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Polytope of Type {18,6,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6,9}*1944a
if this polytope has a name.
Group : SmallGroup(1944,940)
Rank : 4
Schlafli Type : {18,6,9}
Number of vertices, edges, etc : 18, 54, 27, 9
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 6
Special Properties :
   Universal
   Orientable
   Flat
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 : {9,6,9}*972
   3-fold quotients : {18,2,9}*648, {6,6,9}*648a, {18,6,3}*648a
   6-fold quotients : {9,2,9}*324, {3,6,9}*324, {9,6,3}*324
   9-fold quotients : {6,2,9}*216, {18,2,3}*216, {6,6,3}*216a
   18-fold quotients : {3,2,9}*108, {9,2,3}*108, {3,6,3}*108
   27-fold quotients : {2,2,9}*72, {6,2,3}*72
   54-fold quotients : {3,2,3}*36
   81-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  3)(  5,  6)(  8,  9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)
( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)( 37, 46)
( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)( 45, 53)
( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)( 68, 78)
( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 82,172)( 83,174)( 84,173)( 85,175)
( 86,177)( 87,176)( 88,178)( 89,180)( 90,179)( 91,163)( 92,165)( 93,164)
( 94,166)( 95,168)( 96,167)( 97,169)( 98,171)( 99,170)(100,181)(101,183)
(102,182)(103,184)(104,186)(105,185)(106,187)(107,189)(108,188)(109,199)
(110,201)(111,200)(112,202)(113,204)(114,203)(115,205)(116,207)(117,206)
(118,190)(119,192)(120,191)(121,193)(122,195)(123,194)(124,196)(125,198)
(126,197)(127,208)(128,210)(129,209)(130,211)(131,213)(132,212)(133,214)
(134,216)(135,215)(136,226)(137,228)(138,227)(139,229)(140,231)(141,230)
(142,232)(143,234)(144,233)(145,217)(146,219)(147,218)(148,220)(149,222)
(150,221)(151,223)(152,225)(153,224)(154,235)(155,237)(156,236)(157,238)
(158,240)(159,239)(160,241)(161,243)(162,242)(245,246)(248,249)(251,252)
(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)
(261,269)(272,273)(275,276)(278,279)(280,289)(281,291)(282,290)(283,292)
(284,294)(285,293)(286,295)(287,297)(288,296)(299,300)(302,303)(305,306)
(307,316)(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)
(315,323)(325,415)(326,417)(327,416)(328,418)(329,420)(330,419)(331,421)
(332,423)(333,422)(334,406)(335,408)(336,407)(337,409)(338,411)(339,410)
(340,412)(341,414)(342,413)(343,424)(344,426)(345,425)(346,427)(347,429)
(348,428)(349,430)(350,432)(351,431)(352,442)(353,444)(354,443)(355,445)
(356,447)(357,446)(358,448)(359,450)(360,449)(361,433)(362,435)(363,434)
(364,436)(365,438)(366,437)(367,439)(368,441)(369,440)(370,451)(371,453)
(372,452)(373,454)(374,456)(375,455)(376,457)(377,459)(378,458)(379,469)
(380,471)(381,470)(382,472)(383,474)(384,473)(385,475)(386,477)(387,476)
(388,460)(389,462)(390,461)(391,463)(392,465)(393,464)(394,466)(395,468)
(396,467)(397,478)(398,480)(399,479)(400,481)(401,483)(402,482)(403,484)
(404,486)(405,485);;
s1 := (  1,325)(  2,327)(  3,326)(  4,328)(  5,330)(  6,329)(  7,331)(  8,333)
(  9,332)( 10,343)( 11,345)( 12,344)( 13,346)( 14,348)( 15,347)( 16,349)
( 17,351)( 18,350)( 19,334)( 20,336)( 21,335)( 22,337)( 23,339)( 24,338)
( 25,340)( 26,342)( 27,341)( 28,353)( 29,352)( 30,354)( 31,356)( 32,355)
( 33,357)( 34,359)( 35,358)( 36,360)( 37,371)( 38,370)( 39,372)( 40,374)
( 41,373)( 42,375)( 43,377)( 44,376)( 45,378)( 46,362)( 47,361)( 48,363)
( 49,365)( 50,364)( 51,366)( 52,368)( 53,367)( 54,369)( 55,381)( 56,380)
( 57,379)( 58,384)( 59,383)( 60,382)( 61,387)( 62,386)( 63,385)( 64,399)
( 65,398)( 66,397)( 67,402)( 68,401)( 69,400)( 70,405)( 71,404)( 72,403)
( 73,390)( 74,389)( 75,388)( 76,393)( 77,392)( 78,391)( 79,396)( 80,395)
( 81,394)( 82,244)( 83,246)( 84,245)( 85,247)( 86,249)( 87,248)( 88,250)
( 89,252)( 90,251)( 91,262)( 92,264)( 93,263)( 94,265)( 95,267)( 96,266)
( 97,268)( 98,270)( 99,269)(100,253)(101,255)(102,254)(103,256)(104,258)
(105,257)(106,259)(107,261)(108,260)(109,272)(110,271)(111,273)(112,275)
(113,274)(114,276)(115,278)(116,277)(117,279)(118,290)(119,289)(120,291)
(121,293)(122,292)(123,294)(124,296)(125,295)(126,297)(127,281)(128,280)
(129,282)(130,284)(131,283)(132,285)(133,287)(134,286)(135,288)(136,300)
(137,299)(138,298)(139,303)(140,302)(141,301)(142,306)(143,305)(144,304)
(145,318)(146,317)(147,316)(148,321)(149,320)(150,319)(151,324)(152,323)
(153,322)(154,309)(155,308)(156,307)(157,312)(158,311)(159,310)(160,315)
(161,314)(162,313)(163,415)(164,417)(165,416)(166,418)(167,420)(168,419)
(169,421)(170,423)(171,422)(172,406)(173,408)(174,407)(175,409)(176,411)
(177,410)(178,412)(179,414)(180,413)(181,424)(182,426)(183,425)(184,427)
(185,429)(186,428)(187,430)(188,432)(189,431)(190,443)(191,442)(192,444)
(193,446)(194,445)(195,447)(196,449)(197,448)(198,450)(199,434)(200,433)
(201,435)(202,437)(203,436)(204,438)(205,440)(206,439)(207,441)(208,452)
(209,451)(210,453)(211,455)(212,454)(213,456)(214,458)(215,457)(216,459)
(217,471)(218,470)(219,469)(220,474)(221,473)(222,472)(223,477)(224,476)
(225,475)(226,462)(227,461)(228,460)(229,465)(230,464)(231,463)(232,468)
(233,467)(234,466)(235,480)(236,479)(237,478)(238,483)(239,482)(240,481)
(241,486)(242,485)(243,484);;
s2 := (  1, 28)(  2, 30)(  3, 29)(  4, 34)(  5, 36)(  6, 35)(  7, 31)(  8, 33)
(  9, 32)( 10, 37)( 11, 39)( 12, 38)( 13, 43)( 14, 45)( 15, 44)( 16, 40)
( 17, 42)( 18, 41)( 19, 46)( 20, 48)( 21, 47)( 22, 52)( 23, 54)( 24, 53)
( 25, 49)( 26, 51)( 27, 50)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)
( 65, 69)( 66, 68)( 71, 72)( 73, 76)( 74, 78)( 75, 77)( 80, 81)( 82,109)
( 83,111)( 84,110)( 85,115)( 86,117)( 87,116)( 88,112)( 89,114)( 90,113)
( 91,118)( 92,120)( 93,119)( 94,124)( 95,126)( 96,125)( 97,121)( 98,123)
( 99,122)(100,127)(101,129)(102,128)(103,133)(104,135)(105,134)(106,130)
(107,132)(108,131)(136,139)(137,141)(138,140)(143,144)(145,148)(146,150)
(147,149)(152,153)(154,157)(155,159)(156,158)(161,162)(163,190)(164,192)
(165,191)(166,196)(167,198)(168,197)(169,193)(170,195)(171,194)(172,199)
(173,201)(174,200)(175,205)(176,207)(177,206)(178,202)(179,204)(180,203)
(181,208)(182,210)(183,209)(184,214)(185,216)(186,215)(187,211)(188,213)
(189,212)(217,220)(218,222)(219,221)(224,225)(226,229)(227,231)(228,230)
(233,234)(235,238)(236,240)(237,239)(242,243)(244,271)(245,273)(246,272)
(247,277)(248,279)(249,278)(250,274)(251,276)(252,275)(253,280)(254,282)
(255,281)(256,286)(257,288)(258,287)(259,283)(260,285)(261,284)(262,289)
(263,291)(264,290)(265,295)(266,297)(267,296)(268,292)(269,294)(270,293)
(298,301)(299,303)(300,302)(305,306)(307,310)(308,312)(309,311)(314,315)
(316,319)(317,321)(318,320)(323,324)(325,352)(326,354)(327,353)(328,358)
(329,360)(330,359)(331,355)(332,357)(333,356)(334,361)(335,363)(336,362)
(337,367)(338,369)(339,368)(340,364)(341,366)(342,365)(343,370)(344,372)
(345,371)(346,376)(347,378)(348,377)(349,373)(350,375)(351,374)(379,382)
(380,384)(381,383)(386,387)(388,391)(389,393)(390,392)(395,396)(397,400)
(398,402)(399,401)(404,405)(406,433)(407,435)(408,434)(409,439)(410,441)
(411,440)(412,436)(413,438)(414,437)(415,442)(416,444)(417,443)(418,448)
(419,450)(420,449)(421,445)(422,447)(423,446)(424,451)(425,453)(426,452)
(427,457)(428,459)(429,458)(430,454)(431,456)(432,455)(460,463)(461,465)
(462,464)(467,468)(469,472)(470,474)(471,473)(476,477)(478,481)(479,483)
(480,482)(485,486);;
s3 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 58)( 29, 60)( 30, 59)( 31, 55)
( 32, 57)( 33, 56)( 34, 61)( 35, 63)( 36, 62)( 37, 67)( 38, 69)( 39, 68)
( 40, 64)( 41, 66)( 42, 65)( 43, 70)( 44, 72)( 45, 71)( 46, 76)( 47, 78)
( 48, 77)( 49, 73)( 50, 75)( 51, 74)( 52, 79)( 53, 81)( 54, 80)( 83, 84)
( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)
(103,106)(104,108)(105,107)(109,139)(110,141)(111,140)(112,136)(113,138)
(114,137)(115,142)(116,144)(117,143)(118,148)(119,150)(120,149)(121,145)
(122,147)(123,146)(124,151)(125,153)(126,152)(127,157)(128,159)(129,158)
(130,154)(131,156)(132,155)(133,160)(134,162)(135,161)(164,165)(166,169)
(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)
(185,189)(186,188)(190,220)(191,222)(192,221)(193,217)(194,219)(195,218)
(196,223)(197,225)(198,224)(199,229)(200,231)(201,230)(202,226)(203,228)
(204,227)(205,232)(206,234)(207,233)(208,238)(209,240)(210,239)(211,235)
(212,237)(213,236)(214,241)(215,243)(216,242)(245,246)(247,250)(248,252)
(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)
(267,269)(271,301)(272,303)(273,302)(274,298)(275,300)(276,299)(277,304)
(278,306)(279,305)(280,310)(281,312)(282,311)(283,307)(284,309)(285,308)
(286,313)(287,315)(288,314)(289,319)(290,321)(291,320)(292,316)(293,318)
(294,317)(295,322)(296,324)(297,323)(326,327)(328,331)(329,333)(330,332)
(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)(348,350)
(352,382)(353,384)(354,383)(355,379)(356,381)(357,380)(358,385)(359,387)
(360,386)(361,391)(362,393)(363,392)(364,388)(365,390)(366,389)(367,394)
(368,396)(369,395)(370,400)(371,402)(372,401)(373,397)(374,399)(375,398)
(376,403)(377,405)(378,404)(407,408)(409,412)(410,414)(411,413)(416,417)
(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)(433,463)
(434,465)(435,464)(436,460)(437,462)(438,461)(439,466)(440,468)(441,467)
(442,472)(443,474)(444,473)(445,469)(446,471)(447,470)(448,475)(449,477)
(450,476)(451,481)(452,483)(453,482)(454,478)(455,480)(456,479)(457,484)
(458,486)(459,485);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(486)!(  2,  3)(  5,  6)(  8,  9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)
( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)
( 37, 46)( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)
( 45, 53)( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)
( 68, 78)( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 82,172)( 83,174)( 84,173)
( 85,175)( 86,177)( 87,176)( 88,178)( 89,180)( 90,179)( 91,163)( 92,165)
( 93,164)( 94,166)( 95,168)( 96,167)( 97,169)( 98,171)( 99,170)(100,181)
(101,183)(102,182)(103,184)(104,186)(105,185)(106,187)(107,189)(108,188)
(109,199)(110,201)(111,200)(112,202)(113,204)(114,203)(115,205)(116,207)
(117,206)(118,190)(119,192)(120,191)(121,193)(122,195)(123,194)(124,196)
(125,198)(126,197)(127,208)(128,210)(129,209)(130,211)(131,213)(132,212)
(133,214)(134,216)(135,215)(136,226)(137,228)(138,227)(139,229)(140,231)
(141,230)(142,232)(143,234)(144,233)(145,217)(146,219)(147,218)(148,220)
(149,222)(150,221)(151,223)(152,225)(153,224)(154,235)(155,237)(156,236)
(157,238)(158,240)(159,239)(160,241)(161,243)(162,242)(245,246)(248,249)
(251,252)(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)
(260,270)(261,269)(272,273)(275,276)(278,279)(280,289)(281,291)(282,290)
(283,292)(284,294)(285,293)(286,295)(287,297)(288,296)(299,300)(302,303)
(305,306)(307,316)(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)
(314,324)(315,323)(325,415)(326,417)(327,416)(328,418)(329,420)(330,419)
(331,421)(332,423)(333,422)(334,406)(335,408)(336,407)(337,409)(338,411)
(339,410)(340,412)(341,414)(342,413)(343,424)(344,426)(345,425)(346,427)
(347,429)(348,428)(349,430)(350,432)(351,431)(352,442)(353,444)(354,443)
(355,445)(356,447)(357,446)(358,448)(359,450)(360,449)(361,433)(362,435)
(363,434)(364,436)(365,438)(366,437)(367,439)(368,441)(369,440)(370,451)
(371,453)(372,452)(373,454)(374,456)(375,455)(376,457)(377,459)(378,458)
(379,469)(380,471)(381,470)(382,472)(383,474)(384,473)(385,475)(386,477)
(387,476)(388,460)(389,462)(390,461)(391,463)(392,465)(393,464)(394,466)
(395,468)(396,467)(397,478)(398,480)(399,479)(400,481)(401,483)(402,482)
(403,484)(404,486)(405,485);
s1 := Sym(486)!(  1,325)(  2,327)(  3,326)(  4,328)(  5,330)(  6,329)(  7,331)
(  8,333)(  9,332)( 10,343)( 11,345)( 12,344)( 13,346)( 14,348)( 15,347)
( 16,349)( 17,351)( 18,350)( 19,334)( 20,336)( 21,335)( 22,337)( 23,339)
( 24,338)( 25,340)( 26,342)( 27,341)( 28,353)( 29,352)( 30,354)( 31,356)
( 32,355)( 33,357)( 34,359)( 35,358)( 36,360)( 37,371)( 38,370)( 39,372)
( 40,374)( 41,373)( 42,375)( 43,377)( 44,376)( 45,378)( 46,362)( 47,361)
( 48,363)( 49,365)( 50,364)( 51,366)( 52,368)( 53,367)( 54,369)( 55,381)
( 56,380)( 57,379)( 58,384)( 59,383)( 60,382)( 61,387)( 62,386)( 63,385)
( 64,399)( 65,398)( 66,397)( 67,402)( 68,401)( 69,400)( 70,405)( 71,404)
( 72,403)( 73,390)( 74,389)( 75,388)( 76,393)( 77,392)( 78,391)( 79,396)
( 80,395)( 81,394)( 82,244)( 83,246)( 84,245)( 85,247)( 86,249)( 87,248)
( 88,250)( 89,252)( 90,251)( 91,262)( 92,264)( 93,263)( 94,265)( 95,267)
( 96,266)( 97,268)( 98,270)( 99,269)(100,253)(101,255)(102,254)(103,256)
(104,258)(105,257)(106,259)(107,261)(108,260)(109,272)(110,271)(111,273)
(112,275)(113,274)(114,276)(115,278)(116,277)(117,279)(118,290)(119,289)
(120,291)(121,293)(122,292)(123,294)(124,296)(125,295)(126,297)(127,281)
(128,280)(129,282)(130,284)(131,283)(132,285)(133,287)(134,286)(135,288)
(136,300)(137,299)(138,298)(139,303)(140,302)(141,301)(142,306)(143,305)
(144,304)(145,318)(146,317)(147,316)(148,321)(149,320)(150,319)(151,324)
(152,323)(153,322)(154,309)(155,308)(156,307)(157,312)(158,311)(159,310)
(160,315)(161,314)(162,313)(163,415)(164,417)(165,416)(166,418)(167,420)
(168,419)(169,421)(170,423)(171,422)(172,406)(173,408)(174,407)(175,409)
(176,411)(177,410)(178,412)(179,414)(180,413)(181,424)(182,426)(183,425)
(184,427)(185,429)(186,428)(187,430)(188,432)(189,431)(190,443)(191,442)
(192,444)(193,446)(194,445)(195,447)(196,449)(197,448)(198,450)(199,434)
(200,433)(201,435)(202,437)(203,436)(204,438)(205,440)(206,439)(207,441)
(208,452)(209,451)(210,453)(211,455)(212,454)(213,456)(214,458)(215,457)
(216,459)(217,471)(218,470)(219,469)(220,474)(221,473)(222,472)(223,477)
(224,476)(225,475)(226,462)(227,461)(228,460)(229,465)(230,464)(231,463)
(232,468)(233,467)(234,466)(235,480)(236,479)(237,478)(238,483)(239,482)
(240,481)(241,486)(242,485)(243,484);
s2 := Sym(486)!(  1, 28)(  2, 30)(  3, 29)(  4, 34)(  5, 36)(  6, 35)(  7, 31)
(  8, 33)(  9, 32)( 10, 37)( 11, 39)( 12, 38)( 13, 43)( 14, 45)( 15, 44)
( 16, 40)( 17, 42)( 18, 41)( 19, 46)( 20, 48)( 21, 47)( 22, 52)( 23, 54)
( 24, 53)( 25, 49)( 26, 51)( 27, 50)( 55, 58)( 56, 60)( 57, 59)( 62, 63)
( 64, 67)( 65, 69)( 66, 68)( 71, 72)( 73, 76)( 74, 78)( 75, 77)( 80, 81)
( 82,109)( 83,111)( 84,110)( 85,115)( 86,117)( 87,116)( 88,112)( 89,114)
( 90,113)( 91,118)( 92,120)( 93,119)( 94,124)( 95,126)( 96,125)( 97,121)
( 98,123)( 99,122)(100,127)(101,129)(102,128)(103,133)(104,135)(105,134)
(106,130)(107,132)(108,131)(136,139)(137,141)(138,140)(143,144)(145,148)
(146,150)(147,149)(152,153)(154,157)(155,159)(156,158)(161,162)(163,190)
(164,192)(165,191)(166,196)(167,198)(168,197)(169,193)(170,195)(171,194)
(172,199)(173,201)(174,200)(175,205)(176,207)(177,206)(178,202)(179,204)
(180,203)(181,208)(182,210)(183,209)(184,214)(185,216)(186,215)(187,211)
(188,213)(189,212)(217,220)(218,222)(219,221)(224,225)(226,229)(227,231)
(228,230)(233,234)(235,238)(236,240)(237,239)(242,243)(244,271)(245,273)
(246,272)(247,277)(248,279)(249,278)(250,274)(251,276)(252,275)(253,280)
(254,282)(255,281)(256,286)(257,288)(258,287)(259,283)(260,285)(261,284)
(262,289)(263,291)(264,290)(265,295)(266,297)(267,296)(268,292)(269,294)
(270,293)(298,301)(299,303)(300,302)(305,306)(307,310)(308,312)(309,311)
(314,315)(316,319)(317,321)(318,320)(323,324)(325,352)(326,354)(327,353)
(328,358)(329,360)(330,359)(331,355)(332,357)(333,356)(334,361)(335,363)
(336,362)(337,367)(338,369)(339,368)(340,364)(341,366)(342,365)(343,370)
(344,372)(345,371)(346,376)(347,378)(348,377)(349,373)(350,375)(351,374)
(379,382)(380,384)(381,383)(386,387)(388,391)(389,393)(390,392)(395,396)
(397,400)(398,402)(399,401)(404,405)(406,433)(407,435)(408,434)(409,439)
(410,441)(411,440)(412,436)(413,438)(414,437)(415,442)(416,444)(417,443)
(418,448)(419,450)(420,449)(421,445)(422,447)(423,446)(424,451)(425,453)
(426,452)(427,457)(428,459)(429,458)(430,454)(431,456)(432,455)(460,463)
(461,465)(462,464)(467,468)(469,472)(470,474)(471,473)(476,477)(478,481)
(479,483)(480,482)(485,486);
s3 := Sym(486)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 58)( 29, 60)( 30, 59)
( 31, 55)( 32, 57)( 33, 56)( 34, 61)( 35, 63)( 36, 62)( 37, 67)( 38, 69)
( 39, 68)( 40, 64)( 41, 66)( 42, 65)( 43, 70)( 44, 72)( 45, 71)( 46, 76)
( 47, 78)( 48, 77)( 49, 73)( 50, 75)( 51, 74)( 52, 79)( 53, 81)( 54, 80)
( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)
(101,102)(103,106)(104,108)(105,107)(109,139)(110,141)(111,140)(112,136)
(113,138)(114,137)(115,142)(116,144)(117,143)(118,148)(119,150)(120,149)
(121,145)(122,147)(123,146)(124,151)(125,153)(126,152)(127,157)(128,159)
(129,158)(130,154)(131,156)(132,155)(133,160)(134,162)(135,161)(164,165)
(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)
(184,187)(185,189)(186,188)(190,220)(191,222)(192,221)(193,217)(194,219)
(195,218)(196,223)(197,225)(198,224)(199,229)(200,231)(201,230)(202,226)
(203,228)(204,227)(205,232)(206,234)(207,233)(208,238)(209,240)(210,239)
(211,235)(212,237)(213,236)(214,241)(215,243)(216,242)(245,246)(247,250)
(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)
(266,270)(267,269)(271,301)(272,303)(273,302)(274,298)(275,300)(276,299)
(277,304)(278,306)(279,305)(280,310)(281,312)(282,311)(283,307)(284,309)
(285,308)(286,313)(287,315)(288,314)(289,319)(290,321)(291,320)(292,316)
(293,318)(294,317)(295,322)(296,324)(297,323)(326,327)(328,331)(329,333)
(330,332)(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)
(348,350)(352,382)(353,384)(354,383)(355,379)(356,381)(357,380)(358,385)
(359,387)(360,386)(361,391)(362,393)(363,392)(364,388)(365,390)(366,389)
(367,394)(368,396)(369,395)(370,400)(371,402)(372,401)(373,397)(374,399)
(375,398)(376,403)(377,405)(378,404)(407,408)(409,412)(410,414)(411,413)
(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)
(433,463)(434,465)(435,464)(436,460)(437,462)(438,461)(439,466)(440,468)
(441,467)(442,472)(443,474)(444,473)(445,469)(446,471)(447,470)(448,475)
(449,477)(450,476)(451,481)(452,483)(453,482)(454,478)(455,480)(456,479)
(457,484)(458,486)(459,485);
poly := sub<Sym(486)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope