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# Polytope of Type {2,12,12}

Atlas Canonical Name : {2,12,12}*1728h
if this polytope has a name.
Group : SmallGroup(1728,38382)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 36, 216, 36
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,12}*864g, {2,12,6}*864g
3-fold quotients : {2,12,12}*576a, {2,12,12}*576b, {2,12,12}*576c
4-fold quotients : {2,6,6}*432d
6-fold quotients : {2,6,12}*288a, {2,6,12}*288b, {2,12,6}*288a, {2,12,6}*288b, {2,6,12}*288c, {2,12,6}*288c
9-fold quotients : {2,4,12}*192a, {2,12,4}*192a
12-fold quotients : {2,6,6}*144a, {2,6,6}*144b, {2,6,6}*144c
18-fold quotients : {2,2,12}*96, {2,12,2}*96, {2,4,6}*96a, {2,6,4}*96a
24-fold quotients : {2,3,6}*72, {2,6,3}*72
27-fold quotients : {2,4,4}*64
36-fold quotients : {2,2,6}*48, {2,6,2}*48
54-fold quotients : {2,2,4}*32, {2,4,2}*32
72-fold quotients : {2,2,3}*24, {2,3,2}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  3,651)(  4,653)(  5,652)(  6,657)(  7,659)(  8,658)(  9,654)( 10,656)
( 11,655)( 12,660)( 13,662)( 14,661)( 15,666)( 16,668)( 17,667)( 18,663)
( 19,665)( 20,664)( 21,669)( 22,671)( 23,670)( 24,675)( 25,677)( 26,676)
( 27,672)( 28,674)( 29,673)( 30,678)( 31,680)( 32,679)( 33,684)( 34,686)
( 35,685)( 36,681)( 37,683)( 38,682)( 39,687)( 40,689)( 41,688)( 42,693)
( 43,695)( 44,694)( 45,690)( 46,692)( 47,691)( 48,696)( 49,698)( 50,697)
( 51,702)( 52,704)( 53,703)( 54,699)( 55,701)( 56,700)( 57,705)( 58,707)
( 59,706)( 60,711)( 61,713)( 62,712)( 63,708)( 64,710)( 65,709)( 66,714)
( 67,716)( 68,715)( 69,720)( 70,722)( 71,721)( 72,717)( 73,719)( 74,718)
( 75,723)( 76,725)( 77,724)( 78,729)( 79,731)( 80,730)( 81,726)( 82,728)
( 83,727)( 84,732)( 85,734)( 86,733)( 87,738)( 88,740)( 89,739)( 90,735)
( 91,737)( 92,736)( 93,741)( 94,743)( 95,742)( 96,747)( 97,749)( 98,748)
( 99,744)(100,746)(101,745)(102,750)(103,752)(104,751)(105,756)(106,758)
(107,757)(108,753)(109,755)(110,754)(111,813)(112,815)(113,814)(114,819)
(115,821)(116,820)(117,816)(118,818)(119,817)(120,822)(121,824)(122,823)
(123,828)(124,830)(125,829)(126,825)(127,827)(128,826)(129,831)(130,833)
(131,832)(132,837)(133,839)(134,838)(135,834)(136,836)(137,835)(138,840)
(139,842)(140,841)(141,846)(142,848)(143,847)(144,843)(145,845)(146,844)
(147,849)(148,851)(149,850)(150,855)(151,857)(152,856)(153,852)(154,854)
(155,853)(156,858)(157,860)(158,859)(159,864)(160,866)(161,865)(162,861)
(163,863)(164,862)(165,759)(166,761)(167,760)(168,765)(169,767)(170,766)
(171,762)(172,764)(173,763)(174,768)(175,770)(176,769)(177,774)(178,776)
(179,775)(180,771)(181,773)(182,772)(183,777)(184,779)(185,778)(186,783)
(187,785)(188,784)(189,780)(190,782)(191,781)(192,786)(193,788)(194,787)
(195,792)(196,794)(197,793)(198,789)(199,791)(200,790)(201,795)(202,797)
(203,796)(204,801)(205,803)(206,802)(207,798)(208,800)(209,799)(210,804)
(211,806)(212,805)(213,810)(214,812)(215,811)(216,807)(217,809)(218,808)
(219,462)(220,464)(221,463)(222,468)(223,470)(224,469)(225,465)(226,467)
(227,466)(228,471)(229,473)(230,472)(231,477)(232,479)(233,478)(234,474)
(235,476)(236,475)(237,480)(238,482)(239,481)(240,486)(241,488)(242,487)
(243,483)(244,485)(245,484)(246,435)(247,437)(248,436)(249,441)(250,443)
(251,442)(252,438)(253,440)(254,439)(255,444)(256,446)(257,445)(258,450)
(259,452)(260,451)(261,447)(262,449)(263,448)(264,453)(265,455)(266,454)
(267,459)(268,461)(269,460)(270,456)(271,458)(272,457)(273,516)(274,518)
(275,517)(276,522)(277,524)(278,523)(279,519)(280,521)(281,520)(282,525)
(283,527)(284,526)(285,531)(286,533)(287,532)(288,528)(289,530)(290,529)
(291,534)(292,536)(293,535)(294,540)(295,542)(296,541)(297,537)(298,539)
(299,538)(300,489)(301,491)(302,490)(303,495)(304,497)(305,496)(306,492)
(307,494)(308,493)(309,498)(310,500)(311,499)(312,504)(313,506)(314,505)
(315,501)(316,503)(317,502)(318,507)(319,509)(320,508)(321,513)(322,515)
(323,514)(324,510)(325,512)(326,511)(327,624)(328,626)(329,625)(330,630)
(331,632)(332,631)(333,627)(334,629)(335,628)(336,633)(337,635)(338,634)
(339,639)(340,641)(341,640)(342,636)(343,638)(344,637)(345,642)(346,644)
(347,643)(348,648)(349,650)(350,649)(351,645)(352,647)(353,646)(354,597)
(355,599)(356,598)(357,603)(358,605)(359,604)(360,600)(361,602)(362,601)
(363,606)(364,608)(365,607)(366,612)(367,614)(368,613)(369,609)(370,611)
(371,610)(372,615)(373,617)(374,616)(375,621)(376,623)(377,622)(378,618)
(379,620)(380,619)(381,570)(382,572)(383,571)(384,576)(385,578)(386,577)
(387,573)(388,575)(389,574)(390,579)(391,581)(392,580)(393,585)(394,587)
(395,586)(396,582)(397,584)(398,583)(399,588)(400,590)(401,589)(402,594)
(403,596)(404,595)(405,591)(406,593)(407,592)(408,543)(409,545)(410,544)
(411,549)(412,551)(413,550)(414,546)(415,548)(416,547)(417,552)(418,554)
(419,553)(420,558)(421,560)(422,559)(423,555)(424,557)(425,556)(426,561)
(427,563)(428,562)(429,567)(430,569)(431,568)(432,564)(433,566)(434,565);;
s2 := (  3,763)(  4,762)(  5,764)(  6,760)(  7,759)(  8,761)(  9,766)( 10,765)
( 11,767)( 12,781)( 13,780)( 14,782)( 15,778)( 16,777)( 17,779)( 18,784)
( 19,783)( 20,785)( 21,772)( 22,771)( 23,773)( 24,769)( 25,768)( 26,770)
( 27,775)( 28,774)( 29,776)( 30,790)( 31,789)( 32,791)( 33,787)( 34,786)
( 35,788)( 36,793)( 37,792)( 38,794)( 39,808)( 40,807)( 41,809)( 42,805)
( 43,804)( 44,806)( 45,811)( 46,810)( 47,812)( 48,799)( 49,798)( 50,800)
( 51,796)( 52,795)( 53,797)( 54,802)( 55,801)( 56,803)( 57,817)( 58,816)
( 59,818)( 60,814)( 61,813)( 62,815)( 63,820)( 64,819)( 65,821)( 66,835)
( 67,834)( 68,836)( 69,832)( 70,831)( 71,833)( 72,838)( 73,837)( 74,839)
( 75,826)( 76,825)( 77,827)( 78,823)( 79,822)( 80,824)( 81,829)( 82,828)
( 83,830)( 84,844)( 85,843)( 86,845)( 87,841)( 88,840)( 89,842)( 90,847)
( 91,846)( 92,848)( 93,862)( 94,861)( 95,863)( 96,859)( 97,858)( 98,860)
( 99,865)(100,864)(101,866)(102,853)(103,852)(104,854)(105,850)(106,849)
(107,851)(108,856)(109,855)(110,857)(111,655)(112,654)(113,656)(114,652)
(115,651)(116,653)(117,658)(118,657)(119,659)(120,673)(121,672)(122,674)
(123,670)(124,669)(125,671)(126,676)(127,675)(128,677)(129,664)(130,663)
(131,665)(132,661)(133,660)(134,662)(135,667)(136,666)(137,668)(138,682)
(139,681)(140,683)(141,679)(142,678)(143,680)(144,685)(145,684)(146,686)
(147,700)(148,699)(149,701)(150,697)(151,696)(152,698)(153,703)(154,702)
(155,704)(156,691)(157,690)(158,692)(159,688)(160,687)(161,689)(162,694)
(163,693)(164,695)(165,709)(166,708)(167,710)(168,706)(169,705)(170,707)
(171,712)(172,711)(173,713)(174,727)(175,726)(176,728)(177,724)(178,723)
(179,725)(180,730)(181,729)(182,731)(183,718)(184,717)(185,719)(186,715)
(187,714)(188,716)(189,721)(190,720)(191,722)(192,736)(193,735)(194,737)
(195,733)(196,732)(197,734)(198,739)(199,738)(200,740)(201,754)(202,753)
(203,755)(204,751)(205,750)(206,752)(207,757)(208,756)(209,758)(210,745)
(211,744)(212,746)(213,742)(214,741)(215,743)(216,748)(217,747)(218,749)
(219,574)(220,573)(221,575)(222,571)(223,570)(224,572)(225,577)(226,576)
(227,578)(228,592)(229,591)(230,593)(231,589)(232,588)(233,590)(234,595)
(235,594)(236,596)(237,583)(238,582)(239,584)(240,580)(241,579)(242,581)
(243,586)(244,585)(245,587)(246,547)(247,546)(248,548)(249,544)(250,543)
(251,545)(252,550)(253,549)(254,551)(255,565)(256,564)(257,566)(258,562)
(259,561)(260,563)(261,568)(262,567)(263,569)(264,556)(265,555)(266,557)
(267,553)(268,552)(269,554)(270,559)(271,558)(272,560)(273,628)(274,627)
(275,629)(276,625)(277,624)(278,626)(279,631)(280,630)(281,632)(282,646)
(283,645)(284,647)(285,643)(286,642)(287,644)(288,649)(289,648)(290,650)
(291,637)(292,636)(293,638)(294,634)(295,633)(296,635)(297,640)(298,639)
(299,641)(300,601)(301,600)(302,602)(303,598)(304,597)(305,599)(306,604)
(307,603)(308,605)(309,619)(310,618)(311,620)(312,616)(313,615)(314,617)
(315,622)(316,621)(317,623)(318,610)(319,609)(320,611)(321,607)(322,606)
(323,608)(324,613)(325,612)(326,614)(327,466)(328,465)(329,467)(330,463)
(331,462)(332,464)(333,469)(334,468)(335,470)(336,484)(337,483)(338,485)
(339,481)(340,480)(341,482)(342,487)(343,486)(344,488)(345,475)(346,474)
(347,476)(348,472)(349,471)(350,473)(351,478)(352,477)(353,479)(354,439)
(355,438)(356,440)(357,436)(358,435)(359,437)(360,442)(361,441)(362,443)
(363,457)(364,456)(365,458)(366,454)(367,453)(368,455)(369,460)(370,459)
(371,461)(372,448)(373,447)(374,449)(375,445)(376,444)(377,446)(378,451)
(379,450)(380,452)(381,520)(382,519)(383,521)(384,517)(385,516)(386,518)
(387,523)(388,522)(389,524)(390,538)(391,537)(392,539)(393,535)(394,534)
(395,536)(396,541)(397,540)(398,542)(399,529)(400,528)(401,530)(402,526)
(403,525)(404,527)(405,532)(406,531)(407,533)(408,493)(409,492)(410,494)
(411,490)(412,489)(413,491)(414,496)(415,495)(416,497)(417,511)(418,510)
(419,512)(420,508)(421,507)(422,509)(423,514)(424,513)(425,515)(426,502)
(427,501)(428,503)(429,499)(430,498)(431,500)(432,505)(433,504)(434,506);;
s3 := (  3,552)(  4,554)(  5,553)(  6,555)(  7,557)(  8,556)(  9,558)( 10,560)
( 11,559)( 12,543)( 13,545)( 14,544)( 15,546)( 16,548)( 17,547)( 18,549)
( 19,551)( 20,550)( 21,561)( 22,563)( 23,562)( 24,564)( 25,566)( 26,565)
( 27,567)( 28,569)( 29,568)( 30,579)( 31,581)( 32,580)( 33,582)( 34,584)
( 35,583)( 36,585)( 37,587)( 38,586)( 39,570)( 40,572)( 41,571)( 42,573)
( 43,575)( 44,574)( 45,576)( 46,578)( 47,577)( 48,588)( 49,590)( 50,589)
( 51,591)( 52,593)( 53,592)( 54,594)( 55,596)( 56,595)( 57,606)( 58,608)
( 59,607)( 60,609)( 61,611)( 62,610)( 63,612)( 64,614)( 65,613)( 66,597)
( 67,599)( 68,598)( 69,600)( 70,602)( 71,601)( 72,603)( 73,605)( 74,604)
( 75,615)( 76,617)( 77,616)( 78,618)( 79,620)( 80,619)( 81,621)( 82,623)
( 83,622)( 84,633)( 85,635)( 86,634)( 87,636)( 88,638)( 89,637)( 90,639)
( 91,641)( 92,640)( 93,624)( 94,626)( 95,625)( 96,627)( 97,629)( 98,628)
( 99,630)(100,632)(101,631)(102,642)(103,644)(104,643)(105,645)(106,647)
(107,646)(108,648)(109,650)(110,649)(111,471)(112,473)(113,472)(114,474)
(115,476)(116,475)(117,477)(118,479)(119,478)(120,462)(121,464)(122,463)
(123,465)(124,467)(125,466)(126,468)(127,470)(128,469)(129,480)(130,482)
(131,481)(132,483)(133,485)(134,484)(135,486)(136,488)(137,487)(138,444)
(139,446)(140,445)(141,447)(142,449)(143,448)(144,450)(145,452)(146,451)
(147,435)(148,437)(149,436)(150,438)(151,440)(152,439)(153,441)(154,443)
(155,442)(156,453)(157,455)(158,454)(159,456)(160,458)(161,457)(162,459)
(163,461)(164,460)(165,525)(166,527)(167,526)(168,528)(169,530)(170,529)
(171,531)(172,533)(173,532)(174,516)(175,518)(176,517)(177,519)(178,521)
(179,520)(180,522)(181,524)(182,523)(183,534)(184,536)(185,535)(186,537)
(187,539)(188,538)(189,540)(190,542)(191,541)(192,498)(193,500)(194,499)
(195,501)(196,503)(197,502)(198,504)(199,506)(200,505)(201,489)(202,491)
(203,490)(204,492)(205,494)(206,493)(207,495)(208,497)(209,496)(210,507)
(211,509)(212,508)(213,510)(214,512)(215,511)(216,513)(217,515)(218,514)
(219,822)(220,824)(221,823)(222,825)(223,827)(224,826)(225,828)(226,830)
(227,829)(228,813)(229,815)(230,814)(231,816)(232,818)(233,817)(234,819)
(235,821)(236,820)(237,831)(238,833)(239,832)(240,834)(241,836)(242,835)
(243,837)(244,839)(245,838)(246,849)(247,851)(248,850)(249,852)(250,854)
(251,853)(252,855)(253,857)(254,856)(255,840)(256,842)(257,841)(258,843)
(259,845)(260,844)(261,846)(262,848)(263,847)(264,858)(265,860)(266,859)
(267,861)(268,863)(269,862)(270,864)(271,866)(272,865)(273,768)(274,770)
(275,769)(276,771)(277,773)(278,772)(279,774)(280,776)(281,775)(282,759)
(283,761)(284,760)(285,762)(286,764)(287,763)(288,765)(289,767)(290,766)
(291,777)(292,779)(293,778)(294,780)(295,782)(296,781)(297,783)(298,785)
(299,784)(300,795)(301,797)(302,796)(303,798)(304,800)(305,799)(306,801)
(307,803)(308,802)(309,786)(310,788)(311,787)(312,789)(313,791)(314,790)
(315,792)(316,794)(317,793)(318,804)(319,806)(320,805)(321,807)(322,809)
(323,808)(324,810)(325,812)(326,811)(327,741)(328,743)(329,742)(330,744)
(331,746)(332,745)(333,747)(334,749)(335,748)(336,732)(337,734)(338,733)
(339,735)(340,737)(341,736)(342,738)(343,740)(344,739)(345,750)(346,752)
(347,751)(348,753)(349,755)(350,754)(351,756)(352,758)(353,757)(354,714)
(355,716)(356,715)(357,717)(358,719)(359,718)(360,720)(361,722)(362,721)
(363,705)(364,707)(365,706)(366,708)(367,710)(368,709)(369,711)(370,713)
(371,712)(372,723)(373,725)(374,724)(375,726)(376,728)(377,727)(378,729)
(379,731)(380,730)(381,687)(382,689)(383,688)(384,690)(385,692)(386,691)
(387,693)(388,695)(389,694)(390,678)(391,680)(392,679)(393,681)(394,683)
(395,682)(396,684)(397,686)(398,685)(399,696)(400,698)(401,697)(402,699)
(403,701)(404,700)(405,702)(406,704)(407,703)(408,660)(409,662)(410,661)
(411,663)(412,665)(413,664)(414,666)(415,668)(416,667)(417,651)(418,653)
(419,652)(420,654)(421,656)(422,655)(423,657)(424,659)(425,658)(426,669)
(427,671)(428,670)(429,672)(430,674)(431,673)(432,675)(433,677)(434,676);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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(866)!(1,2);
s1 := Sym(866)!(  3,651)(  4,653)(  5,652)(  6,657)(  7,659)(  8,658)(  9,654)
( 10,656)( 11,655)( 12,660)( 13,662)( 14,661)( 15,666)( 16,668)( 17,667)
( 18,663)( 19,665)( 20,664)( 21,669)( 22,671)( 23,670)( 24,675)( 25,677)
( 26,676)( 27,672)( 28,674)( 29,673)( 30,678)( 31,680)( 32,679)( 33,684)
( 34,686)( 35,685)( 36,681)( 37,683)( 38,682)( 39,687)( 40,689)( 41,688)
( 42,693)( 43,695)( 44,694)( 45,690)( 46,692)( 47,691)( 48,696)( 49,698)
( 50,697)( 51,702)( 52,704)( 53,703)( 54,699)( 55,701)( 56,700)( 57,705)
( 58,707)( 59,706)( 60,711)( 61,713)( 62,712)( 63,708)( 64,710)( 65,709)
( 66,714)( 67,716)( 68,715)( 69,720)( 70,722)( 71,721)( 72,717)( 73,719)
( 74,718)( 75,723)( 76,725)( 77,724)( 78,729)( 79,731)( 80,730)( 81,726)
( 82,728)( 83,727)( 84,732)( 85,734)( 86,733)( 87,738)( 88,740)( 89,739)
( 90,735)( 91,737)( 92,736)( 93,741)( 94,743)( 95,742)( 96,747)( 97,749)
( 98,748)( 99,744)(100,746)(101,745)(102,750)(103,752)(104,751)(105,756)
(106,758)(107,757)(108,753)(109,755)(110,754)(111,813)(112,815)(113,814)
(114,819)(115,821)(116,820)(117,816)(118,818)(119,817)(120,822)(121,824)
(122,823)(123,828)(124,830)(125,829)(126,825)(127,827)(128,826)(129,831)
(130,833)(131,832)(132,837)(133,839)(134,838)(135,834)(136,836)(137,835)
(138,840)(139,842)(140,841)(141,846)(142,848)(143,847)(144,843)(145,845)
(146,844)(147,849)(148,851)(149,850)(150,855)(151,857)(152,856)(153,852)
(154,854)(155,853)(156,858)(157,860)(158,859)(159,864)(160,866)(161,865)
(162,861)(163,863)(164,862)(165,759)(166,761)(167,760)(168,765)(169,767)
(170,766)(171,762)(172,764)(173,763)(174,768)(175,770)(176,769)(177,774)
(178,776)(179,775)(180,771)(181,773)(182,772)(183,777)(184,779)(185,778)
(186,783)(187,785)(188,784)(189,780)(190,782)(191,781)(192,786)(193,788)
(194,787)(195,792)(196,794)(197,793)(198,789)(199,791)(200,790)(201,795)
(202,797)(203,796)(204,801)(205,803)(206,802)(207,798)(208,800)(209,799)
(210,804)(211,806)(212,805)(213,810)(214,812)(215,811)(216,807)(217,809)
(218,808)(219,462)(220,464)(221,463)(222,468)(223,470)(224,469)(225,465)
(226,467)(227,466)(228,471)(229,473)(230,472)(231,477)(232,479)(233,478)
(234,474)(235,476)(236,475)(237,480)(238,482)(239,481)(240,486)(241,488)
(242,487)(243,483)(244,485)(245,484)(246,435)(247,437)(248,436)(249,441)
(250,443)(251,442)(252,438)(253,440)(254,439)(255,444)(256,446)(257,445)
(258,450)(259,452)(260,451)(261,447)(262,449)(263,448)(264,453)(265,455)
(266,454)(267,459)(268,461)(269,460)(270,456)(271,458)(272,457)(273,516)
(274,518)(275,517)(276,522)(277,524)(278,523)(279,519)(280,521)(281,520)
(282,525)(283,527)(284,526)(285,531)(286,533)(287,532)(288,528)(289,530)
(290,529)(291,534)(292,536)(293,535)(294,540)(295,542)(296,541)(297,537)
(298,539)(299,538)(300,489)(301,491)(302,490)(303,495)(304,497)(305,496)
(306,492)(307,494)(308,493)(309,498)(310,500)(311,499)(312,504)(313,506)
(314,505)(315,501)(316,503)(317,502)(318,507)(319,509)(320,508)(321,513)
(322,515)(323,514)(324,510)(325,512)(326,511)(327,624)(328,626)(329,625)
(330,630)(331,632)(332,631)(333,627)(334,629)(335,628)(336,633)(337,635)
(338,634)(339,639)(340,641)(341,640)(342,636)(343,638)(344,637)(345,642)
(346,644)(347,643)(348,648)(349,650)(350,649)(351,645)(352,647)(353,646)
(354,597)(355,599)(356,598)(357,603)(358,605)(359,604)(360,600)(361,602)
(362,601)(363,606)(364,608)(365,607)(366,612)(367,614)(368,613)(369,609)
(370,611)(371,610)(372,615)(373,617)(374,616)(375,621)(376,623)(377,622)
(378,618)(379,620)(380,619)(381,570)(382,572)(383,571)(384,576)(385,578)
(386,577)(387,573)(388,575)(389,574)(390,579)(391,581)(392,580)(393,585)
(394,587)(395,586)(396,582)(397,584)(398,583)(399,588)(400,590)(401,589)
(402,594)(403,596)(404,595)(405,591)(406,593)(407,592)(408,543)(409,545)
(410,544)(411,549)(412,551)(413,550)(414,546)(415,548)(416,547)(417,552)
(418,554)(419,553)(420,558)(421,560)(422,559)(423,555)(424,557)(425,556)
(426,561)(427,563)(428,562)(429,567)(430,569)(431,568)(432,564)(433,566)
(434,565);
s2 := Sym(866)!(  3,763)(  4,762)(  5,764)(  6,760)(  7,759)(  8,761)(  9,766)
( 10,765)( 11,767)( 12,781)( 13,780)( 14,782)( 15,778)( 16,777)( 17,779)
( 18,784)( 19,783)( 20,785)( 21,772)( 22,771)( 23,773)( 24,769)( 25,768)
( 26,770)( 27,775)( 28,774)( 29,776)( 30,790)( 31,789)( 32,791)( 33,787)
( 34,786)( 35,788)( 36,793)( 37,792)( 38,794)( 39,808)( 40,807)( 41,809)
( 42,805)( 43,804)( 44,806)( 45,811)( 46,810)( 47,812)( 48,799)( 49,798)
( 50,800)( 51,796)( 52,795)( 53,797)( 54,802)( 55,801)( 56,803)( 57,817)
( 58,816)( 59,818)( 60,814)( 61,813)( 62,815)( 63,820)( 64,819)( 65,821)
( 66,835)( 67,834)( 68,836)( 69,832)( 70,831)( 71,833)( 72,838)( 73,837)
( 74,839)( 75,826)( 76,825)( 77,827)( 78,823)( 79,822)( 80,824)( 81,829)
( 82,828)( 83,830)( 84,844)( 85,843)( 86,845)( 87,841)( 88,840)( 89,842)
( 90,847)( 91,846)( 92,848)( 93,862)( 94,861)( 95,863)( 96,859)( 97,858)
( 98,860)( 99,865)(100,864)(101,866)(102,853)(103,852)(104,854)(105,850)
(106,849)(107,851)(108,856)(109,855)(110,857)(111,655)(112,654)(113,656)
(114,652)(115,651)(116,653)(117,658)(118,657)(119,659)(120,673)(121,672)
(122,674)(123,670)(124,669)(125,671)(126,676)(127,675)(128,677)(129,664)
(130,663)(131,665)(132,661)(133,660)(134,662)(135,667)(136,666)(137,668)
(138,682)(139,681)(140,683)(141,679)(142,678)(143,680)(144,685)(145,684)
(146,686)(147,700)(148,699)(149,701)(150,697)(151,696)(152,698)(153,703)
(154,702)(155,704)(156,691)(157,690)(158,692)(159,688)(160,687)(161,689)
(162,694)(163,693)(164,695)(165,709)(166,708)(167,710)(168,706)(169,705)
(170,707)(171,712)(172,711)(173,713)(174,727)(175,726)(176,728)(177,724)
(178,723)(179,725)(180,730)(181,729)(182,731)(183,718)(184,717)(185,719)
(186,715)(187,714)(188,716)(189,721)(190,720)(191,722)(192,736)(193,735)
(194,737)(195,733)(196,732)(197,734)(198,739)(199,738)(200,740)(201,754)
(202,753)(203,755)(204,751)(205,750)(206,752)(207,757)(208,756)(209,758)
(210,745)(211,744)(212,746)(213,742)(214,741)(215,743)(216,748)(217,747)
(218,749)(219,574)(220,573)(221,575)(222,571)(223,570)(224,572)(225,577)
(226,576)(227,578)(228,592)(229,591)(230,593)(231,589)(232,588)(233,590)
(234,595)(235,594)(236,596)(237,583)(238,582)(239,584)(240,580)(241,579)
(242,581)(243,586)(244,585)(245,587)(246,547)(247,546)(248,548)(249,544)
(250,543)(251,545)(252,550)(253,549)(254,551)(255,565)(256,564)(257,566)
(258,562)(259,561)(260,563)(261,568)(262,567)(263,569)(264,556)(265,555)
(266,557)(267,553)(268,552)(269,554)(270,559)(271,558)(272,560)(273,628)
(274,627)(275,629)(276,625)(277,624)(278,626)(279,631)(280,630)(281,632)
(282,646)(283,645)(284,647)(285,643)(286,642)(287,644)(288,649)(289,648)
(290,650)(291,637)(292,636)(293,638)(294,634)(295,633)(296,635)(297,640)
(298,639)(299,641)(300,601)(301,600)(302,602)(303,598)(304,597)(305,599)
(306,604)(307,603)(308,605)(309,619)(310,618)(311,620)(312,616)(313,615)
(314,617)(315,622)(316,621)(317,623)(318,610)(319,609)(320,611)(321,607)
(322,606)(323,608)(324,613)(325,612)(326,614)(327,466)(328,465)(329,467)
(330,463)(331,462)(332,464)(333,469)(334,468)(335,470)(336,484)(337,483)
(338,485)(339,481)(340,480)(341,482)(342,487)(343,486)(344,488)(345,475)
(346,474)(347,476)(348,472)(349,471)(350,473)(351,478)(352,477)(353,479)
(354,439)(355,438)(356,440)(357,436)(358,435)(359,437)(360,442)(361,441)
(362,443)(363,457)(364,456)(365,458)(366,454)(367,453)(368,455)(369,460)
(370,459)(371,461)(372,448)(373,447)(374,449)(375,445)(376,444)(377,446)
(378,451)(379,450)(380,452)(381,520)(382,519)(383,521)(384,517)(385,516)
(386,518)(387,523)(388,522)(389,524)(390,538)(391,537)(392,539)(393,535)
(394,534)(395,536)(396,541)(397,540)(398,542)(399,529)(400,528)(401,530)
(402,526)(403,525)(404,527)(405,532)(406,531)(407,533)(408,493)(409,492)
(410,494)(411,490)(412,489)(413,491)(414,496)(415,495)(416,497)(417,511)
(418,510)(419,512)(420,508)(421,507)(422,509)(423,514)(424,513)(425,515)
(426,502)(427,501)(428,503)(429,499)(430,498)(431,500)(432,505)(433,504)
(434,506);
s3 := Sym(866)!(  3,552)(  4,554)(  5,553)(  6,555)(  7,557)(  8,556)(  9,558)
( 10,560)( 11,559)( 12,543)( 13,545)( 14,544)( 15,546)( 16,548)( 17,547)
( 18,549)( 19,551)( 20,550)( 21,561)( 22,563)( 23,562)( 24,564)( 25,566)
( 26,565)( 27,567)( 28,569)( 29,568)( 30,579)( 31,581)( 32,580)( 33,582)
( 34,584)( 35,583)( 36,585)( 37,587)( 38,586)( 39,570)( 40,572)( 41,571)
( 42,573)( 43,575)( 44,574)( 45,576)( 46,578)( 47,577)( 48,588)( 49,590)
( 50,589)( 51,591)( 52,593)( 53,592)( 54,594)( 55,596)( 56,595)( 57,606)
( 58,608)( 59,607)( 60,609)( 61,611)( 62,610)( 63,612)( 64,614)( 65,613)
( 66,597)( 67,599)( 68,598)( 69,600)( 70,602)( 71,601)( 72,603)( 73,605)
( 74,604)( 75,615)( 76,617)( 77,616)( 78,618)( 79,620)( 80,619)( 81,621)
( 82,623)( 83,622)( 84,633)( 85,635)( 86,634)( 87,636)( 88,638)( 89,637)
( 90,639)( 91,641)( 92,640)( 93,624)( 94,626)( 95,625)( 96,627)( 97,629)
( 98,628)( 99,630)(100,632)(101,631)(102,642)(103,644)(104,643)(105,645)
(106,647)(107,646)(108,648)(109,650)(110,649)(111,471)(112,473)(113,472)
(114,474)(115,476)(116,475)(117,477)(118,479)(119,478)(120,462)(121,464)
(122,463)(123,465)(124,467)(125,466)(126,468)(127,470)(128,469)(129,480)
(130,482)(131,481)(132,483)(133,485)(134,484)(135,486)(136,488)(137,487)
(138,444)(139,446)(140,445)(141,447)(142,449)(143,448)(144,450)(145,452)
(146,451)(147,435)(148,437)(149,436)(150,438)(151,440)(152,439)(153,441)
(154,443)(155,442)(156,453)(157,455)(158,454)(159,456)(160,458)(161,457)
(162,459)(163,461)(164,460)(165,525)(166,527)(167,526)(168,528)(169,530)
(170,529)(171,531)(172,533)(173,532)(174,516)(175,518)(176,517)(177,519)
(178,521)(179,520)(180,522)(181,524)(182,523)(183,534)(184,536)(185,535)
(186,537)(187,539)(188,538)(189,540)(190,542)(191,541)(192,498)(193,500)
(194,499)(195,501)(196,503)(197,502)(198,504)(199,506)(200,505)(201,489)
(202,491)(203,490)(204,492)(205,494)(206,493)(207,495)(208,497)(209,496)
(210,507)(211,509)(212,508)(213,510)(214,512)(215,511)(216,513)(217,515)
(218,514)(219,822)(220,824)(221,823)(222,825)(223,827)(224,826)(225,828)
(226,830)(227,829)(228,813)(229,815)(230,814)(231,816)(232,818)(233,817)
(234,819)(235,821)(236,820)(237,831)(238,833)(239,832)(240,834)(241,836)
(242,835)(243,837)(244,839)(245,838)(246,849)(247,851)(248,850)(249,852)
(250,854)(251,853)(252,855)(253,857)(254,856)(255,840)(256,842)(257,841)
(258,843)(259,845)(260,844)(261,846)(262,848)(263,847)(264,858)(265,860)
(266,859)(267,861)(268,863)(269,862)(270,864)(271,866)(272,865)(273,768)
(274,770)(275,769)(276,771)(277,773)(278,772)(279,774)(280,776)(281,775)
(282,759)(283,761)(284,760)(285,762)(286,764)(287,763)(288,765)(289,767)
(290,766)(291,777)(292,779)(293,778)(294,780)(295,782)(296,781)(297,783)
(298,785)(299,784)(300,795)(301,797)(302,796)(303,798)(304,800)(305,799)
(306,801)(307,803)(308,802)(309,786)(310,788)(311,787)(312,789)(313,791)
(314,790)(315,792)(316,794)(317,793)(318,804)(319,806)(320,805)(321,807)
(322,809)(323,808)(324,810)(325,812)(326,811)(327,741)(328,743)(329,742)
(330,744)(331,746)(332,745)(333,747)(334,749)(335,748)(336,732)(337,734)
(338,733)(339,735)(340,737)(341,736)(342,738)(343,740)(344,739)(345,750)
(346,752)(347,751)(348,753)(349,755)(350,754)(351,756)(352,758)(353,757)
(354,714)(355,716)(356,715)(357,717)(358,719)(359,718)(360,720)(361,722)
(362,721)(363,705)(364,707)(365,706)(366,708)(367,710)(368,709)(369,711)
(370,713)(371,712)(372,723)(373,725)(374,724)(375,726)(376,728)(377,727)
(378,729)(379,731)(380,730)(381,687)(382,689)(383,688)(384,690)(385,692)
(386,691)(387,693)(388,695)(389,694)(390,678)(391,680)(392,679)(393,681)
(394,683)(395,682)(396,684)(397,686)(398,685)(399,696)(400,698)(401,697)
(402,699)(403,701)(404,700)(405,702)(406,704)(407,703)(408,660)(409,662)
(410,661)(411,663)(412,665)(413,664)(414,666)(415,668)(416,667)(417,651)
(418,653)(419,652)(420,654)(421,656)(422,655)(423,657)(424,659)(425,658)
(426,669)(427,671)(428,670)(429,672)(430,674)(431,673)(432,675)(433,677)
(434,676);
poly := sub<Sym(866)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope