Polytope of Type {2,8,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6,3}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46634)
Rank : 5
Schlafli Type : {2,8,6,3}
Number of vertices, edges, etc : 2, 24, 72, 27, 3
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,4,6,3}*864b
9-fold quotients : {2,8,2,3}*192
18-fold quotients : {2,4,2,3}*96
36-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,219)( 4,220)( 5,221)( 6,240)( 7,241)( 8,242)( 9,234)( 10,235)
( 11,236)( 12,237)( 13,238)( 14,239)( 15,231)( 16,232)( 17,233)( 18,225)
( 19,226)( 20,227)( 21,228)( 22,229)( 23,230)( 24,222)( 25,223)( 26,224)
( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)( 33,267)( 34,268)
( 35,269)( 36,261)( 37,262)( 38,263)( 39,264)( 40,265)( 41,266)( 42,258)
( 43,259)( 44,260)( 45,252)( 46,253)( 47,254)( 48,255)( 49,256)( 50,257)
( 51,249)( 52,250)( 53,251)( 54,270)( 55,271)( 56,272)( 57,300)( 58,301)
( 59,302)( 60,321)( 61,322)( 62,323)( 63,315)( 64,316)( 65,317)( 66,318)
( 67,319)( 68,320)( 69,312)( 70,313)( 71,314)( 72,306)( 73,307)( 74,308)
( 75,309)( 76,310)( 77,311)( 78,303)( 79,304)( 80,305)( 81,324)( 82,325)
( 83,326)( 84,273)( 85,274)( 86,275)( 87,294)( 88,295)( 89,296)( 90,288)
( 91,289)( 92,290)( 93,291)( 94,292)( 95,293)( 96,285)( 97,286)( 98,287)
( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)(105,276)(106,277)
(107,278)(108,297)(109,298)(110,299)(111,381)(112,382)(113,383)(114,402)
(115,403)(116,404)(117,396)(118,397)(119,398)(120,399)(121,400)(122,401)
(123,393)(124,394)(125,395)(126,387)(127,388)(128,389)(129,390)(130,391)
(131,392)(132,384)(133,385)(134,386)(135,405)(136,406)(137,407)(138,408)
(139,409)(140,410)(141,429)(142,430)(143,431)(144,423)(145,424)(146,425)
(147,426)(148,427)(149,428)(150,420)(151,421)(152,422)(153,414)(154,415)
(155,416)(156,417)(157,418)(158,419)(159,411)(160,412)(161,413)(162,432)
(163,433)(164,434)(165,327)(166,328)(167,329)(168,348)(169,349)(170,350)
(171,342)(172,343)(173,344)(174,345)(175,346)(176,347)(177,339)(178,340)
(179,341)(180,333)(181,334)(182,335)(183,336)(184,337)(185,338)(186,330)
(187,331)(188,332)(189,351)(190,352)(191,353)(192,354)(193,355)(194,356)
(195,375)(196,376)(197,377)(198,369)(199,370)(200,371)(201,372)(202,373)
(203,374)(204,366)(205,367)(206,368)(207,360)(208,361)(209,362)(210,363)
(211,364)(212,365)(213,357)(214,358)(215,359)(216,378)(217,379)(218,380)
(435,651)(436,652)(437,653)(438,672)(439,673)(440,674)(441,666)(442,667)
(443,668)(444,669)(445,670)(446,671)(447,663)(448,664)(449,665)(450,657)
(451,658)(452,659)(453,660)(454,661)(455,662)(456,654)(457,655)(458,656)
(459,675)(460,676)(461,677)(462,678)(463,679)(464,680)(465,699)(466,700)
(467,701)(468,693)(469,694)(470,695)(471,696)(472,697)(473,698)(474,690)
(475,691)(476,692)(477,684)(478,685)(479,686)(480,687)(481,688)(482,689)
(483,681)(484,682)(485,683)(486,702)(487,703)(488,704)(489,732)(490,733)
(491,734)(492,753)(493,754)(494,755)(495,747)(496,748)(497,749)(498,750)
(499,751)(500,752)(501,744)(502,745)(503,746)(504,738)(505,739)(506,740)
(507,741)(508,742)(509,743)(510,735)(511,736)(512,737)(513,756)(514,757)
(515,758)(516,705)(517,706)(518,707)(519,726)(520,727)(521,728)(522,720)
(523,721)(524,722)(525,723)(526,724)(527,725)(528,717)(529,718)(530,719)
(531,711)(532,712)(533,713)(534,714)(535,715)(536,716)(537,708)(538,709)
(539,710)(540,729)(541,730)(542,731)(543,813)(544,814)(545,815)(546,834)
(547,835)(548,836)(549,828)(550,829)(551,830)(552,831)(553,832)(554,833)
(555,825)(556,826)(557,827)(558,819)(559,820)(560,821)(561,822)(562,823)
(563,824)(564,816)(565,817)(566,818)(567,837)(568,838)(569,839)(570,840)
(571,841)(572,842)(573,861)(574,862)(575,863)(576,855)(577,856)(578,857)
(579,858)(580,859)(581,860)(582,852)(583,853)(584,854)(585,846)(586,847)
(587,848)(588,849)(589,850)(590,851)(591,843)(592,844)(593,845)(594,864)
(595,865)(596,866)(597,759)(598,760)(599,761)(600,780)(601,781)(602,782)
(603,774)(604,775)(605,776)(606,777)(607,778)(608,779)(609,771)(610,772)
(611,773)(612,765)(613,766)(614,767)(615,768)(616,769)(617,770)(618,762)
(619,763)(620,764)(621,783)(622,784)(623,785)(624,786)(625,787)(626,788)
(627,807)(628,808)(629,809)(630,801)(631,802)(632,803)(633,804)(634,805)
(635,806)(636,798)(637,799)(638,800)(639,792)(640,793)(641,794)(642,795)
(643,796)(644,797)(645,789)(646,790)(647,791)(648,810)(649,811)(650,812);;
s2 := ( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)( 8,116)( 9,117)( 10,118)
( 11,119)( 12,135)( 13,136)( 14,137)( 15,129)( 16,130)( 17,131)( 18,132)
( 19,133)( 20,134)( 21,123)( 22,124)( 23,125)( 24,126)( 25,127)( 26,128)
( 27,120)( 28,121)( 29,122)( 30,138)( 31,139)( 32,140)( 33,141)( 34,142)
( 35,143)( 36,144)( 37,145)( 38,146)( 39,162)( 40,163)( 41,164)( 42,156)
( 43,157)( 44,158)( 45,159)( 46,160)( 47,161)( 48,150)( 49,151)( 50,152)
( 51,153)( 52,154)( 53,155)( 54,147)( 55,148)( 56,149)( 57,192)( 58,193)
( 59,194)( 60,195)( 61,196)( 62,197)( 63,198)( 64,199)( 65,200)( 66,216)
( 67,217)( 68,218)( 69,210)( 70,211)( 71,212)( 72,213)( 73,214)( 74,215)
( 75,204)( 76,205)( 77,206)( 78,207)( 79,208)( 80,209)( 81,201)( 82,202)
( 83,203)( 84,165)( 85,166)( 86,167)( 87,168)( 88,169)( 89,170)( 90,171)
( 91,172)( 92,173)( 93,189)( 94,190)( 95,191)( 96,183)( 97,184)( 98,185)
( 99,186)(100,187)(101,188)(102,177)(103,178)(104,179)(105,180)(106,181)
(107,182)(108,174)(109,175)(110,176)(219,327)(220,328)(221,329)(222,330)
(223,331)(224,332)(225,333)(226,334)(227,335)(228,351)(229,352)(230,353)
(231,345)(232,346)(233,347)(234,348)(235,349)(236,350)(237,339)(238,340)
(239,341)(240,342)(241,343)(242,344)(243,336)(244,337)(245,338)(246,354)
(247,355)(248,356)(249,357)(250,358)(251,359)(252,360)(253,361)(254,362)
(255,378)(256,379)(257,380)(258,372)(259,373)(260,374)(261,375)(262,376)
(263,377)(264,366)(265,367)(266,368)(267,369)(268,370)(269,371)(270,363)
(271,364)(272,365)(273,408)(274,409)(275,410)(276,411)(277,412)(278,413)
(279,414)(280,415)(281,416)(282,432)(283,433)(284,434)(285,426)(286,427)
(287,428)(288,429)(289,430)(290,431)(291,420)(292,421)(293,422)(294,423)
(295,424)(296,425)(297,417)(298,418)(299,419)(300,381)(301,382)(302,383)
(303,384)(304,385)(305,386)(306,387)(307,388)(308,389)(309,405)(310,406)
(311,407)(312,399)(313,400)(314,401)(315,402)(316,403)(317,404)(318,393)
(319,394)(320,395)(321,396)(322,397)(323,398)(324,390)(325,391)(326,392)
(435,543)(436,544)(437,545)(438,546)(439,547)(440,548)(441,549)(442,550)
(443,551)(444,567)(445,568)(446,569)(447,561)(448,562)(449,563)(450,564)
(451,565)(452,566)(453,555)(454,556)(455,557)(456,558)(457,559)(458,560)
(459,552)(460,553)(461,554)(462,570)(463,571)(464,572)(465,573)(466,574)
(467,575)(468,576)(469,577)(470,578)(471,594)(472,595)(473,596)(474,588)
(475,589)(476,590)(477,591)(478,592)(479,593)(480,582)(481,583)(482,584)
(483,585)(484,586)(485,587)(486,579)(487,580)(488,581)(489,624)(490,625)
(491,626)(492,627)(493,628)(494,629)(495,630)(496,631)(497,632)(498,648)
(499,649)(500,650)(501,642)(502,643)(503,644)(504,645)(505,646)(506,647)
(507,636)(508,637)(509,638)(510,639)(511,640)(512,641)(513,633)(514,634)
(515,635)(516,597)(517,598)(518,599)(519,600)(520,601)(521,602)(522,603)
(523,604)(524,605)(525,621)(526,622)(527,623)(528,615)(529,616)(530,617)
(531,618)(532,619)(533,620)(534,609)(535,610)(536,611)(537,612)(538,613)
(539,614)(540,606)(541,607)(542,608)(651,759)(652,760)(653,761)(654,762)
(655,763)(656,764)(657,765)(658,766)(659,767)(660,783)(661,784)(662,785)
(663,777)(664,778)(665,779)(666,780)(667,781)(668,782)(669,771)(670,772)
(671,773)(672,774)(673,775)(674,776)(675,768)(676,769)(677,770)(678,786)
(679,787)(680,788)(681,789)(682,790)(683,791)(684,792)(685,793)(686,794)
(687,810)(688,811)(689,812)(690,804)(691,805)(692,806)(693,807)(694,808)
(695,809)(696,798)(697,799)(698,800)(699,801)(700,802)(701,803)(702,795)
(703,796)(704,797)(705,840)(706,841)(707,842)(708,843)(709,844)(710,845)
(711,846)(712,847)(713,848)(714,864)(715,865)(716,866)(717,858)(718,859)
(719,860)(720,861)(721,862)(722,863)(723,852)(724,853)(725,854)(726,855)
(727,856)(728,857)(729,849)(730,850)(731,851)(732,813)(733,814)(734,815)
(735,816)(736,817)(737,818)(738,819)(739,820)(740,821)(741,837)(742,838)
(743,839)(744,831)(745,832)(746,833)(747,834)(748,835)(749,836)(750,825)
(751,826)(752,827)(753,828)(754,829)(755,830)(756,822)(757,823)(758,824);;
s3 := ( 3,501)( 4,503)( 5,502)( 6,498)( 7,500)( 8,499)( 9,504)( 10,506)
( 11,505)( 12,492)( 13,494)( 14,493)( 15,489)( 16,491)( 17,490)( 18,495)
( 19,497)( 20,496)( 21,510)( 22,512)( 23,511)( 24,507)( 25,509)( 26,508)
( 27,513)( 28,515)( 29,514)( 30,528)( 31,530)( 32,529)( 33,525)( 34,527)
( 35,526)( 36,531)( 37,533)( 38,532)( 39,519)( 40,521)( 41,520)( 42,516)
( 43,518)( 44,517)( 45,522)( 46,524)( 47,523)( 48,537)( 49,539)( 50,538)
( 51,534)( 52,536)( 53,535)( 54,540)( 55,542)( 56,541)( 57,474)( 58,476)
( 59,475)( 60,471)( 61,473)( 62,472)( 63,477)( 64,479)( 65,478)( 66,465)
( 67,467)( 68,466)( 69,462)( 70,464)( 71,463)( 72,468)( 73,470)( 74,469)
( 75,483)( 76,485)( 77,484)( 78,480)( 79,482)( 80,481)( 81,486)( 82,488)
( 83,487)( 84,447)( 85,449)( 86,448)( 87,444)( 88,446)( 89,445)( 90,450)
( 91,452)( 92,451)( 93,438)( 94,440)( 95,439)( 96,435)( 97,437)( 98,436)
( 99,441)(100,443)(101,442)(102,456)(103,458)(104,457)(105,453)(106,455)
(107,454)(108,459)(109,461)(110,460)(111,636)(112,638)(113,637)(114,633)
(115,635)(116,634)(117,639)(118,641)(119,640)(120,627)(121,629)(122,628)
(123,624)(124,626)(125,625)(126,630)(127,632)(128,631)(129,645)(130,647)
(131,646)(132,642)(133,644)(134,643)(135,648)(136,650)(137,649)(138,609)
(139,611)(140,610)(141,606)(142,608)(143,607)(144,612)(145,614)(146,613)
(147,600)(148,602)(149,601)(150,597)(151,599)(152,598)(153,603)(154,605)
(155,604)(156,618)(157,620)(158,619)(159,615)(160,617)(161,616)(162,621)
(163,623)(164,622)(165,555)(166,557)(167,556)(168,552)(169,554)(170,553)
(171,558)(172,560)(173,559)(174,546)(175,548)(176,547)(177,543)(178,545)
(179,544)(180,549)(181,551)(182,550)(183,564)(184,566)(185,565)(186,561)
(187,563)(188,562)(189,567)(190,569)(191,568)(192,582)(193,584)(194,583)
(195,579)(196,581)(197,580)(198,585)(199,587)(200,586)(201,573)(202,575)
(203,574)(204,570)(205,572)(206,571)(207,576)(208,578)(209,577)(210,591)
(211,593)(212,592)(213,588)(214,590)(215,589)(216,594)(217,596)(218,595)
(219,744)(220,746)(221,745)(222,741)(223,743)(224,742)(225,747)(226,749)
(227,748)(228,735)(229,737)(230,736)(231,732)(232,734)(233,733)(234,738)
(235,740)(236,739)(237,753)(238,755)(239,754)(240,750)(241,752)(242,751)
(243,756)(244,758)(245,757)(246,717)(247,719)(248,718)(249,714)(250,716)
(251,715)(252,720)(253,722)(254,721)(255,708)(256,710)(257,709)(258,705)
(259,707)(260,706)(261,711)(262,713)(263,712)(264,726)(265,728)(266,727)
(267,723)(268,725)(269,724)(270,729)(271,731)(272,730)(273,663)(274,665)
(275,664)(276,660)(277,662)(278,661)(279,666)(280,668)(281,667)(282,654)
(283,656)(284,655)(285,651)(286,653)(287,652)(288,657)(289,659)(290,658)
(291,672)(292,674)(293,673)(294,669)(295,671)(296,670)(297,675)(298,677)
(299,676)(300,690)(301,692)(302,691)(303,687)(304,689)(305,688)(306,693)
(307,695)(308,694)(309,681)(310,683)(311,682)(312,678)(313,680)(314,679)
(315,684)(316,686)(317,685)(318,699)(319,701)(320,700)(321,696)(322,698)
(323,697)(324,702)(325,704)(326,703)(327,825)(328,827)(329,826)(330,822)
(331,824)(332,823)(333,828)(334,830)(335,829)(336,816)(337,818)(338,817)
(339,813)(340,815)(341,814)(342,819)(343,821)(344,820)(345,834)(346,836)
(347,835)(348,831)(349,833)(350,832)(351,837)(352,839)(353,838)(354,852)
(355,854)(356,853)(357,849)(358,851)(359,850)(360,855)(361,857)(362,856)
(363,843)(364,845)(365,844)(366,840)(367,842)(368,841)(369,846)(370,848)
(371,847)(372,861)(373,863)(374,862)(375,858)(376,860)(377,859)(378,864)
(379,866)(380,865)(381,798)(382,800)(383,799)(384,795)(385,797)(386,796)
(387,801)(388,803)(389,802)(390,789)(391,791)(392,790)(393,786)(394,788)
(395,787)(396,792)(397,794)(398,793)(399,807)(400,809)(401,808)(402,804)
(403,806)(404,805)(405,810)(406,812)(407,811)(408,771)(409,773)(410,772)
(411,768)(412,770)(413,769)(414,774)(415,776)(416,775)(417,762)(418,764)
(419,763)(420,759)(421,761)(422,760)(423,765)(424,767)(425,766)(426,780)
(427,782)(428,781)(429,777)(430,779)(431,778)(432,783)(433,785)(434,784);;
s4 := ( 3,490)( 4,489)( 5,491)( 6,496)( 7,495)( 8,497)( 9,493)( 10,492)
( 11,494)( 12,508)( 13,507)( 14,509)( 15,514)( 16,513)( 17,515)( 18,511)
( 19,510)( 20,512)( 21,499)( 22,498)( 23,500)( 24,505)( 25,504)( 26,506)
( 27,502)( 28,501)( 29,503)( 30,517)( 31,516)( 32,518)( 33,523)( 34,522)
( 35,524)( 36,520)( 37,519)( 38,521)( 39,535)( 40,534)( 41,536)( 42,541)
( 43,540)( 44,542)( 45,538)( 46,537)( 47,539)( 48,526)( 49,525)( 50,527)
( 51,532)( 52,531)( 53,533)( 54,529)( 55,528)( 56,530)( 57,463)( 58,462)
( 59,464)( 60,469)( 61,468)( 62,470)( 63,466)( 64,465)( 65,467)( 66,481)
( 67,480)( 68,482)( 69,487)( 70,486)( 71,488)( 72,484)( 73,483)( 74,485)
( 75,472)( 76,471)( 77,473)( 78,478)( 79,477)( 80,479)( 81,475)( 82,474)
( 83,476)( 84,436)( 85,435)( 86,437)( 87,442)( 88,441)( 89,443)( 90,439)
( 91,438)( 92,440)( 93,454)( 94,453)( 95,455)( 96,460)( 97,459)( 98,461)
( 99,457)(100,456)(101,458)(102,445)(103,444)(104,446)(105,451)(106,450)
(107,452)(108,448)(109,447)(110,449)(111,625)(112,624)(113,626)(114,631)
(115,630)(116,632)(117,628)(118,627)(119,629)(120,643)(121,642)(122,644)
(123,649)(124,648)(125,650)(126,646)(127,645)(128,647)(129,634)(130,633)
(131,635)(132,640)(133,639)(134,641)(135,637)(136,636)(137,638)(138,598)
(139,597)(140,599)(141,604)(142,603)(143,605)(144,601)(145,600)(146,602)
(147,616)(148,615)(149,617)(150,622)(151,621)(152,623)(153,619)(154,618)
(155,620)(156,607)(157,606)(158,608)(159,613)(160,612)(161,614)(162,610)
(163,609)(164,611)(165,544)(166,543)(167,545)(168,550)(169,549)(170,551)
(171,547)(172,546)(173,548)(174,562)(175,561)(176,563)(177,568)(178,567)
(179,569)(180,565)(181,564)(182,566)(183,553)(184,552)(185,554)(186,559)
(187,558)(188,560)(189,556)(190,555)(191,557)(192,571)(193,570)(194,572)
(195,577)(196,576)(197,578)(198,574)(199,573)(200,575)(201,589)(202,588)
(203,590)(204,595)(205,594)(206,596)(207,592)(208,591)(209,593)(210,580)
(211,579)(212,581)(213,586)(214,585)(215,587)(216,583)(217,582)(218,584)
(219,733)(220,732)(221,734)(222,739)(223,738)(224,740)(225,736)(226,735)
(227,737)(228,751)(229,750)(230,752)(231,757)(232,756)(233,758)(234,754)
(235,753)(236,755)(237,742)(238,741)(239,743)(240,748)(241,747)(242,749)
(243,745)(244,744)(245,746)(246,706)(247,705)(248,707)(249,712)(250,711)
(251,713)(252,709)(253,708)(254,710)(255,724)(256,723)(257,725)(258,730)
(259,729)(260,731)(261,727)(262,726)(263,728)(264,715)(265,714)(266,716)
(267,721)(268,720)(269,722)(270,718)(271,717)(272,719)(273,652)(274,651)
(275,653)(276,658)(277,657)(278,659)(279,655)(280,654)(281,656)(282,670)
(283,669)(284,671)(285,676)(286,675)(287,677)(288,673)(289,672)(290,674)
(291,661)(292,660)(293,662)(294,667)(295,666)(296,668)(297,664)(298,663)
(299,665)(300,679)(301,678)(302,680)(303,685)(304,684)(305,686)(306,682)
(307,681)(308,683)(309,697)(310,696)(311,698)(312,703)(313,702)(314,704)
(315,700)(316,699)(317,701)(318,688)(319,687)(320,689)(321,694)(322,693)
(323,695)(324,691)(325,690)(326,692)(327,814)(328,813)(329,815)(330,820)
(331,819)(332,821)(333,817)(334,816)(335,818)(336,832)(337,831)(338,833)
(339,838)(340,837)(341,839)(342,835)(343,834)(344,836)(345,823)(346,822)
(347,824)(348,829)(349,828)(350,830)(351,826)(352,825)(353,827)(354,841)
(355,840)(356,842)(357,847)(358,846)(359,848)(360,844)(361,843)(362,845)
(363,859)(364,858)(365,860)(366,865)(367,864)(368,866)(369,862)(370,861)
(371,863)(372,850)(373,849)(374,851)(375,856)(376,855)(377,857)(378,853)
(379,852)(380,854)(381,787)(382,786)(383,788)(384,793)(385,792)(386,794)
(387,790)(388,789)(389,791)(390,805)(391,804)(392,806)(393,811)(394,810)
(395,812)(396,808)(397,807)(398,809)(399,796)(400,795)(401,797)(402,802)
(403,801)(404,803)(405,799)(406,798)(407,800)(408,760)(409,759)(410,761)
(411,766)(412,765)(413,767)(414,763)(415,762)(416,764)(417,778)(418,777)
(419,779)(420,784)(421,783)(422,785)(423,781)(424,780)(425,782)(426,769)
(427,768)(428,770)(429,775)(430,774)(431,776)(432,772)(433,771)(434,773);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*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(866)!(1,2);
s1 := Sym(866)!( 3,219)( 4,220)( 5,221)( 6,240)( 7,241)( 8,242)( 9,234)
( 10,235)( 11,236)( 12,237)( 13,238)( 14,239)( 15,231)( 16,232)( 17,233)
( 18,225)( 19,226)( 20,227)( 21,228)( 22,229)( 23,230)( 24,222)( 25,223)
( 26,224)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)( 33,267)
( 34,268)( 35,269)( 36,261)( 37,262)( 38,263)( 39,264)( 40,265)( 41,266)
( 42,258)( 43,259)( 44,260)( 45,252)( 46,253)( 47,254)( 48,255)( 49,256)
( 50,257)( 51,249)( 52,250)( 53,251)( 54,270)( 55,271)( 56,272)( 57,300)
( 58,301)( 59,302)( 60,321)( 61,322)( 62,323)( 63,315)( 64,316)( 65,317)
( 66,318)( 67,319)( 68,320)( 69,312)( 70,313)( 71,314)( 72,306)( 73,307)
( 74,308)( 75,309)( 76,310)( 77,311)( 78,303)( 79,304)( 80,305)( 81,324)
( 82,325)( 83,326)( 84,273)( 85,274)( 86,275)( 87,294)( 88,295)( 89,296)
( 90,288)( 91,289)( 92,290)( 93,291)( 94,292)( 95,293)( 96,285)( 97,286)
( 98,287)( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)(105,276)
(106,277)(107,278)(108,297)(109,298)(110,299)(111,381)(112,382)(113,383)
(114,402)(115,403)(116,404)(117,396)(118,397)(119,398)(120,399)(121,400)
(122,401)(123,393)(124,394)(125,395)(126,387)(127,388)(128,389)(129,390)
(130,391)(131,392)(132,384)(133,385)(134,386)(135,405)(136,406)(137,407)
(138,408)(139,409)(140,410)(141,429)(142,430)(143,431)(144,423)(145,424)
(146,425)(147,426)(148,427)(149,428)(150,420)(151,421)(152,422)(153,414)
(154,415)(155,416)(156,417)(157,418)(158,419)(159,411)(160,412)(161,413)
(162,432)(163,433)(164,434)(165,327)(166,328)(167,329)(168,348)(169,349)
(170,350)(171,342)(172,343)(173,344)(174,345)(175,346)(176,347)(177,339)
(178,340)(179,341)(180,333)(181,334)(182,335)(183,336)(184,337)(185,338)
(186,330)(187,331)(188,332)(189,351)(190,352)(191,353)(192,354)(193,355)
(194,356)(195,375)(196,376)(197,377)(198,369)(199,370)(200,371)(201,372)
(202,373)(203,374)(204,366)(205,367)(206,368)(207,360)(208,361)(209,362)
(210,363)(211,364)(212,365)(213,357)(214,358)(215,359)(216,378)(217,379)
(218,380)(435,651)(436,652)(437,653)(438,672)(439,673)(440,674)(441,666)
(442,667)(443,668)(444,669)(445,670)(446,671)(447,663)(448,664)(449,665)
(450,657)(451,658)(452,659)(453,660)(454,661)(455,662)(456,654)(457,655)
(458,656)(459,675)(460,676)(461,677)(462,678)(463,679)(464,680)(465,699)
(466,700)(467,701)(468,693)(469,694)(470,695)(471,696)(472,697)(473,698)
(474,690)(475,691)(476,692)(477,684)(478,685)(479,686)(480,687)(481,688)
(482,689)(483,681)(484,682)(485,683)(486,702)(487,703)(488,704)(489,732)
(490,733)(491,734)(492,753)(493,754)(494,755)(495,747)(496,748)(497,749)
(498,750)(499,751)(500,752)(501,744)(502,745)(503,746)(504,738)(505,739)
(506,740)(507,741)(508,742)(509,743)(510,735)(511,736)(512,737)(513,756)
(514,757)(515,758)(516,705)(517,706)(518,707)(519,726)(520,727)(521,728)
(522,720)(523,721)(524,722)(525,723)(526,724)(527,725)(528,717)(529,718)
(530,719)(531,711)(532,712)(533,713)(534,714)(535,715)(536,716)(537,708)
(538,709)(539,710)(540,729)(541,730)(542,731)(543,813)(544,814)(545,815)
(546,834)(547,835)(548,836)(549,828)(550,829)(551,830)(552,831)(553,832)
(554,833)(555,825)(556,826)(557,827)(558,819)(559,820)(560,821)(561,822)
(562,823)(563,824)(564,816)(565,817)(566,818)(567,837)(568,838)(569,839)
(570,840)(571,841)(572,842)(573,861)(574,862)(575,863)(576,855)(577,856)
(578,857)(579,858)(580,859)(581,860)(582,852)(583,853)(584,854)(585,846)
(586,847)(587,848)(588,849)(589,850)(590,851)(591,843)(592,844)(593,845)
(594,864)(595,865)(596,866)(597,759)(598,760)(599,761)(600,780)(601,781)
(602,782)(603,774)(604,775)(605,776)(606,777)(607,778)(608,779)(609,771)
(610,772)(611,773)(612,765)(613,766)(614,767)(615,768)(616,769)(617,770)
(618,762)(619,763)(620,764)(621,783)(622,784)(623,785)(624,786)(625,787)
(626,788)(627,807)(628,808)(629,809)(630,801)(631,802)(632,803)(633,804)
(634,805)(635,806)(636,798)(637,799)(638,800)(639,792)(640,793)(641,794)
(642,795)(643,796)(644,797)(645,789)(646,790)(647,791)(648,810)(649,811)
(650,812);
s2 := Sym(866)!( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)( 8,116)( 9,117)
( 10,118)( 11,119)( 12,135)( 13,136)( 14,137)( 15,129)( 16,130)( 17,131)
( 18,132)( 19,133)( 20,134)( 21,123)( 22,124)( 23,125)( 24,126)( 25,127)
( 26,128)( 27,120)( 28,121)( 29,122)( 30,138)( 31,139)( 32,140)( 33,141)
( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,162)( 40,163)( 41,164)
( 42,156)( 43,157)( 44,158)( 45,159)( 46,160)( 47,161)( 48,150)( 49,151)
( 50,152)( 51,153)( 52,154)( 53,155)( 54,147)( 55,148)( 56,149)( 57,192)
( 58,193)( 59,194)( 60,195)( 61,196)( 62,197)( 63,198)( 64,199)( 65,200)
( 66,216)( 67,217)( 68,218)( 69,210)( 70,211)( 71,212)( 72,213)( 73,214)
( 74,215)( 75,204)( 76,205)( 77,206)( 78,207)( 79,208)( 80,209)( 81,201)
( 82,202)( 83,203)( 84,165)( 85,166)( 86,167)( 87,168)( 88,169)( 89,170)
( 90,171)( 91,172)( 92,173)( 93,189)( 94,190)( 95,191)( 96,183)( 97,184)
( 98,185)( 99,186)(100,187)(101,188)(102,177)(103,178)(104,179)(105,180)
(106,181)(107,182)(108,174)(109,175)(110,176)(219,327)(220,328)(221,329)
(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,351)(229,352)
(230,353)(231,345)(232,346)(233,347)(234,348)(235,349)(236,350)(237,339)
(238,340)(239,341)(240,342)(241,343)(242,344)(243,336)(244,337)(245,338)
(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)(252,360)(253,361)
(254,362)(255,378)(256,379)(257,380)(258,372)(259,373)(260,374)(261,375)
(262,376)(263,377)(264,366)(265,367)(266,368)(267,369)(268,370)(269,371)
(270,363)(271,364)(272,365)(273,408)(274,409)(275,410)(276,411)(277,412)
(278,413)(279,414)(280,415)(281,416)(282,432)(283,433)(284,434)(285,426)
(286,427)(287,428)(288,429)(289,430)(290,431)(291,420)(292,421)(293,422)
(294,423)(295,424)(296,425)(297,417)(298,418)(299,419)(300,381)(301,382)
(302,383)(303,384)(304,385)(305,386)(306,387)(307,388)(308,389)(309,405)
(310,406)(311,407)(312,399)(313,400)(314,401)(315,402)(316,403)(317,404)
(318,393)(319,394)(320,395)(321,396)(322,397)(323,398)(324,390)(325,391)
(326,392)(435,543)(436,544)(437,545)(438,546)(439,547)(440,548)(441,549)
(442,550)(443,551)(444,567)(445,568)(446,569)(447,561)(448,562)(449,563)
(450,564)(451,565)(452,566)(453,555)(454,556)(455,557)(456,558)(457,559)
(458,560)(459,552)(460,553)(461,554)(462,570)(463,571)(464,572)(465,573)
(466,574)(467,575)(468,576)(469,577)(470,578)(471,594)(472,595)(473,596)
(474,588)(475,589)(476,590)(477,591)(478,592)(479,593)(480,582)(481,583)
(482,584)(483,585)(484,586)(485,587)(486,579)(487,580)(488,581)(489,624)
(490,625)(491,626)(492,627)(493,628)(494,629)(495,630)(496,631)(497,632)
(498,648)(499,649)(500,650)(501,642)(502,643)(503,644)(504,645)(505,646)
(506,647)(507,636)(508,637)(509,638)(510,639)(511,640)(512,641)(513,633)
(514,634)(515,635)(516,597)(517,598)(518,599)(519,600)(520,601)(521,602)
(522,603)(523,604)(524,605)(525,621)(526,622)(527,623)(528,615)(529,616)
(530,617)(531,618)(532,619)(533,620)(534,609)(535,610)(536,611)(537,612)
(538,613)(539,614)(540,606)(541,607)(542,608)(651,759)(652,760)(653,761)
(654,762)(655,763)(656,764)(657,765)(658,766)(659,767)(660,783)(661,784)
(662,785)(663,777)(664,778)(665,779)(666,780)(667,781)(668,782)(669,771)
(670,772)(671,773)(672,774)(673,775)(674,776)(675,768)(676,769)(677,770)
(678,786)(679,787)(680,788)(681,789)(682,790)(683,791)(684,792)(685,793)
(686,794)(687,810)(688,811)(689,812)(690,804)(691,805)(692,806)(693,807)
(694,808)(695,809)(696,798)(697,799)(698,800)(699,801)(700,802)(701,803)
(702,795)(703,796)(704,797)(705,840)(706,841)(707,842)(708,843)(709,844)
(710,845)(711,846)(712,847)(713,848)(714,864)(715,865)(716,866)(717,858)
(718,859)(719,860)(720,861)(721,862)(722,863)(723,852)(724,853)(725,854)
(726,855)(727,856)(728,857)(729,849)(730,850)(731,851)(732,813)(733,814)
(734,815)(735,816)(736,817)(737,818)(738,819)(739,820)(740,821)(741,837)
(742,838)(743,839)(744,831)(745,832)(746,833)(747,834)(748,835)(749,836)
(750,825)(751,826)(752,827)(753,828)(754,829)(755,830)(756,822)(757,823)
(758,824);
s3 := Sym(866)!( 3,501)( 4,503)( 5,502)( 6,498)( 7,500)( 8,499)( 9,504)
( 10,506)( 11,505)( 12,492)( 13,494)( 14,493)( 15,489)( 16,491)( 17,490)
( 18,495)( 19,497)( 20,496)( 21,510)( 22,512)( 23,511)( 24,507)( 25,509)
( 26,508)( 27,513)( 28,515)( 29,514)( 30,528)( 31,530)( 32,529)( 33,525)
( 34,527)( 35,526)( 36,531)( 37,533)( 38,532)( 39,519)( 40,521)( 41,520)
( 42,516)( 43,518)( 44,517)( 45,522)( 46,524)( 47,523)( 48,537)( 49,539)
( 50,538)( 51,534)( 52,536)( 53,535)( 54,540)( 55,542)( 56,541)( 57,474)
( 58,476)( 59,475)( 60,471)( 61,473)( 62,472)( 63,477)( 64,479)( 65,478)
( 66,465)( 67,467)( 68,466)( 69,462)( 70,464)( 71,463)( 72,468)( 73,470)
( 74,469)( 75,483)( 76,485)( 77,484)( 78,480)( 79,482)( 80,481)( 81,486)
( 82,488)( 83,487)( 84,447)( 85,449)( 86,448)( 87,444)( 88,446)( 89,445)
( 90,450)( 91,452)( 92,451)( 93,438)( 94,440)( 95,439)( 96,435)( 97,437)
( 98,436)( 99,441)(100,443)(101,442)(102,456)(103,458)(104,457)(105,453)
(106,455)(107,454)(108,459)(109,461)(110,460)(111,636)(112,638)(113,637)
(114,633)(115,635)(116,634)(117,639)(118,641)(119,640)(120,627)(121,629)
(122,628)(123,624)(124,626)(125,625)(126,630)(127,632)(128,631)(129,645)
(130,647)(131,646)(132,642)(133,644)(134,643)(135,648)(136,650)(137,649)
(138,609)(139,611)(140,610)(141,606)(142,608)(143,607)(144,612)(145,614)
(146,613)(147,600)(148,602)(149,601)(150,597)(151,599)(152,598)(153,603)
(154,605)(155,604)(156,618)(157,620)(158,619)(159,615)(160,617)(161,616)
(162,621)(163,623)(164,622)(165,555)(166,557)(167,556)(168,552)(169,554)
(170,553)(171,558)(172,560)(173,559)(174,546)(175,548)(176,547)(177,543)
(178,545)(179,544)(180,549)(181,551)(182,550)(183,564)(184,566)(185,565)
(186,561)(187,563)(188,562)(189,567)(190,569)(191,568)(192,582)(193,584)
(194,583)(195,579)(196,581)(197,580)(198,585)(199,587)(200,586)(201,573)
(202,575)(203,574)(204,570)(205,572)(206,571)(207,576)(208,578)(209,577)
(210,591)(211,593)(212,592)(213,588)(214,590)(215,589)(216,594)(217,596)
(218,595)(219,744)(220,746)(221,745)(222,741)(223,743)(224,742)(225,747)
(226,749)(227,748)(228,735)(229,737)(230,736)(231,732)(232,734)(233,733)
(234,738)(235,740)(236,739)(237,753)(238,755)(239,754)(240,750)(241,752)
(242,751)(243,756)(244,758)(245,757)(246,717)(247,719)(248,718)(249,714)
(250,716)(251,715)(252,720)(253,722)(254,721)(255,708)(256,710)(257,709)
(258,705)(259,707)(260,706)(261,711)(262,713)(263,712)(264,726)(265,728)
(266,727)(267,723)(268,725)(269,724)(270,729)(271,731)(272,730)(273,663)
(274,665)(275,664)(276,660)(277,662)(278,661)(279,666)(280,668)(281,667)
(282,654)(283,656)(284,655)(285,651)(286,653)(287,652)(288,657)(289,659)
(290,658)(291,672)(292,674)(293,673)(294,669)(295,671)(296,670)(297,675)
(298,677)(299,676)(300,690)(301,692)(302,691)(303,687)(304,689)(305,688)
(306,693)(307,695)(308,694)(309,681)(310,683)(311,682)(312,678)(313,680)
(314,679)(315,684)(316,686)(317,685)(318,699)(319,701)(320,700)(321,696)
(322,698)(323,697)(324,702)(325,704)(326,703)(327,825)(328,827)(329,826)
(330,822)(331,824)(332,823)(333,828)(334,830)(335,829)(336,816)(337,818)
(338,817)(339,813)(340,815)(341,814)(342,819)(343,821)(344,820)(345,834)
(346,836)(347,835)(348,831)(349,833)(350,832)(351,837)(352,839)(353,838)
(354,852)(355,854)(356,853)(357,849)(358,851)(359,850)(360,855)(361,857)
(362,856)(363,843)(364,845)(365,844)(366,840)(367,842)(368,841)(369,846)
(370,848)(371,847)(372,861)(373,863)(374,862)(375,858)(376,860)(377,859)
(378,864)(379,866)(380,865)(381,798)(382,800)(383,799)(384,795)(385,797)
(386,796)(387,801)(388,803)(389,802)(390,789)(391,791)(392,790)(393,786)
(394,788)(395,787)(396,792)(397,794)(398,793)(399,807)(400,809)(401,808)
(402,804)(403,806)(404,805)(405,810)(406,812)(407,811)(408,771)(409,773)
(410,772)(411,768)(412,770)(413,769)(414,774)(415,776)(416,775)(417,762)
(418,764)(419,763)(420,759)(421,761)(422,760)(423,765)(424,767)(425,766)
(426,780)(427,782)(428,781)(429,777)(430,779)(431,778)(432,783)(433,785)
(434,784);
s4 := Sym(866)!( 3,490)( 4,489)( 5,491)( 6,496)( 7,495)( 8,497)( 9,493)
( 10,492)( 11,494)( 12,508)( 13,507)( 14,509)( 15,514)( 16,513)( 17,515)
( 18,511)( 19,510)( 20,512)( 21,499)( 22,498)( 23,500)( 24,505)( 25,504)
( 26,506)( 27,502)( 28,501)( 29,503)( 30,517)( 31,516)( 32,518)( 33,523)
( 34,522)( 35,524)( 36,520)( 37,519)( 38,521)( 39,535)( 40,534)( 41,536)
( 42,541)( 43,540)( 44,542)( 45,538)( 46,537)( 47,539)( 48,526)( 49,525)
( 50,527)( 51,532)( 52,531)( 53,533)( 54,529)( 55,528)( 56,530)( 57,463)
( 58,462)( 59,464)( 60,469)( 61,468)( 62,470)( 63,466)( 64,465)( 65,467)
( 66,481)( 67,480)( 68,482)( 69,487)( 70,486)( 71,488)( 72,484)( 73,483)
( 74,485)( 75,472)( 76,471)( 77,473)( 78,478)( 79,477)( 80,479)( 81,475)
( 82,474)( 83,476)( 84,436)( 85,435)( 86,437)( 87,442)( 88,441)( 89,443)
( 90,439)( 91,438)( 92,440)( 93,454)( 94,453)( 95,455)( 96,460)( 97,459)
( 98,461)( 99,457)(100,456)(101,458)(102,445)(103,444)(104,446)(105,451)
(106,450)(107,452)(108,448)(109,447)(110,449)(111,625)(112,624)(113,626)
(114,631)(115,630)(116,632)(117,628)(118,627)(119,629)(120,643)(121,642)
(122,644)(123,649)(124,648)(125,650)(126,646)(127,645)(128,647)(129,634)
(130,633)(131,635)(132,640)(133,639)(134,641)(135,637)(136,636)(137,638)
(138,598)(139,597)(140,599)(141,604)(142,603)(143,605)(144,601)(145,600)
(146,602)(147,616)(148,615)(149,617)(150,622)(151,621)(152,623)(153,619)
(154,618)(155,620)(156,607)(157,606)(158,608)(159,613)(160,612)(161,614)
(162,610)(163,609)(164,611)(165,544)(166,543)(167,545)(168,550)(169,549)
(170,551)(171,547)(172,546)(173,548)(174,562)(175,561)(176,563)(177,568)
(178,567)(179,569)(180,565)(181,564)(182,566)(183,553)(184,552)(185,554)
(186,559)(187,558)(188,560)(189,556)(190,555)(191,557)(192,571)(193,570)
(194,572)(195,577)(196,576)(197,578)(198,574)(199,573)(200,575)(201,589)
(202,588)(203,590)(204,595)(205,594)(206,596)(207,592)(208,591)(209,593)
(210,580)(211,579)(212,581)(213,586)(214,585)(215,587)(216,583)(217,582)
(218,584)(219,733)(220,732)(221,734)(222,739)(223,738)(224,740)(225,736)
(226,735)(227,737)(228,751)(229,750)(230,752)(231,757)(232,756)(233,758)
(234,754)(235,753)(236,755)(237,742)(238,741)(239,743)(240,748)(241,747)
(242,749)(243,745)(244,744)(245,746)(246,706)(247,705)(248,707)(249,712)
(250,711)(251,713)(252,709)(253,708)(254,710)(255,724)(256,723)(257,725)
(258,730)(259,729)(260,731)(261,727)(262,726)(263,728)(264,715)(265,714)
(266,716)(267,721)(268,720)(269,722)(270,718)(271,717)(272,719)(273,652)
(274,651)(275,653)(276,658)(277,657)(278,659)(279,655)(280,654)(281,656)
(282,670)(283,669)(284,671)(285,676)(286,675)(287,677)(288,673)(289,672)
(290,674)(291,661)(292,660)(293,662)(294,667)(295,666)(296,668)(297,664)
(298,663)(299,665)(300,679)(301,678)(302,680)(303,685)(304,684)(305,686)
(306,682)(307,681)(308,683)(309,697)(310,696)(311,698)(312,703)(313,702)
(314,704)(315,700)(316,699)(317,701)(318,688)(319,687)(320,689)(321,694)
(322,693)(323,695)(324,691)(325,690)(326,692)(327,814)(328,813)(329,815)
(330,820)(331,819)(332,821)(333,817)(334,816)(335,818)(336,832)(337,831)
(338,833)(339,838)(340,837)(341,839)(342,835)(343,834)(344,836)(345,823)
(346,822)(347,824)(348,829)(349,828)(350,830)(351,826)(352,825)(353,827)
(354,841)(355,840)(356,842)(357,847)(358,846)(359,848)(360,844)(361,843)
(362,845)(363,859)(364,858)(365,860)(366,865)(367,864)(368,866)(369,862)
(370,861)(371,863)(372,850)(373,849)(374,851)(375,856)(376,855)(377,857)
(378,853)(379,852)(380,854)(381,787)(382,786)(383,788)(384,793)(385,792)
(386,794)(387,790)(388,789)(389,791)(390,805)(391,804)(392,806)(393,811)
(394,810)(395,812)(396,808)(397,807)(398,809)(399,796)(400,795)(401,797)
(402,802)(403,801)(404,803)(405,799)(406,798)(407,800)(408,760)(409,759)
(410,761)(411,766)(412,765)(413,767)(414,763)(415,762)(416,764)(417,778)
(418,777)(419,779)(420,784)(421,783)(422,785)(423,781)(424,780)(425,782)
(426,769)(427,768)(428,770)(429,775)(430,774)(431,776)(432,772)(433,771)
(434,773);
poly := sub<Sym(866)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope