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