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