(406,714)(407,713)
(408,712)(409,711)(410,710)(411,709)(412,708)(413,707)(414,706)(415,705)
(416,704);
s1 := Sym(832)!( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)
( 8,216)( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)
( 16,234)( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)
( 24,226)( 25,225)( 26,224)( 27,236)( 28,235)( 29,247)( 30,246)( 31,245)
( 32,244)( 33,243)( 34,242)( 35,241)( 36,240)( 37,239)( 38,238)( 39,237)
( 40,249)( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)
( 48,254)( 49,253)( 50,252)( 51,251)( 52,250)( 53,262)( 54,261)( 55,273)
( 56,272)( 57,271)( 58,270)( 59,269)( 60,268)( 61,267)( 62,266)( 63,265)
( 64,264)( 65,263)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)
( 72,282)( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,288)
( 80,287)( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)
( 88,292)( 89,291)( 90,290)( 91,289)( 92,301)( 93,300)( 94,312)( 95,311)
( 96,310)( 97,309)( 98,308)( 99,307)(100,306)(101,305)(102,304)(103,303)
(104,302)(105,314)(106,313)(107,325)(108,324)(109,323)(110,322)(111,321)
(112,320)(113,319)(114,318)(115,317)(116,316)(117,315)(118,327)(119,326)
(120,338)(121,337)(122,336)(123,335)(124,334)(125,333)(126,332)(127,331)
(128,330)(129,329)(130,328)(131,340)(132,339)(133,351)(134,350)(135,349)
(136,348)(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)
(144,353)(145,352)(146,364)(147,363)(148,362)(149,361)(150,360)(151,359)
(152,358)(153,357)(154,356)(155,355)(156,354)(157,366)(158,365)(159,377)
(160,376)(161,375)(162,374)(163,373)(164,372)(165,371)(166,370)(167,369)
(168,368)(169,367)(170,379)(171,378)(172,390)(173,389)(174,388)(175,387)
(176,386)(177,385)(178,384)(179,383)(180,382)(181,381)(182,380)(183,392)
(184,391)(185,403)(186,402)(187,401)(188,400)(189,399)(190,398)(191,397)
(192,396)(193,395)(194,394)(195,393)(196,405)(197,404)(198,416)(199,415)
(200,414)(201,413)(202,412)(203,411)(204,410)(205,409)(206,408)(207,407)
(208,406)(417,626)(418,625)(419,637)(420,636)(421,635)(422,634)(423,633)
(424,632)(425,631)(426,630)(427,629)(428,628)(429,627)(430,639)(431,638)
(432,650)(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)(439,643)
(440,642)(441,641)(442,640)(443,652)(444,651)(445,663)(446,662)(447,661)
(448,660)(449,659)(450,658)(451,657)(452,656)(453,655)(454,654)(455,653)
(456,665)(457,664)(458,676)(459,675)(460,674)(461,673)(462,672)(463,671)
(464,670)(465,669)(466,668)(467,667)(468,666)(469,678)(470,677)(471,689)
(472,688)(473,687)(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)
(480,680)(481,679)(482,691)(483,690)(484,702)(485,701)(486,700)(487,699)
(488,698)(489,697)(490,696)(491,695)(492,694)(493,693)(494,692)(495,704)
(496,703)(497,715)(498,714)(499,713)(500,712)(501,711)(502,710)(503,709)
(504,708)(505,707)(506,706)(507,705)(508,717)(509,716)(510,728)(511,727)
(512,726)(513,725)(514,724)(515,723)(516,722)(517,721)(518,720)(519,719)
(520,718)(521,730)(522,729)(523,741)(524,740)(525,739)(526,738)(527,737)
(528,736)(529,735)(530,734)(531,733)(532,732)(533,731)(534,743)(535,742)
(536,754)(537,753)(538,752)(539,751)(540,750)(541,749)(542,748)(543,747)
(544,746)(545,745)(546,744)(547,756)(548,755)(549,767)(550,766)(551,765)
(552,764)(553,763)(554,762)(555,761)(556,760)(557,759)(558,758)(559,757)
(560,769)(561,768)(562,780)(563,779)(564,778)(565,777)(566,776)(567,775)
(568,774)(569,773)(570,772)(571,771)(572,770)(573,782)(574,781)(575,793)
(576,792)(577,791)(578,790)(579,789)(580,788)(581,787)(582,786)(583,785)
(584,784)(585,783)(586,795)(587,794)(588,806)(589,805)(590,804)(591,803)
(592,802)(593,801)(594,800)(595,799)(596,798)(597,797)(598,796)(599,808)
(600,807)(601,819)(602,818)(603,817)(604,816)(605,815)(606,814)(607,813)
(608,812)(609,811)(610,810)(611,809)(612,821)(613,820)(614,832)(615,831)
(616,830)(617,829)(618,828)(619,827)(620,826)(621,825)(622,824)(623,823)
(624,822);
s2 := Sym(832)!(105,157)(106,158)(107,159)(108,160)(109,161)(110,162)(111,163)
(112,164)(113,165)(114,166)(115,167)(116,168)(117,169)(118,170)(119,171)
(120,172)(121,173)(122,174)(123,175)(124,176)(125,177)(126,178)(127,179)
(128,180)(129,181)(130,182)(131,183)(132,184)(133,185)(134,186)(135,187)
(136,188)(137,189)(138,190)(139,191)(140,192)(141,193)(142,194)(143,195)
(144,196)(145,197)(146,198)(147,199)(148,200)(149,201)(150,202)(151,203)
(152,204)(153,205)(154,206)(155,207)(156,208)(209,235)(210,236)(211,237)
(212,238)(213,239)(214,240)(215,241)(216,242)(217,243)(218,244)(219,245)
(220,246)(221,247)(222,248)(223,249)(224,250)(225,251)(226,252)(227,253)
(228,254)(229,255)(230,256)(231,257)(232,258)(233,259)(234,260)(261,287)
(262,288)(263,289)(264,290)(265,291)(266,292)(267,293)(268,294)(269,295)
(270,296)(271,297)(272,298)(273,299)(274,300)(275,301)(276,302)(277,303)
(278,304)(279,305)(280,306)(281,307)(282,308)(283,309)(284,310)(285,311)
(286,312)(313,391)(314,392)(315,393)(316,394)(317,395)(318,396)(319,397)
(320,398)(321,399)(322,400)(323,401)(324,402)(325,403)(326,404)(327,405)
(328,406)(329,407)(330,408)(331,409)(332,410)(333,411)(334,412)(335,413)
(336,414)(337,415)(338,416)(339,365)(340,366)(341,367)(342,368)(343,369)
(344,370)(345,371)(346,372)(347,373)(348,374)(349,375)(350,376)(351,377)
(352,378)(353,379)(354,380)(355,381)(356,382)(357,383)(358,384)(359,385)
(360,386)(361,387)(362,388)(363,389)(364,390)(417,469)(418,470)(419,471)
(420,472)(421,473)(422,474)(423,475)(424,476)(425,477)(426,478)(427,479)
(428,480)(429,481)(430,482)(431,483)(432,484)(433,485)(434,486)(435,487)
(436,488)(437,489)(438,490)(439,491)(440,492)(441,493)(442,494)(443,495)
(444,496)(445,497)(446,498)(447,499)(448,500)(449,501)(450,502)(451,503)
(452,504)(453,505)(454,506)(455,507)(456,508)(457,509)(458,510)(459,511)
(460,512)(461,513)(462,514)(463,515)(464,516)(465,517)(466,518)(467,519)
(468,520)(625,703)(626,704)(627,705)(628,706)(629,707)(630,708)(631,709)
(632,710)(633,711)(634,712)(635,713)(636,714)(637,715)(638,716)(639,717)
(640,718)(641,719)(642,720)(643,721)(644,722)(645,723)(646,724)(647,725)
(648,726)(649,727)(650,728)(651,677)(652,678)(653,679)(654,680)(655,681)
(656,682)(657,683)(658,684)(659,685)(660,686)(661,687)(662,688)(663,689)
(664,690)(665,691)(666,692)(667,693)(668,694)(669,695)(670,696)(671,697)
(672,698)(673,699)(674,700)(675,701)(676,702)(729,755)(730,756)(731,757)
(732,758)(733,759)(734,760)(735,761)(736,762)(737,763)(738,764)(739,765)
(740,766)(741,767)(742,768)(743,769)(744,770)(745,771)(746,772)(747,773)
(748,774)(749,775)(750,776)(751,777)(752,778)(753,779)(754,780)(781,807)
(782,808)(783,809)(784,810)(785,811)(786,812)(787,813)(788,814)(789,815)
(790,816)(791,817)(792,818)(793,819)(794,820)(795,821)(796,822)(797,823)
(798,824)(799,825)(800,826)(801,827)(802,828)(803,829)(804,830)(805,831)
(806,832);
s3 := Sym(832)!( 1,105)( 2,106)( 3,107)( 4,108)( 5,109)( 6,110)( 7,111)
( 8,112)( 9,113)( 10,114)( 11,115)( 12,116)( 13,117)( 14,118)( 15,119)
( 16,120)( 17,121)( 18,122)( 19,123)( 20,124)( 21,125)( 22,126)( 23,127)
( 24,128)( 25,129)( 26,130)( 27,131)( 28,132)( 29,133)( 30,134)( 31,135)
( 32,136)( 33,137)( 34,138)( 35,139)( 36,140)( 37,141)( 38,142)( 39,143)
( 40,144)( 41,145)( 42,146)( 43,147)( 44,148)( 45,149)( 46,150)( 47,151)
( 48,152)( 49,153)( 50,154)( 51,155)( 52,156)( 53,157)( 54,158)( 55,159)
( 56,160)( 57,161)( 58,162)( 59,163)( 60,164)( 61,165)( 62,166)( 63,167)
( 64,168)( 65,169)( 66,170)( 67,171)( 68,172)( 69,173)( 70,174)( 71,175)
( 72,176)( 73,177)( 74,178)( 75,179)( 76,180)( 77,181)( 78,182)( 79,183)
( 80,184)( 81,185)( 82,186)( 83,187)( 84,188)( 85,189)( 86,190)( 87,191)
( 88,192)( 89,193)( 90,194)( 91,195)( 92,196)( 93,197)( 94,198)( 95,199)
( 96,200)( 97,201)( 98,202)( 99,203)(100,204)(101,205)(102,206)(103,207)
(104,208)(209,313)(210,314)(211,315)(212,316)(213,317)(214,318)(215,319)
(216,320)(217,321)(218,322)(219,323)(220,324)(221,325)(222,326)(223,327)
(224,328)(225,329)(226,330)(227,331)(228,332)(229,333)(230,334)(231,335)
(232,336)(233,337)(234,338)(235,339)(236,340)(237,341)(238,342)(239,343)
(240,344)(241,345)(242,346)(243,347)(244,348)(245,349)(246,350)(247,351)
(248,352)(249,353)(250,354)(251,355)(252,356)(253,357)(254,358)(255,359)
(256,360)(257,361)(258,362)(259,363)(260,364)(261,365)(262,366)(263,367)
(264,368)(265,369)(266,370)(267,371)(268,372)(269,373)(270,374)(271,375)
(272,376)(273,377)(274,378)(275,379)(276,380)(277,381)(278,382)(279,383)
(280,384)(281,385)(282,386)(283,387)(284,388)(285,389)(286,390)(287,391)
(288,392)(289,393)(290,394)(291,395)(292,396)(293,397)(294,398)(295,399)
(296,400)(297,401)(298,402)(299,403)(300,404)(301,405)(302,406)(303,407)
(304,408)(305,409)(306,410)(307,411)(308,412)(309,413)(310,414)(311,415)
(312,416)(417,521)(418,522)(419,523)(420,524)(421,525)(422,526)(423,527)
(424,528)(425,529)(426,530)(427,531)(428,532)(429,533)(430,534)(431,535)
(432,536)(433,537)(434,538)(435,539)(436,540)(437,541)(438,542)(439,543)
(440,544)(441,545)(442,546)(443,547)(444,548)(445,549)(446,550)(447,551)
(448,552)(449,553)(450,554)(451,555)(452,556)(453,557)(454,558)(455,559)
(456,560)(457,561)(458,562)(459,563)(460,564)(461,565)(462,566)(463,567)
(464,568)(465,569)(466,570)(467,571)(468,572)(469,573)(470,574)(471,575)
(472,576)(473,577)(474,578)(475,579)(476,580)(477,581)(478,582)(479,583)
(480,584)(481,585)(482,586)(483,587)(484,588)(485,589)(486,590)(487,591)
(488,592)(489,593)(490,594)(491,595)(492,596)(493,597)(494,598)(495,599)
(496,600)(497,601)(498,602)(499,603)(500,604)(501,605)(502,606)(503,607)
(504,608)(505,609)(506,610)(507,611)(508,612)(509,613)(510,614)(511,615)
(512,616)(513,617)(514,618)(515,619)(516,620)(517,621)(518,622)(519,623)
(520,624)(625,729)(626,730)(627,731)(628,732)(629,733)(630,734)(631,735)
(632,736)(633,737)(634,738)(635,739)(636,740)(637,741)(638,742)(639,743)
(640,744)(641,745)(642,746)(643,747)(644,748)(645,749)(646,750)(647,751)
(648,752)(649,753)(650,754)(651,755)(652,756)(653,757)(654,758)(655,759)
(656,760)(657,761)(658,762)(659,763)(660,764)(661,765)(662,766)(663,767)
(664,768)(665,769)(666,770)(667,771)(668,772)(669,773)(670,774)(671,775)
(672,776)(673,777)(674,778)(675,779)(676,780)(677,781)(678,782)(679,783)
(680,784)(681,785)(682,786)(683,787)(684,788)(685,789)(686,790)(687,791)
(688,792)(689,793)(690,794)(691,795)(692,796)(693,797)(694,798)(695,799)
(696,800)(697,801)(698,802)(699,803)(700,804)(701,805)(702,806)(703,807)
(704,808)(705,809)(706,810)(707,811)(708,812)(709,813)(710,814)(711,815)
(712,816)(713,817)(714,818)(715,819)(716,820)(717,821)(718,822)(719,823)
(720,824)(721,825)(722,826)(723,827)(724,828)(725,829)(726,830)(727,831)
(728,832);
poly := sub<Sym(832)|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*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope