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# Polytope of Type {6,12}

Atlas Canonical Name : {6,12}*1296i
if this polytope has a name.
Group : SmallGroup(1296,2077)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 54, 324, 108
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {6,6}*648e
3-fold quotients : {6,12}*432c, {6,12}*432g
6-fold quotients : {6,6}*216c, {6,6}*216d
9-fold quotients : {6,12}*144a, {6,12}*144b, {6,12}*144c
12-fold quotients : {3,6}*108
18-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
27-fold quotients : {2,12}*48, {6,4}*48a
36-fold quotients : {3,6}*36, {6,3}*36
54-fold quotients : {2,6}*24, {6,2}*24
81-fold quotients : {2,4}*16
108-fold quotients : {2,3}*12, {3,2}*12
162-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,487)(  2,488)(  3,489)(  4,490)(  5,491)(  6,492)(  7,493)(  8,494)
(  9,495)( 10,505)( 11,506)( 12,507)( 13,508)( 14,509)( 15,510)( 16,511)
( 17,512)( 18,513)( 19,496)( 20,497)( 21,498)( 22,499)( 23,500)( 24,501)
( 25,502)( 26,503)( 27,504)( 28,541)( 29,542)( 30,543)( 31,544)( 32,545)
( 33,546)( 34,547)( 35,548)( 36,549)( 37,559)( 38,560)( 39,561)( 40,562)
( 41,563)( 42,564)( 43,565)( 44,566)( 45,567)( 46,550)( 47,551)( 48,552)
( 49,553)( 50,554)( 51,555)( 52,556)( 53,557)( 54,558)( 55,514)( 56,515)
( 57,516)( 58,517)( 59,518)( 60,519)( 61,520)( 62,521)( 63,522)( 64,532)
( 65,533)( 66,534)( 67,535)( 68,536)( 69,537)( 70,538)( 71,539)( 72,540)
( 73,523)( 74,524)( 75,525)( 76,526)( 77,527)( 78,528)( 79,529)( 80,530)
( 81,531)( 82,568)( 83,569)( 84,570)( 85,571)( 86,572)( 87,573)( 88,574)
( 89,575)( 90,576)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,577)(101,578)(102,579)(103,580)(104,581)
(105,582)(106,583)(107,584)(108,585)(109,622)(110,623)(111,624)(112,625)
(113,626)(114,627)(115,628)(116,629)(117,630)(118,640)(119,641)(120,642)
(121,643)(122,644)(123,645)(124,646)(125,647)(126,648)(127,631)(128,632)
(129,633)(130,634)(131,635)(132,636)(133,637)(134,638)(135,639)(136,595)
(137,596)(138,597)(139,598)(140,599)(141,600)(142,601)(143,602)(144,603)
(145,613)(146,614)(147,615)(148,616)(149,617)(150,618)(151,619)(152,620)
(153,621)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(161,611)(162,612)(163,406)(164,407)(165,408)(166,409)(167,410)(168,411)
(169,412)(170,413)(171,414)(172,424)(173,425)(174,426)(175,427)(176,428)
(177,429)(178,430)(179,431)(180,432)(181,415)(182,416)(183,417)(184,418)
(185,419)(186,420)(187,421)(188,422)(189,423)(190,460)(191,461)(192,462)
(193,463)(194,464)(195,465)(196,466)(197,467)(198,468)(199,478)(200,479)
(201,480)(202,481)(203,482)(204,483)(205,484)(206,485)(207,486)(208,469)
(209,470)(210,471)(211,472)(212,473)(213,474)(214,475)(215,476)(216,477)
(217,433)(218,434)(219,435)(220,436)(221,437)(222,438)(223,439)(224,440)
(225,441)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)(232,457)
(233,458)(234,459)(235,442)(236,443)(237,444)(238,445)(239,446)(240,447)
(241,448)(242,449)(243,450)(244,325)(245,326)(246,327)(247,328)(248,329)
(249,330)(250,331)(251,332)(252,333)(253,343)(254,344)(255,345)(256,346)
(257,347)(258,348)(259,349)(260,350)(261,351)(262,334)(263,335)(264,336)
(265,337)(266,338)(267,339)(268,340)(269,341)(270,342)(271,379)(272,380)
(273,381)(274,382)(275,383)(276,384)(277,385)(278,386)(279,387)(280,397)
(281,398)(282,399)(283,400)(284,401)(285,402)(286,403)(287,404)(288,405)
(289,388)(290,389)(291,390)(292,391)(293,392)(294,393)(295,394)(296,395)
(297,396)(298,352)(299,353)(300,354)(301,355)(302,356)(303,357)(304,358)
(305,359)(306,360)(307,370)(308,371)(309,372)(310,373)(311,374)(312,375)
(313,376)(314,377)(315,378)(316,361)(317,362)(318,363)(319,364)(320,365)
(321,366)(322,367)(323,368)(324,369);;
s1 := (  1,551)(  2,552)(  3,550)(  4,557)(  5,558)(  6,556)(  7,554)(  8,555)
(  9,553)( 10,543)( 11,541)( 12,542)( 13,549)( 14,547)( 15,548)( 16,546)
( 17,544)( 18,545)( 19,559)( 20,560)( 21,561)( 22,565)( 23,566)( 24,567)
( 25,562)( 26,563)( 27,564)( 28,524)( 29,525)( 30,523)( 31,530)( 32,531)
( 33,529)( 34,527)( 35,528)( 36,526)( 37,516)( 38,514)( 39,515)( 40,522)
( 41,520)( 42,521)( 43,519)( 44,517)( 45,518)( 46,532)( 47,533)( 48,534)
( 49,538)( 50,539)( 51,540)( 52,535)( 53,536)( 54,537)( 55,497)( 56,498)
( 57,496)( 58,503)( 59,504)( 60,502)( 61,500)( 62,501)( 63,499)( 64,489)
( 65,487)( 66,488)( 67,495)( 68,493)( 69,494)( 70,492)( 71,490)( 72,491)
( 73,505)( 74,506)( 75,507)( 76,511)( 77,512)( 78,513)( 79,508)( 80,509)
( 81,510)( 82,632)( 83,633)( 84,631)( 85,638)( 86,639)( 87,637)( 88,635)
( 89,636)( 90,634)( 91,624)( 92,622)( 93,623)( 94,630)( 95,628)( 96,629)
( 97,627)( 98,625)( 99,626)(100,640)(101,641)(102,642)(103,646)(104,647)
(105,648)(106,643)(107,644)(108,645)(109,605)(110,606)(111,604)(112,611)
(113,612)(114,610)(115,608)(116,609)(117,607)(118,597)(119,595)(120,596)
(121,603)(122,601)(123,602)(124,600)(125,598)(126,599)(127,613)(128,614)
(129,615)(130,619)(131,620)(132,621)(133,616)(134,617)(135,618)(136,578)
(137,579)(138,577)(139,584)(140,585)(141,583)(142,581)(143,582)(144,580)
(145,570)(146,568)(147,569)(148,576)(149,574)(150,575)(151,573)(152,571)
(153,572)(154,586)(155,587)(156,588)(157,592)(158,593)(159,594)(160,589)
(161,590)(162,591)(163,389)(164,390)(165,388)(166,395)(167,396)(168,394)
(169,392)(170,393)(171,391)(172,381)(173,379)(174,380)(175,387)(176,385)
(177,386)(178,384)(179,382)(180,383)(181,397)(182,398)(183,399)(184,403)
(185,404)(186,405)(187,400)(188,401)(189,402)(190,362)(191,363)(192,361)
(193,368)(194,369)(195,367)(196,365)(197,366)(198,364)(199,354)(200,352)
(201,353)(202,360)(203,358)(204,359)(205,357)(206,355)(207,356)(208,370)
(209,371)(210,372)(211,376)(212,377)(213,378)(214,373)(215,374)(216,375)
(217,335)(218,336)(219,334)(220,341)(221,342)(222,340)(223,338)(224,339)
(225,337)(226,327)(227,325)(228,326)(229,333)(230,331)(231,332)(232,330)
(233,328)(234,329)(235,343)(236,344)(237,345)(238,349)(239,350)(240,351)
(241,346)(242,347)(243,348)(244,470)(245,471)(246,469)(247,476)(248,477)
(249,475)(250,473)(251,474)(252,472)(253,462)(254,460)(255,461)(256,468)
(257,466)(258,467)(259,465)(260,463)(261,464)(262,478)(263,479)(264,480)
(265,484)(266,485)(267,486)(268,481)(269,482)(270,483)(271,443)(272,444)
(273,442)(274,449)(275,450)(276,448)(277,446)(278,447)(279,445)(280,435)
(281,433)(282,434)(283,441)(284,439)(285,440)(286,438)(287,436)(288,437)
(289,451)(290,452)(291,453)(292,457)(293,458)(294,459)(295,454)(296,455)
(297,456)(298,416)(299,417)(300,415)(301,422)(302,423)(303,421)(304,419)
(305,420)(306,418)(307,408)(308,406)(309,407)(310,414)(311,412)(312,413)
(313,411)(314,409)(315,410)(316,424)(317,425)(318,426)(319,430)(320,431)
(321,432)(322,427)(323,428)(324,429);;
s2 := (  1,328)(  2,330)(  3,329)(  4,325)(  5,327)(  6,326)(  7,331)(  8,333)
(  9,332)( 10,337)( 11,339)( 12,338)( 13,334)( 14,336)( 15,335)( 16,340)
( 17,342)( 18,341)( 19,346)( 20,348)( 21,347)( 22,343)( 23,345)( 24,344)
( 25,349)( 26,351)( 27,350)( 28,382)( 29,384)( 30,383)( 31,379)( 32,381)
( 33,380)( 34,385)( 35,387)( 36,386)( 37,391)( 38,393)( 39,392)( 40,388)
( 41,390)( 42,389)( 43,394)( 44,396)( 45,395)( 46,400)( 47,402)( 48,401)
( 49,397)( 50,399)( 51,398)( 52,403)( 53,405)( 54,404)( 55,355)( 56,357)
( 57,356)( 58,352)( 59,354)( 60,353)( 61,358)( 62,360)( 63,359)( 64,364)
( 65,366)( 66,365)( 67,361)( 68,363)( 69,362)( 70,367)( 71,369)( 72,368)
( 73,373)( 74,375)( 75,374)( 76,370)( 77,372)( 78,371)( 79,376)( 80,378)
( 81,377)( 82,409)( 83,411)( 84,410)( 85,406)( 86,408)( 87,407)( 88,412)
( 89,414)( 90,413)( 91,418)( 92,420)( 93,419)( 94,415)( 95,417)( 96,416)
( 97,421)( 98,423)( 99,422)(100,427)(101,429)(102,428)(103,424)(104,426)
(105,425)(106,430)(107,432)(108,431)(109,463)(110,465)(111,464)(112,460)
(113,462)(114,461)(115,466)(116,468)(117,467)(118,472)(119,474)(120,473)
(121,469)(122,471)(123,470)(124,475)(125,477)(126,476)(127,481)(128,483)
(129,482)(130,478)(131,480)(132,479)(133,484)(134,486)(135,485)(136,436)
(137,438)(138,437)(139,433)(140,435)(141,434)(142,439)(143,441)(144,440)
(145,445)(146,447)(147,446)(148,442)(149,444)(150,443)(151,448)(152,450)
(153,449)(154,454)(155,456)(156,455)(157,451)(158,453)(159,452)(160,457)
(161,459)(162,458)(163,571)(164,573)(165,572)(166,568)(167,570)(168,569)
(169,574)(170,576)(171,575)(172,580)(173,582)(174,581)(175,577)(176,579)
(177,578)(178,583)(179,585)(180,584)(181,589)(182,591)(183,590)(184,586)
(185,588)(186,587)(187,592)(188,594)(189,593)(190,625)(191,627)(192,626)
(193,622)(194,624)(195,623)(196,628)(197,630)(198,629)(199,634)(200,636)
(201,635)(202,631)(203,633)(204,632)(205,637)(206,639)(207,638)(208,643)
(209,645)(210,644)(211,640)(212,642)(213,641)(214,646)(215,648)(216,647)
(217,598)(218,600)(219,599)(220,595)(221,597)(222,596)(223,601)(224,603)
(225,602)(226,607)(227,609)(228,608)(229,604)(230,606)(231,605)(232,610)
(233,612)(234,611)(235,616)(236,618)(237,617)(238,613)(239,615)(240,614)
(241,619)(242,621)(243,620)(244,490)(245,492)(246,491)(247,487)(248,489)
(249,488)(250,493)(251,495)(252,494)(253,499)(254,501)(255,500)(256,496)
(257,498)(258,497)(259,502)(260,504)(261,503)(262,508)(263,510)(264,509)
(265,505)(266,507)(267,506)(268,511)(269,513)(270,512)(271,544)(272,546)
(273,545)(274,541)(275,543)(276,542)(277,547)(278,549)(279,548)(280,553)
(281,555)(282,554)(283,550)(284,552)(285,551)(286,556)(287,558)(288,557)
(289,562)(290,564)(291,563)(292,559)(293,561)(294,560)(295,565)(296,567)
(297,566)(298,517)(299,519)(300,518)(301,514)(302,516)(303,515)(304,520)
(305,522)(306,521)(307,526)(308,528)(309,527)(310,523)(311,525)(312,524)
(313,529)(314,531)(315,530)(316,535)(317,537)(318,536)(319,532)(320,534)
(321,533)(322,538)(323,540)(324,539);;
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*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope