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Polytope of Type {18,12}

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