Polytope of Type {18,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,12}*1296l
if this polytope has a name.
Group : SmallGroup(1296,2020)
Rank : 3
Schlafli Type : {18,12}
Number of vertices, edges, etc : 54, 324, 36
Order of s0s1s2 : 36
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 : {18,6}*648i
3-fold quotients : {18,12}*432a, {18,12}*432b, {6,12}*432g
6-fold quotients : {18,6}*216a, {18,6}*216b, {6,6}*216d
9-fold quotients : {18,4}*144a, {6,12}*144a, {6,12}*144b, {6,12}*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 : {2,12}*48, {6,4}*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 : {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)( 28,543)( 29,542)( 30,541)( 31,546)( 32,545)
( 33,544)( 34,549)( 35,548)( 36,547)( 37,561)( 38,560)( 39,559)( 40,564)
( 41,563)( 42,562)( 43,567)( 44,566)( 45,565)( 46,552)( 47,551)( 48,550)
( 49,555)( 50,554)( 51,553)( 52,558)( 53,557)( 54,556)( 55,516)( 56,515)
( 57,514)( 58,519)( 59,518)( 60,517)( 61,522)( 62,521)( 63,520)( 64,534)
( 65,533)( 66,532)( 67,537)( 68,536)( 69,535)( 70,540)( 71,539)( 72,538)
( 73,525)( 74,524)( 75,523)( 76,528)( 77,527)( 78,526)( 79,531)( 80,530)
( 81,529)( 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)(109,624)(110,623)(111,622)(112,627)
(113,626)(114,625)(115,630)(116,629)(117,628)(118,642)(119,641)(120,640)
(121,645)(122,644)(123,643)(124,648)(125,647)(126,646)(127,633)(128,632)
(129,631)(130,636)(131,635)(132,634)(133,639)(134,638)(135,637)(136,597)
(137,596)(138,595)(139,600)(140,599)(141,598)(142,603)(143,602)(144,601)
(145,615)(146,614)(147,613)(148,618)(149,617)(150,616)(151,621)(152,620)
(153,619)(154,606)(155,605)(156,604)(157,609)(158,608)(159,607)(160,612)
(161,611)(162,610)(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)(190,462)(191,461)(192,460)
(193,465)(194,464)(195,463)(196,468)(197,467)(198,466)(199,480)(200,479)
(201,478)(202,483)(203,482)(204,481)(205,486)(206,485)(207,484)(208,471)
(209,470)(210,469)(211,474)(212,473)(213,472)(214,477)(215,476)(216,475)
(217,435)(218,434)(219,433)(220,438)(221,437)(222,436)(223,441)(224,440)
(225,439)(226,453)(227,452)(228,451)(229,456)(230,455)(231,454)(232,459)
(233,458)(234,457)(235,444)(236,443)(237,442)(238,447)(239,446)(240,445)
(241,450)(242,449)(243,448)(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)(271,381)(272,380)
(273,379)(274,384)(275,383)(276,382)(277,387)(278,386)(279,385)(280,399)
(281,398)(282,397)(283,402)(284,401)(285,400)(286,405)(287,404)(288,403)
(289,390)(290,389)(291,388)(292,393)(293,392)(294,391)(295,396)(296,395)
(297,394)(298,354)(299,353)(300,352)(301,357)(302,356)(303,355)(304,360)
(305,359)(306,358)(307,372)(308,371)(309,370)(310,375)(311,374)(312,373)
(313,378)(314,377)(315,376)(316,363)(317,362)(318,361)(319,366)(320,365)
(321,364)(322,369)(323,368)(324,367);;
s1 := ( 1,523)( 2,525)( 3,524)( 4,529)( 5,531)( 6,530)( 7,526)( 8,528)
( 9,527)( 10,514)( 11,516)( 12,515)( 13,520)( 14,522)( 15,521)( 16,517)
( 17,519)( 18,518)( 19,532)( 20,534)( 21,533)( 22,538)( 23,540)( 24,539)
( 25,535)( 26,537)( 27,536)( 28,496)( 29,498)( 30,497)( 31,502)( 32,504)
( 33,503)( 34,499)( 35,501)( 36,500)( 37,487)( 38,489)( 39,488)( 40,493)
( 41,495)( 42,494)( 43,490)( 44,492)( 45,491)( 46,505)( 47,507)( 48,506)
( 49,511)( 50,513)( 51,512)( 52,508)( 53,510)( 54,509)( 55,552)( 56,551)
( 57,550)( 58,558)( 59,557)( 60,556)( 61,555)( 62,554)( 63,553)( 64,543)
( 65,542)( 66,541)( 67,549)( 68,548)( 69,547)( 70,546)( 71,545)( 72,544)
( 73,561)( 74,560)( 75,559)( 76,567)( 77,566)( 78,565)( 79,564)( 80,563)
( 81,562)( 82,604)( 83,606)( 84,605)( 85,610)( 86,612)( 87,611)( 88,607)
( 89,609)( 90,608)( 91,595)( 92,597)( 93,596)( 94,601)( 95,603)( 96,602)
( 97,598)( 98,600)( 99,599)(100,613)(101,615)(102,614)(103,619)(104,621)
(105,620)(106,616)(107,618)(108,617)(109,577)(110,579)(111,578)(112,583)
(113,585)(114,584)(115,580)(116,582)(117,581)(118,568)(119,570)(120,569)
(121,574)(122,576)(123,575)(124,571)(125,573)(126,572)(127,586)(128,588)
(129,587)(130,592)(131,594)(132,593)(133,589)(134,591)(135,590)(136,633)
(137,632)(138,631)(139,639)(140,638)(141,637)(142,636)(143,635)(144,634)
(145,624)(146,623)(147,622)(148,630)(149,629)(150,628)(151,627)(152,626)
(153,625)(154,642)(155,641)(156,640)(157,648)(158,647)(159,646)(160,645)
(161,644)(162,643)(163,361)(164,363)(165,362)(166,367)(167,369)(168,368)
(169,364)(170,366)(171,365)(172,352)(173,354)(174,353)(175,358)(176,360)
(177,359)(178,355)(179,357)(180,356)(181,370)(182,372)(183,371)(184,376)
(185,378)(186,377)(187,373)(188,375)(189,374)(190,334)(191,336)(192,335)
(193,340)(194,342)(195,341)(196,337)(197,339)(198,338)(199,325)(200,327)
(201,326)(202,331)(203,333)(204,332)(205,328)(206,330)(207,329)(208,343)
(209,345)(210,344)(211,349)(212,351)(213,350)(214,346)(215,348)(216,347)
(217,390)(218,389)(219,388)(220,396)(221,395)(222,394)(223,393)(224,392)
(225,391)(226,381)(227,380)(228,379)(229,387)(230,386)(231,385)(232,384)
(233,383)(234,382)(235,399)(236,398)(237,397)(238,405)(239,404)(240,403)
(241,402)(242,401)(243,400)(244,442)(245,444)(246,443)(247,448)(248,450)
(249,449)(250,445)(251,447)(252,446)(253,433)(254,435)(255,434)(256,439)
(257,441)(258,440)(259,436)(260,438)(261,437)(262,451)(263,453)(264,452)
(265,457)(266,459)(267,458)(268,454)(269,456)(270,455)(271,415)(272,417)
(273,416)(274,421)(275,423)(276,422)(277,418)(278,420)(279,419)(280,406)
(281,408)(282,407)(283,412)(284,414)(285,413)(286,409)(287,411)(288,410)
(289,424)(290,426)(291,425)(292,430)(293,432)(294,431)(295,427)(296,429)
(297,428)(298,471)(299,470)(300,469)(301,477)(302,476)(303,475)(304,474)
(305,473)(306,472)(307,462)(308,461)(309,460)(310,468)(311,467)(312,466)
(313,465)(314,464)(315,463)(316,480)(317,479)(318,478)(319,486)(320,485)
(321,484)(322,483)(323,482)(324,481);;
s2 := ( 1,166)( 2,167)( 3,168)( 4,163)( 5,164)( 6,165)( 7,169)( 8,170)
( 9,171)( 10,184)( 11,185)( 12,186)( 13,181)( 14,182)( 15,183)( 16,187)
( 17,188)( 18,189)( 19,175)( 20,176)( 21,177)( 22,172)( 23,173)( 24,174)
( 25,178)( 26,179)( 27,180)( 28,193)( 29,194)( 30,195)( 31,190)( 32,191)
( 33,192)( 34,196)( 35,197)( 36,198)( 37,211)( 38,212)( 39,213)( 40,208)
( 41,209)( 42,210)( 43,214)( 44,215)( 45,216)( 46,202)( 47,203)( 48,204)
( 49,199)( 50,200)( 51,201)( 52,205)( 53,206)( 54,207)( 55,220)( 56,221)
( 57,222)( 58,217)( 59,218)( 60,219)( 61,223)( 62,224)( 63,225)( 64,238)
( 65,239)( 66,240)( 67,235)( 68,236)( 69,237)( 70,241)( 71,242)( 72,243)
( 73,229)( 74,230)( 75,231)( 76,226)( 77,227)( 78,228)( 79,232)( 80,233)
( 81,234)( 82,247)( 83,248)( 84,249)( 85,244)( 86,245)( 87,246)( 88,250)
( 89,251)( 90,252)( 91,265)( 92,266)( 93,267)( 94,262)( 95,263)( 96,264)
( 97,268)( 98,269)( 99,270)(100,256)(101,257)(102,258)(103,253)(104,254)
(105,255)(106,259)(107,260)(108,261)(109,274)(110,275)(111,276)(112,271)
(113,272)(114,273)(115,277)(116,278)(117,279)(118,292)(119,293)(120,294)
(121,289)(122,290)(123,291)(124,295)(125,296)(126,297)(127,283)(128,284)
(129,285)(130,280)(131,281)(132,282)(133,286)(134,287)(135,288)(136,301)
(137,302)(138,303)(139,298)(140,299)(141,300)(142,304)(143,305)(144,306)
(145,319)(146,320)(147,321)(148,316)(149,317)(150,318)(151,322)(152,323)
(153,324)(154,310)(155,311)(156,312)(157,307)(158,308)(159,309)(160,313)
(161,314)(162,315)(325,571)(326,572)(327,573)(328,568)(329,569)(330,570)
(331,574)(332,575)(333,576)(334,589)(335,590)(336,591)(337,586)(338,587)
(339,588)(340,592)(341,593)(342,594)(343,580)(344,581)(345,582)(346,577)
(347,578)(348,579)(349,583)(350,584)(351,585)(352,598)(353,599)(354,600)
(355,595)(356,596)(357,597)(358,601)(359,602)(360,603)(361,616)(362,617)
(363,618)(364,613)(365,614)(366,615)(367,619)(368,620)(369,621)(370,607)
(371,608)(372,609)(373,604)(374,605)(375,606)(376,610)(377,611)(378,612)
(379,625)(380,626)(381,627)(382,622)(383,623)(384,624)(385,628)(386,629)
(387,630)(388,643)(389,644)(390,645)(391,640)(392,641)(393,642)(394,646)
(395,647)(396,648)(397,634)(398,635)(399,636)(400,631)(401,632)(402,633)
(403,637)(404,638)(405,639)(406,490)(407,491)(408,492)(409,487)(410,488)
(411,489)(412,493)(413,494)(414,495)(415,508)(416,509)(417,510)(418,505)
(419,506)(420,507)(421,511)(422,512)(423,513)(424,499)(425,500)(426,501)
(427,496)(428,497)(429,498)(430,502)(431,503)(432,504)(433,517)(434,518)
(435,519)(436,514)(437,515)(438,516)(439,520)(440,521)(441,522)(442,535)
(443,536)(444,537)(445,532)(446,533)(447,534)(448,538)(449,539)(450,540)
(451,526)(452,527)(453,528)(454,523)(455,524)(456,525)(457,529)(458,530)
(459,531)(460,544)(461,545)(462,546)(463,541)(464,542)(465,543)(466,547)
(467,548)(468,549)(469,562)(470,563)(471,564)(472,559)(473,560)(474,561)
(475,565)(476,566)(477,567)(478,553)(479,554)(480,555)(481,550)(482,551)
(483,552)(484,556)(485,557)(486,558);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*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,
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)!( 1,487)( 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)( 28,543)( 29,542)( 30,541)( 31,546)
( 32,545)( 33,544)( 34,549)( 35,548)( 36,547)( 37,561)( 38,560)( 39,559)
( 40,564)( 41,563)( 42,562)( 43,567)( 44,566)( 45,565)( 46,552)( 47,551)
( 48,550)( 49,555)( 50,554)( 51,553)( 52,558)( 53,557)( 54,556)( 55,516)
( 56,515)( 57,514)( 58,519)( 59,518)( 60,517)( 61,522)( 62,521)( 63,520)
( 64,534)( 65,533)( 66,532)( 67,537)( 68,536)( 69,535)( 70,540)( 71,539)
( 72,538)( 73,525)( 74,524)( 75,523)( 76,528)( 77,527)( 78,526)( 79,531)
( 80,530)( 81,529)( 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)(109,624)(110,623)(111,622)
(112,627)(113,626)(114,625)(115,630)(116,629)(117,628)(118,642)(119,641)
(120,640)(121,645)(122,644)(123,643)(124,648)(125,647)(126,646)(127,633)
(128,632)(129,631)(130,636)(131,635)(132,634)(133,639)(134,638)(135,637)
(136,597)(137,596)(138,595)(139,600)(140,599)(141,598)(142,603)(143,602)
(144,601)(145,615)(146,614)(147,613)(148,618)(149,617)(150,616)(151,621)
(152,620)(153,619)(154,606)(155,605)(156,604)(157,609)(158,608)(159,607)
(160,612)(161,611)(162,610)(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)(190,462)(191,461)
(192,460)(193,465)(194,464)(195,463)(196,468)(197,467)(198,466)(199,480)
(200,479)(201,478)(202,483)(203,482)(204,481)(205,486)(206,485)(207,484)
(208,471)(209,470)(210,469)(211,474)(212,473)(213,472)(214,477)(215,476)
(216,475)(217,435)(218,434)(219,433)(220,438)(221,437)(222,436)(223,441)
(224,440)(225,439)(226,453)(227,452)(228,451)(229,456)(230,455)(231,454)
(232,459)(233,458)(234,457)(235,444)(236,443)(237,442)(238,447)(239,446)
(240,445)(241,450)(242,449)(243,448)(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)(271,381)
(272,380)(273,379)(274,384)(275,383)(276,382)(277,387)(278,386)(279,385)
(280,399)(281,398)(282,397)(283,402)(284,401)(285,400)(286,405)(287,404)
(288,403)(289,390)(290,389)(291,388)(292,393)(293,392)(294,391)(295,396)
(296,395)(297,394)(298,354)(299,353)(300,352)(301,357)(302,356)(303,355)
(304,360)(305,359)(306,358)(307,372)(308,371)(309,370)(310,375)(311,374)
(312,373)(313,378)(314,377)(315,376)(316,363)(317,362)(318,361)(319,366)
(320,365)(321,364)(322,369)(323,368)(324,367);
s1 := Sym(648)!( 1,523)( 2,525)( 3,524)( 4,529)( 5,531)( 6,530)( 7,526)
( 8,528)( 9,527)( 10,514)( 11,516)( 12,515)( 13,520)( 14,522)( 15,521)
( 16,517)( 17,519)( 18,518)( 19,532)( 20,534)( 21,533)( 22,538)( 23,540)
( 24,539)( 25,535)( 26,537)( 27,536)( 28,496)( 29,498)( 30,497)( 31,502)
( 32,504)( 33,503)( 34,499)( 35,501)( 36,500)( 37,487)( 38,489)( 39,488)
( 40,493)( 41,495)( 42,494)( 43,490)( 44,492)( 45,491)( 46,505)( 47,507)
( 48,506)( 49,511)( 50,513)( 51,512)( 52,508)( 53,510)( 54,509)( 55,552)
( 56,551)( 57,550)( 58,558)( 59,557)( 60,556)( 61,555)( 62,554)( 63,553)
( 64,543)( 65,542)( 66,541)( 67,549)( 68,548)( 69,547)( 70,546)( 71,545)
( 72,544)( 73,561)( 74,560)( 75,559)( 76,567)( 77,566)( 78,565)( 79,564)
( 80,563)( 81,562)( 82,604)( 83,606)( 84,605)( 85,610)( 86,612)( 87,611)
( 88,607)( 89,609)( 90,608)( 91,595)( 92,597)( 93,596)( 94,601)( 95,603)
( 96,602)( 97,598)( 98,600)( 99,599)(100,613)(101,615)(102,614)(103,619)
(104,621)(105,620)(106,616)(107,618)(108,617)(109,577)(110,579)(111,578)
(112,583)(113,585)(114,584)(115,580)(116,582)(117,581)(118,568)(119,570)
(120,569)(121,574)(122,576)(123,575)(124,571)(125,573)(126,572)(127,586)
(128,588)(129,587)(130,592)(131,594)(132,593)(133,589)(134,591)(135,590)
(136,633)(137,632)(138,631)(139,639)(140,638)(141,637)(142,636)(143,635)
(144,634)(145,624)(146,623)(147,622)(148,630)(149,629)(150,628)(151,627)
(152,626)(153,625)(154,642)(155,641)(156,640)(157,648)(158,647)(159,646)
(160,645)(161,644)(162,643)(163,361)(164,363)(165,362)(166,367)(167,369)
(168,368)(169,364)(170,366)(171,365)(172,352)(173,354)(174,353)(175,358)
(176,360)(177,359)(178,355)(179,357)(180,356)(181,370)(182,372)(183,371)
(184,376)(185,378)(186,377)(187,373)(188,375)(189,374)(190,334)(191,336)
(192,335)(193,340)(194,342)(195,341)(196,337)(197,339)(198,338)(199,325)
(200,327)(201,326)(202,331)(203,333)(204,332)(205,328)(206,330)(207,329)
(208,343)(209,345)(210,344)(211,349)(212,351)(213,350)(214,346)(215,348)
(216,347)(217,390)(218,389)(219,388)(220,396)(221,395)(222,394)(223,393)
(224,392)(225,391)(226,381)(227,380)(228,379)(229,387)(230,386)(231,385)
(232,384)(233,383)(234,382)(235,399)(236,398)(237,397)(238,405)(239,404)
(240,403)(241,402)(242,401)(243,400)(244,442)(245,444)(246,443)(247,448)
(248,450)(249,449)(250,445)(251,447)(252,446)(253,433)(254,435)(255,434)
(256,439)(257,441)(258,440)(259,436)(260,438)(261,437)(262,451)(263,453)
(264,452)(265,457)(266,459)(267,458)(268,454)(269,456)(270,455)(271,415)
(272,417)(273,416)(274,421)(275,423)(276,422)(277,418)(278,420)(279,419)
(280,406)(281,408)(282,407)(283,412)(284,414)(285,413)(286,409)(287,411)
(288,410)(289,424)(290,426)(291,425)(292,430)(293,432)(294,431)(295,427)
(296,429)(297,428)(298,471)(299,470)(300,469)(301,477)(302,476)(303,475)
(304,474)(305,473)(306,472)(307,462)(308,461)(309,460)(310,468)(311,467)
(312,466)(313,465)(314,464)(315,463)(316,480)(317,479)(318,478)(319,486)
(320,485)(321,484)(322,483)(323,482)(324,481);
s2 := Sym(648)!( 1,166)( 2,167)( 3,168)( 4,163)( 5,164)( 6,165)( 7,169)
( 8,170)( 9,171)( 10,184)( 11,185)( 12,186)( 13,181)( 14,182)( 15,183)
( 16,187)( 17,188)( 18,189)( 19,175)( 20,176)( 21,177)( 22,172)( 23,173)
( 24,174)( 25,178)( 26,179)( 27,180)( 28,193)( 29,194)( 30,195)( 31,190)
( 32,191)( 33,192)( 34,196)( 35,197)( 36,198)( 37,211)( 38,212)( 39,213)
( 40,208)( 41,209)( 42,210)( 43,214)( 44,215)( 45,216)( 46,202)( 47,203)
( 48,204)( 49,199)( 50,200)( 51,201)( 52,205)( 53,206)( 54,207)( 55,220)
( 56,221)( 57,222)( 58,217)( 59,218)( 60,219)( 61,223)( 62,224)( 63,225)
( 64,238)( 65,239)( 66,240)( 67,235)( 68,236)( 69,237)( 70,241)( 71,242)
( 72,243)( 73,229)( 74,230)( 75,231)( 76,226)( 77,227)( 78,228)( 79,232)
( 80,233)( 81,234)( 82,247)( 83,248)( 84,249)( 85,244)( 86,245)( 87,246)
( 88,250)( 89,251)( 90,252)( 91,265)( 92,266)( 93,267)( 94,262)( 95,263)
( 96,264)( 97,268)( 98,269)( 99,270)(100,256)(101,257)(102,258)(103,253)
(104,254)(105,255)(106,259)(107,260)(108,261)(109,274)(110,275)(111,276)
(112,271)(113,272)(114,273)(115,277)(116,278)(117,279)(118,292)(119,293)
(120,294)(121,289)(122,290)(123,291)(124,295)(125,296)(126,297)(127,283)
(128,284)(129,285)(130,280)(131,281)(132,282)(133,286)(134,287)(135,288)
(136,301)(137,302)(138,303)(139,298)(140,299)(141,300)(142,304)(143,305)
(144,306)(145,319)(146,320)(147,321)(148,316)(149,317)(150,318)(151,322)
(152,323)(153,324)(154,310)(155,311)(156,312)(157,307)(158,308)(159,309)
(160,313)(161,314)(162,315)(325,571)(326,572)(327,573)(328,568)(329,569)
(330,570)(331,574)(332,575)(333,576)(334,589)(335,590)(336,591)(337,586)
(338,587)(339,588)(340,592)(341,593)(342,594)(343,580)(344,581)(345,582)
(346,577)(347,578)(348,579)(349,583)(350,584)(351,585)(352,598)(353,599)
(354,600)(355,595)(356,596)(357,597)(358,601)(359,602)(360,603)(361,616)
(362,617)(363,618)(364,613)(365,614)(366,615)(367,619)(368,620)(369,621)
(370,607)(371,608)(372,609)(373,604)(374,605)(375,606)(376,610)(377,611)
(378,612)(379,625)(380,626)(381,627)(382,622)(383,623)(384,624)(385,628)
(386,629)(387,630)(388,643)(389,644)(390,645)(391,640)(392,641)(393,642)
(394,646)(395,647)(396,648)(397,634)(398,635)(399,636)(400,631)(401,632)
(402,633)(403,637)(404,638)(405,639)(406,490)(407,491)(408,492)(409,487)
(410,488)(411,489)(412,493)(413,494)(414,495)(415,508)(416,509)(417,510)
(418,505)(419,506)(420,507)(421,511)(422,512)(423,513)(424,499)(425,500)
(426,501)(427,496)(428,497)(429,498)(430,502)(431,503)(432,504)(433,517)
(434,518)(435,519)(436,514)(437,515)(438,516)(439,520)(440,521)(441,522)
(442,535)(443,536)(444,537)(445,532)(446,533)(447,534)(448,538)(449,539)
(450,540)(451,526)(452,527)(453,528)(454,523)(455,524)(456,525)(457,529)
(458,530)(459,531)(460,544)(461,545)(462,546)(463,541)(464,542)(465,543)
(466,547)(467,548)(468,549)(469,562)(470,563)(471,564)(472,559)(473,560)
(474,561)(475,565)(476,566)(477,567)(478,553)(479,554)(480,555)(481,550)
(482,551)(483,552)(484,556)(485,557)(486,558);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*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,
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