Questions?
See the FAQ
or other info.

Polytope of Type {4,18}

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