Polytope of Type {3,6,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,18}*1944b
if this polytope has a name.
Group : SmallGroup(1944,952)
Rank : 4
Schlafli Type : {3,6,18}
Number of vertices, edges, etc : 9, 27, 162, 18
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}*972b
3-fold quotients : {3,6,18}*648a, {3,6,6}*648a
6-fold quotients : {3,6,9}*324, {3,6,3}*324b
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 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 28, 55)( 29, 56)( 30, 57)( 31, 61)( 32, 62)( 33, 63)( 34, 58)
( 35, 59)( 36, 60)( 37, 64)( 38, 65)( 39, 66)( 40, 70)( 41, 71)( 42, 72)
( 43, 67)( 44, 68)( 45, 69)( 46, 73)( 47, 74)( 48, 75)( 49, 79)( 50, 80)
( 51, 81)( 52, 76)( 53, 77)( 54, 78)( 85, 88)( 86, 89)( 87, 90)( 94, 97)
( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)
(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)
(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)
(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)
(166,169)(167,170)(168,171)(175,178)(176,179)(177,180)(184,187)(185,188)
(186,189)(190,217)(191,218)(192,219)(193,223)(194,224)(195,225)(196,220)
(197,221)(198,222)(199,226)(200,227)(201,228)(202,232)(203,233)(204,234)
(205,229)(206,230)(207,231)(208,235)(209,236)(210,237)(211,241)(212,242)
(213,243)(214,238)(215,239)(216,240)(247,250)(248,251)(249,252)(256,259)
(257,260)(258,261)(265,268)(266,269)(267,270)(271,298)(272,299)(273,300)
(274,304)(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)(281,308)
(282,309)(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)(289,316)
(290,317)(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)(297,321)
(328,331)(329,332)(330,333)(337,340)(338,341)(339,342)(346,349)(347,350)
(348,351)(352,379)(353,380)(354,381)(355,385)(356,386)(357,387)(358,382)
(359,383)(360,384)(361,388)(362,389)(363,390)(364,394)(365,395)(366,396)
(367,391)(368,392)(369,393)(370,397)(371,398)(372,399)(373,403)(374,404)
(375,405)(376,400)(377,401)(378,402)(409,412)(410,413)(411,414)(418,421)
(419,422)(420,423)(427,430)(428,431)(429,432)(433,460)(434,461)(435,462)
(436,466)(437,467)(438,468)(439,463)(440,464)(441,465)(442,469)(443,470)
(444,471)(445,475)(446,476)(447,477)(448,472)(449,473)(450,474)(451,478)
(452,479)(453,480)(454,484)(455,485)(456,486)(457,481)(458,482)(459,483);;
s1 := ( 1, 28)( 2, 29)( 3, 30)( 4, 35)( 5, 36)( 6, 34)( 7, 33)( 8, 31)
( 9, 32)( 10, 37)( 11, 38)( 12, 39)( 13, 44)( 14, 45)( 15, 43)( 16, 42)
( 17, 40)( 18, 41)( 19, 46)( 20, 47)( 21, 48)( 22, 53)( 23, 54)( 24, 52)
( 25, 51)( 26, 49)( 27, 50)( 58, 62)( 59, 63)( 60, 61)( 67, 71)( 68, 72)
( 69, 70)( 76, 80)( 77, 81)( 78, 79)( 82,109)( 83,110)( 84,111)( 85,116)
( 86,117)( 87,115)( 88,114)( 89,112)( 90,113)( 91,118)( 92,119)( 93,120)
( 94,125)( 95,126)( 96,124)( 97,123)( 98,121)( 99,122)(100,127)(101,128)
(102,129)(103,134)(104,135)(105,133)(106,132)(107,130)(108,131)(139,143)
(140,144)(141,142)(148,152)(149,153)(150,151)(157,161)(158,162)(159,160)
(163,190)(164,191)(165,192)(166,197)(167,198)(168,196)(169,195)(170,193)
(171,194)(172,199)(173,200)(174,201)(175,206)(176,207)(177,205)(178,204)
(179,202)(180,203)(181,208)(182,209)(183,210)(184,215)(185,216)(186,214)
(187,213)(188,211)(189,212)(220,224)(221,225)(222,223)(229,233)(230,234)
(231,232)(238,242)(239,243)(240,241)(244,271)(245,272)(246,273)(247,278)
(248,279)(249,277)(250,276)(251,274)(252,275)(253,280)(254,281)(255,282)
(256,287)(257,288)(258,286)(259,285)(260,283)(261,284)(262,289)(263,290)
(264,291)(265,296)(266,297)(267,295)(268,294)(269,292)(270,293)(301,305)
(302,306)(303,304)(310,314)(311,315)(312,313)(319,323)(320,324)(321,322)
(325,352)(326,353)(327,354)(328,359)(329,360)(330,358)(331,357)(332,355)
(333,356)(334,361)(335,362)(336,363)(337,368)(338,369)(339,367)(340,366)
(341,364)(342,365)(343,370)(344,371)(345,372)(346,377)(347,378)(348,376)
(349,375)(350,373)(351,374)(382,386)(383,387)(384,385)(391,395)(392,396)
(393,394)(400,404)(401,405)(402,403)(406,433)(407,434)(408,435)(409,440)
(410,441)(411,439)(412,438)(413,436)(414,437)(415,442)(416,443)(417,444)
(418,449)(419,450)(420,448)(421,447)(422,445)(423,446)(424,451)(425,452)
(426,453)(427,458)(428,459)(429,457)(430,456)(431,454)(432,455)(463,467)
(464,468)(465,466)(472,476)(473,477)(474,475)(481,485)(482,486)(483,484);;
s2 := ( 1, 82)( 2, 84)( 3, 83)( 4, 88)( 5, 90)( 6, 89)( 7, 85)( 8, 87)
( 9, 86)( 10,100)( 11,102)( 12,101)( 13,106)( 14,108)( 15,107)( 16,103)
( 17,105)( 18,104)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)
( 25, 94)( 26, 96)( 27, 95)( 28,113)( 29,112)( 30,114)( 31,110)( 32,109)
( 33,111)( 34,116)( 35,115)( 36,117)( 37,131)( 38,130)( 39,132)( 40,128)
( 41,127)( 42,129)( 43,134)( 44,133)( 45,135)( 46,122)( 47,121)( 48,123)
( 49,119)( 50,118)( 51,120)( 52,125)( 53,124)( 54,126)( 55,143)( 56,142)
( 57,144)( 58,140)( 59,139)( 60,141)( 61,137)( 62,136)( 63,138)( 64,161)
( 65,160)( 66,162)( 67,158)( 68,157)( 69,159)( 70,155)( 71,154)( 72,156)
( 73,152)( 74,151)( 75,153)( 76,149)( 77,148)( 78,150)( 79,146)( 80,145)
( 81,147)(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)
(170,177)(171,176)(182,183)(184,187)(185,189)(186,188)(190,203)(191,202)
(192,204)(193,200)(194,199)(195,201)(196,206)(197,205)(198,207)(208,212)
(209,211)(210,213)(214,215)(217,233)(218,232)(219,234)(220,230)(221,229)
(222,231)(223,227)(224,226)(225,228)(235,242)(236,241)(237,243)(238,239)
(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)(251,330)
(252,329)(253,343)(254,345)(255,344)(256,349)(257,351)(258,350)(259,346)
(260,348)(261,347)(262,334)(263,336)(264,335)(265,340)(266,342)(267,341)
(268,337)(269,339)(270,338)(271,356)(272,355)(273,357)(274,353)(275,352)
(276,354)(277,359)(278,358)(279,360)(280,374)(281,373)(282,375)(283,371)
(284,370)(285,372)(286,377)(287,376)(288,378)(289,365)(290,364)(291,366)
(292,362)(293,361)(294,363)(295,368)(296,367)(297,369)(298,386)(299,385)
(300,387)(301,383)(302,382)(303,384)(304,380)(305,379)(306,381)(307,404)
(308,403)(309,405)(310,401)(311,400)(312,402)(313,398)(314,397)(315,399)
(316,395)(317,394)(318,396)(319,392)(320,391)(321,393)(322,389)(323,388)
(324,390)(406,415)(407,417)(408,416)(409,421)(410,423)(411,422)(412,418)
(413,420)(414,419)(425,426)(427,430)(428,432)(429,431)(433,446)(434,445)
(435,447)(436,443)(437,442)(438,444)(439,449)(440,448)(441,450)(451,455)
(452,454)(453,456)(457,458)(460,476)(461,475)(462,477)(463,473)(464,472)
(465,474)(466,470)(467,469)(468,471)(478,485)(479,484)(480,486)(481,482);;
s3 := ( 1,244)( 2,246)( 3,245)( 4,250)( 5,252)( 6,251)( 7,247)( 8,249)
( 9,248)( 10,262)( 11,264)( 12,263)( 13,268)( 14,270)( 15,269)( 16,265)
( 17,267)( 18,266)( 19,253)( 20,255)( 21,254)( 22,259)( 23,261)( 24,260)
( 25,256)( 26,258)( 27,257)( 28,271)( 29,273)( 30,272)( 31,277)( 32,279)
( 33,278)( 34,274)( 35,276)( 36,275)( 37,289)( 38,291)( 39,290)( 40,295)
( 41,297)( 42,296)( 43,292)( 44,294)( 45,293)( 46,280)( 47,282)( 48,281)
( 49,286)( 50,288)( 51,287)( 52,283)( 53,285)( 54,284)( 55,298)( 56,300)
( 57,299)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)( 64,316)
( 65,318)( 66,317)( 67,322)( 68,324)( 69,323)( 70,319)( 71,321)( 72,320)
( 73,307)( 74,309)( 75,308)( 76,313)( 77,315)( 78,314)( 79,310)( 80,312)
( 81,311)( 82,415)( 83,417)( 84,416)( 85,421)( 86,423)( 87,422)( 88,418)
( 89,420)( 90,419)( 91,406)( 92,408)( 93,407)( 94,412)( 95,414)( 96,413)
( 97,409)( 98,411)( 99,410)(100,424)(101,426)(102,425)(103,430)(104,432)
(105,431)(106,427)(107,429)(108,428)(109,442)(110,444)(111,443)(112,448)
(113,450)(114,449)(115,445)(116,447)(117,446)(118,433)(119,435)(120,434)
(121,439)(122,441)(123,440)(124,436)(125,438)(126,437)(127,451)(128,453)
(129,452)(130,457)(131,459)(132,458)(133,454)(134,456)(135,455)(136,469)
(137,471)(138,470)(139,475)(140,477)(141,476)(142,472)(143,474)(144,473)
(145,460)(146,462)(147,461)(148,466)(149,468)(150,467)(151,463)(152,465)
(153,464)(154,478)(155,480)(156,479)(157,484)(158,486)(159,485)(160,481)
(161,483)(162,482)(163,334)(164,336)(165,335)(166,340)(167,342)(168,341)
(169,337)(170,339)(171,338)(172,325)(173,327)(174,326)(175,331)(176,333)
(177,332)(178,328)(179,330)(180,329)(181,343)(182,345)(183,344)(184,349)
(185,351)(186,350)(187,346)(188,348)(189,347)(190,361)(191,363)(192,362)
(193,367)(194,369)(195,368)(196,364)(197,366)(198,365)(199,352)(200,354)
(201,353)(202,358)(203,360)(204,359)(205,355)(206,357)(207,356)(208,370)
(209,372)(210,371)(211,376)(212,378)(213,377)(214,373)(215,375)(216,374)
(217,388)(218,390)(219,389)(220,394)(221,396)(222,395)(223,391)(224,393)
(225,392)(226,379)(227,381)(228,380)(229,385)(230,387)(231,386)(232,382)
(233,384)(234,383)(235,397)(236,399)(237,398)(238,403)(239,405)(240,404)
(241,400)(242,402)(243,401);;
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,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)
( 23, 26)( 24, 27)( 28, 55)( 29, 56)( 30, 57)( 31, 61)( 32, 62)( 33, 63)
( 34, 58)( 35, 59)( 36, 60)( 37, 64)( 38, 65)( 39, 66)( 40, 70)( 41, 71)
( 42, 72)( 43, 67)( 44, 68)( 45, 69)( 46, 73)( 47, 74)( 48, 75)( 49, 79)
( 50, 80)( 51, 81)( 52, 76)( 53, 77)( 54, 78)( 85, 88)( 86, 89)( 87, 90)
( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)
(111,138)(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)
(119,146)(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)
(127,154)(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)
(135,159)(166,169)(167,170)(168,171)(175,178)(176,179)(177,180)(184,187)
(185,188)(186,189)(190,217)(191,218)(192,219)(193,223)(194,224)(195,225)
(196,220)(197,221)(198,222)(199,226)(200,227)(201,228)(202,232)(203,233)
(204,234)(205,229)(206,230)(207,231)(208,235)(209,236)(210,237)(211,241)
(212,242)(213,243)(214,238)(215,239)(216,240)(247,250)(248,251)(249,252)
(256,259)(257,260)(258,261)(265,268)(266,269)(267,270)(271,298)(272,299)
(273,300)(274,304)(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)
(281,308)(282,309)(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)
(289,316)(290,317)(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)
(297,321)(328,331)(329,332)(330,333)(337,340)(338,341)(339,342)(346,349)
(347,350)(348,351)(352,379)(353,380)(354,381)(355,385)(356,386)(357,387)
(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)(364,394)(365,395)
(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)(372,399)(373,403)
(374,404)(375,405)(376,400)(377,401)(378,402)(409,412)(410,413)(411,414)
(418,421)(419,422)(420,423)(427,430)(428,431)(429,432)(433,460)(434,461)
(435,462)(436,466)(437,467)(438,468)(439,463)(440,464)(441,465)(442,469)
(443,470)(444,471)(445,475)(446,476)(447,477)(448,472)(449,473)(450,474)
(451,478)(452,479)(453,480)(454,484)(455,485)(456,486)(457,481)(458,482)
(459,483);
s1 := Sym(486)!( 1, 28)( 2, 29)( 3, 30)( 4, 35)( 5, 36)( 6, 34)( 7, 33)
( 8, 31)( 9, 32)( 10, 37)( 11, 38)( 12, 39)( 13, 44)( 14, 45)( 15, 43)
( 16, 42)( 17, 40)( 18, 41)( 19, 46)( 20, 47)( 21, 48)( 22, 53)( 23, 54)
( 24, 52)( 25, 51)( 26, 49)( 27, 50)( 58, 62)( 59, 63)( 60, 61)( 67, 71)
( 68, 72)( 69, 70)( 76, 80)( 77, 81)( 78, 79)( 82,109)( 83,110)( 84,111)
( 85,116)( 86,117)( 87,115)( 88,114)( 89,112)( 90,113)( 91,118)( 92,119)
( 93,120)( 94,125)( 95,126)( 96,124)( 97,123)( 98,121)( 99,122)(100,127)
(101,128)(102,129)(103,134)(104,135)(105,133)(106,132)(107,130)(108,131)
(139,143)(140,144)(141,142)(148,152)(149,153)(150,151)(157,161)(158,162)
(159,160)(163,190)(164,191)(165,192)(166,197)(167,198)(168,196)(169,195)
(170,193)(171,194)(172,199)(173,200)(174,201)(175,206)(176,207)(177,205)
(178,204)(179,202)(180,203)(181,208)(182,209)(183,210)(184,215)(185,216)
(186,214)(187,213)(188,211)(189,212)(220,224)(221,225)(222,223)(229,233)
(230,234)(231,232)(238,242)(239,243)(240,241)(244,271)(245,272)(246,273)
(247,278)(248,279)(249,277)(250,276)(251,274)(252,275)(253,280)(254,281)
(255,282)(256,287)(257,288)(258,286)(259,285)(260,283)(261,284)(262,289)
(263,290)(264,291)(265,296)(266,297)(267,295)(268,294)(269,292)(270,293)
(301,305)(302,306)(303,304)(310,314)(311,315)(312,313)(319,323)(320,324)
(321,322)(325,352)(326,353)(327,354)(328,359)(329,360)(330,358)(331,357)
(332,355)(333,356)(334,361)(335,362)(336,363)(337,368)(338,369)(339,367)
(340,366)(341,364)(342,365)(343,370)(344,371)(345,372)(346,377)(347,378)
(348,376)(349,375)(350,373)(351,374)(382,386)(383,387)(384,385)(391,395)
(392,396)(393,394)(400,404)(401,405)(402,403)(406,433)(407,434)(408,435)
(409,440)(410,441)(411,439)(412,438)(413,436)(414,437)(415,442)(416,443)
(417,444)(418,449)(419,450)(420,448)(421,447)(422,445)(423,446)(424,451)
(425,452)(426,453)(427,458)(428,459)(429,457)(430,456)(431,454)(432,455)
(463,467)(464,468)(465,466)(472,476)(473,477)(474,475)(481,485)(482,486)
(483,484);
s2 := Sym(486)!( 1, 82)( 2, 84)( 3, 83)( 4, 88)( 5, 90)( 6, 89)( 7, 85)
( 8, 87)( 9, 86)( 10,100)( 11,102)( 12,101)( 13,106)( 14,108)( 15,107)
( 16,103)( 17,105)( 18,104)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)
( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,113)( 29,112)( 30,114)( 31,110)
( 32,109)( 33,111)( 34,116)( 35,115)( 36,117)( 37,131)( 38,130)( 39,132)
( 40,128)( 41,127)( 42,129)( 43,134)( 44,133)( 45,135)( 46,122)( 47,121)
( 48,123)( 49,119)( 50,118)( 51,120)( 52,125)( 53,124)( 54,126)( 55,143)
( 56,142)( 57,144)( 58,140)( 59,139)( 60,141)( 61,137)( 62,136)( 63,138)
( 64,161)( 65,160)( 66,162)( 67,158)( 68,157)( 69,159)( 70,155)( 71,154)
( 72,156)( 73,152)( 74,151)( 75,153)( 76,149)( 77,148)( 78,150)( 79,146)
( 80,145)( 81,147)(163,172)(164,174)(165,173)(166,178)(167,180)(168,179)
(169,175)(170,177)(171,176)(182,183)(184,187)(185,189)(186,188)(190,203)
(191,202)(192,204)(193,200)(194,199)(195,201)(196,206)(197,205)(198,207)
(208,212)(209,211)(210,213)(214,215)(217,233)(218,232)(219,234)(220,230)
(221,229)(222,231)(223,227)(224,226)(225,228)(235,242)(236,241)(237,243)
(238,239)(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)
(251,330)(252,329)(253,343)(254,345)(255,344)(256,349)(257,351)(258,350)
(259,346)(260,348)(261,347)(262,334)(263,336)(264,335)(265,340)(266,342)
(267,341)(268,337)(269,339)(270,338)(271,356)(272,355)(273,357)(274,353)
(275,352)(276,354)(277,359)(278,358)(279,360)(280,374)(281,373)(282,375)
(283,371)(284,370)(285,372)(286,377)(287,376)(288,378)(289,365)(290,364)
(291,366)(292,362)(293,361)(294,363)(295,368)(296,367)(297,369)(298,386)
(299,385)(300,387)(301,383)(302,382)(303,384)(304,380)(305,379)(306,381)
(307,404)(308,403)(309,405)(310,401)(311,400)(312,402)(313,398)(314,397)
(315,399)(316,395)(317,394)(318,396)(319,392)(320,391)(321,393)(322,389)
(323,388)(324,390)(406,415)(407,417)(408,416)(409,421)(410,423)(411,422)
(412,418)(413,420)(414,419)(425,426)(427,430)(428,432)(429,431)(433,446)
(434,445)(435,447)(436,443)(437,442)(438,444)(439,449)(440,448)(441,450)
(451,455)(452,454)(453,456)(457,458)(460,476)(461,475)(462,477)(463,473)
(464,472)(465,474)(466,470)(467,469)(468,471)(478,485)(479,484)(480,486)
(481,482);
s3 := Sym(486)!( 1,244)( 2,246)( 3,245)( 4,250)( 5,252)( 6,251)( 7,247)
( 8,249)( 9,248)( 10,262)( 11,264)( 12,263)( 13,268)( 14,270)( 15,269)
( 16,265)( 17,267)( 18,266)( 19,253)( 20,255)( 21,254)( 22,259)( 23,261)
( 24,260)( 25,256)( 26,258)( 27,257)( 28,271)( 29,273)( 30,272)( 31,277)
( 32,279)( 33,278)( 34,274)( 35,276)( 36,275)( 37,289)( 38,291)( 39,290)
( 40,295)( 41,297)( 42,296)( 43,292)( 44,294)( 45,293)( 46,280)( 47,282)
( 48,281)( 49,286)( 50,288)( 51,287)( 52,283)( 53,285)( 54,284)( 55,298)
( 56,300)( 57,299)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)
( 64,316)( 65,318)( 66,317)( 67,322)( 68,324)( 69,323)( 70,319)( 71,321)
( 72,320)( 73,307)( 74,309)( 75,308)( 76,313)( 77,315)( 78,314)( 79,310)
( 80,312)( 81,311)( 82,415)( 83,417)( 84,416)( 85,421)( 86,423)( 87,422)
( 88,418)( 89,420)( 90,419)( 91,406)( 92,408)( 93,407)( 94,412)( 95,414)
( 96,413)( 97,409)( 98,411)( 99,410)(100,424)(101,426)(102,425)(103,430)
(104,432)(105,431)(106,427)(107,429)(108,428)(109,442)(110,444)(111,443)
(112,448)(113,450)(114,449)(115,445)(116,447)(117,446)(118,433)(119,435)
(120,434)(121,439)(122,441)(123,440)(124,436)(125,438)(126,437)(127,451)
(128,453)(129,452)(130,457)(131,459)(132,458)(133,454)(134,456)(135,455)
(136,469)(137,471)(138,470)(139,475)(140,477)(141,476)(142,472)(143,474)
(144,473)(145,460)(146,462)(147,461)(148,466)(149,468)(150,467)(151,463)
(152,465)(153,464)(154,478)(155,480)(156,479)(157,484)(158,486)(159,485)
(160,481)(161,483)(162,482)(163,334)(164,336)(165,335)(166,340)(167,342)
(168,341)(169,337)(170,339)(171,338)(172,325)(173,327)(174,326)(175,331)
(176,333)(177,332)(178,328)(179,330)(180,329)(181,343)(182,345)(183,344)
(184,349)(185,351)(186,350)(187,346)(188,348)(189,347)(190,361)(191,363)
(192,362)(193,367)(194,369)(195,368)(196,364)(197,366)(198,365)(199,352)
(200,354)(201,353)(202,358)(203,360)(204,359)(205,355)(206,357)(207,356)
(208,370)(209,372)(210,371)(211,376)(212,378)(213,377)(214,373)(215,375)
(216,374)(217,388)(218,390)(219,389)(220,394)(221,396)(222,395)(223,391)
(224,393)(225,392)(226,379)(227,381)(228,380)(229,385)(230,387)(231,386)
(232,382)(233,384)(234,383)(235,397)(236,399)(237,398)(238,403)(239,405)
(240,404)(241,400)(242,402)(243,401);
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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