Polytope of Type {3,6,44}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,44}*1584
if this polytope has a name.
Group : SmallGroup(1584,417)
Rank : 4
Schlafli Type : {3,6,44}
Number of vertices, edges, etc : 3, 9, 132, 44
Order of s0s1s2s3 : 132
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 : {3,6,22}*792
3-fold quotients : {3,2,44}*528
6-fold quotients : {3,2,22}*264
11-fold quotients : {3,6,4}*144
12-fold quotients : {3,2,11}*132
22-fold quotients : {3,6,2}*72
33-fold quotients : {3,2,4}*48
66-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,595)( 2,596)( 3,597)( 4,598)( 5,599)( 6,600)( 7,601)( 8,602)
( 9,603)( 10,604)( 11,605)( 12,617)( 13,618)( 14,619)( 15,620)( 16,621)
( 17,622)( 18,623)( 19,624)( 20,625)( 21,626)( 22,627)( 23,606)( 24,607)
( 25,608)( 26,609)( 27,610)( 28,611)( 29,612)( 30,613)( 31,614)( 32,615)
( 33,616)( 34,661)( 35,662)( 36,663)( 37,664)( 38,665)( 39,666)( 40,667)
( 41,668)( 42,669)( 43,670)( 44,671)( 45,683)( 46,684)( 47,685)( 48,686)
( 49,687)( 50,688)( 51,689)( 52,690)( 53,691)( 54,692)( 55,693)( 56,672)
( 57,673)( 58,674)( 59,675)( 60,676)( 61,677)( 62,678)( 63,679)( 64,680)
( 65,681)( 66,682)( 67,628)( 68,629)( 69,630)( 70,631)( 71,632)( 72,633)
( 73,634)( 74,635)( 75,636)( 76,637)( 77,638)( 78,650)( 79,651)( 80,652)
( 81,653)( 82,654)( 83,655)( 84,656)( 85,657)( 86,658)( 87,659)( 88,660)
( 89,639)( 90,640)( 91,641)( 92,642)( 93,643)( 94,644)( 95,645)( 96,646)
( 97,647)( 98,648)( 99,649)(100,694)(101,695)(102,696)(103,697)(104,698)
(105,699)(106,700)(107,701)(108,702)(109,703)(110,704)(111,716)(112,717)
(113,718)(114,719)(115,720)(116,721)(117,722)(118,723)(119,724)(120,725)
(121,726)(122,705)(123,706)(124,707)(125,708)(126,709)(127,710)(128,711)
(129,712)(130,713)(131,714)(132,715)(133,760)(134,761)(135,762)(136,763)
(137,764)(138,765)(139,766)(140,767)(141,768)(142,769)(143,770)(144,782)
(145,783)(146,784)(147,785)(148,786)(149,787)(150,788)(151,789)(152,790)
(153,791)(154,792)(155,771)(156,772)(157,773)(158,774)(159,775)(160,776)
(161,777)(162,778)(163,779)(164,780)(165,781)(166,727)(167,728)(168,729)
(169,730)(170,731)(171,732)(172,733)(173,734)(174,735)(175,736)(176,737)
(177,749)(178,750)(179,751)(180,752)(181,753)(182,754)(183,755)(184,756)
(185,757)(186,758)(187,759)(188,738)(189,739)(190,740)(191,741)(192,742)
(193,743)(194,744)(195,745)(196,746)(197,747)(198,748)(199,496)(200,497)
(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,505)
(209,506)(210,518)(211,519)(212,520)(213,521)(214,522)(215,523)(216,524)
(217,525)(218,526)(219,527)(220,528)(221,507)(222,508)(223,509)(224,510)
(225,511)(226,512)(227,513)(228,514)(229,515)(230,516)(231,517)(232,562)
(233,563)(234,564)(235,565)(236,566)(237,567)(238,568)(239,569)(240,570)
(241,571)(242,572)(243,584)(244,585)(245,586)(246,587)(247,588)(248,589)
(249,590)(250,591)(251,592)(252,593)(253,594)(254,573)(255,574)(256,575)
(257,576)(258,577)(259,578)(260,579)(261,580)(262,581)(263,582)(264,583)
(265,529)(266,530)(267,531)(268,532)(269,533)(270,534)(271,535)(272,536)
(273,537)(274,538)(275,539)(276,551)(277,552)(278,553)(279,554)(280,555)
(281,556)(282,557)(283,558)(284,559)(285,560)(286,561)(287,540)(288,541)
(289,542)(290,543)(291,544)(292,545)(293,546)(294,547)(295,548)(296,549)
(297,550)(298,397)(299,398)(300,399)(301,400)(302,401)(303,402)(304,403)
(305,404)(306,405)(307,406)(308,407)(309,419)(310,420)(311,421)(312,422)
(313,423)(314,424)(315,425)(316,426)(317,427)(318,428)(319,429)(320,408)
(321,409)(322,410)(323,411)(324,412)(325,413)(326,414)(327,415)(328,416)
(329,417)(330,418)(331,463)(332,464)(333,465)(334,466)(335,467)(336,468)
(337,469)(338,470)(339,471)(340,472)(341,473)(342,485)(343,486)(344,487)
(345,488)(346,489)(347,490)(348,491)(349,492)(350,493)(351,494)(352,495)
(353,474)(354,475)(355,476)(356,477)(357,478)(358,479)(359,480)(360,481)
(361,482)(362,483)(363,484)(364,430)(365,431)(366,432)(367,433)(368,434)
(369,435)(370,436)(371,437)(372,438)(373,439)(374,440)(375,452)(376,453)
(377,454)(378,455)(379,456)(380,457)(381,458)(382,459)(383,460)(384,461)
(385,462)(386,441)(387,442)(388,443)(389,444)(390,445)(391,446)(392,447)
(393,448)(394,449)(395,450)(396,451);;
s1 := ( 1,639)( 2,640)( 3,641)( 4,642)( 5,643)( 6,644)( 7,645)( 8,646)
( 9,647)( 10,648)( 11,649)( 12,628)( 13,629)( 14,630)( 15,631)( 16,632)
( 17,633)( 18,634)( 19,635)( 20,636)( 21,637)( 22,638)( 23,650)( 24,651)
( 25,652)( 26,653)( 27,654)( 28,655)( 29,656)( 30,657)( 31,658)( 32,659)
( 33,660)( 34,606)( 35,607)( 36,608)( 37,609)( 38,610)( 39,611)( 40,612)
( 41,613)( 42,614)( 43,615)( 44,616)( 45,595)( 46,596)( 47,597)( 48,598)
( 49,599)( 50,600)( 51,601)( 52,602)( 53,603)( 54,604)( 55,605)( 56,617)
( 57,618)( 58,619)( 59,620)( 60,621)( 61,622)( 62,623)( 63,624)( 64,625)
( 65,626)( 66,627)( 67,672)( 68,673)( 69,674)( 70,675)( 71,676)( 72,677)
( 73,678)( 74,679)( 75,680)( 76,681)( 77,682)( 78,661)( 79,662)( 80,663)
( 81,664)( 82,665)( 83,666)( 84,667)( 85,668)( 86,669)( 87,670)( 88,671)
( 89,683)( 90,684)( 91,685)( 92,686)( 93,687)( 94,688)( 95,689)( 96,690)
( 97,691)( 98,692)( 99,693)(100,738)(101,739)(102,740)(103,741)(104,742)
(105,743)(106,744)(107,745)(108,746)(109,747)(110,748)(111,727)(112,728)
(113,729)(114,730)(115,731)(116,732)(117,733)(118,734)(119,735)(120,736)
(121,737)(122,749)(123,750)(124,751)(125,752)(126,753)(127,754)(128,755)
(129,756)(130,757)(131,758)(132,759)(133,705)(134,706)(135,707)(136,708)
(137,709)(138,710)(139,711)(140,712)(141,713)(142,714)(143,715)(144,694)
(145,695)(146,696)(147,697)(148,698)(149,699)(150,700)(151,701)(152,702)
(153,703)(154,704)(155,716)(156,717)(157,718)(158,719)(159,720)(160,721)
(161,722)(162,723)(163,724)(164,725)(165,726)(166,771)(167,772)(168,773)
(169,774)(170,775)(171,776)(172,777)(173,778)(174,779)(175,780)(176,781)
(177,760)(178,761)(179,762)(180,763)(181,764)(182,765)(183,766)(184,767)
(185,768)(186,769)(187,770)(188,782)(189,783)(190,784)(191,785)(192,786)
(193,787)(194,788)(195,789)(196,790)(197,791)(198,792)(199,540)(200,541)
(201,542)(202,543)(203,544)(204,545)(205,546)(206,547)(207,548)(208,549)
(209,550)(210,529)(211,530)(212,531)(213,532)(214,533)(215,534)(216,535)
(217,536)(218,537)(219,538)(220,539)(221,551)(222,552)(223,553)(224,554)
(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,561)(232,507)
(233,508)(234,509)(235,510)(236,511)(237,512)(238,513)(239,514)(240,515)
(241,516)(242,517)(243,496)(244,497)(245,498)(246,499)(247,500)(248,501)
(249,502)(250,503)(251,504)(252,505)(253,506)(254,518)(255,519)(256,520)
(257,521)(258,522)(259,523)(260,524)(261,525)(262,526)(263,527)(264,528)
(265,573)(266,574)(267,575)(268,576)(269,577)(270,578)(271,579)(272,580)
(273,581)(274,582)(275,583)(276,562)(277,563)(278,564)(279,565)(280,566)
(281,567)(282,568)(283,569)(284,570)(285,571)(286,572)(287,584)(288,585)
(289,586)(290,587)(291,588)(292,589)(293,590)(294,591)(295,592)(296,593)
(297,594)(298,441)(299,442)(300,443)(301,444)(302,445)(303,446)(304,447)
(305,448)(306,449)(307,450)(308,451)(309,430)(310,431)(311,432)(312,433)
(313,434)(314,435)(315,436)(316,437)(317,438)(318,439)(319,440)(320,452)
(321,453)(322,454)(323,455)(324,456)(325,457)(326,458)(327,459)(328,460)
(329,461)(330,462)(331,408)(332,409)(333,410)(334,411)(335,412)(336,413)
(337,414)(338,415)(339,416)(340,417)(341,418)(342,397)(343,398)(344,399)
(345,400)(346,401)(347,402)(348,403)(349,404)(350,405)(351,406)(352,407)
(353,419)(354,420)(355,421)(356,422)(357,423)(358,424)(359,425)(360,426)
(361,427)(362,428)(363,429)(364,474)(365,475)(366,476)(367,477)(368,478)
(369,479)(370,480)(371,481)(372,482)(373,483)(374,484)(375,463)(376,464)
(377,465)(378,466)(379,467)(380,468)(381,469)(382,470)(383,471)(384,472)
(385,473)(386,485)(387,486)(388,487)(389,488)(390,489)(391,490)(392,491)
(393,492)(394,493)(395,494)(396,495);;
s2 := ( 1,397)( 2,407)( 3,406)( 4,405)( 5,404)( 6,403)( 7,402)( 8,401)
( 9,400)( 10,399)( 11,398)( 12,408)( 13,418)( 14,417)( 15,416)( 16,415)
( 17,414)( 18,413)( 19,412)( 20,411)( 21,410)( 22,409)( 23,419)( 24,429)
( 25,428)( 26,427)( 27,426)( 28,425)( 29,424)( 30,423)( 31,422)( 32,421)
( 33,420)( 34,463)( 35,473)( 36,472)( 37,471)( 38,470)( 39,469)( 40,468)
( 41,467)( 42,466)( 43,465)( 44,464)( 45,474)( 46,484)( 47,483)( 48,482)
( 49,481)( 50,480)( 51,479)( 52,478)( 53,477)( 54,476)( 55,475)( 56,485)
( 57,495)( 58,494)( 59,493)( 60,492)( 61,491)( 62,490)( 63,489)( 64,488)
( 65,487)( 66,486)( 67,430)( 68,440)( 69,439)( 70,438)( 71,437)( 72,436)
( 73,435)( 74,434)( 75,433)( 76,432)( 77,431)( 78,441)( 79,451)( 80,450)
( 81,449)( 82,448)( 83,447)( 84,446)( 85,445)( 86,444)( 87,443)( 88,442)
( 89,452)( 90,462)( 91,461)( 92,460)( 93,459)( 94,458)( 95,457)( 96,456)
( 97,455)( 98,454)( 99,453)(100,496)(101,506)(102,505)(103,504)(104,503)
(105,502)(106,501)(107,500)(108,499)(109,498)(110,497)(111,507)(112,517)
(113,516)(114,515)(115,514)(116,513)(117,512)(118,511)(119,510)(120,509)
(121,508)(122,518)(123,528)(124,527)(125,526)(126,525)(127,524)(128,523)
(129,522)(130,521)(131,520)(132,519)(133,562)(134,572)(135,571)(136,570)
(137,569)(138,568)(139,567)(140,566)(141,565)(142,564)(143,563)(144,573)
(145,583)(146,582)(147,581)(148,580)(149,579)(150,578)(151,577)(152,576)
(153,575)(154,574)(155,584)(156,594)(157,593)(158,592)(159,591)(160,590)
(161,589)(162,588)(163,587)(164,586)(165,585)(166,529)(167,539)(168,538)
(169,537)(170,536)(171,535)(172,534)(173,533)(174,532)(175,531)(176,530)
(177,540)(178,550)(179,549)(180,548)(181,547)(182,546)(183,545)(184,544)
(185,543)(186,542)(187,541)(188,551)(189,561)(190,560)(191,559)(192,558)
(193,557)(194,556)(195,555)(196,554)(197,553)(198,552)(199,694)(200,704)
(201,703)(202,702)(203,701)(204,700)(205,699)(206,698)(207,697)(208,696)
(209,695)(210,705)(211,715)(212,714)(213,713)(214,712)(215,711)(216,710)
(217,709)(218,708)(219,707)(220,706)(221,716)(222,726)(223,725)(224,724)
(225,723)(226,722)(227,721)(228,720)(229,719)(230,718)(231,717)(232,760)
(233,770)(234,769)(235,768)(236,767)(237,766)(238,765)(239,764)(240,763)
(241,762)(242,761)(243,771)(244,781)(245,780)(246,779)(247,778)(248,777)
(249,776)(250,775)(251,774)(252,773)(253,772)(254,782)(255,792)(256,791)
(257,790)(258,789)(259,788)(260,787)(261,786)(262,785)(263,784)(264,783)
(265,727)(266,737)(267,736)(268,735)(269,734)(270,733)(271,732)(272,731)
(273,730)(274,729)(275,728)(276,738)(277,748)(278,747)(279,746)(280,745)
(281,744)(282,743)(283,742)(284,741)(285,740)(286,739)(287,749)(288,759)
(289,758)(290,757)(291,756)(292,755)(293,754)(294,753)(295,752)(296,751)
(297,750)(298,595)(299,605)(300,604)(301,603)(302,602)(303,601)(304,600)
(305,599)(306,598)(307,597)(308,596)(309,606)(310,616)(311,615)(312,614)
(313,613)(314,612)(315,611)(316,610)(317,609)(318,608)(319,607)(320,617)
(321,627)(322,626)(323,625)(324,624)(325,623)(326,622)(327,621)(328,620)
(329,619)(330,618)(331,661)(332,671)(333,670)(334,669)(335,668)(336,667)
(337,666)(338,665)(339,664)(340,663)(341,662)(342,672)(343,682)(344,681)
(345,680)(346,679)(347,678)(348,677)(349,676)(350,675)(351,674)(352,673)
(353,683)(354,693)(355,692)(356,691)(357,690)(358,689)(359,688)(360,687)
(361,686)(362,685)(363,684)(364,628)(365,638)(366,637)(367,636)(368,635)
(369,634)(370,633)(371,632)(372,631)(373,630)(374,629)(375,639)(376,649)
(377,648)(378,647)(379,646)(380,645)(381,644)(382,643)(383,642)(384,641)
(385,640)(386,650)(387,660)(388,659)(389,658)(390,657)(391,656)(392,655)
(393,654)(394,653)(395,652)(396,651);;
s3 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)
( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)( 49, 53)
( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)( 69, 77)
( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)
( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)
(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)
(124,132)(125,131)(126,130)(127,129)(133,134)(135,143)(136,142)(137,141)
(138,140)(144,145)(146,154)(147,153)(148,152)(149,151)(155,156)(157,165)
(158,164)(159,163)(160,162)(166,167)(168,176)(169,175)(170,174)(171,173)
(177,178)(179,187)(180,186)(181,185)(182,184)(188,189)(190,198)(191,197)
(192,196)(193,195)(199,299)(200,298)(201,308)(202,307)(203,306)(204,305)
(205,304)(206,303)(207,302)(208,301)(209,300)(210,310)(211,309)(212,319)
(213,318)(214,317)(215,316)(216,315)(217,314)(218,313)(219,312)(220,311)
(221,321)(222,320)(223,330)(224,329)(225,328)(226,327)(227,326)(228,325)
(229,324)(230,323)(231,322)(232,332)(233,331)(234,341)(235,340)(236,339)
(237,338)(238,337)(239,336)(240,335)(241,334)(242,333)(243,343)(244,342)
(245,352)(246,351)(247,350)(248,349)(249,348)(250,347)(251,346)(252,345)
(253,344)(254,354)(255,353)(256,363)(257,362)(258,361)(259,360)(260,359)
(261,358)(262,357)(263,356)(264,355)(265,365)(266,364)(267,374)(268,373)
(269,372)(270,371)(271,370)(272,369)(273,368)(274,367)(275,366)(276,376)
(277,375)(278,385)(279,384)(280,383)(281,382)(282,381)(283,380)(284,379)
(285,378)(286,377)(287,387)(288,386)(289,396)(290,395)(291,394)(292,393)
(293,392)(294,391)(295,390)(296,389)(297,388)(397,497)(398,496)(399,506)
(400,505)(401,504)(402,503)(403,502)(404,501)(405,500)(406,499)(407,498)
(408,508)(409,507)(410,517)(411,516)(412,515)(413,514)(414,513)(415,512)
(416,511)(417,510)(418,509)(419,519)(420,518)(421,528)(422,527)(423,526)
(424,525)(425,524)(426,523)(427,522)(428,521)(429,520)(430,530)(431,529)
(432,539)(433,538)(434,537)(435,536)(436,535)(437,534)(438,533)(439,532)
(440,531)(441,541)(442,540)(443,550)(444,549)(445,548)(446,547)(447,546)
(448,545)(449,544)(450,543)(451,542)(452,552)(453,551)(454,561)(455,560)
(456,559)(457,558)(458,557)(459,556)(460,555)(461,554)(462,553)(463,563)
(464,562)(465,572)(466,571)(467,570)(468,569)(469,568)(470,567)(471,566)
(472,565)(473,564)(474,574)(475,573)(476,583)(477,582)(478,581)(479,580)
(480,579)(481,578)(482,577)(483,576)(484,575)(485,585)(486,584)(487,594)
(488,593)(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)(495,586)
(595,596)(597,605)(598,604)(599,603)(600,602)(606,607)(608,616)(609,615)
(610,614)(611,613)(617,618)(619,627)(620,626)(621,625)(622,624)(628,629)
(630,638)(631,637)(632,636)(633,635)(639,640)(641,649)(642,648)(643,647)
(644,646)(650,651)(652,660)(653,659)(654,658)(655,657)(661,662)(663,671)
(664,670)(665,669)(666,668)(672,673)(674,682)(675,681)(676,680)(677,679)
(683,684)(685,693)(686,692)(687,691)(688,690)(694,695)(696,704)(697,703)
(698,702)(699,701)(705,706)(707,715)(708,714)(709,713)(710,712)(716,717)
(718,726)(719,725)(720,724)(721,723)(727,728)(729,737)(730,736)(731,735)
(732,734)(738,739)(740,748)(741,747)(742,746)(743,745)(749,750)(751,759)
(752,758)(753,757)(754,756)(760,761)(762,770)(763,769)(764,768)(765,767)
(771,772)(773,781)(774,780)(775,779)(776,778)(782,783)(784,792)(785,791)
(786,790)(787,789);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(792)!( 1,595)( 2,596)( 3,597)( 4,598)( 5,599)( 6,600)( 7,601)
( 8,602)( 9,603)( 10,604)( 11,605)( 12,617)( 13,618)( 14,619)( 15,620)
( 16,621)( 17,622)( 18,623)( 19,624)( 20,625)( 21,626)( 22,627)( 23,606)
( 24,607)( 25,608)( 26,609)( 27,610)( 28,611)( 29,612)( 30,613)( 31,614)
( 32,615)( 33,616)( 34,661)( 35,662)( 36,663)( 37,664)( 38,665)( 39,666)
( 40,667)( 41,668)( 42,669)( 43,670)( 44,671)( 45,683)( 46,684)( 47,685)
( 48,686)( 49,687)( 50,688)( 51,689)( 52,690)( 53,691)( 54,692)( 55,693)
( 56,672)( 57,673)( 58,674)( 59,675)( 60,676)( 61,677)( 62,678)( 63,679)
( 64,680)( 65,681)( 66,682)( 67,628)( 68,629)( 69,630)( 70,631)( 71,632)
( 72,633)( 73,634)( 74,635)( 75,636)( 76,637)( 77,638)( 78,650)( 79,651)
( 80,652)( 81,653)( 82,654)( 83,655)( 84,656)( 85,657)( 86,658)( 87,659)
( 88,660)( 89,639)( 90,640)( 91,641)( 92,642)( 93,643)( 94,644)( 95,645)
( 96,646)( 97,647)( 98,648)( 99,649)(100,694)(101,695)(102,696)(103,697)
(104,698)(105,699)(106,700)(107,701)(108,702)(109,703)(110,704)(111,716)
(112,717)(113,718)(114,719)(115,720)(116,721)(117,722)(118,723)(119,724)
(120,725)(121,726)(122,705)(123,706)(124,707)(125,708)(126,709)(127,710)
(128,711)(129,712)(130,713)(131,714)(132,715)(133,760)(134,761)(135,762)
(136,763)(137,764)(138,765)(139,766)(140,767)(141,768)(142,769)(143,770)
(144,782)(145,783)(146,784)(147,785)(148,786)(149,787)(150,788)(151,789)
(152,790)(153,791)(154,792)(155,771)(156,772)(157,773)(158,774)(159,775)
(160,776)(161,777)(162,778)(163,779)(164,780)(165,781)(166,727)(167,728)
(168,729)(169,730)(170,731)(171,732)(172,733)(173,734)(174,735)(175,736)
(176,737)(177,749)(178,750)(179,751)(180,752)(181,753)(182,754)(183,755)
(184,756)(185,757)(186,758)(187,759)(188,738)(189,739)(190,740)(191,741)
(192,742)(193,743)(194,744)(195,745)(196,746)(197,747)(198,748)(199,496)
(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)
(208,505)(209,506)(210,518)(211,519)(212,520)(213,521)(214,522)(215,523)
(216,524)(217,525)(218,526)(219,527)(220,528)(221,507)(222,508)(223,509)
(224,510)(225,511)(226,512)(227,513)(228,514)(229,515)(230,516)(231,517)
(232,562)(233,563)(234,564)(235,565)(236,566)(237,567)(238,568)(239,569)
(240,570)(241,571)(242,572)(243,584)(244,585)(245,586)(246,587)(247,588)
(248,589)(249,590)(250,591)(251,592)(252,593)(253,594)(254,573)(255,574)
(256,575)(257,576)(258,577)(259,578)(260,579)(261,580)(262,581)(263,582)
(264,583)(265,529)(266,530)(267,531)(268,532)(269,533)(270,534)(271,535)
(272,536)(273,537)(274,538)(275,539)(276,551)(277,552)(278,553)(279,554)
(280,555)(281,556)(282,557)(283,558)(284,559)(285,560)(286,561)(287,540)
(288,541)(289,542)(290,543)(291,544)(292,545)(293,546)(294,547)(295,548)
(296,549)(297,550)(298,397)(299,398)(300,399)(301,400)(302,401)(303,402)
(304,403)(305,404)(306,405)(307,406)(308,407)(309,419)(310,420)(311,421)
(312,422)(313,423)(314,424)(315,425)(316,426)(317,427)(318,428)(319,429)
(320,408)(321,409)(322,410)(323,411)(324,412)(325,413)(326,414)(327,415)
(328,416)(329,417)(330,418)(331,463)(332,464)(333,465)(334,466)(335,467)
(336,468)(337,469)(338,470)(339,471)(340,472)(341,473)(342,485)(343,486)
(344,487)(345,488)(346,489)(347,490)(348,491)(349,492)(350,493)(351,494)
(352,495)(353,474)(354,475)(355,476)(356,477)(357,478)(358,479)(359,480)
(360,481)(361,482)(362,483)(363,484)(364,430)(365,431)(366,432)(367,433)
(368,434)(369,435)(370,436)(371,437)(372,438)(373,439)(374,440)(375,452)
(376,453)(377,454)(378,455)(379,456)(380,457)(381,458)(382,459)(383,460)
(384,461)(385,462)(386,441)(387,442)(388,443)(389,444)(390,445)(391,446)
(392,447)(393,448)(394,449)(395,450)(396,451);
s1 := Sym(792)!( 1,639)( 2,640)( 3,641)( 4,642)( 5,643)( 6,644)( 7,645)
( 8,646)( 9,647)( 10,648)( 11,649)( 12,628)( 13,629)( 14,630)( 15,631)
( 16,632)( 17,633)( 18,634)( 19,635)( 20,636)( 21,637)( 22,638)( 23,650)
( 24,651)( 25,652)( 26,653)( 27,654)( 28,655)( 29,656)( 30,657)( 31,658)
( 32,659)( 33,660)( 34,606)( 35,607)( 36,608)( 37,609)( 38,610)( 39,611)
( 40,612)( 41,613)( 42,614)( 43,615)( 44,616)( 45,595)( 46,596)( 47,597)
( 48,598)( 49,599)( 50,600)( 51,601)( 52,602)( 53,603)( 54,604)( 55,605)
( 56,617)( 57,618)( 58,619)( 59,620)( 60,621)( 61,622)( 62,623)( 63,624)
( 64,625)( 65,626)( 66,627)( 67,672)( 68,673)( 69,674)( 70,675)( 71,676)
( 72,677)( 73,678)( 74,679)( 75,680)( 76,681)( 77,682)( 78,661)( 79,662)
( 80,663)( 81,664)( 82,665)( 83,666)( 84,667)( 85,668)( 86,669)( 87,670)
( 88,671)( 89,683)( 90,684)( 91,685)( 92,686)( 93,687)( 94,688)( 95,689)
( 96,690)( 97,691)( 98,692)( 99,693)(100,738)(101,739)(102,740)(103,741)
(104,742)(105,743)(106,744)(107,745)(108,746)(109,747)(110,748)(111,727)
(112,728)(113,729)(114,730)(115,731)(116,732)(117,733)(118,734)(119,735)
(120,736)(121,737)(122,749)(123,750)(124,751)(125,752)(126,753)(127,754)
(128,755)(129,756)(130,757)(131,758)(132,759)(133,705)(134,706)(135,707)
(136,708)(137,709)(138,710)(139,711)(140,712)(141,713)(142,714)(143,715)
(144,694)(145,695)(146,696)(147,697)(148,698)(149,699)(150,700)(151,701)
(152,702)(153,703)(154,704)(155,716)(156,717)(157,718)(158,719)(159,720)
(160,721)(161,722)(162,723)(163,724)(164,725)(165,726)(166,771)(167,772)
(168,773)(169,774)(170,775)(171,776)(172,777)(173,778)(174,779)(175,780)
(176,781)(177,760)(178,761)(179,762)(180,763)(181,764)(182,765)(183,766)
(184,767)(185,768)(186,769)(187,770)(188,782)(189,783)(190,784)(191,785)
(192,786)(193,787)(194,788)(195,789)(196,790)(197,791)(198,792)(199,540)
(200,541)(201,542)(202,543)(203,544)(204,545)(205,546)(206,547)(207,548)
(208,549)(209,550)(210,529)(211,530)(212,531)(213,532)(214,533)(215,534)
(216,535)(217,536)(218,537)(219,538)(220,539)(221,551)(222,552)(223,553)
(224,554)(225,555)(226,556)(227,557)(228,558)(229,559)(230,560)(231,561)
(232,507)(233,508)(234,509)(235,510)(236,511)(237,512)(238,513)(239,514)
(240,515)(241,516)(242,517)(243,496)(244,497)(245,498)(246,499)(247,500)
(248,501)(249,502)(250,503)(251,504)(252,505)(253,506)(254,518)(255,519)
(256,520)(257,521)(258,522)(259,523)(260,524)(261,525)(262,526)(263,527)
(264,528)(265,573)(266,574)(267,575)(268,576)(269,577)(270,578)(271,579)
(272,580)(273,581)(274,582)(275,583)(276,562)(277,563)(278,564)(279,565)
(280,566)(281,567)(282,568)(283,569)(284,570)(285,571)(286,572)(287,584)
(288,585)(289,586)(290,587)(291,588)(292,589)(293,590)(294,591)(295,592)
(296,593)(297,594)(298,441)(299,442)(300,443)(301,444)(302,445)(303,446)
(304,447)(305,448)(306,449)(307,450)(308,451)(309,430)(310,431)(311,432)
(312,433)(313,434)(314,435)(315,436)(316,437)(317,438)(318,439)(319,440)
(320,452)(321,453)(322,454)(323,455)(324,456)(325,457)(326,458)(327,459)
(328,460)(329,461)(330,462)(331,408)(332,409)(333,410)(334,411)(335,412)
(336,413)(337,414)(338,415)(339,416)(340,417)(341,418)(342,397)(343,398)
(344,399)(345,400)(346,401)(347,402)(348,403)(349,404)(350,405)(351,406)
(352,407)(353,419)(354,420)(355,421)(356,422)(357,423)(358,424)(359,425)
(360,426)(361,427)(362,428)(363,429)(364,474)(365,475)(366,476)(367,477)
(368,478)(369,479)(370,480)(371,481)(372,482)(373,483)(374,484)(375,463)
(376,464)(377,465)(378,466)(379,467)(380,468)(381,469)(382,470)(383,471)
(384,472)(385,473)(386,485)(387,486)(388,487)(389,488)(390,489)(391,490)
(392,491)(393,492)(394,493)(395,494)(396,495);
s2 := Sym(792)!( 1,397)( 2,407)( 3,406)( 4,405)( 5,404)( 6,403)( 7,402)
( 8,401)( 9,400)( 10,399)( 11,398)( 12,408)( 13,418)( 14,417)( 15,416)
( 16,415)( 17,414)( 18,413)( 19,412)( 20,411)( 21,410)( 22,409)( 23,419)
( 24,429)( 25,428)( 26,427)( 27,426)( 28,425)( 29,424)( 30,423)( 31,422)
( 32,421)( 33,420)( 34,463)( 35,473)( 36,472)( 37,471)( 38,470)( 39,469)
( 40,468)( 41,467)( 42,466)( 43,465)( 44,464)( 45,474)( 46,484)( 47,483)
( 48,482)( 49,481)( 50,480)( 51,479)( 52,478)( 53,477)( 54,476)( 55,475)
( 56,485)( 57,495)( 58,494)( 59,493)( 60,492)( 61,491)( 62,490)( 63,489)
( 64,488)( 65,487)( 66,486)( 67,430)( 68,440)( 69,439)( 70,438)( 71,437)
( 72,436)( 73,435)( 74,434)( 75,433)( 76,432)( 77,431)( 78,441)( 79,451)
( 80,450)( 81,449)( 82,448)( 83,447)( 84,446)( 85,445)( 86,444)( 87,443)
( 88,442)( 89,452)( 90,462)( 91,461)( 92,460)( 93,459)( 94,458)( 95,457)
( 96,456)( 97,455)( 98,454)( 99,453)(100,496)(101,506)(102,505)(103,504)
(104,503)(105,502)(106,501)(107,500)(108,499)(109,498)(110,497)(111,507)
(112,517)(113,516)(114,515)(115,514)(116,513)(117,512)(118,511)(119,510)
(120,509)(121,508)(122,518)(123,528)(124,527)(125,526)(126,525)(127,524)
(128,523)(129,522)(130,521)(131,520)(132,519)(133,562)(134,572)(135,571)
(136,570)(137,569)(138,568)(139,567)(140,566)(141,565)(142,564)(143,563)
(144,573)(145,583)(146,582)(147,581)(148,580)(149,579)(150,578)(151,577)
(152,576)(153,575)(154,574)(155,584)(156,594)(157,593)(158,592)(159,591)
(160,590)(161,589)(162,588)(163,587)(164,586)(165,585)(166,529)(167,539)
(168,538)(169,537)(170,536)(171,535)(172,534)(173,533)(174,532)(175,531)
(176,530)(177,540)(178,550)(179,549)(180,548)(181,547)(182,546)(183,545)
(184,544)(185,543)(186,542)(187,541)(188,551)(189,561)(190,560)(191,559)
(192,558)(193,557)(194,556)(195,555)(196,554)(197,553)(198,552)(199,694)
(200,704)(201,703)(202,702)(203,701)(204,700)(205,699)(206,698)(207,697)
(208,696)(209,695)(210,705)(211,715)(212,714)(213,713)(214,712)(215,711)
(216,710)(217,709)(218,708)(219,707)(220,706)(221,716)(222,726)(223,725)
(224,724)(225,723)(226,722)(227,721)(228,720)(229,719)(230,718)(231,717)
(232,760)(233,770)(234,769)(235,768)(236,767)(237,766)(238,765)(239,764)
(240,763)(241,762)(242,761)(243,771)(244,781)(245,780)(246,779)(247,778)
(248,777)(249,776)(250,775)(251,774)(252,773)(253,772)(254,782)(255,792)
(256,791)(257,790)(258,789)(259,788)(260,787)(261,786)(262,785)(263,784)
(264,783)(265,727)(266,737)(267,736)(268,735)(269,734)(270,733)(271,732)
(272,731)(273,730)(274,729)(275,728)(276,738)(277,748)(278,747)(279,746)
(280,745)(281,744)(282,743)(283,742)(284,741)(285,740)(286,739)(287,749)
(288,759)(289,758)(290,757)(291,756)(292,755)(293,754)(294,753)(295,752)
(296,751)(297,750)(298,595)(299,605)(300,604)(301,603)(302,602)(303,601)
(304,600)(305,599)(306,598)(307,597)(308,596)(309,606)(310,616)(311,615)
(312,614)(313,613)(314,612)(315,611)(316,610)(317,609)(318,608)(319,607)
(320,617)(321,627)(322,626)(323,625)(324,624)(325,623)(326,622)(327,621)
(328,620)(329,619)(330,618)(331,661)(332,671)(333,670)(334,669)(335,668)
(336,667)(337,666)(338,665)(339,664)(340,663)(341,662)(342,672)(343,682)
(344,681)(345,680)(346,679)(347,678)(348,677)(349,676)(350,675)(351,674)
(352,673)(353,683)(354,693)(355,692)(356,691)(357,690)(358,689)(359,688)
(360,687)(361,686)(362,685)(363,684)(364,628)(365,638)(366,637)(367,636)
(368,635)(369,634)(370,633)(371,632)(372,631)(373,630)(374,629)(375,639)
(376,649)(377,648)(378,647)(379,646)(380,645)(381,644)(382,643)(383,642)
(384,641)(385,640)(386,650)(387,660)(388,659)(389,658)(390,657)(391,656)
(392,655)(393,654)(394,653)(395,652)(396,651);
s3 := Sym(792)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 13)( 14, 22)
( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 46)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 68)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 78, 79)( 80, 88)( 81, 87)( 82, 86)
( 83, 85)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)
(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)
(122,123)(124,132)(125,131)(126,130)(127,129)(133,134)(135,143)(136,142)
(137,141)(138,140)(144,145)(146,154)(147,153)(148,152)(149,151)(155,156)
(157,165)(158,164)(159,163)(160,162)(166,167)(168,176)(169,175)(170,174)
(171,173)(177,178)(179,187)(180,186)(181,185)(182,184)(188,189)(190,198)
(191,197)(192,196)(193,195)(199,299)(200,298)(201,308)(202,307)(203,306)
(204,305)(205,304)(206,303)(207,302)(208,301)(209,300)(210,310)(211,309)
(212,319)(213,318)(214,317)(215,316)(216,315)(217,314)(218,313)(219,312)
(220,311)(221,321)(222,320)(223,330)(224,329)(225,328)(226,327)(227,326)
(228,325)(229,324)(230,323)(231,322)(232,332)(233,331)(234,341)(235,340)
(236,339)(237,338)(238,337)(239,336)(240,335)(241,334)(242,333)(243,343)
(244,342)(245,352)(246,351)(247,350)(248,349)(249,348)(250,347)(251,346)
(252,345)(253,344)(254,354)(255,353)(256,363)(257,362)(258,361)(259,360)
(260,359)(261,358)(262,357)(263,356)(264,355)(265,365)(266,364)(267,374)
(268,373)(269,372)(270,371)(271,370)(272,369)(273,368)(274,367)(275,366)
(276,376)(277,375)(278,385)(279,384)(280,383)(281,382)(282,381)(283,380)
(284,379)(285,378)(286,377)(287,387)(288,386)(289,396)(290,395)(291,394)
(292,393)(293,392)(294,391)(295,390)(296,389)(297,388)(397,497)(398,496)
(399,506)(400,505)(401,504)(402,503)(403,502)(404,501)(405,500)(406,499)
(407,498)(408,508)(409,507)(410,517)(411,516)(412,515)(413,514)(414,513)
(415,512)(416,511)(417,510)(418,509)(419,519)(420,518)(421,528)(422,527)
(423,526)(424,525)(425,524)(426,523)(427,522)(428,521)(429,520)(430,530)
(431,529)(432,539)(433,538)(434,537)(435,536)(436,535)(437,534)(438,533)
(439,532)(440,531)(441,541)(442,540)(443,550)(444,549)(445,548)(446,547)
(447,546)(448,545)(449,544)(450,543)(451,542)(452,552)(453,551)(454,561)
(455,560)(456,559)(457,558)(458,557)(459,556)(460,555)(461,554)(462,553)
(463,563)(464,562)(465,572)(466,571)(467,570)(468,569)(469,568)(470,567)
(471,566)(472,565)(473,564)(474,574)(475,573)(476,583)(477,582)(478,581)
(479,580)(480,579)(481,578)(482,577)(483,576)(484,575)(485,585)(486,584)
(487,594)(488,593)(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)
(495,586)(595,596)(597,605)(598,604)(599,603)(600,602)(606,607)(608,616)
(609,615)(610,614)(611,613)(617,618)(619,627)(620,626)(621,625)(622,624)
(628,629)(630,638)(631,637)(632,636)(633,635)(639,640)(641,649)(642,648)
(643,647)(644,646)(650,651)(652,660)(653,659)(654,658)(655,657)(661,662)
(663,671)(664,670)(665,669)(666,668)(672,673)(674,682)(675,681)(676,680)
(677,679)(683,684)(685,693)(686,692)(687,691)(688,690)(694,695)(696,704)
(697,703)(698,702)(699,701)(705,706)(707,715)(708,714)(709,713)(710,712)
(716,717)(718,726)(719,725)(720,724)(721,723)(727,728)(729,737)(730,736)
(731,735)(732,734)(738,739)(740,748)(741,747)(742,746)(743,745)(749,750)
(751,759)(752,758)(753,757)(754,756)(760,761)(762,770)(763,769)(764,768)
(765,767)(771,772)(773,781)(774,780)(775,779)(776,778)(782,783)(784,792)
(785,791)(786,790)(787,789);
poly := sub<Sym(792)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope