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