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