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