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