Polytope of Type {12,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,18}*1296n
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 : 6
Order of s0s1s2s1 : 12
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}*648b
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 := ( 1,604)( 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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*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)!( 1,604)( 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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1 >;
References : None.
to this polytope