Polytope of Type {132,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {132,6}*1584a
if this polytope has a name.
Group : SmallGroup(1584,417)
Rank : 3
Schlafli Type : {132,6}
Number of vertices, edges, etc : 132, 396, 6
Order of s₀s₁s₂ : 132
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {66,6}*792a
   3-fold quotients : {44,6}*528a
   6-fold quotients : {22,6}*264
   9-fold quotients : {44,2}*176
   11-fold quotients : {12,6}*144c
   18-fold quotients : {22,2}*88
   22-fold quotients : {6,6}*72b
   33-fold quotients : {4,6}*48a
   36-fold quotients : {11,2}*44
   44-fold quotients : {6,3}*36
   66-fold quotients : {2,6}*24
   99-fold quotients : {4,2}*16
   132-fold quotients : {2,3}*12
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  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);;
s1 := (  1,629)(  2,628)(  3,638)(  4,637)(  5,636)(  6,635)(  7,634)(  8,633)
(  9,632)( 10,631)( 11,630)( 12,651)( 13,650)( 14,660)( 15,659)( 16,658)
( 17,657)( 18,656)( 19,655)( 20,654)( 21,653)( 22,652)( 23,640)( 24,639)
( 25,649)( 26,648)( 27,647)( 28,646)( 29,645)( 30,644)( 31,643)( 32,642)
( 33,641)( 34,596)( 35,595)( 36,605)( 37,604)( 38,603)( 39,602)( 40,601)
( 41,600)( 42,599)( 43,598)( 44,597)( 45,618)( 46,617)( 47,627)( 48,626)
( 49,625)( 50,624)( 51,623)( 52,622)( 53,621)( 54,620)( 55,619)( 56,607)
( 57,606)( 58,616)( 59,615)( 60,614)( 61,613)( 62,612)( 63,611)( 64,610)
( 65,609)( 66,608)( 67,662)( 68,661)( 69,671)( 70,670)( 71,669)( 72,668)
( 73,667)( 74,666)( 75,665)( 76,664)( 77,663)( 78,684)( 79,683)( 80,693)
( 81,692)( 82,691)( 83,690)( 84,689)( 85,688)( 86,687)( 87,686)( 88,685)
( 89,673)( 90,672)( 91,682)( 92,681)( 93,680)( 94,679)( 95,678)( 96,677)
( 97,676)( 98,675)( 99,674)(100,728)(101,727)(102,737)(103,736)(104,735)
(105,734)(106,733)(107,732)(108,731)(109,730)(110,729)(111,750)(112,749)
(113,759)(114,758)(115,757)(116,756)(117,755)(118,754)(119,753)(120,752)
(121,751)(122,739)(123,738)(124,748)(125,747)(126,746)(127,745)(128,744)
(129,743)(130,742)(131,741)(132,740)(133,695)(134,694)(135,704)(136,703)
(137,702)(138,701)(139,700)(140,699)(141,698)(142,697)(143,696)(144,717)
(145,716)(146,726)(147,725)(148,724)(149,723)(150,722)(151,721)(152,720)
(153,719)(154,718)(155,706)(156,705)(157,715)(158,714)(159,713)(160,712)
(161,711)(162,710)(163,709)(164,708)(165,707)(166,761)(167,760)(168,770)
(169,769)(170,768)(171,767)(172,766)(173,765)(174,764)(175,763)(176,762)
(177,783)(178,782)(179,792)(180,791)(181,790)(182,789)(183,788)(184,787)
(185,786)(186,785)(187,784)(188,772)(189,771)(190,781)(191,780)(192,779)
(193,778)(194,777)(195,776)(196,775)(197,774)(198,773)(199,431)(200,430)
(201,440)(202,439)(203,438)(204,437)(205,436)(206,435)(207,434)(208,433)
(209,432)(210,453)(211,452)(212,462)(213,461)(214,460)(215,459)(216,458)
(217,457)(218,456)(219,455)(220,454)(221,442)(222,441)(223,451)(224,450)
(225,449)(226,448)(227,447)(228,446)(229,445)(230,444)(231,443)(232,398)
(233,397)(234,407)(235,406)(236,405)(237,404)(238,403)(239,402)(240,401)
(241,400)(242,399)(243,420)(244,419)(245,429)(246,428)(247,427)(248,426)
(249,425)(250,424)(251,423)(252,422)(253,421)(254,409)(255,408)(256,418)
(257,417)(258,416)(259,415)(260,414)(261,413)(262,412)(263,411)(264,410)
(265,464)(266,463)(267,473)(268,472)(269,471)(270,470)(271,469)(272,468)
(273,467)(274,466)(275,465)(276,486)(277,485)(278,495)(279,494)(280,493)
(281,492)(282,491)(283,490)(284,489)(285,488)(286,487)(287,475)(288,474)
(289,484)(290,483)(291,482)(292,481)(293,480)(294,479)(295,478)(296,477)
(297,476)(298,530)(299,529)(300,539)(301,538)(302,537)(303,536)(304,535)
(305,534)(306,533)(307,532)(308,531)(309,552)(310,551)(311,561)(312,560)
(313,559)(314,558)(315,557)(316,556)(317,555)(318,554)(319,553)(320,541)
(321,540)(322,550)(323,549)(324,548)(325,547)(326,546)(327,545)(328,544)
(329,543)(330,542)(331,497)(332,496)(333,506)(334,505)(335,504)(336,503)
(337,502)(338,501)(339,500)(340,499)(341,498)(342,519)(343,518)(344,528)
(345,527)(346,526)(347,525)(348,524)(349,523)(350,522)(351,521)(352,520)
(353,508)(354,507)(355,517)(356,516)(357,515)(358,514)(359,513)(360,512)
(361,511)(362,510)(363,509)(364,563)(365,562)(366,572)(367,571)(368,570)
(369,569)(370,568)(371,567)(372,566)(373,565)(374,564)(375,585)(376,584)
(377,594)(378,593)(379,592)(380,591)(381,590)(382,589)(383,588)(384,587)
(385,586)(386,574)(387,573)(388,583)(389,582)(390,581)(391,580)(392,579)
(393,578)(394,577)(395,576)(396,575);;
s2 := (  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]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*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*s2*s0*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := 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);
s1 := Sym(792)!(  1,629)(  2,628)(  3,638)(  4,637)(  5,636)(  6,635)(  7,634)
(  8,633)(  9,632)( 10,631)( 11,630)( 12,651)( 13,650)( 14,660)( 15,659)
( 16,658)( 17,657)( 18,656)( 19,655)( 20,654)( 21,653)( 22,652)( 23,640)
( 24,639)( 25,649)( 26,648)( 27,647)( 28,646)( 29,645)( 30,644)( 31,643)
( 32,642)( 33,641)( 34,596)( 35,595)( 36,605)( 37,604)( 38,603)( 39,602)
( 40,601)( 41,600)( 42,599)( 43,598)( 44,597)( 45,618)( 46,617)( 47,627)
( 48,626)( 49,625)( 50,624)( 51,623)( 52,622)( 53,621)( 54,620)( 55,619)
( 56,607)( 57,606)( 58,616)( 59,615)( 60,614)( 61,613)( 62,612)( 63,611)
( 64,610)( 65,609)( 66,608)( 67,662)( 68,661)( 69,671)( 70,670)( 71,669)
( 72,668)( 73,667)( 74,666)( 75,665)( 76,664)( 77,663)( 78,684)( 79,683)
( 80,693)( 81,692)( 82,691)( 83,690)( 84,689)( 85,688)( 86,687)( 87,686)
( 88,685)( 89,673)( 90,672)( 91,682)( 92,681)( 93,680)( 94,679)( 95,678)
( 96,677)( 97,676)( 98,675)( 99,674)(100,728)(101,727)(102,737)(103,736)
(104,735)(105,734)(106,733)(107,732)(108,731)(109,730)(110,729)(111,750)
(112,749)(113,759)(114,758)(115,757)(116,756)(117,755)(118,754)(119,753)
(120,752)(121,751)(122,739)(123,738)(124,748)(125,747)(126,746)(127,745)
(128,744)(129,743)(130,742)(131,741)(132,740)(133,695)(134,694)(135,704)
(136,703)(137,702)(138,701)(139,700)(140,699)(141,698)(142,697)(143,696)
(144,717)(145,716)(146,726)(147,725)(148,724)(149,723)(150,722)(151,721)
(152,720)(153,719)(154,718)(155,706)(156,705)(157,715)(158,714)(159,713)
(160,712)(161,711)(162,710)(163,709)(164,708)(165,707)(166,761)(167,760)
(168,770)(169,769)(170,768)(171,767)(172,766)(173,765)(174,764)(175,763)
(176,762)(177,783)(178,782)(179,792)(180,791)(181,790)(182,789)(183,788)
(184,787)(185,786)(186,785)(187,784)(188,772)(189,771)(190,781)(191,780)
(192,779)(193,778)(194,777)(195,776)(196,775)(197,774)(198,773)(199,431)
(200,430)(201,440)(202,439)(203,438)(204,437)(205,436)(206,435)(207,434)
(208,433)(209,432)(210,453)(211,452)(212,462)(213,461)(214,460)(215,459)
(216,458)(217,457)(218,456)(219,455)(220,454)(221,442)(222,441)(223,451)
(224,450)(225,449)(226,448)(227,447)(228,446)(229,445)(230,444)(231,443)
(232,398)(233,397)(234,407)(235,406)(236,405)(237,404)(238,403)(239,402)
(240,401)(241,400)(242,399)(243,420)(244,419)(245,429)(246,428)(247,427)
(248,426)(249,425)(250,424)(251,423)(252,422)(253,421)(254,409)(255,408)
(256,418)(257,417)(258,416)(259,415)(260,414)(261,413)(262,412)(263,411)
(264,410)(265,464)(266,463)(267,473)(268,472)(269,471)(270,470)(271,469)
(272,468)(273,467)(274,466)(275,465)(276,486)(277,485)(278,495)(279,494)
(280,493)(281,492)(282,491)(283,490)(284,489)(285,488)(286,487)(287,475)
(288,474)(289,484)(290,483)(291,482)(292,481)(293,480)(294,479)(295,478)
(296,477)(297,476)(298,530)(299,529)(300,539)(301,538)(302,537)(303,536)
(304,535)(305,534)(306,533)(307,532)(308,531)(309,552)(310,551)(311,561)
(312,560)(313,559)(314,558)(315,557)(316,556)(317,555)(318,554)(319,553)
(320,541)(321,540)(322,550)(323,549)(324,548)(325,547)(326,546)(327,545)
(328,544)(329,543)(330,542)(331,497)(332,496)(333,506)(334,505)(335,504)
(336,503)(337,502)(338,501)(339,500)(340,499)(341,498)(342,519)(343,518)
(344,528)(345,527)(346,526)(347,525)(348,524)(349,523)(350,522)(351,521)
(352,520)(353,508)(354,507)(355,517)(356,516)(357,515)(358,514)(359,513)
(360,512)(361,511)(362,510)(363,509)(364,563)(365,562)(366,572)(367,571)
(368,570)(369,569)(370,568)(371,567)(372,566)(373,565)(374,564)(375,585)
(376,584)(377,594)(378,593)(379,592)(380,591)(381,590)(382,589)(383,588)
(384,587)(385,586)(386,574)(387,573)(388,583)(389,582)(390,581)(391,580)
(392,579)(393,578)(394,577)(395,576)(396,575);
s2 := 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>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*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*s2*s0*s1*s0*s1*s0*s1*s0*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 >;

References : None.
to this polytope