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