Polytope of Type {12,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,18}*1296p
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 3
Schlafli Type : {12,18}
Number of vertices, edges, etc : 36, 324, 54
Order of s0s1s2 : 3
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {12,9}*648b
27-fold quotients : {4,6}*48b
54-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,379)( 2,381)( 3,380)( 4,385)( 5,387)( 6,386)( 7,382)( 8,384)
( 9,383)( 10,388)( 11,390)( 12,389)( 13,394)( 14,396)( 15,395)( 16,391)
( 17,393)( 18,392)( 19,397)( 20,399)( 21,398)( 22,403)( 23,405)( 24,404)
( 25,400)( 26,402)( 27,401)( 28,406)( 29,408)( 30,407)( 31,412)( 32,414)
( 33,413)( 34,409)( 35,411)( 36,410)( 37,415)( 38,417)( 39,416)( 40,421)
( 41,423)( 42,422)( 43,418)( 44,420)( 45,419)( 46,424)( 47,426)( 48,425)
( 49,430)( 50,432)( 51,431)( 52,427)( 53,429)( 54,428)( 55,325)( 56,327)
( 57,326)( 58,331)( 59,333)( 60,332)( 61,328)( 62,330)( 63,329)( 64,334)
( 65,336)( 66,335)( 67,340)( 68,342)( 69,341)( 70,337)( 71,339)( 72,338)
( 73,343)( 74,345)( 75,344)( 76,349)( 77,351)( 78,350)( 79,346)( 80,348)
( 81,347)( 82,352)( 83,354)( 84,353)( 85,358)( 86,360)( 87,359)( 88,355)
( 89,357)( 90,356)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)
( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)
(105,377)(106,373)(107,375)(108,374)(109,487)(110,489)(111,488)(112,493)
(113,495)(114,494)(115,490)(116,492)(117,491)(118,496)(119,498)(120,497)
(121,502)(122,504)(123,503)(124,499)(125,501)(126,500)(127,505)(128,507)
(129,506)(130,511)(131,513)(132,512)(133,508)(134,510)(135,509)(136,514)
(137,516)(138,515)(139,520)(140,522)(141,521)(142,517)(143,519)(144,518)
(145,523)(146,525)(147,524)(148,529)(149,531)(150,530)(151,526)(152,528)
(153,527)(154,532)(155,534)(156,533)(157,538)(158,540)(159,539)(160,535)
(161,537)(162,536)(163,433)(164,435)(165,434)(166,439)(167,441)(168,440)
(169,436)(170,438)(171,437)(172,442)(173,444)(174,443)(175,448)(176,450)
(177,449)(178,445)(179,447)(180,446)(181,451)(182,453)(183,452)(184,457)
(185,459)(186,458)(187,454)(188,456)(189,455)(190,460)(191,462)(192,461)
(193,466)(194,468)(195,467)(196,463)(197,465)(198,464)(199,469)(200,471)
(201,470)(202,475)(203,477)(204,476)(205,472)(206,474)(207,473)(208,478)
(209,480)(210,479)(211,484)(212,486)(213,485)(214,481)(215,483)(216,482)
(217,595)(218,597)(219,596)(220,601)(221,603)(222,602)(223,598)(224,600)
(225,599)(226,604)(227,606)(228,605)(229,610)(230,612)(231,611)(232,607)
(233,609)(234,608)(235,613)(236,615)(237,614)(238,619)(239,621)(240,620)
(241,616)(242,618)(243,617)(244,622)(245,624)(246,623)(247,628)(248,630)
(249,629)(250,625)(251,627)(252,626)(253,631)(254,633)(255,632)(256,637)
(257,639)(258,638)(259,634)(260,636)(261,635)(262,640)(263,642)(264,641)
(265,646)(266,648)(267,647)(268,643)(269,645)(270,644)(271,541)(272,543)
(273,542)(274,547)(275,549)(276,548)(277,544)(278,546)(279,545)(280,550)
(281,552)(282,551)(283,556)(284,558)(285,557)(286,553)(287,555)(288,554)
(289,559)(290,561)(291,560)(292,565)(293,567)(294,566)(295,562)(296,564)
(297,563)(298,568)(299,570)(300,569)(301,574)(302,576)(303,575)(304,571)
(305,573)(306,572)(307,577)(308,579)(309,578)(310,583)(311,585)(312,584)
(313,580)(314,582)(315,581)(316,586)(317,588)(318,587)(319,592)(320,594)
(321,593)(322,589)(323,591)(324,590);;
s1 := ( 1, 2)( 4, 20)( 5, 19)( 6, 21)( 7, 11)( 8, 10)( 9, 12)( 13, 26)
( 14, 25)( 15, 27)( 16, 17)( 22, 23)( 28, 56)( 29, 55)( 30, 57)( 31, 74)
( 32, 73)( 33, 75)( 34, 65)( 35, 64)( 36, 66)( 37, 62)( 38, 61)( 39, 63)
( 40, 80)( 41, 79)( 42, 81)( 43, 71)( 44, 70)( 45, 72)( 46, 59)( 47, 58)
( 48, 60)( 49, 77)( 50, 76)( 51, 78)( 52, 68)( 53, 67)( 54, 69)( 82, 83)
( 85,101)( 86,100)( 87,102)( 88, 92)( 89, 91)( 90, 93)( 94,107)( 95,106)
( 96,108)( 97, 98)(103,104)(109,218)(110,217)(111,219)(112,236)(113,235)
(114,237)(115,227)(116,226)(117,228)(118,224)(119,223)(120,225)(121,242)
(122,241)(123,243)(124,233)(125,232)(126,234)(127,221)(128,220)(129,222)
(130,239)(131,238)(132,240)(133,230)(134,229)(135,231)(136,272)(137,271)
(138,273)(139,290)(140,289)(141,291)(142,281)(143,280)(144,282)(145,278)
(146,277)(147,279)(148,296)(149,295)(150,297)(151,287)(152,286)(153,288)
(154,275)(155,274)(156,276)(157,293)(158,292)(159,294)(160,284)(161,283)
(162,285)(163,245)(164,244)(165,246)(166,263)(167,262)(168,264)(169,254)
(170,253)(171,255)(172,251)(173,250)(174,252)(175,269)(176,268)(177,270)
(178,260)(179,259)(180,261)(181,248)(182,247)(183,249)(184,266)(185,265)
(186,267)(187,257)(188,256)(189,258)(190,299)(191,298)(192,300)(193,317)
(194,316)(195,318)(196,308)(197,307)(198,309)(199,305)(200,304)(201,306)
(202,323)(203,322)(204,324)(205,314)(206,313)(207,315)(208,302)(209,301)
(210,303)(211,320)(212,319)(213,321)(214,311)(215,310)(216,312)(325,326)
(328,344)(329,343)(330,345)(331,335)(332,334)(333,336)(337,350)(338,349)
(339,351)(340,341)(346,347)(352,380)(353,379)(354,381)(355,398)(356,397)
(357,399)(358,389)(359,388)(360,390)(361,386)(362,385)(363,387)(364,404)
(365,403)(366,405)(367,395)(368,394)(369,396)(370,383)(371,382)(372,384)
(373,401)(374,400)(375,402)(376,392)(377,391)(378,393)(406,407)(409,425)
(410,424)(411,426)(412,416)(413,415)(414,417)(418,431)(419,430)(420,432)
(421,422)(427,428)(433,542)(434,541)(435,543)(436,560)(437,559)(438,561)
(439,551)(440,550)(441,552)(442,548)(443,547)(444,549)(445,566)(446,565)
(447,567)(448,557)(449,556)(450,558)(451,545)(452,544)(453,546)(454,563)
(455,562)(456,564)(457,554)(458,553)(459,555)(460,596)(461,595)(462,597)
(463,614)(464,613)(465,615)(466,605)(467,604)(468,606)(469,602)(470,601)
(471,603)(472,620)(473,619)(474,621)(475,611)(476,610)(477,612)(478,599)
(479,598)(480,600)(481,617)(482,616)(483,618)(484,608)(485,607)(486,609)
(487,569)(488,568)(489,570)(490,587)(491,586)(492,588)(493,578)(494,577)
(495,579)(496,575)(497,574)(498,576)(499,593)(500,592)(501,594)(502,584)
(503,583)(504,585)(505,572)(506,571)(507,573)(508,590)(509,589)(510,591)
(511,581)(512,580)(513,582)(514,623)(515,622)(516,624)(517,641)(518,640)
(519,642)(520,632)(521,631)(522,633)(523,629)(524,628)(525,630)(526,647)
(527,646)(528,648)(529,638)(530,637)(531,639)(532,626)(533,625)(534,627)
(535,644)(536,643)(537,645)(538,635)(539,634)(540,636);;
s2 := ( 1,604)( 2,607)( 3,610)( 4,605)( 5,608)( 6,611)( 7,606)( 8,609)
( 9,612)( 10,595)( 11,598)( 12,601)( 13,596)( 14,599)( 15,602)( 16,597)
( 17,600)( 18,603)( 19,613)( 20,616)( 21,619)( 22,614)( 23,617)( 24,620)
( 25,615)( 26,618)( 27,621)( 28,577)( 29,580)( 30,583)( 31,578)( 32,581)
( 33,584)( 34,579)( 35,582)( 36,585)( 37,568)( 38,571)( 39,574)( 40,569)
( 41,572)( 42,575)( 43,570)( 44,573)( 45,576)( 46,586)( 47,589)( 48,592)
( 49,587)( 50,590)( 51,593)( 52,588)( 53,591)( 54,594)( 55,550)( 56,553)
( 57,556)( 58,551)( 59,554)( 60,557)( 61,552)( 62,555)( 63,558)( 64,541)
( 65,544)( 66,547)( 67,542)( 68,545)( 69,548)( 70,543)( 71,546)( 72,549)
( 73,559)( 74,562)( 75,565)( 76,560)( 77,563)( 78,566)( 79,561)( 80,564)
( 81,567)( 82,631)( 83,634)( 84,637)( 85,632)( 86,635)( 87,638)( 88,633)
( 89,636)( 90,639)( 91,622)( 92,625)( 93,628)( 94,623)( 95,626)( 96,629)
( 97,624)( 98,627)( 99,630)(100,640)(101,643)(102,646)(103,641)(104,644)
(105,647)(106,642)(107,645)(108,648)(109,496)(110,499)(111,502)(112,497)
(113,500)(114,503)(115,498)(116,501)(117,504)(118,487)(119,490)(120,493)
(121,488)(122,491)(123,494)(124,489)(125,492)(126,495)(127,505)(128,508)
(129,511)(130,506)(131,509)(132,512)(133,507)(134,510)(135,513)(136,469)
(137,472)(138,475)(139,470)(140,473)(141,476)(142,471)(143,474)(144,477)
(145,460)(146,463)(147,466)(148,461)(149,464)(150,467)(151,462)(152,465)
(153,468)(154,478)(155,481)(156,484)(157,479)(158,482)(159,485)(160,480)
(161,483)(162,486)(163,442)(164,445)(165,448)(166,443)(167,446)(168,449)
(169,444)(170,447)(171,450)(172,433)(173,436)(174,439)(175,434)(176,437)
(177,440)(178,435)(179,438)(180,441)(181,451)(182,454)(183,457)(184,452)
(185,455)(186,458)(187,453)(188,456)(189,459)(190,523)(191,526)(192,529)
(193,524)(194,527)(195,530)(196,525)(197,528)(198,531)(199,514)(200,517)
(201,520)(202,515)(203,518)(204,521)(205,516)(206,519)(207,522)(208,532)
(209,535)(210,538)(211,533)(212,536)(213,539)(214,534)(215,537)(216,540)
(217,388)(218,391)(219,394)(220,389)(221,392)(222,395)(223,390)(224,393)
(225,396)(226,379)(227,382)(228,385)(229,380)(230,383)(231,386)(232,381)
(233,384)(234,387)(235,397)(236,400)(237,403)(238,398)(239,401)(240,404)
(241,399)(242,402)(243,405)(244,361)(245,364)(246,367)(247,362)(248,365)
(249,368)(250,363)(251,366)(252,369)(253,352)(254,355)(255,358)(256,353)
(257,356)(258,359)(259,354)(260,357)(261,360)(262,370)(263,373)(264,376)
(265,371)(266,374)(267,377)(268,372)(269,375)(270,378)(271,334)(272,337)
(273,340)(274,335)(275,338)(276,341)(277,336)(278,339)(279,342)(280,325)
(281,328)(282,331)(283,326)(284,329)(285,332)(286,327)(287,330)(288,333)
(289,343)(290,346)(291,349)(292,344)(293,347)(294,350)(295,345)(296,348)
(297,351)(298,415)(299,418)(300,421)(301,416)(302,419)(303,422)(304,417)
(305,420)(306,423)(307,406)(308,409)(309,412)(310,407)(311,410)(312,413)
(313,408)(314,411)(315,414)(316,424)(317,427)(318,430)(319,425)(320,428)
(321,431)(322,426)(323,429)(324,432);;
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*s2*s0*s1*s2*s0*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(648)!( 1,379)( 2,381)( 3,380)( 4,385)( 5,387)( 6,386)( 7,382)
( 8,384)( 9,383)( 10,388)( 11,390)( 12,389)( 13,394)( 14,396)( 15,395)
( 16,391)( 17,393)( 18,392)( 19,397)( 20,399)( 21,398)( 22,403)( 23,405)
( 24,404)( 25,400)( 26,402)( 27,401)( 28,406)( 29,408)( 30,407)( 31,412)
( 32,414)( 33,413)( 34,409)( 35,411)( 36,410)( 37,415)( 38,417)( 39,416)
( 40,421)( 41,423)( 42,422)( 43,418)( 44,420)( 45,419)( 46,424)( 47,426)
( 48,425)( 49,430)( 50,432)( 51,431)( 52,427)( 53,429)( 54,428)( 55,325)
( 56,327)( 57,326)( 58,331)( 59,333)( 60,332)( 61,328)( 62,330)( 63,329)
( 64,334)( 65,336)( 66,335)( 67,340)( 68,342)( 69,341)( 70,337)( 71,339)
( 72,338)( 73,343)( 74,345)( 75,344)( 76,349)( 77,351)( 78,350)( 79,346)
( 80,348)( 81,347)( 82,352)( 83,354)( 84,353)( 85,358)( 86,360)( 87,359)
( 88,355)( 89,357)( 90,356)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)
( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)
(104,378)(105,377)(106,373)(107,375)(108,374)(109,487)(110,489)(111,488)
(112,493)(113,495)(114,494)(115,490)(116,492)(117,491)(118,496)(119,498)
(120,497)(121,502)(122,504)(123,503)(124,499)(125,501)(126,500)(127,505)
(128,507)(129,506)(130,511)(131,513)(132,512)(133,508)(134,510)(135,509)
(136,514)(137,516)(138,515)(139,520)(140,522)(141,521)(142,517)(143,519)
(144,518)(145,523)(146,525)(147,524)(148,529)(149,531)(150,530)(151,526)
(152,528)(153,527)(154,532)(155,534)(156,533)(157,538)(158,540)(159,539)
(160,535)(161,537)(162,536)(163,433)(164,435)(165,434)(166,439)(167,441)
(168,440)(169,436)(170,438)(171,437)(172,442)(173,444)(174,443)(175,448)
(176,450)(177,449)(178,445)(179,447)(180,446)(181,451)(182,453)(183,452)
(184,457)(185,459)(186,458)(187,454)(188,456)(189,455)(190,460)(191,462)
(192,461)(193,466)(194,468)(195,467)(196,463)(197,465)(198,464)(199,469)
(200,471)(201,470)(202,475)(203,477)(204,476)(205,472)(206,474)(207,473)
(208,478)(209,480)(210,479)(211,484)(212,486)(213,485)(214,481)(215,483)
(216,482)(217,595)(218,597)(219,596)(220,601)(221,603)(222,602)(223,598)
(224,600)(225,599)(226,604)(227,606)(228,605)(229,610)(230,612)(231,611)
(232,607)(233,609)(234,608)(235,613)(236,615)(237,614)(238,619)(239,621)
(240,620)(241,616)(242,618)(243,617)(244,622)(245,624)(246,623)(247,628)
(248,630)(249,629)(250,625)(251,627)(252,626)(253,631)(254,633)(255,632)
(256,637)(257,639)(258,638)(259,634)(260,636)(261,635)(262,640)(263,642)
(264,641)(265,646)(266,648)(267,647)(268,643)(269,645)(270,644)(271,541)
(272,543)(273,542)(274,547)(275,549)(276,548)(277,544)(278,546)(279,545)
(280,550)(281,552)(282,551)(283,556)(284,558)(285,557)(286,553)(287,555)
(288,554)(289,559)(290,561)(291,560)(292,565)(293,567)(294,566)(295,562)
(296,564)(297,563)(298,568)(299,570)(300,569)(301,574)(302,576)(303,575)
(304,571)(305,573)(306,572)(307,577)(308,579)(309,578)(310,583)(311,585)
(312,584)(313,580)(314,582)(315,581)(316,586)(317,588)(318,587)(319,592)
(320,594)(321,593)(322,589)(323,591)(324,590);
s1 := Sym(648)!( 1, 2)( 4, 20)( 5, 19)( 6, 21)( 7, 11)( 8, 10)( 9, 12)
( 13, 26)( 14, 25)( 15, 27)( 16, 17)( 22, 23)( 28, 56)( 29, 55)( 30, 57)
( 31, 74)( 32, 73)( 33, 75)( 34, 65)( 35, 64)( 36, 66)( 37, 62)( 38, 61)
( 39, 63)( 40, 80)( 41, 79)( 42, 81)( 43, 71)( 44, 70)( 45, 72)( 46, 59)
( 47, 58)( 48, 60)( 49, 77)( 50, 76)( 51, 78)( 52, 68)( 53, 67)( 54, 69)
( 82, 83)( 85,101)( 86,100)( 87,102)( 88, 92)( 89, 91)( 90, 93)( 94,107)
( 95,106)( 96,108)( 97, 98)(103,104)(109,218)(110,217)(111,219)(112,236)
(113,235)(114,237)(115,227)(116,226)(117,228)(118,224)(119,223)(120,225)
(121,242)(122,241)(123,243)(124,233)(125,232)(126,234)(127,221)(128,220)
(129,222)(130,239)(131,238)(132,240)(133,230)(134,229)(135,231)(136,272)
(137,271)(138,273)(139,290)(140,289)(141,291)(142,281)(143,280)(144,282)
(145,278)(146,277)(147,279)(148,296)(149,295)(150,297)(151,287)(152,286)
(153,288)(154,275)(155,274)(156,276)(157,293)(158,292)(159,294)(160,284)
(161,283)(162,285)(163,245)(164,244)(165,246)(166,263)(167,262)(168,264)
(169,254)(170,253)(171,255)(172,251)(173,250)(174,252)(175,269)(176,268)
(177,270)(178,260)(179,259)(180,261)(181,248)(182,247)(183,249)(184,266)
(185,265)(186,267)(187,257)(188,256)(189,258)(190,299)(191,298)(192,300)
(193,317)(194,316)(195,318)(196,308)(197,307)(198,309)(199,305)(200,304)
(201,306)(202,323)(203,322)(204,324)(205,314)(206,313)(207,315)(208,302)
(209,301)(210,303)(211,320)(212,319)(213,321)(214,311)(215,310)(216,312)
(325,326)(328,344)(329,343)(330,345)(331,335)(332,334)(333,336)(337,350)
(338,349)(339,351)(340,341)(346,347)(352,380)(353,379)(354,381)(355,398)
(356,397)(357,399)(358,389)(359,388)(360,390)(361,386)(362,385)(363,387)
(364,404)(365,403)(366,405)(367,395)(368,394)(369,396)(370,383)(371,382)
(372,384)(373,401)(374,400)(375,402)(376,392)(377,391)(378,393)(406,407)
(409,425)(410,424)(411,426)(412,416)(413,415)(414,417)(418,431)(419,430)
(420,432)(421,422)(427,428)(433,542)(434,541)(435,543)(436,560)(437,559)
(438,561)(439,551)(440,550)(441,552)(442,548)(443,547)(444,549)(445,566)
(446,565)(447,567)(448,557)(449,556)(450,558)(451,545)(452,544)(453,546)
(454,563)(455,562)(456,564)(457,554)(458,553)(459,555)(460,596)(461,595)
(462,597)(463,614)(464,613)(465,615)(466,605)(467,604)(468,606)(469,602)
(470,601)(471,603)(472,620)(473,619)(474,621)(475,611)(476,610)(477,612)
(478,599)(479,598)(480,600)(481,617)(482,616)(483,618)(484,608)(485,607)
(486,609)(487,569)(488,568)(489,570)(490,587)(491,586)(492,588)(493,578)
(494,577)(495,579)(496,575)(497,574)(498,576)(499,593)(500,592)(501,594)
(502,584)(503,583)(504,585)(505,572)(506,571)(507,573)(508,590)(509,589)
(510,591)(511,581)(512,580)(513,582)(514,623)(515,622)(516,624)(517,641)
(518,640)(519,642)(520,632)(521,631)(522,633)(523,629)(524,628)(525,630)
(526,647)(527,646)(528,648)(529,638)(530,637)(531,639)(532,626)(533,625)
(534,627)(535,644)(536,643)(537,645)(538,635)(539,634)(540,636);
s2 := Sym(648)!( 1,604)( 2,607)( 3,610)( 4,605)( 5,608)( 6,611)( 7,606)
( 8,609)( 9,612)( 10,595)( 11,598)( 12,601)( 13,596)( 14,599)( 15,602)
( 16,597)( 17,600)( 18,603)( 19,613)( 20,616)( 21,619)( 22,614)( 23,617)
( 24,620)( 25,615)( 26,618)( 27,621)( 28,577)( 29,580)( 30,583)( 31,578)
( 32,581)( 33,584)( 34,579)( 35,582)( 36,585)( 37,568)( 38,571)( 39,574)
( 40,569)( 41,572)( 42,575)( 43,570)( 44,573)( 45,576)( 46,586)( 47,589)
( 48,592)( 49,587)( 50,590)( 51,593)( 52,588)( 53,591)( 54,594)( 55,550)
( 56,553)( 57,556)( 58,551)( 59,554)( 60,557)( 61,552)( 62,555)( 63,558)
( 64,541)( 65,544)( 66,547)( 67,542)( 68,545)( 69,548)( 70,543)( 71,546)
( 72,549)( 73,559)( 74,562)( 75,565)( 76,560)( 77,563)( 78,566)( 79,561)
( 80,564)( 81,567)( 82,631)( 83,634)( 84,637)( 85,632)( 86,635)( 87,638)
( 88,633)( 89,636)( 90,639)( 91,622)( 92,625)( 93,628)( 94,623)( 95,626)
( 96,629)( 97,624)( 98,627)( 99,630)(100,640)(101,643)(102,646)(103,641)
(104,644)(105,647)(106,642)(107,645)(108,648)(109,496)(110,499)(111,502)
(112,497)(113,500)(114,503)(115,498)(116,501)(117,504)(118,487)(119,490)
(120,493)(121,488)(122,491)(123,494)(124,489)(125,492)(126,495)(127,505)
(128,508)(129,511)(130,506)(131,509)(132,512)(133,507)(134,510)(135,513)
(136,469)(137,472)(138,475)(139,470)(140,473)(141,476)(142,471)(143,474)
(144,477)(145,460)(146,463)(147,466)(148,461)(149,464)(150,467)(151,462)
(152,465)(153,468)(154,478)(155,481)(156,484)(157,479)(158,482)(159,485)
(160,480)(161,483)(162,486)(163,442)(164,445)(165,448)(166,443)(167,446)
(168,449)(169,444)(170,447)(171,450)(172,433)(173,436)(174,439)(175,434)
(176,437)(177,440)(178,435)(179,438)(180,441)(181,451)(182,454)(183,457)
(184,452)(185,455)(186,458)(187,453)(188,456)(189,459)(190,523)(191,526)
(192,529)(193,524)(194,527)(195,530)(196,525)(197,528)(198,531)(199,514)
(200,517)(201,520)(202,515)(203,518)(204,521)(205,516)(206,519)(207,522)
(208,532)(209,535)(210,538)(211,533)(212,536)(213,539)(214,534)(215,537)
(216,540)(217,388)(218,391)(219,394)(220,389)(221,392)(222,395)(223,390)
(224,393)(225,396)(226,379)(227,382)(228,385)(229,380)(230,383)(231,386)
(232,381)(233,384)(234,387)(235,397)(236,400)(237,403)(238,398)(239,401)
(240,404)(241,399)(242,402)(243,405)(244,361)(245,364)(246,367)(247,362)
(248,365)(249,368)(250,363)(251,366)(252,369)(253,352)(254,355)(255,358)
(256,353)(257,356)(258,359)(259,354)(260,357)(261,360)(262,370)(263,373)
(264,376)(265,371)(266,374)(267,377)(268,372)(269,375)(270,378)(271,334)
(272,337)(273,340)(274,335)(275,338)(276,341)(277,336)(278,339)(279,342)
(280,325)(281,328)(282,331)(283,326)(284,329)(285,332)(286,327)(287,330)
(288,333)(289,343)(290,346)(291,349)(292,344)(293,347)(294,350)(295,345)
(296,348)(297,351)(298,415)(299,418)(300,421)(301,416)(302,419)(303,422)
(304,417)(305,420)(306,423)(307,406)(308,409)(309,412)(310,407)(311,410)
(312,413)(313,408)(314,411)(315,414)(316,424)(317,427)(318,430)(319,425)
(320,428)(321,431)(322,426)(323,429)(324,432);
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*s2*s0*s1*s2*s0*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*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 >;
References : None.
to this polytope