Polytope of Type {18,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6,3}*1944a
if this polytope has a name.
Group : SmallGroup(1944,949)
Rank : 4
Schlafli Type : {18,6,3}
Number of vertices, edges, etc : 54, 162, 27, 3
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 : {9,6,3}*972a
3-fold quotients : {18,6,3}*648a, {6,6,3}*648a
6-fold quotients : {9,6,3}*324, {3,6,3}*324b
9-fold quotients : {18,2,3}*216, {6,6,3}*216a
18-fold quotients : {9,2,3}*108, {3,6,3}*108
27-fold quotients : {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 := ( 4, 7)( 5, 8)( 6, 9)( 10, 19)( 11, 20)( 12, 21)( 13, 25)( 14, 26)
( 15, 27)( 16, 22)( 17, 23)( 18, 24)( 31, 34)( 32, 35)( 33, 36)( 37, 46)
( 38, 47)( 39, 48)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)( 45, 51)
( 58, 61)( 59, 62)( 60, 63)( 64, 73)( 65, 74)( 66, 75)( 67, 79)( 68, 80)
( 69, 81)( 70, 76)( 71, 77)( 72, 78)( 82,172)( 83,173)( 84,174)( 85,178)
( 86,179)( 87,180)( 88,175)( 89,176)( 90,177)( 91,163)( 92,164)( 93,165)
( 94,169)( 95,170)( 96,171)( 97,166)( 98,167)( 99,168)(100,181)(101,182)
(102,183)(103,187)(104,188)(105,189)(106,184)(107,185)(108,186)(109,199)
(110,200)(111,201)(112,205)(113,206)(114,207)(115,202)(116,203)(117,204)
(118,190)(119,191)(120,192)(121,196)(122,197)(123,198)(124,193)(125,194)
(126,195)(127,208)(128,209)(129,210)(130,214)(131,215)(132,216)(133,211)
(134,212)(135,213)(136,226)(137,227)(138,228)(139,232)(140,233)(141,234)
(142,229)(143,230)(144,231)(145,217)(146,218)(147,219)(148,223)(149,224)
(150,225)(151,220)(152,221)(153,222)(154,235)(155,236)(156,237)(157,241)
(158,242)(159,243)(160,238)(161,239)(162,240)(247,250)(248,251)(249,252)
(253,262)(254,263)(255,264)(256,268)(257,269)(258,270)(259,265)(260,266)
(261,267)(274,277)(275,278)(276,279)(280,289)(281,290)(282,291)(283,295)
(284,296)(285,297)(286,292)(287,293)(288,294)(301,304)(302,305)(303,306)
(307,316)(308,317)(309,318)(310,322)(311,323)(312,324)(313,319)(314,320)
(315,321)(325,415)(326,416)(327,417)(328,421)(329,422)(330,423)(331,418)
(332,419)(333,420)(334,406)(335,407)(336,408)(337,412)(338,413)(339,414)
(340,409)(341,410)(342,411)(343,424)(344,425)(345,426)(346,430)(347,431)
(348,432)(349,427)(350,428)(351,429)(352,442)(353,443)(354,444)(355,448)
(356,449)(357,450)(358,445)(359,446)(360,447)(361,433)(362,434)(363,435)
(364,439)(365,440)(366,441)(367,436)(368,437)(369,438)(370,451)(371,452)
(372,453)(373,457)(374,458)(375,459)(376,454)(377,455)(378,456)(379,469)
(380,470)(381,471)(382,475)(383,476)(384,477)(385,472)(386,473)(387,474)
(388,460)(389,461)(390,462)(391,466)(392,467)(393,468)(394,463)(395,464)
(396,465)(397,478)(398,479)(399,480)(400,484)(401,485)(402,486)(403,481)
(404,482)(405,483);;
s1 := ( 1,325)( 2,326)( 3,327)( 4,332)( 5,333)( 6,331)( 7,330)( 8,328)
( 9,329)( 10,343)( 11,344)( 12,345)( 13,350)( 14,351)( 15,349)( 16,348)
( 17,346)( 18,347)( 19,334)( 20,335)( 21,336)( 22,341)( 23,342)( 24,340)
( 25,339)( 26,337)( 27,338)( 28,356)( 29,357)( 30,355)( 31,354)( 32,352)
( 33,353)( 34,358)( 35,359)( 36,360)( 37,374)( 38,375)( 39,373)( 40,372)
( 41,370)( 42,371)( 43,376)( 44,377)( 45,378)( 46,365)( 47,366)( 48,364)
( 49,363)( 50,361)( 51,362)( 52,367)( 53,368)( 54,369)( 55,387)( 56,385)
( 57,386)( 58,382)( 59,383)( 60,384)( 61,380)( 62,381)( 63,379)( 64,405)
( 65,403)( 66,404)( 67,400)( 68,401)( 69,402)( 70,398)( 71,399)( 72,397)
( 73,396)( 74,394)( 75,395)( 76,391)( 77,392)( 78,393)( 79,389)( 80,390)
( 81,388)( 82,244)( 83,245)( 84,246)( 85,251)( 86,252)( 87,250)( 88,249)
( 89,247)( 90,248)( 91,262)( 92,263)( 93,264)( 94,269)( 95,270)( 96,268)
( 97,267)( 98,265)( 99,266)(100,253)(101,254)(102,255)(103,260)(104,261)
(105,259)(106,258)(107,256)(108,257)(109,275)(110,276)(111,274)(112,273)
(113,271)(114,272)(115,277)(116,278)(117,279)(118,293)(119,294)(120,292)
(121,291)(122,289)(123,290)(124,295)(125,296)(126,297)(127,284)(128,285)
(129,283)(130,282)(131,280)(132,281)(133,286)(134,287)(135,288)(136,306)
(137,304)(138,305)(139,301)(140,302)(141,303)(142,299)(143,300)(144,298)
(145,324)(146,322)(147,323)(148,319)(149,320)(150,321)(151,317)(152,318)
(153,316)(154,315)(155,313)(156,314)(157,310)(158,311)(159,312)(160,308)
(161,309)(162,307)(163,415)(164,416)(165,417)(166,422)(167,423)(168,421)
(169,420)(170,418)(171,419)(172,406)(173,407)(174,408)(175,413)(176,414)
(177,412)(178,411)(179,409)(180,410)(181,424)(182,425)(183,426)(184,431)
(185,432)(186,430)(187,429)(188,427)(189,428)(190,446)(191,447)(192,445)
(193,444)(194,442)(195,443)(196,448)(197,449)(198,450)(199,437)(200,438)
(201,436)(202,435)(203,433)(204,434)(205,439)(206,440)(207,441)(208,455)
(209,456)(210,454)(211,453)(212,451)(213,452)(214,457)(215,458)(216,459)
(217,477)(218,475)(219,476)(220,472)(221,473)(222,474)(223,470)(224,471)
(225,469)(226,468)(227,466)(228,467)(229,463)(230,464)(231,465)(232,461)
(233,462)(234,460)(235,486)(236,484)(237,485)(238,481)(239,482)(240,483)
(241,479)(242,480)(243,478);;
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)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)
( 67, 70)( 68, 72)( 69, 71)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 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)(137,138)(139,142)(140,144)(141,143)(146,147)(148,151)
(149,153)(150,152)(155,156)(157,160)(158,162)(159,161)(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)(218,219)(220,223)(221,225)(222,224)(227,228)(229,232)(230,234)
(231,233)(236,237)(238,241)(239,243)(240,242)(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)
(299,300)(301,304)(302,306)(303,305)(308,309)(310,313)(311,315)(312,314)
(317,318)(319,322)(320,324)(321,323)(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)(380,381)
(382,385)(383,387)(384,386)(389,390)(391,394)(392,396)(393,395)(398,399)
(400,403)(401,405)(402,404)(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)(461,462)(463,466)
(464,468)(465,467)(470,471)(472,475)(473,477)(474,476)(479,480)(481,484)
(482,486)(483,485);;
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, 55)( 29, 57)( 30, 56)( 31, 61)
( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)( 39, 65)
( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)( 47, 75)
( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)( 83, 84)
( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)
(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)
(114,143)(115,139)(116,141)(117,140)(118,145)(119,147)(120,146)(121,151)
(122,153)(123,152)(124,148)(125,150)(126,149)(127,154)(128,156)(129,155)
(130,160)(131,162)(132,161)(133,157)(134,159)(135,158)(164,165)(166,169)
(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)
(185,189)(186,188)(190,217)(191,219)(192,218)(193,223)(194,225)(195,224)
(196,220)(197,222)(198,221)(199,226)(200,228)(201,227)(202,232)(203,234)
(204,233)(205,229)(206,231)(207,230)(208,235)(209,237)(210,236)(211,241)
(212,243)(213,242)(214,238)(215,240)(216,239)(245,246)(247,250)(248,252)
(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)
(267,269)(271,298)(272,300)(273,299)(274,304)(275,306)(276,305)(277,301)
(278,303)(279,302)(280,307)(281,309)(282,308)(283,313)(284,315)(285,314)
(286,310)(287,312)(288,311)(289,316)(290,318)(291,317)(292,322)(293,324)
(294,323)(295,319)(296,321)(297,320)(326,327)(328,331)(329,333)(330,332)
(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)(348,350)
(352,379)(353,381)(354,380)(355,385)(356,387)(357,386)(358,382)(359,384)
(360,383)(361,388)(362,390)(363,389)(364,394)(365,396)(366,395)(367,391)
(368,393)(369,392)(370,397)(371,399)(372,398)(373,403)(374,405)(375,404)
(376,400)(377,402)(378,401)(407,408)(409,412)(410,414)(411,413)(416,417)
(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)(433,460)
(434,462)(435,461)(436,466)(437,468)(438,467)(439,463)(440,465)(441,464)
(442,469)(443,471)(444,470)(445,475)(446,477)(447,476)(448,472)(449,474)
(450,473)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)(457,481)
(458,483)(459,482);;
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*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(486)!( 4, 7)( 5, 8)( 6, 9)( 10, 19)( 11, 20)( 12, 21)( 13, 25)
( 14, 26)( 15, 27)( 16, 22)( 17, 23)( 18, 24)( 31, 34)( 32, 35)( 33, 36)
( 37, 46)( 38, 47)( 39, 48)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)
( 45, 51)( 58, 61)( 59, 62)( 60, 63)( 64, 73)( 65, 74)( 66, 75)( 67, 79)
( 68, 80)( 69, 81)( 70, 76)( 71, 77)( 72, 78)( 82,172)( 83,173)( 84,174)
( 85,178)( 86,179)( 87,180)( 88,175)( 89,176)( 90,177)( 91,163)( 92,164)
( 93,165)( 94,169)( 95,170)( 96,171)( 97,166)( 98,167)( 99,168)(100,181)
(101,182)(102,183)(103,187)(104,188)(105,189)(106,184)(107,185)(108,186)
(109,199)(110,200)(111,201)(112,205)(113,206)(114,207)(115,202)(116,203)
(117,204)(118,190)(119,191)(120,192)(121,196)(122,197)(123,198)(124,193)
(125,194)(126,195)(127,208)(128,209)(129,210)(130,214)(131,215)(132,216)
(133,211)(134,212)(135,213)(136,226)(137,227)(138,228)(139,232)(140,233)
(141,234)(142,229)(143,230)(144,231)(145,217)(146,218)(147,219)(148,223)
(149,224)(150,225)(151,220)(152,221)(153,222)(154,235)(155,236)(156,237)
(157,241)(158,242)(159,243)(160,238)(161,239)(162,240)(247,250)(248,251)
(249,252)(253,262)(254,263)(255,264)(256,268)(257,269)(258,270)(259,265)
(260,266)(261,267)(274,277)(275,278)(276,279)(280,289)(281,290)(282,291)
(283,295)(284,296)(285,297)(286,292)(287,293)(288,294)(301,304)(302,305)
(303,306)(307,316)(308,317)(309,318)(310,322)(311,323)(312,324)(313,319)
(314,320)(315,321)(325,415)(326,416)(327,417)(328,421)(329,422)(330,423)
(331,418)(332,419)(333,420)(334,406)(335,407)(336,408)(337,412)(338,413)
(339,414)(340,409)(341,410)(342,411)(343,424)(344,425)(345,426)(346,430)
(347,431)(348,432)(349,427)(350,428)(351,429)(352,442)(353,443)(354,444)
(355,448)(356,449)(357,450)(358,445)(359,446)(360,447)(361,433)(362,434)
(363,435)(364,439)(365,440)(366,441)(367,436)(368,437)(369,438)(370,451)
(371,452)(372,453)(373,457)(374,458)(375,459)(376,454)(377,455)(378,456)
(379,469)(380,470)(381,471)(382,475)(383,476)(384,477)(385,472)(386,473)
(387,474)(388,460)(389,461)(390,462)(391,466)(392,467)(393,468)(394,463)
(395,464)(396,465)(397,478)(398,479)(399,480)(400,484)(401,485)(402,486)
(403,481)(404,482)(405,483);
s1 := Sym(486)!( 1,325)( 2,326)( 3,327)( 4,332)( 5,333)( 6,331)( 7,330)
( 8,328)( 9,329)( 10,343)( 11,344)( 12,345)( 13,350)( 14,351)( 15,349)
( 16,348)( 17,346)( 18,347)( 19,334)( 20,335)( 21,336)( 22,341)( 23,342)
( 24,340)( 25,339)( 26,337)( 27,338)( 28,356)( 29,357)( 30,355)( 31,354)
( 32,352)( 33,353)( 34,358)( 35,359)( 36,360)( 37,374)( 38,375)( 39,373)
( 40,372)( 41,370)( 42,371)( 43,376)( 44,377)( 45,378)( 46,365)( 47,366)
( 48,364)( 49,363)( 50,361)( 51,362)( 52,367)( 53,368)( 54,369)( 55,387)
( 56,385)( 57,386)( 58,382)( 59,383)( 60,384)( 61,380)( 62,381)( 63,379)
( 64,405)( 65,403)( 66,404)( 67,400)( 68,401)( 69,402)( 70,398)( 71,399)
( 72,397)( 73,396)( 74,394)( 75,395)( 76,391)( 77,392)( 78,393)( 79,389)
( 80,390)( 81,388)( 82,244)( 83,245)( 84,246)( 85,251)( 86,252)( 87,250)
( 88,249)( 89,247)( 90,248)( 91,262)( 92,263)( 93,264)( 94,269)( 95,270)
( 96,268)( 97,267)( 98,265)( 99,266)(100,253)(101,254)(102,255)(103,260)
(104,261)(105,259)(106,258)(107,256)(108,257)(109,275)(110,276)(111,274)
(112,273)(113,271)(114,272)(115,277)(116,278)(117,279)(118,293)(119,294)
(120,292)(121,291)(122,289)(123,290)(124,295)(125,296)(126,297)(127,284)
(128,285)(129,283)(130,282)(131,280)(132,281)(133,286)(134,287)(135,288)
(136,306)(137,304)(138,305)(139,301)(140,302)(141,303)(142,299)(143,300)
(144,298)(145,324)(146,322)(147,323)(148,319)(149,320)(150,321)(151,317)
(152,318)(153,316)(154,315)(155,313)(156,314)(157,310)(158,311)(159,312)
(160,308)(161,309)(162,307)(163,415)(164,416)(165,417)(166,422)(167,423)
(168,421)(169,420)(170,418)(171,419)(172,406)(173,407)(174,408)(175,413)
(176,414)(177,412)(178,411)(179,409)(180,410)(181,424)(182,425)(183,426)
(184,431)(185,432)(186,430)(187,429)(188,427)(189,428)(190,446)(191,447)
(192,445)(193,444)(194,442)(195,443)(196,448)(197,449)(198,450)(199,437)
(200,438)(201,436)(202,435)(203,433)(204,434)(205,439)(206,440)(207,441)
(208,455)(209,456)(210,454)(211,453)(212,451)(213,452)(214,457)(215,458)
(216,459)(217,477)(218,475)(219,476)(220,472)(221,473)(222,474)(223,470)
(224,471)(225,469)(226,468)(227,466)(228,467)(229,463)(230,464)(231,465)
(232,461)(233,462)(234,460)(235,486)(236,484)(237,485)(238,481)(239,482)
(240,483)(241,479)(242,480)(243,478);
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)( 56, 57)( 58, 61)( 59, 63)( 60, 62)
( 65, 66)( 67, 70)( 68, 72)( 69, 71)( 74, 75)( 76, 79)( 77, 81)( 78, 80)
( 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)(137,138)(139,142)(140,144)(141,143)(146,147)
(148,151)(149,153)(150,152)(155,156)(157,160)(158,162)(159,161)(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)(218,219)(220,223)(221,225)(222,224)(227,228)(229,232)
(230,234)(231,233)(236,237)(238,241)(239,243)(240,242)(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)(299,300)(301,304)(302,306)(303,305)(308,309)(310,313)(311,315)
(312,314)(317,318)(319,322)(320,324)(321,323)(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)
(380,381)(382,385)(383,387)(384,386)(389,390)(391,394)(392,396)(393,395)
(398,399)(400,403)(401,405)(402,404)(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)(461,462)
(463,466)(464,468)(465,467)(470,471)(472,475)(473,477)(474,476)(479,480)
(481,484)(482,486)(483,485);
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, 55)( 29, 57)( 30, 56)
( 31, 61)( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)
( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)
( 47, 75)( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)
( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)
(101,102)(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)
(113,144)(114,143)(115,139)(116,141)(117,140)(118,145)(119,147)(120,146)
(121,151)(122,153)(123,152)(124,148)(125,150)(126,149)(127,154)(128,156)
(129,155)(130,160)(131,162)(132,161)(133,157)(134,159)(135,158)(164,165)
(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)
(184,187)(185,189)(186,188)(190,217)(191,219)(192,218)(193,223)(194,225)
(195,224)(196,220)(197,222)(198,221)(199,226)(200,228)(201,227)(202,232)
(203,234)(204,233)(205,229)(206,231)(207,230)(208,235)(209,237)(210,236)
(211,241)(212,243)(213,242)(214,238)(215,240)(216,239)(245,246)(247,250)
(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)
(266,270)(267,269)(271,298)(272,300)(273,299)(274,304)(275,306)(276,305)
(277,301)(278,303)(279,302)(280,307)(281,309)(282,308)(283,313)(284,315)
(285,314)(286,310)(287,312)(288,311)(289,316)(290,318)(291,317)(292,322)
(293,324)(294,323)(295,319)(296,321)(297,320)(326,327)(328,331)(329,333)
(330,332)(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)
(348,350)(352,379)(353,381)(354,380)(355,385)(356,387)(357,386)(358,382)
(359,384)(360,383)(361,388)(362,390)(363,389)(364,394)(365,396)(366,395)
(367,391)(368,393)(369,392)(370,397)(371,399)(372,398)(373,403)(374,405)
(375,404)(376,400)(377,402)(378,401)(407,408)(409,412)(410,414)(411,413)
(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)
(433,460)(434,462)(435,461)(436,466)(437,468)(438,467)(439,463)(440,465)
(441,464)(442,469)(443,471)(444,470)(445,475)(446,477)(447,476)(448,472)
(449,474)(450,473)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)
(457,481)(458,483)(459,482);
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*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1 >;
References : None.
to this polytope