Polytope of Type {6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*1296h
if this polytope has a name.
Group : SmallGroup(1296,2061)
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}*648f
3-fold quotients : {6,12}*432a, {6,12}*432g
6-fold quotients : {6,6}*216a, {6,6}*216d
9-fold quotients : {6,12}*144a, {6,12}*144b, {6,12}*144c
12-fold quotients : {6,3}*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)( 2,489)( 3,488)( 4,490)( 5,492)( 6,491)( 7,493)( 8,495)
( 9,494)( 10,505)( 11,507)( 12,506)( 13,508)( 14,510)( 15,509)( 16,511)
( 17,513)( 18,512)( 19,496)( 20,498)( 21,497)( 22,499)( 23,501)( 24,500)
( 25,502)( 26,504)( 27,503)( 28,541)( 29,543)( 30,542)( 31,544)( 32,546)
( 33,545)( 34,547)( 35,549)( 36,548)( 37,559)( 38,561)( 39,560)( 40,562)
( 41,564)( 42,563)( 43,565)( 44,567)( 45,566)( 46,550)( 47,552)( 48,551)
( 49,553)( 50,555)( 51,554)( 52,556)( 53,558)( 54,557)( 55,514)( 56,516)
( 57,515)( 58,517)( 59,519)( 60,518)( 61,520)( 62,522)( 63,521)( 64,532)
( 65,534)( 66,533)( 67,535)( 68,537)( 69,536)( 70,538)( 71,540)( 72,539)
( 73,523)( 74,525)( 75,524)( 76,526)( 77,528)( 78,527)( 79,529)( 80,531)
( 81,530)( 82,568)( 83,570)( 84,569)( 85,571)( 86,573)( 87,572)( 88,574)
( 89,576)( 90,575)( 91,586)( 92,588)( 93,587)( 94,589)( 95,591)( 96,590)
( 97,592)( 98,594)( 99,593)(100,577)(101,579)(102,578)(103,580)(104,582)
(105,581)(106,583)(107,585)(108,584)(109,622)(110,624)(111,623)(112,625)
(113,627)(114,626)(115,628)(116,630)(117,629)(118,640)(119,642)(120,641)
(121,643)(122,645)(123,644)(124,646)(125,648)(126,647)(127,631)(128,633)
(129,632)(130,634)(131,636)(132,635)(133,637)(134,639)(135,638)(136,595)
(137,597)(138,596)(139,598)(140,600)(141,599)(142,601)(143,603)(144,602)
(145,613)(146,615)(147,614)(148,616)(149,618)(150,617)(151,619)(152,621)
(153,620)(154,604)(155,606)(156,605)(157,607)(158,609)(159,608)(160,610)
(161,612)(162,611)(163,406)(164,408)(165,407)(166,409)(167,411)(168,410)
(169,412)(170,414)(171,413)(172,424)(173,426)(174,425)(175,427)(176,429)
(177,428)(178,430)(179,432)(180,431)(181,415)(182,417)(183,416)(184,418)
(185,420)(186,419)(187,421)(188,423)(189,422)(190,460)(191,462)(192,461)
(193,463)(194,465)(195,464)(196,466)(197,468)(198,467)(199,478)(200,480)
(201,479)(202,481)(203,483)(204,482)(205,484)(206,486)(207,485)(208,469)
(209,471)(210,470)(211,472)(212,474)(213,473)(214,475)(215,477)(216,476)
(217,433)(218,435)(219,434)(220,436)(221,438)(222,437)(223,439)(224,441)
(225,440)(226,451)(227,453)(228,452)(229,454)(230,456)(231,455)(232,457)
(233,459)(234,458)(235,442)(236,444)(237,443)(238,445)(239,447)(240,446)
(241,448)(242,450)(243,449)(244,325)(245,327)(246,326)(247,328)(248,330)
(249,329)(250,331)(251,333)(252,332)(253,343)(254,345)(255,344)(256,346)
(257,348)(258,347)(259,349)(260,351)(261,350)(262,334)(263,336)(264,335)
(265,337)(266,339)(267,338)(268,340)(269,342)(270,341)(271,379)(272,381)
(273,380)(274,382)(275,384)(276,383)(277,385)(278,387)(279,386)(280,397)
(281,399)(282,398)(283,400)(284,402)(285,401)(286,403)(287,405)(288,404)
(289,388)(290,390)(291,389)(292,391)(293,393)(294,392)(295,394)(296,396)
(297,395)(298,352)(299,354)(300,353)(301,355)(302,357)(303,356)(304,358)
(305,360)(306,359)(307,370)(308,372)(309,371)(310,373)(311,375)(312,374)
(313,376)(314,378)(315,377)(316,361)(317,363)(318,362)(319,364)(320,366)
(321,365)(322,367)(323,369)(324,368);;
s1 := ( 1,523)( 2,524)( 3,525)( 4,531)( 5,529)( 6,530)( 7,527)( 8,528)
( 9,526)( 10,514)( 11,515)( 12,516)( 13,522)( 14,520)( 15,521)( 16,518)
( 17,519)( 18,517)( 19,532)( 20,533)( 21,534)( 22,540)( 23,538)( 24,539)
( 25,536)( 26,537)( 27,535)( 28,496)( 29,497)( 30,498)( 31,504)( 32,502)
( 33,503)( 34,500)( 35,501)( 36,499)( 37,487)( 38,488)( 39,489)( 40,495)
( 41,493)( 42,494)( 43,491)( 44,492)( 45,490)( 46,505)( 47,506)( 48,507)
( 49,513)( 50,511)( 51,512)( 52,509)( 53,510)( 54,508)( 55,550)( 56,551)
( 57,552)( 58,558)( 59,556)( 60,557)( 61,554)( 62,555)( 63,553)( 64,541)
( 65,542)( 66,543)( 67,549)( 68,547)( 69,548)( 70,545)( 71,546)( 72,544)
( 73,559)( 74,560)( 75,561)( 76,567)( 77,565)( 78,566)( 79,563)( 80,564)
( 81,562)( 82,604)( 83,605)( 84,606)( 85,612)( 86,610)( 87,611)( 88,608)
( 89,609)( 90,607)( 91,595)( 92,596)( 93,597)( 94,603)( 95,601)( 96,602)
( 97,599)( 98,600)( 99,598)(100,613)(101,614)(102,615)(103,621)(104,619)
(105,620)(106,617)(107,618)(108,616)(109,577)(110,578)(111,579)(112,585)
(113,583)(114,584)(115,581)(116,582)(117,580)(118,568)(119,569)(120,570)
(121,576)(122,574)(123,575)(124,572)(125,573)(126,571)(127,586)(128,587)
(129,588)(130,594)(131,592)(132,593)(133,590)(134,591)(135,589)(136,631)
(137,632)(138,633)(139,639)(140,637)(141,638)(142,635)(143,636)(144,634)
(145,622)(146,623)(147,624)(148,630)(149,628)(150,629)(151,626)(152,627)
(153,625)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)
(161,645)(162,643)(163,361)(164,362)(165,363)(166,369)(167,367)(168,368)
(169,365)(170,366)(171,364)(172,352)(173,353)(174,354)(175,360)(176,358)
(177,359)(178,356)(179,357)(180,355)(181,370)(182,371)(183,372)(184,378)
(185,376)(186,377)(187,374)(188,375)(189,373)(190,334)(191,335)(192,336)
(193,342)(194,340)(195,341)(196,338)(197,339)(198,337)(199,325)(200,326)
(201,327)(202,333)(203,331)(204,332)(205,329)(206,330)(207,328)(208,343)
(209,344)(210,345)(211,351)(212,349)(213,350)(214,347)(215,348)(216,346)
(217,388)(218,389)(219,390)(220,396)(221,394)(222,395)(223,392)(224,393)
(225,391)(226,379)(227,380)(228,381)(229,387)(230,385)(231,386)(232,383)
(233,384)(234,382)(235,397)(236,398)(237,399)(238,405)(239,403)(240,404)
(241,401)(242,402)(243,400)(244,442)(245,443)(246,444)(247,450)(248,448)
(249,449)(250,446)(251,447)(252,445)(253,433)(254,434)(255,435)(256,441)
(257,439)(258,440)(259,437)(260,438)(261,436)(262,451)(263,452)(264,453)
(265,459)(266,457)(267,458)(268,455)(269,456)(270,454)(271,415)(272,416)
(273,417)(274,423)(275,421)(276,422)(277,419)(278,420)(279,418)(280,406)
(281,407)(282,408)(283,414)(284,412)(285,413)(286,410)(287,411)(288,409)
(289,424)(290,425)(291,426)(292,432)(293,430)(294,431)(295,428)(296,429)
(297,427)(298,469)(299,470)(300,471)(301,477)(302,475)(303,476)(304,473)
(305,474)(306,472)(307,460)(308,461)(309,462)(310,468)(311,466)(312,467)
(313,464)(314,465)(315,463)(316,478)(317,479)(318,480)(319,486)(320,484)
(321,485)(322,482)(323,483)(324,481);;
s2 := ( 1,328)( 2,329)( 3,330)( 4,325)( 5,326)( 6,327)( 7,331)( 8,332)
( 9,333)( 10,337)( 11,338)( 12,339)( 13,334)( 14,335)( 15,336)( 16,340)
( 17,341)( 18,342)( 19,346)( 20,347)( 21,348)( 22,343)( 23,344)( 24,345)
( 25,349)( 26,350)( 27,351)( 28,382)( 29,383)( 30,384)( 31,379)( 32,380)
( 33,381)( 34,385)( 35,386)( 36,387)( 37,391)( 38,392)( 39,393)( 40,388)
( 41,389)( 42,390)( 43,394)( 44,395)( 45,396)( 46,400)( 47,401)( 48,402)
( 49,397)( 50,398)( 51,399)( 52,403)( 53,404)( 54,405)( 55,355)( 56,356)
( 57,357)( 58,352)( 59,353)( 60,354)( 61,358)( 62,359)( 63,360)( 64,364)
( 65,365)( 66,366)( 67,361)( 68,362)( 69,363)( 70,367)( 71,368)( 72,369)
( 73,373)( 74,374)( 75,375)( 76,370)( 77,371)( 78,372)( 79,376)( 80,377)
( 81,378)( 82,409)( 83,410)( 84,411)( 85,406)( 86,407)( 87,408)( 88,412)
( 89,413)( 90,414)( 91,418)( 92,419)( 93,420)( 94,415)( 95,416)( 96,417)
( 97,421)( 98,422)( 99,423)(100,427)(101,428)(102,429)(103,424)(104,425)
(105,426)(106,430)(107,431)(108,432)(109,463)(110,464)(111,465)(112,460)
(113,461)(114,462)(115,466)(116,467)(117,468)(118,472)(119,473)(120,474)
(121,469)(122,470)(123,471)(124,475)(125,476)(126,477)(127,481)(128,482)
(129,483)(130,478)(131,479)(132,480)(133,484)(134,485)(135,486)(136,436)
(137,437)(138,438)(139,433)(140,434)(141,435)(142,439)(143,440)(144,441)
(145,445)(146,446)(147,447)(148,442)(149,443)(150,444)(151,448)(152,449)
(153,450)(154,454)(155,455)(156,456)(157,451)(158,452)(159,453)(160,457)
(161,458)(162,459)(163,571)(164,572)(165,573)(166,568)(167,569)(168,570)
(169,574)(170,575)(171,576)(172,580)(173,581)(174,582)(175,577)(176,578)
(177,579)(178,583)(179,584)(180,585)(181,589)(182,590)(183,591)(184,586)
(185,587)(186,588)(187,592)(188,593)(189,594)(190,625)(191,626)(192,627)
(193,622)(194,623)(195,624)(196,628)(197,629)(198,630)(199,634)(200,635)
(201,636)(202,631)(203,632)(204,633)(205,637)(206,638)(207,639)(208,643)
(209,644)(210,645)(211,640)(212,641)(213,642)(214,646)(215,647)(216,648)
(217,598)(218,599)(219,600)(220,595)(221,596)(222,597)(223,601)(224,602)
(225,603)(226,607)(227,608)(228,609)(229,604)(230,605)(231,606)(232,610)
(233,611)(234,612)(235,616)(236,617)(237,618)(238,613)(239,614)(240,615)
(241,619)(242,620)(243,621)(244,490)(245,491)(246,492)(247,487)(248,488)
(249,489)(250,493)(251,494)(252,495)(253,499)(254,500)(255,501)(256,496)
(257,497)(258,498)(259,502)(260,503)(261,504)(262,508)(263,509)(264,510)
(265,505)(266,506)(267,507)(268,511)(269,512)(270,513)(271,544)(272,545)
(273,546)(274,541)(275,542)(276,543)(277,547)(278,548)(279,549)(280,553)
(281,554)(282,555)(283,550)(284,551)(285,552)(286,556)(287,557)(288,558)
(289,562)(290,563)(291,564)(292,559)(293,560)(294,561)(295,565)(296,566)
(297,567)(298,517)(299,518)(300,519)(301,514)(302,515)(303,516)(304,520)
(305,521)(306,522)(307,526)(308,527)(309,528)(310,523)(311,524)(312,525)
(313,529)(314,530)(315,531)(316,535)(317,536)(318,537)(319,532)(320,533)
(321,534)(322,538)(323,539)(324,540);;
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*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*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)( 2,489)( 3,488)( 4,490)( 5,492)( 6,491)( 7,493)
( 8,495)( 9,494)( 10,505)( 11,507)( 12,506)( 13,508)( 14,510)( 15,509)
( 16,511)( 17,513)( 18,512)( 19,496)( 20,498)( 21,497)( 22,499)( 23,501)
( 24,500)( 25,502)( 26,504)( 27,503)( 28,541)( 29,543)( 30,542)( 31,544)
( 32,546)( 33,545)( 34,547)( 35,549)( 36,548)( 37,559)( 38,561)( 39,560)
( 40,562)( 41,564)( 42,563)( 43,565)( 44,567)( 45,566)( 46,550)( 47,552)
( 48,551)( 49,553)( 50,555)( 51,554)( 52,556)( 53,558)( 54,557)( 55,514)
( 56,516)( 57,515)( 58,517)( 59,519)( 60,518)( 61,520)( 62,522)( 63,521)
( 64,532)( 65,534)( 66,533)( 67,535)( 68,537)( 69,536)( 70,538)( 71,540)
( 72,539)( 73,523)( 74,525)( 75,524)( 76,526)( 77,528)( 78,527)( 79,529)
( 80,531)( 81,530)( 82,568)( 83,570)( 84,569)( 85,571)( 86,573)( 87,572)
( 88,574)( 89,576)( 90,575)( 91,586)( 92,588)( 93,587)( 94,589)( 95,591)
( 96,590)( 97,592)( 98,594)( 99,593)(100,577)(101,579)(102,578)(103,580)
(104,582)(105,581)(106,583)(107,585)(108,584)(109,622)(110,624)(111,623)
(112,625)(113,627)(114,626)(115,628)(116,630)(117,629)(118,640)(119,642)
(120,641)(121,643)(122,645)(123,644)(124,646)(125,648)(126,647)(127,631)
(128,633)(129,632)(130,634)(131,636)(132,635)(133,637)(134,639)(135,638)
(136,595)(137,597)(138,596)(139,598)(140,600)(141,599)(142,601)(143,603)
(144,602)(145,613)(146,615)(147,614)(148,616)(149,618)(150,617)(151,619)
(152,621)(153,620)(154,604)(155,606)(156,605)(157,607)(158,609)(159,608)
(160,610)(161,612)(162,611)(163,406)(164,408)(165,407)(166,409)(167,411)
(168,410)(169,412)(170,414)(171,413)(172,424)(173,426)(174,425)(175,427)
(176,429)(177,428)(178,430)(179,432)(180,431)(181,415)(182,417)(183,416)
(184,418)(185,420)(186,419)(187,421)(188,423)(189,422)(190,460)(191,462)
(192,461)(193,463)(194,465)(195,464)(196,466)(197,468)(198,467)(199,478)
(200,480)(201,479)(202,481)(203,483)(204,482)(205,484)(206,486)(207,485)
(208,469)(209,471)(210,470)(211,472)(212,474)(213,473)(214,475)(215,477)
(216,476)(217,433)(218,435)(219,434)(220,436)(221,438)(222,437)(223,439)
(224,441)(225,440)(226,451)(227,453)(228,452)(229,454)(230,456)(231,455)
(232,457)(233,459)(234,458)(235,442)(236,444)(237,443)(238,445)(239,447)
(240,446)(241,448)(242,450)(243,449)(244,325)(245,327)(246,326)(247,328)
(248,330)(249,329)(250,331)(251,333)(252,332)(253,343)(254,345)(255,344)
(256,346)(257,348)(258,347)(259,349)(260,351)(261,350)(262,334)(263,336)
(264,335)(265,337)(266,339)(267,338)(268,340)(269,342)(270,341)(271,379)
(272,381)(273,380)(274,382)(275,384)(276,383)(277,385)(278,387)(279,386)
(280,397)(281,399)(282,398)(283,400)(284,402)(285,401)(286,403)(287,405)
(288,404)(289,388)(290,390)(291,389)(292,391)(293,393)(294,392)(295,394)
(296,396)(297,395)(298,352)(299,354)(300,353)(301,355)(302,357)(303,356)
(304,358)(305,360)(306,359)(307,370)(308,372)(309,371)(310,373)(311,375)
(312,374)(313,376)(314,378)(315,377)(316,361)(317,363)(318,362)(319,364)
(320,366)(321,365)(322,367)(323,369)(324,368);
s1 := Sym(648)!( 1,523)( 2,524)( 3,525)( 4,531)( 5,529)( 6,530)( 7,527)
( 8,528)( 9,526)( 10,514)( 11,515)( 12,516)( 13,522)( 14,520)( 15,521)
( 16,518)( 17,519)( 18,517)( 19,532)( 20,533)( 21,534)( 22,540)( 23,538)
( 24,539)( 25,536)( 26,537)( 27,535)( 28,496)( 29,497)( 30,498)( 31,504)
( 32,502)( 33,503)( 34,500)( 35,501)( 36,499)( 37,487)( 38,488)( 39,489)
( 40,495)( 41,493)( 42,494)( 43,491)( 44,492)( 45,490)( 46,505)( 47,506)
( 48,507)( 49,513)( 50,511)( 51,512)( 52,509)( 53,510)( 54,508)( 55,550)
( 56,551)( 57,552)( 58,558)( 59,556)( 60,557)( 61,554)( 62,555)( 63,553)
( 64,541)( 65,542)( 66,543)( 67,549)( 68,547)( 69,548)( 70,545)( 71,546)
( 72,544)( 73,559)( 74,560)( 75,561)( 76,567)( 77,565)( 78,566)( 79,563)
( 80,564)( 81,562)( 82,604)( 83,605)( 84,606)( 85,612)( 86,610)( 87,611)
( 88,608)( 89,609)( 90,607)( 91,595)( 92,596)( 93,597)( 94,603)( 95,601)
( 96,602)( 97,599)( 98,600)( 99,598)(100,613)(101,614)(102,615)(103,621)
(104,619)(105,620)(106,617)(107,618)(108,616)(109,577)(110,578)(111,579)
(112,585)(113,583)(114,584)(115,581)(116,582)(117,580)(118,568)(119,569)
(120,570)(121,576)(122,574)(123,575)(124,572)(125,573)(126,571)(127,586)
(128,587)(129,588)(130,594)(131,592)(132,593)(133,590)(134,591)(135,589)
(136,631)(137,632)(138,633)(139,639)(140,637)(141,638)(142,635)(143,636)
(144,634)(145,622)(146,623)(147,624)(148,630)(149,628)(150,629)(151,626)
(152,627)(153,625)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)
(160,644)(161,645)(162,643)(163,361)(164,362)(165,363)(166,369)(167,367)
(168,368)(169,365)(170,366)(171,364)(172,352)(173,353)(174,354)(175,360)
(176,358)(177,359)(178,356)(179,357)(180,355)(181,370)(182,371)(183,372)
(184,378)(185,376)(186,377)(187,374)(188,375)(189,373)(190,334)(191,335)
(192,336)(193,342)(194,340)(195,341)(196,338)(197,339)(198,337)(199,325)
(200,326)(201,327)(202,333)(203,331)(204,332)(205,329)(206,330)(207,328)
(208,343)(209,344)(210,345)(211,351)(212,349)(213,350)(214,347)(215,348)
(216,346)(217,388)(218,389)(219,390)(220,396)(221,394)(222,395)(223,392)
(224,393)(225,391)(226,379)(227,380)(228,381)(229,387)(230,385)(231,386)
(232,383)(233,384)(234,382)(235,397)(236,398)(237,399)(238,405)(239,403)
(240,404)(241,401)(242,402)(243,400)(244,442)(245,443)(246,444)(247,450)
(248,448)(249,449)(250,446)(251,447)(252,445)(253,433)(254,434)(255,435)
(256,441)(257,439)(258,440)(259,437)(260,438)(261,436)(262,451)(263,452)
(264,453)(265,459)(266,457)(267,458)(268,455)(269,456)(270,454)(271,415)
(272,416)(273,417)(274,423)(275,421)(276,422)(277,419)(278,420)(279,418)
(280,406)(281,407)(282,408)(283,414)(284,412)(285,413)(286,410)(287,411)
(288,409)(289,424)(290,425)(291,426)(292,432)(293,430)(294,431)(295,428)
(296,429)(297,427)(298,469)(299,470)(300,471)(301,477)(302,475)(303,476)
(304,473)(305,474)(306,472)(307,460)(308,461)(309,462)(310,468)(311,466)
(312,467)(313,464)(314,465)(315,463)(316,478)(317,479)(318,480)(319,486)
(320,484)(321,485)(322,482)(323,483)(324,481);
s2 := Sym(648)!( 1,328)( 2,329)( 3,330)( 4,325)( 5,326)( 6,327)( 7,331)
( 8,332)( 9,333)( 10,337)( 11,338)( 12,339)( 13,334)( 14,335)( 15,336)
( 16,340)( 17,341)( 18,342)( 19,346)( 20,347)( 21,348)( 22,343)( 23,344)
( 24,345)( 25,349)( 26,350)( 27,351)( 28,382)( 29,383)( 30,384)( 31,379)
( 32,380)( 33,381)( 34,385)( 35,386)( 36,387)( 37,391)( 38,392)( 39,393)
( 40,388)( 41,389)( 42,390)( 43,394)( 44,395)( 45,396)( 46,400)( 47,401)
( 48,402)( 49,397)( 50,398)( 51,399)( 52,403)( 53,404)( 54,405)( 55,355)
( 56,356)( 57,357)( 58,352)( 59,353)( 60,354)( 61,358)( 62,359)( 63,360)
( 64,364)( 65,365)( 66,366)( 67,361)( 68,362)( 69,363)( 70,367)( 71,368)
( 72,369)( 73,373)( 74,374)( 75,375)( 76,370)( 77,371)( 78,372)( 79,376)
( 80,377)( 81,378)( 82,409)( 83,410)( 84,411)( 85,406)( 86,407)( 87,408)
( 88,412)( 89,413)( 90,414)( 91,418)( 92,419)( 93,420)( 94,415)( 95,416)
( 96,417)( 97,421)( 98,422)( 99,423)(100,427)(101,428)(102,429)(103,424)
(104,425)(105,426)(106,430)(107,431)(108,432)(109,463)(110,464)(111,465)
(112,460)(113,461)(114,462)(115,466)(116,467)(117,468)(118,472)(119,473)
(120,474)(121,469)(122,470)(123,471)(124,475)(125,476)(126,477)(127,481)
(128,482)(129,483)(130,478)(131,479)(132,480)(133,484)(134,485)(135,486)
(136,436)(137,437)(138,438)(139,433)(140,434)(141,435)(142,439)(143,440)
(144,441)(145,445)(146,446)(147,447)(148,442)(149,443)(150,444)(151,448)
(152,449)(153,450)(154,454)(155,455)(156,456)(157,451)(158,452)(159,453)
(160,457)(161,458)(162,459)(163,571)(164,572)(165,573)(166,568)(167,569)
(168,570)(169,574)(170,575)(171,576)(172,580)(173,581)(174,582)(175,577)
(176,578)(177,579)(178,583)(179,584)(180,585)(181,589)(182,590)(183,591)
(184,586)(185,587)(186,588)(187,592)(188,593)(189,594)(190,625)(191,626)
(192,627)(193,622)(194,623)(195,624)(196,628)(197,629)(198,630)(199,634)
(200,635)(201,636)(202,631)(203,632)(204,633)(205,637)(206,638)(207,639)
(208,643)(209,644)(210,645)(211,640)(212,641)(213,642)(214,646)(215,647)
(216,648)(217,598)(218,599)(219,600)(220,595)(221,596)(222,597)(223,601)
(224,602)(225,603)(226,607)(227,608)(228,609)(229,604)(230,605)(231,606)
(232,610)(233,611)(234,612)(235,616)(236,617)(237,618)(238,613)(239,614)
(240,615)(241,619)(242,620)(243,621)(244,490)(245,491)(246,492)(247,487)
(248,488)(249,489)(250,493)(251,494)(252,495)(253,499)(254,500)(255,501)
(256,496)(257,497)(258,498)(259,502)(260,503)(261,504)(262,508)(263,509)
(264,510)(265,505)(266,506)(267,507)(268,511)(269,512)(270,513)(271,544)
(272,545)(273,546)(274,541)(275,542)(276,543)(277,547)(278,548)(279,549)
(280,553)(281,554)(282,555)(283,550)(284,551)(285,552)(286,556)(287,557)
(288,558)(289,562)(290,563)(291,564)(292,559)(293,560)(294,561)(295,565)
(296,566)(297,567)(298,517)(299,518)(300,519)(301,514)(302,515)(303,516)
(304,520)(305,521)(306,522)(307,526)(308,527)(309,528)(310,523)(311,524)
(312,525)(313,529)(314,530)(315,531)(316,535)(317,536)(318,537)(319,532)
(320,533)(321,534)(322,538)(323,539)(324,540);
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*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*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