Polytope of Type {36,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,6}*1296l
if this polytope has a name.
Group : SmallGroup(1296,2007)
Rank : 3
Schlafli Type : {36,6}
Number of vertices, edges, etc : 108, 324, 18
Order of s₀s₁s₂ : 36
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   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 : {18,6}*648i
   3-fold quotients : {36,6}*432a, {36,6}*432b, {12,6}*432g
   6-fold quotients : {18,6}*216a, {18,6}*216b, {6,6}*216d
   9-fold quotients : {36,2}*144, {12,6}*144a, {12,6}*144b, {12,6}*144c
   12-fold quotients : {9,6}*108
   18-fold quotients : {18,2}*72, {6,6}*72a, {6,6}*72b, {6,6}*72c
   27-fold quotients : {12,2}*48, {4,6}*48a
   36-fold quotients : {9,2}*36, {3,6}*36, {6,3}*36
   54-fold quotients : {2,6}*24, {6,2}*24
   81-fold quotients : {4,2}*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 := (  1,325)(  2,327)(  3,326)(  4,333)(  5,332)(  6,331)(  7,330)(  8,329)
(  9,328)( 10,334)( 11,336)( 12,335)( 13,342)( 14,341)( 15,340)( 16,339)
( 17,338)( 18,337)( 19,343)( 20,345)( 21,344)( 22,351)( 23,350)( 24,349)
( 25,348)( 26,347)( 27,346)( 28,379)( 29,381)( 30,380)( 31,387)( 32,386)
( 33,385)( 34,384)( 35,383)( 36,382)( 37,388)( 38,390)( 39,389)( 40,396)
( 41,395)( 42,394)( 43,393)( 44,392)( 45,391)( 46,397)( 47,399)( 48,398)
( 49,405)( 50,404)( 51,403)( 52,402)( 53,401)( 54,400)( 55,352)( 56,354)
( 57,353)( 58,360)( 59,359)( 60,358)( 61,357)( 62,356)( 63,355)( 64,361)
( 65,363)( 66,362)( 67,369)( 68,368)( 69,367)( 70,366)( 71,365)( 72,364)
( 73,370)( 74,372)( 75,371)( 76,378)( 77,377)( 78,376)( 79,375)( 80,374)
( 81,373)( 82,406)( 83,408)( 84,407)( 85,414)( 86,413)( 87,412)( 88,411)
( 89,410)( 90,409)( 91,415)( 92,417)( 93,416)( 94,423)( 95,422)( 96,421)
( 97,420)( 98,419)( 99,418)(100,424)(101,426)(102,425)(103,432)(104,431)
(105,430)(106,429)(107,428)(108,427)(109,460)(110,462)(111,461)(112,468)
(113,467)(114,466)(115,465)(116,464)(117,463)(118,469)(119,471)(120,470)
(121,477)(122,476)(123,475)(124,474)(125,473)(126,472)(127,478)(128,480)
(129,479)(130,486)(131,485)(132,484)(133,483)(134,482)(135,481)(136,433)
(137,435)(138,434)(139,441)(140,440)(141,439)(142,438)(143,437)(144,436)
(145,442)(146,444)(147,443)(148,450)(149,449)(150,448)(151,447)(152,446)
(153,445)(154,451)(155,453)(156,452)(157,459)(158,458)(159,457)(160,456)
(161,455)(162,454)(163,568)(164,570)(165,569)(166,576)(167,575)(168,574)
(169,573)(170,572)(171,571)(172,577)(173,579)(174,578)(175,585)(176,584)
(177,583)(178,582)(179,581)(180,580)(181,586)(182,588)(183,587)(184,594)
(185,593)(186,592)(187,591)(188,590)(189,589)(190,622)(191,624)(192,623)
(193,630)(194,629)(195,628)(196,627)(197,626)(198,625)(199,631)(200,633)
(201,632)(202,639)(203,638)(204,637)(205,636)(206,635)(207,634)(208,640)
(209,642)(210,641)(211,648)(212,647)(213,646)(214,645)(215,644)(216,643)
(217,595)(218,597)(219,596)(220,603)(221,602)(222,601)(223,600)(224,599)
(225,598)(226,604)(227,606)(228,605)(229,612)(230,611)(231,610)(232,609)
(233,608)(234,607)(235,613)(236,615)(237,614)(238,621)(239,620)(240,619)
(241,618)(242,617)(243,616)(244,487)(245,489)(246,488)(247,495)(248,494)
(249,493)(250,492)(251,491)(252,490)(253,496)(254,498)(255,497)(256,504)
(257,503)(258,502)(259,501)(260,500)(261,499)(262,505)(263,507)(264,506)
(265,513)(266,512)(267,511)(268,510)(269,509)(270,508)(271,541)(272,543)
(273,542)(274,549)(275,548)(276,547)(277,546)(278,545)(279,544)(280,550)
(281,552)(282,551)(283,558)(284,557)(285,556)(286,555)(287,554)(288,553)
(289,559)(290,561)(291,560)(292,567)(293,566)(294,565)(295,564)(296,563)
(297,562)(298,514)(299,516)(300,515)(301,522)(302,521)(303,520)(304,519)
(305,518)(306,517)(307,523)(308,525)(309,524)(310,531)(311,530)(312,529)
(313,528)(314,527)(315,526)(316,532)(317,534)(318,533)(319,540)(320,539)
(321,538)(322,537)(323,536)(324,535);;
s1 := (  1,517)(  2,519)(  3,518)(  4,514)(  5,516)(  6,515)(  7,522)(  8,521)
(  9,520)( 10,535)( 11,537)( 12,536)( 13,532)( 14,534)( 15,533)( 16,540)
( 17,539)( 18,538)( 19,526)( 20,528)( 21,527)( 22,523)( 23,525)( 24,524)
( 25,531)( 26,530)( 27,529)( 28,490)( 29,492)( 30,491)( 31,487)( 32,489)
( 33,488)( 34,495)( 35,494)( 36,493)( 37,508)( 38,510)( 39,509)( 40,505)
( 41,507)( 42,506)( 43,513)( 44,512)( 45,511)( 46,499)( 47,501)( 48,500)
( 49,496)( 50,498)( 51,497)( 52,504)( 53,503)( 54,502)( 55,544)( 56,546)
( 57,545)( 58,541)( 59,543)( 60,542)( 61,549)( 62,548)( 63,547)( 64,562)
( 65,564)( 66,563)( 67,559)( 68,561)( 69,560)( 70,567)( 71,566)( 72,565)
( 73,553)( 74,555)( 75,554)( 76,550)( 77,552)( 78,551)( 79,558)( 80,557)
( 81,556)( 82,598)( 83,600)( 84,599)( 85,595)( 86,597)( 87,596)( 88,603)
( 89,602)( 90,601)( 91,616)( 92,618)( 93,617)( 94,613)( 95,615)( 96,614)
( 97,621)( 98,620)( 99,619)(100,607)(101,609)(102,608)(103,604)(104,606)
(105,605)(106,612)(107,611)(108,610)(109,571)(110,573)(111,572)(112,568)
(113,570)(114,569)(115,576)(116,575)(117,574)(118,589)(119,591)(120,590)
(121,586)(122,588)(123,587)(124,594)(125,593)(126,592)(127,580)(128,582)
(129,581)(130,577)(131,579)(132,578)(133,585)(134,584)(135,583)(136,625)
(137,627)(138,626)(139,622)(140,624)(141,623)(142,630)(143,629)(144,628)
(145,643)(146,645)(147,644)(148,640)(149,642)(150,641)(151,648)(152,647)
(153,646)(154,634)(155,636)(156,635)(157,631)(158,633)(159,632)(160,639)
(161,638)(162,637)(163,355)(164,357)(165,356)(166,352)(167,354)(168,353)
(169,360)(170,359)(171,358)(172,373)(173,375)(174,374)(175,370)(176,372)
(177,371)(178,378)(179,377)(180,376)(181,364)(182,366)(183,365)(184,361)
(185,363)(186,362)(187,369)(188,368)(189,367)(190,328)(191,330)(192,329)
(193,325)(194,327)(195,326)(196,333)(197,332)(198,331)(199,346)(200,348)
(201,347)(202,343)(203,345)(204,344)(205,351)(206,350)(207,349)(208,337)
(209,339)(210,338)(211,334)(212,336)(213,335)(214,342)(215,341)(216,340)
(217,382)(218,384)(219,383)(220,379)(221,381)(222,380)(223,387)(224,386)
(225,385)(226,400)(227,402)(228,401)(229,397)(230,399)(231,398)(232,405)
(233,404)(234,403)(235,391)(236,393)(237,392)(238,388)(239,390)(240,389)
(241,396)(242,395)(243,394)(244,436)(245,438)(246,437)(247,433)(248,435)
(249,434)(250,441)(251,440)(252,439)(253,454)(254,456)(255,455)(256,451)
(257,453)(258,452)(259,459)(260,458)(261,457)(262,445)(263,447)(264,446)
(265,442)(266,444)(267,443)(268,450)(269,449)(270,448)(271,409)(272,411)
(273,410)(274,406)(275,408)(276,407)(277,414)(278,413)(279,412)(280,427)
(281,429)(282,428)(283,424)(284,426)(285,425)(286,432)(287,431)(288,430)
(289,418)(290,420)(291,419)(292,415)(293,417)(294,416)(295,423)(296,422)
(297,421)(298,463)(299,465)(300,464)(301,460)(302,462)(303,461)(304,468)
(305,467)(306,466)(307,481)(308,483)(309,482)(310,478)(311,480)(312,479)
(313,486)(314,485)(315,484)(316,472)(317,474)(318,473)(319,469)(320,471)
(321,470)(322,477)(323,476)(324,475);;
s2 := (  1,496)(  2,497)(  3,498)(  4,499)(  5,500)(  6,501)(  7,502)(  8,503)
(  9,504)( 10,487)( 11,488)( 12,489)( 13,490)( 14,491)( 15,492)( 16,493)
( 17,494)( 18,495)( 19,505)( 20,506)( 21,507)( 22,508)( 23,509)( 24,510)
( 25,511)( 26,512)( 27,513)( 28,550)( 29,551)( 30,552)( 31,553)( 32,554)
( 33,555)( 34,556)( 35,557)( 36,558)( 37,541)( 38,542)( 39,543)( 40,544)
( 41,545)( 42,546)( 43,547)( 44,548)( 45,549)( 46,559)( 47,560)( 48,561)
( 49,562)( 50,563)( 51,564)( 52,565)( 53,566)( 54,567)( 55,523)( 56,524)
( 57,525)( 58,526)( 59,527)( 60,528)( 61,529)( 62,530)( 63,531)( 64,514)
( 65,515)( 66,516)( 67,517)( 68,518)( 69,519)( 70,520)( 71,521)( 72,522)
( 73,532)( 74,533)( 75,534)( 76,535)( 77,536)( 78,537)( 79,538)( 80,539)
( 81,540)( 82,577)( 83,578)( 84,579)( 85,580)( 86,581)( 87,582)( 88,583)
( 89,584)( 90,585)( 91,568)( 92,569)( 93,570)( 94,571)( 95,572)( 96,573)
( 97,574)( 98,575)( 99,576)(100,586)(101,587)(102,588)(103,589)(104,590)
(105,591)(106,592)(107,593)(108,594)(109,631)(110,632)(111,633)(112,634)
(113,635)(114,636)(115,637)(116,638)(117,639)(118,622)(119,623)(120,624)
(121,625)(122,626)(123,627)(124,628)(125,629)(126,630)(127,640)(128,641)
(129,642)(130,643)(131,644)(132,645)(133,646)(134,647)(135,648)(136,604)
(137,605)(138,606)(139,607)(140,608)(141,609)(142,610)(143,611)(144,612)
(145,595)(146,596)(147,597)(148,598)(149,599)(150,600)(151,601)(152,602)
(153,603)(154,613)(155,614)(156,615)(157,616)(158,617)(159,618)(160,619)
(161,620)(162,621)(163,415)(164,416)(165,417)(166,418)(167,419)(168,420)
(169,421)(170,422)(171,423)(172,406)(173,407)(174,408)(175,409)(176,410)
(177,411)(178,412)(179,413)(180,414)(181,424)(182,425)(183,426)(184,427)
(185,428)(186,429)(187,430)(188,431)(189,432)(190,469)(191,470)(192,471)
(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,460)(200,461)
(201,462)(202,463)(203,464)(204,465)(205,466)(206,467)(207,468)(208,478)
(209,479)(210,480)(211,481)(212,482)(213,483)(214,484)(215,485)(216,486)
(217,442)(218,443)(219,444)(220,445)(221,446)(222,447)(223,448)(224,449)
(225,450)(226,433)(227,434)(228,435)(229,436)(230,437)(231,438)(232,439)
(233,440)(234,441)(235,451)(236,452)(237,453)(238,454)(239,455)(240,456)
(241,457)(242,458)(243,459)(244,334)(245,335)(246,336)(247,337)(248,338)
(249,339)(250,340)(251,341)(252,342)(253,325)(254,326)(255,327)(256,328)
(257,329)(258,330)(259,331)(260,332)(261,333)(262,343)(263,344)(264,345)
(265,346)(266,347)(267,348)(268,349)(269,350)(270,351)(271,388)(272,389)
(273,390)(274,391)(275,392)(276,393)(277,394)(278,395)(279,396)(280,379)
(281,380)(282,381)(283,382)(284,383)(285,384)(286,385)(287,386)(288,387)
(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)(296,404)
(297,405)(298,361)(299,362)(300,363)(301,364)(302,365)(303,366)(304,367)
(305,368)(306,369)(307,352)(308,353)(309,354)(310,355)(311,356)(312,357)
(313,358)(314,359)(315,360)(316,370)(317,371)(318,372)(319,373)(320,374)
(321,375)(322,376)(323,377)(324,378);;
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*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(648)!(  1,325)(  2,327)(  3,326)(  4,333)(  5,332)(  6,331)(  7,330)
(  8,329)(  9,328)( 10,334)( 11,336)( 12,335)( 13,342)( 14,341)( 15,340)
( 16,339)( 17,338)( 18,337)( 19,343)( 20,345)( 21,344)( 22,351)( 23,350)
( 24,349)( 25,348)( 26,347)( 27,346)( 28,379)( 29,381)( 30,380)( 31,387)
( 32,386)( 33,385)( 34,384)( 35,383)( 36,382)( 37,388)( 38,390)( 39,389)
( 40,396)( 41,395)( 42,394)( 43,393)( 44,392)( 45,391)( 46,397)( 47,399)
( 48,398)( 49,405)( 50,404)( 51,403)( 52,402)( 53,401)( 54,400)( 55,352)
( 56,354)( 57,353)( 58,360)( 59,359)( 60,358)( 61,357)( 62,356)( 63,355)
( 64,361)( 65,363)( 66,362)( 67,369)( 68,368)( 69,367)( 70,366)( 71,365)
( 72,364)( 73,370)( 74,372)( 75,371)( 76,378)( 77,377)( 78,376)( 79,375)
( 80,374)( 81,373)( 82,406)( 83,408)( 84,407)( 85,414)( 86,413)( 87,412)
( 88,411)( 89,410)( 90,409)( 91,415)( 92,417)( 93,416)( 94,423)( 95,422)
( 96,421)( 97,420)( 98,419)( 99,418)(100,424)(101,426)(102,425)(103,432)
(104,431)(105,430)(106,429)(107,428)(108,427)(109,460)(110,462)(111,461)
(112,468)(113,467)(114,466)(115,465)(116,464)(117,463)(118,469)(119,471)
(120,470)(121,477)(122,476)(123,475)(124,474)(125,473)(126,472)(127,478)
(128,480)(129,479)(130,486)(131,485)(132,484)(133,483)(134,482)(135,481)
(136,433)(137,435)(138,434)(139,441)(140,440)(141,439)(142,438)(143,437)
(144,436)(145,442)(146,444)(147,443)(148,450)(149,449)(150,448)(151,447)
(152,446)(153,445)(154,451)(155,453)(156,452)(157,459)(158,458)(159,457)
(160,456)(161,455)(162,454)(163,568)(164,570)(165,569)(166,576)(167,575)
(168,574)(169,573)(170,572)(171,571)(172,577)(173,579)(174,578)(175,585)
(176,584)(177,583)(178,582)(179,581)(180,580)(181,586)(182,588)(183,587)
(184,594)(185,593)(186,592)(187,591)(188,590)(189,589)(190,622)(191,624)
(192,623)(193,630)(194,629)(195,628)(196,627)(197,626)(198,625)(199,631)
(200,633)(201,632)(202,639)(203,638)(204,637)(205,636)(206,635)(207,634)
(208,640)(209,642)(210,641)(211,648)(212,647)(213,646)(214,645)(215,644)
(216,643)(217,595)(218,597)(219,596)(220,603)(221,602)(222,601)(223,600)
(224,599)(225,598)(226,604)(227,606)(228,605)(229,612)(230,611)(231,610)
(232,609)(233,608)(234,607)(235,613)(236,615)(237,614)(238,621)(239,620)
(240,619)(241,618)(242,617)(243,616)(244,487)(245,489)(246,488)(247,495)
(248,494)(249,493)(250,492)(251,491)(252,490)(253,496)(254,498)(255,497)
(256,504)(257,503)(258,502)(259,501)(260,500)(261,499)(262,505)(263,507)
(264,506)(265,513)(266,512)(267,511)(268,510)(269,509)(270,508)(271,541)
(272,543)(273,542)(274,549)(275,548)(276,547)(277,546)(278,545)(279,544)
(280,550)(281,552)(282,551)(283,558)(284,557)(285,556)(286,555)(287,554)
(288,553)(289,559)(290,561)(291,560)(292,567)(293,566)(294,565)(295,564)
(296,563)(297,562)(298,514)(299,516)(300,515)(301,522)(302,521)(303,520)
(304,519)(305,518)(306,517)(307,523)(308,525)(309,524)(310,531)(311,530)
(312,529)(313,528)(314,527)(315,526)(316,532)(317,534)(318,533)(319,540)
(320,539)(321,538)(322,537)(323,536)(324,535);
s1 := Sym(648)!(  1,517)(  2,519)(  3,518)(  4,514)(  5,516)(  6,515)(  7,522)
(  8,521)(  9,520)( 10,535)( 11,537)( 12,536)( 13,532)( 14,534)( 15,533)
( 16,540)( 17,539)( 18,538)( 19,526)( 20,528)( 21,527)( 22,523)( 23,525)
( 24,524)( 25,531)( 26,530)( 27,529)( 28,490)( 29,492)( 30,491)( 31,487)
( 32,489)( 33,488)( 34,495)( 35,494)( 36,493)( 37,508)( 38,510)( 39,509)
( 40,505)( 41,507)( 42,506)( 43,513)( 44,512)( 45,511)( 46,499)( 47,501)
( 48,500)( 49,496)( 50,498)( 51,497)( 52,504)( 53,503)( 54,502)( 55,544)
( 56,546)( 57,545)( 58,541)( 59,543)( 60,542)( 61,549)( 62,548)( 63,547)
( 64,562)( 65,564)( 66,563)( 67,559)( 68,561)( 69,560)( 70,567)( 71,566)
( 72,565)( 73,553)( 74,555)( 75,554)( 76,550)( 77,552)( 78,551)( 79,558)
( 80,557)( 81,556)( 82,598)( 83,600)( 84,599)( 85,595)( 86,597)( 87,596)
( 88,603)( 89,602)( 90,601)( 91,616)( 92,618)( 93,617)( 94,613)( 95,615)
( 96,614)( 97,621)( 98,620)( 99,619)(100,607)(101,609)(102,608)(103,604)
(104,606)(105,605)(106,612)(107,611)(108,610)(109,571)(110,573)(111,572)
(112,568)(113,570)(114,569)(115,576)(116,575)(117,574)(118,589)(119,591)
(120,590)(121,586)(122,588)(123,587)(124,594)(125,593)(126,592)(127,580)
(128,582)(129,581)(130,577)(131,579)(132,578)(133,585)(134,584)(135,583)
(136,625)(137,627)(138,626)(139,622)(140,624)(141,623)(142,630)(143,629)
(144,628)(145,643)(146,645)(147,644)(148,640)(149,642)(150,641)(151,648)
(152,647)(153,646)(154,634)(155,636)(156,635)(157,631)(158,633)(159,632)
(160,639)(161,638)(162,637)(163,355)(164,357)(165,356)(166,352)(167,354)
(168,353)(169,360)(170,359)(171,358)(172,373)(173,375)(174,374)(175,370)
(176,372)(177,371)(178,378)(179,377)(180,376)(181,364)(182,366)(183,365)
(184,361)(185,363)(186,362)(187,369)(188,368)(189,367)(190,328)(191,330)
(192,329)(193,325)(194,327)(195,326)(196,333)(197,332)(198,331)(199,346)
(200,348)(201,347)(202,343)(203,345)(204,344)(205,351)(206,350)(207,349)
(208,337)(209,339)(210,338)(211,334)(212,336)(213,335)(214,342)(215,341)
(216,340)(217,382)(218,384)(219,383)(220,379)(221,381)(222,380)(223,387)
(224,386)(225,385)(226,400)(227,402)(228,401)(229,397)(230,399)(231,398)
(232,405)(233,404)(234,403)(235,391)(236,393)(237,392)(238,388)(239,390)
(240,389)(241,396)(242,395)(243,394)(244,436)(245,438)(246,437)(247,433)
(248,435)(249,434)(250,441)(251,440)(252,439)(253,454)(254,456)(255,455)
(256,451)(257,453)(258,452)(259,459)(260,458)(261,457)(262,445)(263,447)
(264,446)(265,442)(266,444)(267,443)(268,450)(269,449)(270,448)(271,409)
(272,411)(273,410)(274,406)(275,408)(276,407)(277,414)(278,413)(279,412)
(280,427)(281,429)(282,428)(283,424)(284,426)(285,425)(286,432)(287,431)
(288,430)(289,418)(290,420)(291,419)(292,415)(293,417)(294,416)(295,423)
(296,422)(297,421)(298,463)(299,465)(300,464)(301,460)(302,462)(303,461)
(304,468)(305,467)(306,466)(307,481)(308,483)(309,482)(310,478)(311,480)
(312,479)(313,486)(314,485)(315,484)(316,472)(317,474)(318,473)(319,469)
(320,471)(321,470)(322,477)(323,476)(324,475);
s2 := Sym(648)!(  1,496)(  2,497)(  3,498)(  4,499)(  5,500)(  6,501)(  7,502)
(  8,503)(  9,504)( 10,487)( 11,488)( 12,489)( 13,490)( 14,491)( 15,492)
( 16,493)( 17,494)( 18,495)( 19,505)( 20,506)( 21,507)( 22,508)( 23,509)
( 24,510)( 25,511)( 26,512)( 27,513)( 28,550)( 29,551)( 30,552)( 31,553)
( 32,554)( 33,555)( 34,556)( 35,557)( 36,558)( 37,541)( 38,542)( 39,543)
( 40,544)( 41,545)( 42,546)( 43,547)( 44,548)( 45,549)( 46,559)( 47,560)
( 48,561)( 49,562)( 50,563)( 51,564)( 52,565)( 53,566)( 54,567)( 55,523)
( 56,524)( 57,525)( 58,526)( 59,527)( 60,528)( 61,529)( 62,530)( 63,531)
( 64,514)( 65,515)( 66,516)( 67,517)( 68,518)( 69,519)( 70,520)( 71,521)
( 72,522)( 73,532)( 74,533)( 75,534)( 76,535)( 77,536)( 78,537)( 79,538)
( 80,539)( 81,540)( 82,577)( 83,578)( 84,579)( 85,580)( 86,581)( 87,582)
( 88,583)( 89,584)( 90,585)( 91,568)( 92,569)( 93,570)( 94,571)( 95,572)
( 96,573)( 97,574)( 98,575)( 99,576)(100,586)(101,587)(102,588)(103,589)
(104,590)(105,591)(106,592)(107,593)(108,594)(109,631)(110,632)(111,633)
(112,634)(113,635)(114,636)(115,637)(116,638)(117,639)(118,622)(119,623)
(120,624)(121,625)(122,626)(123,627)(124,628)(125,629)(126,630)(127,640)
(128,641)(129,642)(130,643)(131,644)(132,645)(133,646)(134,647)(135,648)
(136,604)(137,605)(138,606)(139,607)(140,608)(141,609)(142,610)(143,611)
(144,612)(145,595)(146,596)(147,597)(148,598)(149,599)(150,600)(151,601)
(152,602)(153,603)(154,613)(155,614)(156,615)(157,616)(158,617)(159,618)
(160,619)(161,620)(162,621)(163,415)(164,416)(165,417)(166,418)(167,419)
(168,420)(169,421)(170,422)(171,423)(172,406)(173,407)(174,408)(175,409)
(176,410)(177,411)(178,412)(179,413)(180,414)(181,424)(182,425)(183,426)
(184,427)(185,428)(186,429)(187,430)(188,431)(189,432)(190,469)(191,470)
(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,460)
(200,461)(201,462)(202,463)(203,464)(204,465)(205,466)(206,467)(207,468)
(208,478)(209,479)(210,480)(211,481)(212,482)(213,483)(214,484)(215,485)
(216,486)(217,442)(218,443)(219,444)(220,445)(221,446)(222,447)(223,448)
(224,449)(225,450)(226,433)(227,434)(228,435)(229,436)(230,437)(231,438)
(232,439)(233,440)(234,441)(235,451)(236,452)(237,453)(238,454)(239,455)
(240,456)(241,457)(242,458)(243,459)(244,334)(245,335)(246,336)(247,337)
(248,338)(249,339)(250,340)(251,341)(252,342)(253,325)(254,326)(255,327)
(256,328)(257,329)(258,330)(259,331)(260,332)(261,333)(262,343)(263,344)
(264,345)(265,346)(266,347)(267,348)(268,349)(269,350)(270,351)(271,388)
(272,389)(273,390)(274,391)(275,392)(276,393)(277,394)(278,395)(279,396)
(280,379)(281,380)(282,381)(283,382)(284,383)(285,384)(286,385)(287,386)
(288,387)(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)
(296,404)(297,405)(298,361)(299,362)(300,363)(301,364)(302,365)(303,366)
(304,367)(305,368)(306,369)(307,352)(308,353)(309,354)(310,355)(311,356)
(312,357)(313,358)(314,359)(315,360)(316,370)(317,371)(318,372)(319,373)
(320,374)(321,375)(322,376)(323,377)(324,378);
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, 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*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