Polytope of Type {6,132}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,132}*1584a
if this polytope has a name.
Group : SmallGroup(1584,417)
Rank : 3
Schlafli Type : {6,132}
Number of vertices, edges, etc : 6, 396, 132
Order of s0s1s2 : 132
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {6,66}*792a
3-fold quotients : {6,44}*528a
6-fold quotients : {6,22}*264
9-fold quotients : {2,44}*176
11-fold quotients : {6,12}*144c
18-fold quotients : {2,22}*88
22-fold quotients : {6,6}*72c
33-fold quotients : {6,4}*48a
36-fold quotients : {2,11}*44
44-fold quotients : {3,6}*36
66-fold quotients : {6,2}*24
99-fold quotients : {2,4}*16
132-fold quotients : {3,2}*12
198-fold quotients : {2,2}*8
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)( 2,649)( 3,648)( 4,647)( 5,646)( 6,645)( 7,644)( 8,643)
( 9,642)( 10,641)( 11,640)( 12,628)( 13,638)( 14,637)( 15,636)( 16,635)
( 17,634)( 18,633)( 19,632)( 20,631)( 21,630)( 22,629)( 23,650)( 24,660)
( 25,659)( 26,658)( 27,657)( 28,656)( 29,655)( 30,654)( 31,653)( 32,652)
( 33,651)( 34,606)( 35,616)( 36,615)( 37,614)( 38,613)( 39,612)( 40,611)
( 41,610)( 42,609)( 43,608)( 44,607)( 45,595)( 46,605)( 47,604)( 48,603)
( 49,602)( 50,601)( 51,600)( 52,599)( 53,598)( 54,597)( 55,596)( 56,617)
( 57,627)( 58,626)( 59,625)( 60,624)( 61,623)( 62,622)( 63,621)( 64,620)
( 65,619)( 66,618)( 67,672)( 68,682)( 69,681)( 70,680)( 71,679)( 72,678)
( 73,677)( 74,676)( 75,675)( 76,674)( 77,673)( 78,661)( 79,671)( 80,670)
( 81,669)( 82,668)( 83,667)( 84,666)( 85,665)( 86,664)( 87,663)( 88,662)
( 89,683)( 90,693)( 91,692)( 92,691)( 93,690)( 94,689)( 95,688)( 96,687)
( 97,686)( 98,685)( 99,684)(100,738)(101,748)(102,747)(103,746)(104,745)
(105,744)(106,743)(107,742)(108,741)(109,740)(110,739)(111,727)(112,737)
(113,736)(114,735)(115,734)(116,733)(117,732)(118,731)(119,730)(120,729)
(121,728)(122,749)(123,759)(124,758)(125,757)(126,756)(127,755)(128,754)
(129,753)(130,752)(131,751)(132,750)(133,705)(134,715)(135,714)(136,713)
(137,712)(138,711)(139,710)(140,709)(141,708)(142,707)(143,706)(144,694)
(145,704)(146,703)(147,702)(148,701)(149,700)(150,699)(151,698)(152,697)
(153,696)(154,695)(155,716)(156,726)(157,725)(158,724)(159,723)(160,722)
(161,721)(162,720)(163,719)(164,718)(165,717)(166,771)(167,781)(168,780)
(169,779)(170,778)(171,777)(172,776)(173,775)(174,774)(175,773)(176,772)
(177,760)(178,770)(179,769)(180,768)(181,767)(182,766)(183,765)(184,764)
(185,763)(186,762)(187,761)(188,782)(189,792)(190,791)(191,790)(192,789)
(193,788)(194,787)(195,786)(196,785)(197,784)(198,783)(199,441)(200,451)
(201,450)(202,449)(203,448)(204,447)(205,446)(206,445)(207,444)(208,443)
(209,442)(210,430)(211,440)(212,439)(213,438)(214,437)(215,436)(216,435)
(217,434)(218,433)(219,432)(220,431)(221,452)(222,462)(223,461)(224,460)
(225,459)(226,458)(227,457)(228,456)(229,455)(230,454)(231,453)(232,408)
(233,418)(234,417)(235,416)(236,415)(237,414)(238,413)(239,412)(240,411)
(241,410)(242,409)(243,397)(244,407)(245,406)(246,405)(247,404)(248,403)
(249,402)(250,401)(251,400)(252,399)(253,398)(254,419)(255,429)(256,428)
(257,427)(258,426)(259,425)(260,424)(261,423)(262,422)(263,421)(264,420)
(265,474)(266,484)(267,483)(268,482)(269,481)(270,480)(271,479)(272,478)
(273,477)(274,476)(275,475)(276,463)(277,473)(278,472)(279,471)(280,470)
(281,469)(282,468)(283,467)(284,466)(285,465)(286,464)(287,485)(288,495)
(289,494)(290,493)(291,492)(292,491)(293,490)(294,489)(295,488)(296,487)
(297,486)(298,540)(299,550)(300,549)(301,548)(302,547)(303,546)(304,545)
(305,544)(306,543)(307,542)(308,541)(309,529)(310,539)(311,538)(312,537)
(313,536)(314,535)(315,534)(316,533)(317,532)(318,531)(319,530)(320,551)
(321,561)(322,560)(323,559)(324,558)(325,557)(326,556)(327,555)(328,554)
(329,553)(330,552)(331,507)(332,517)(333,516)(334,515)(335,514)(336,513)
(337,512)(338,511)(339,510)(340,509)(341,508)(342,496)(343,506)(344,505)
(345,504)(346,503)(347,502)(348,501)(349,500)(350,499)(351,498)(352,497)
(353,518)(354,528)(355,527)(356,526)(357,525)(358,524)(359,523)(360,522)
(361,521)(362,520)(363,519)(364,573)(365,583)(366,582)(367,581)(368,580)
(369,579)(370,578)(371,577)(372,576)(373,575)(374,574)(375,562)(376,572)
(377,571)(378,570)(379,569)(380,568)(381,567)(382,566)(383,565)(384,564)
(385,563)(386,584)(387,594)(388,593)(389,592)(390,591)(391,590)(392,589)
(393,588)(394,587)(395,586)(396,585);;
s2 := ( 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);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
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)( 2,649)( 3,648)( 4,647)( 5,646)( 6,645)( 7,644)
( 8,643)( 9,642)( 10,641)( 11,640)( 12,628)( 13,638)( 14,637)( 15,636)
( 16,635)( 17,634)( 18,633)( 19,632)( 20,631)( 21,630)( 22,629)( 23,650)
( 24,660)( 25,659)( 26,658)( 27,657)( 28,656)( 29,655)( 30,654)( 31,653)
( 32,652)( 33,651)( 34,606)( 35,616)( 36,615)( 37,614)( 38,613)( 39,612)
( 40,611)( 41,610)( 42,609)( 43,608)( 44,607)( 45,595)( 46,605)( 47,604)
( 48,603)( 49,602)( 50,601)( 51,600)( 52,599)( 53,598)( 54,597)( 55,596)
( 56,617)( 57,627)( 58,626)( 59,625)( 60,624)( 61,623)( 62,622)( 63,621)
( 64,620)( 65,619)( 66,618)( 67,672)( 68,682)( 69,681)( 70,680)( 71,679)
( 72,678)( 73,677)( 74,676)( 75,675)( 76,674)( 77,673)( 78,661)( 79,671)
( 80,670)( 81,669)( 82,668)( 83,667)( 84,666)( 85,665)( 86,664)( 87,663)
( 88,662)( 89,683)( 90,693)( 91,692)( 92,691)( 93,690)( 94,689)( 95,688)
( 96,687)( 97,686)( 98,685)( 99,684)(100,738)(101,748)(102,747)(103,746)
(104,745)(105,744)(106,743)(107,742)(108,741)(109,740)(110,739)(111,727)
(112,737)(113,736)(114,735)(115,734)(116,733)(117,732)(118,731)(119,730)
(120,729)(121,728)(122,749)(123,759)(124,758)(125,757)(126,756)(127,755)
(128,754)(129,753)(130,752)(131,751)(132,750)(133,705)(134,715)(135,714)
(136,713)(137,712)(138,711)(139,710)(140,709)(141,708)(142,707)(143,706)
(144,694)(145,704)(146,703)(147,702)(148,701)(149,700)(150,699)(151,698)
(152,697)(153,696)(154,695)(155,716)(156,726)(157,725)(158,724)(159,723)
(160,722)(161,721)(162,720)(163,719)(164,718)(165,717)(166,771)(167,781)
(168,780)(169,779)(170,778)(171,777)(172,776)(173,775)(174,774)(175,773)
(176,772)(177,760)(178,770)(179,769)(180,768)(181,767)(182,766)(183,765)
(184,764)(185,763)(186,762)(187,761)(188,782)(189,792)(190,791)(191,790)
(192,789)(193,788)(194,787)(195,786)(196,785)(197,784)(198,783)(199,441)
(200,451)(201,450)(202,449)(203,448)(204,447)(205,446)(206,445)(207,444)
(208,443)(209,442)(210,430)(211,440)(212,439)(213,438)(214,437)(215,436)
(216,435)(217,434)(218,433)(219,432)(220,431)(221,452)(222,462)(223,461)
(224,460)(225,459)(226,458)(227,457)(228,456)(229,455)(230,454)(231,453)
(232,408)(233,418)(234,417)(235,416)(236,415)(237,414)(238,413)(239,412)
(240,411)(241,410)(242,409)(243,397)(244,407)(245,406)(246,405)(247,404)
(248,403)(249,402)(250,401)(251,400)(252,399)(253,398)(254,419)(255,429)
(256,428)(257,427)(258,426)(259,425)(260,424)(261,423)(262,422)(263,421)
(264,420)(265,474)(266,484)(267,483)(268,482)(269,481)(270,480)(271,479)
(272,478)(273,477)(274,476)(275,475)(276,463)(277,473)(278,472)(279,471)
(280,470)(281,469)(282,468)(283,467)(284,466)(285,465)(286,464)(287,485)
(288,495)(289,494)(290,493)(291,492)(292,491)(293,490)(294,489)(295,488)
(296,487)(297,486)(298,540)(299,550)(300,549)(301,548)(302,547)(303,546)
(304,545)(305,544)(306,543)(307,542)(308,541)(309,529)(310,539)(311,538)
(312,537)(313,536)(314,535)(315,534)(316,533)(317,532)(318,531)(319,530)
(320,551)(321,561)(322,560)(323,559)(324,558)(325,557)(326,556)(327,555)
(328,554)(329,553)(330,552)(331,507)(332,517)(333,516)(334,515)(335,514)
(336,513)(337,512)(338,511)(339,510)(340,509)(341,508)(342,496)(343,506)
(344,505)(345,504)(346,503)(347,502)(348,501)(349,500)(350,499)(351,498)
(352,497)(353,518)(354,528)(355,527)(356,526)(357,525)(358,524)(359,523)
(360,522)(361,521)(362,520)(363,519)(364,573)(365,583)(366,582)(367,581)
(368,580)(369,579)(370,578)(371,577)(372,576)(373,575)(374,574)(375,562)
(376,572)(377,571)(378,570)(379,569)(380,568)(381,567)(382,566)(383,565)
(384,564)(385,563)(386,584)(387,594)(388,593)(389,592)(390,591)(391,590)
(392,589)(393,588)(394,587)(395,586)(396,585);
s2 := 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);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >;
References : None.
to this polytope