Polytope of Type {9,6,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,6,18}*1944a
if this polytope has a name.
Group : SmallGroup(1944,940)
Rank : 4
Schlafli Type : {9,6,18}
Number of vertices, edges, etc : 9, 27, 54, 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 : {9,6,9}*972
3-fold quotients : {9,2,18}*648, {3,6,18}*648a, {9,6,6}*648a
6-fold quotients : {9,2,9}*324, {3,6,9}*324, {9,6,3}*324
9-fold quotients : {3,2,18}*216, {9,2,6}*216, {3,6,6}*216a
18-fold quotients : {3,2,9}*108, {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 := ( 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, 82)( 2, 84)( 3, 83)( 4, 85)( 5, 87)( 6, 86)( 7, 88)( 8, 90)
( 9, 89)( 10,100)( 11,102)( 12,101)( 13,103)( 14,105)( 15,104)( 16,106)
( 17,108)( 18,107)( 19, 91)( 20, 93)( 21, 92)( 22, 94)( 23, 96)( 24, 95)
( 25, 97)( 26, 99)( 27, 98)( 28,110)( 29,109)( 30,111)( 31,113)( 32,112)
( 33,114)( 34,116)( 35,115)( 36,117)( 37,128)( 38,127)( 39,129)( 40,131)
( 41,130)( 42,132)( 43,134)( 44,133)( 45,135)( 46,119)( 47,118)( 48,120)
( 49,122)( 50,121)( 51,123)( 52,125)( 53,124)( 54,126)( 55,138)( 56,137)
( 57,136)( 58,141)( 59,140)( 60,139)( 61,144)( 62,143)( 63,142)( 64,156)
( 65,155)( 66,154)( 67,159)( 68,158)( 69,157)( 70,162)( 71,161)( 72,160)
( 73,147)( 74,146)( 75,145)( 76,150)( 77,149)( 78,148)( 79,153)( 80,152)
( 81,151)(163,172)(164,174)(165,173)(166,175)(167,177)(168,176)(169,178)
(170,180)(171,179)(182,183)(185,186)(188,189)(190,200)(191,199)(192,201)
(193,203)(194,202)(195,204)(196,206)(197,205)(198,207)(208,209)(211,212)
(214,215)(217,228)(218,227)(219,226)(220,231)(221,230)(222,229)(223,234)
(224,233)(225,232)(235,237)(238,240)(241,243)(244,325)(245,327)(246,326)
(247,328)(248,330)(249,329)(250,331)(251,333)(252,332)(253,343)(254,345)
(255,344)(256,346)(257,348)(258,347)(259,349)(260,351)(261,350)(262,334)
(263,336)(264,335)(265,337)(266,339)(267,338)(268,340)(269,342)(270,341)
(271,353)(272,352)(273,354)(274,356)(275,355)(276,357)(277,359)(278,358)
(279,360)(280,371)(281,370)(282,372)(283,374)(284,373)(285,375)(286,377)
(287,376)(288,378)(289,362)(290,361)(291,363)(292,365)(293,364)(294,366)
(295,368)(296,367)(297,369)(298,381)(299,380)(300,379)(301,384)(302,383)
(303,382)(304,387)(305,386)(306,385)(307,399)(308,398)(309,397)(310,402)
(311,401)(312,400)(313,405)(314,404)(315,403)(316,390)(317,389)(318,388)
(319,393)(320,392)(321,391)(322,396)(323,395)(324,394)(406,415)(407,417)
(408,416)(409,418)(410,420)(411,419)(412,421)(413,423)(414,422)(425,426)
(428,429)(431,432)(433,443)(434,442)(435,444)(436,446)(437,445)(438,447)
(439,449)(440,448)(441,450)(451,452)(454,455)(457,458)(460,471)(461,470)
(462,469)(463,474)(464,473)(465,472)(466,477)(467,476)(468,475)(478,480)
(481,483)(484,486);;
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 := ( 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)( 28,301)( 29,303)( 30,302)( 31,298)( 32,300)
( 33,299)( 34,304)( 35,306)( 36,305)( 37,310)( 38,312)( 39,311)( 40,307)
( 41,309)( 42,308)( 43,313)( 44,315)( 45,314)( 46,319)( 47,321)( 48,320)
( 49,316)( 50,318)( 51,317)( 52,322)( 53,324)( 54,323)( 55,274)( 56,276)
( 57,275)( 58,271)( 59,273)( 60,272)( 61,277)( 62,279)( 63,278)( 64,283)
( 65,285)( 66,284)( 67,280)( 68,282)( 69,281)( 70,286)( 71,288)( 72,287)
( 73,292)( 74,294)( 75,293)( 76,289)( 77,291)( 78,290)( 79,295)( 80,297)
( 81,296)( 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)(109,382)(110,384)(111,383)(112,379)
(113,381)(114,380)(115,385)(116,387)(117,386)(118,391)(119,393)(120,392)
(121,388)(122,390)(123,389)(124,394)(125,396)(126,395)(127,400)(128,402)
(129,401)(130,397)(131,399)(132,398)(133,403)(134,405)(135,404)(136,355)
(137,357)(138,356)(139,352)(140,354)(141,353)(142,358)(143,360)(144,359)
(145,364)(146,366)(147,365)(148,361)(149,363)(150,362)(151,367)(152,369)
(153,368)(154,373)(155,375)(156,374)(157,370)(158,372)(159,371)(160,376)
(161,378)(162,377)(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)(190,463)(191,465)(192,464)
(193,460)(194,462)(195,461)(196,466)(197,468)(198,467)(199,472)(200,474)
(201,473)(202,469)(203,471)(204,470)(205,475)(206,477)(207,476)(208,481)
(209,483)(210,482)(211,478)(212,480)(213,479)(214,484)(215,486)(216,485)
(217,436)(218,438)(219,437)(220,433)(221,435)(222,434)(223,439)(224,441)
(225,440)(226,445)(227,447)(228,446)(229,442)(230,444)(231,443)(232,448)
(233,450)(234,449)(235,454)(236,456)(237,455)(238,451)(239,453)(240,452)
(241,457)(242,459)(243,458);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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)( 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, 82)( 2, 84)( 3, 83)( 4, 85)( 5, 87)( 6, 86)( 7, 88)
( 8, 90)( 9, 89)( 10,100)( 11,102)( 12,101)( 13,103)( 14,105)( 15,104)
( 16,106)( 17,108)( 18,107)( 19, 91)( 20, 93)( 21, 92)( 22, 94)( 23, 96)
( 24, 95)( 25, 97)( 26, 99)( 27, 98)( 28,110)( 29,109)( 30,111)( 31,113)
( 32,112)( 33,114)( 34,116)( 35,115)( 36,117)( 37,128)( 38,127)( 39,129)
( 40,131)( 41,130)( 42,132)( 43,134)( 44,133)( 45,135)( 46,119)( 47,118)
( 48,120)( 49,122)( 50,121)( 51,123)( 52,125)( 53,124)( 54,126)( 55,138)
( 56,137)( 57,136)( 58,141)( 59,140)( 60,139)( 61,144)( 62,143)( 63,142)
( 64,156)( 65,155)( 66,154)( 67,159)( 68,158)( 69,157)( 70,162)( 71,161)
( 72,160)( 73,147)( 74,146)( 75,145)( 76,150)( 77,149)( 78,148)( 79,153)
( 80,152)( 81,151)(163,172)(164,174)(165,173)(166,175)(167,177)(168,176)
(169,178)(170,180)(171,179)(182,183)(185,186)(188,189)(190,200)(191,199)
(192,201)(193,203)(194,202)(195,204)(196,206)(197,205)(198,207)(208,209)
(211,212)(214,215)(217,228)(218,227)(219,226)(220,231)(221,230)(222,229)
(223,234)(224,233)(225,232)(235,237)(238,240)(241,243)(244,325)(245,327)
(246,326)(247,328)(248,330)(249,329)(250,331)(251,333)(252,332)(253,343)
(254,345)(255,344)(256,346)(257,348)(258,347)(259,349)(260,351)(261,350)
(262,334)(263,336)(264,335)(265,337)(266,339)(267,338)(268,340)(269,342)
(270,341)(271,353)(272,352)(273,354)(274,356)(275,355)(276,357)(277,359)
(278,358)(279,360)(280,371)(281,370)(282,372)(283,374)(284,373)(285,375)
(286,377)(287,376)(288,378)(289,362)(290,361)(291,363)(292,365)(293,364)
(294,366)(295,368)(296,367)(297,369)(298,381)(299,380)(300,379)(301,384)
(302,383)(303,382)(304,387)(305,386)(306,385)(307,399)(308,398)(309,397)
(310,402)(311,401)(312,400)(313,405)(314,404)(315,403)(316,390)(317,389)
(318,388)(319,393)(320,392)(321,391)(322,396)(323,395)(324,394)(406,415)
(407,417)(408,416)(409,418)(410,420)(411,419)(412,421)(413,423)(414,422)
(425,426)(428,429)(431,432)(433,443)(434,442)(435,444)(436,446)(437,445)
(438,447)(439,449)(440,448)(441,450)(451,452)(454,455)(457,458)(460,471)
(461,470)(462,469)(463,474)(464,473)(465,472)(466,477)(467,476)(468,475)
(478,480)(481,483)(484,486);
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)!( 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)( 28,301)( 29,303)( 30,302)( 31,298)
( 32,300)( 33,299)( 34,304)( 35,306)( 36,305)( 37,310)( 38,312)( 39,311)
( 40,307)( 41,309)( 42,308)( 43,313)( 44,315)( 45,314)( 46,319)( 47,321)
( 48,320)( 49,316)( 50,318)( 51,317)( 52,322)( 53,324)( 54,323)( 55,274)
( 56,276)( 57,275)( 58,271)( 59,273)( 60,272)( 61,277)( 62,279)( 63,278)
( 64,283)( 65,285)( 66,284)( 67,280)( 68,282)( 69,281)( 70,286)( 71,288)
( 72,287)( 73,292)( 74,294)( 75,293)( 76,289)( 77,291)( 78,290)( 79,295)
( 80,297)( 81,296)( 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)(109,382)(110,384)(111,383)
(112,379)(113,381)(114,380)(115,385)(116,387)(117,386)(118,391)(119,393)
(120,392)(121,388)(122,390)(123,389)(124,394)(125,396)(126,395)(127,400)
(128,402)(129,401)(130,397)(131,399)(132,398)(133,403)(134,405)(135,404)
(136,355)(137,357)(138,356)(139,352)(140,354)(141,353)(142,358)(143,360)
(144,359)(145,364)(146,366)(147,365)(148,361)(149,363)(150,362)(151,367)
(152,369)(153,368)(154,373)(155,375)(156,374)(157,370)(158,372)(159,371)
(160,376)(161,378)(162,377)(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)(190,463)(191,465)
(192,464)(193,460)(194,462)(195,461)(196,466)(197,468)(198,467)(199,472)
(200,474)(201,473)(202,469)(203,471)(204,470)(205,475)(206,477)(207,476)
(208,481)(209,483)(210,482)(211,478)(212,480)(213,479)(214,484)(215,486)
(216,485)(217,436)(218,438)(219,437)(220,433)(221,435)(222,434)(223,439)
(224,441)(225,440)(226,445)(227,447)(228,446)(229,442)(230,444)(231,443)
(232,448)(233,450)(234,449)(235,454)(236,456)(237,455)(238,451)(239,453)
(240,452)(241,457)(242,459)(243,458);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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