Polytope of Type {27,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {27,6,6}*1944a
if this polytope has a name.
Group : SmallGroup(1944,948)
Rank : 4
Schlafli Type : {27,6,6}
Number of vertices, edges, etc : 27, 81, 18, 6
Order of s0s1s2s3 : 54
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 : {27,6,3}*972
3-fold quotients : {9,6,6}*648a, {27,2,6}*648
6-fold quotients : {9,6,3}*324, {27,2,3}*324
9-fold quotients : {27,2,2}*216, {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 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 21)( 11, 20)( 12, 19)( 13, 27)
( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)( 43, 51)
( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)( 65, 74)
( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 82,183)
( 83,182)( 84,181)( 85,189)( 86,188)( 87,187)( 88,186)( 89,185)( 90,184)
( 91,174)( 92,173)( 93,172)( 94,180)( 95,179)( 96,178)( 97,177)( 98,176)
( 99,175)(100,165)(101,164)(102,163)(103,171)(104,170)(105,169)(106,168)
(107,167)(108,166)(109,210)(110,209)(111,208)(112,216)(113,215)(114,214)
(115,213)(116,212)(117,211)(118,201)(119,200)(120,199)(121,207)(122,206)
(123,205)(124,204)(125,203)(126,202)(127,192)(128,191)(129,190)(130,198)
(131,197)(132,196)(133,195)(134,194)(135,193)(136,237)(137,236)(138,235)
(139,243)(140,242)(141,241)(142,240)(143,239)(144,238)(145,228)(146,227)
(147,226)(148,234)(149,233)(150,232)(151,231)(152,230)(153,229)(154,219)
(155,218)(156,217)(157,225)(158,224)(159,223)(160,222)(161,221)(162,220)
(245,246)(247,250)(248,252)(249,251)(253,264)(254,263)(255,262)(256,270)
(257,269)(258,268)(259,267)(260,266)(261,265)(272,273)(274,277)(275,279)
(276,278)(280,291)(281,290)(282,289)(283,297)(284,296)(285,295)(286,294)
(287,293)(288,292)(299,300)(301,304)(302,306)(303,305)(307,318)(308,317)
(309,316)(310,324)(311,323)(312,322)(313,321)(314,320)(315,319)(325,426)
(326,425)(327,424)(328,432)(329,431)(330,430)(331,429)(332,428)(333,427)
(334,417)(335,416)(336,415)(337,423)(338,422)(339,421)(340,420)(341,419)
(342,418)(343,408)(344,407)(345,406)(346,414)(347,413)(348,412)(349,411)
(350,410)(351,409)(352,453)(353,452)(354,451)(355,459)(356,458)(357,457)
(358,456)(359,455)(360,454)(361,444)(362,443)(363,442)(364,450)(365,449)
(366,448)(367,447)(368,446)(369,445)(370,435)(371,434)(372,433)(373,441)
(374,440)(375,439)(376,438)(377,437)(378,436)(379,480)(380,479)(381,478)
(382,486)(383,485)(384,484)(385,483)(386,482)(387,481)(388,471)(389,470)
(390,469)(391,477)(392,476)(393,475)(394,474)(395,473)(396,472)(397,462)
(398,461)(399,460)(400,468)(401,467)(402,466)(403,465)(404,464)(405,463);;
s1 := ( 1, 82)( 2, 84)( 3, 83)( 4, 88)( 5, 90)( 6, 89)( 7, 85)( 8, 87)
( 9, 86)( 10,102)( 11,101)( 12,100)( 13,108)( 14,107)( 15,106)( 16,105)
( 17,104)( 18,103)( 19, 93)( 20, 92)( 21, 91)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28,112)( 29,114)( 30,113)( 31,109)( 32,111)
( 33,110)( 34,115)( 35,117)( 36,116)( 37,132)( 38,131)( 39,130)( 40,129)
( 41,128)( 42,127)( 43,135)( 44,134)( 45,133)( 46,123)( 47,122)( 48,121)
( 49,120)( 50,119)( 51,118)( 52,126)( 53,125)( 54,124)( 55,142)( 56,144)
( 57,143)( 58,139)( 59,141)( 60,140)( 61,136)( 62,138)( 63,137)( 64,162)
( 65,161)( 66,160)( 67,159)( 68,158)( 69,157)( 70,156)( 71,155)( 72,154)
( 73,153)( 74,152)( 75,151)( 76,150)( 77,149)( 78,148)( 79,147)( 80,146)
( 81,145)(163,183)(164,182)(165,181)(166,189)(167,188)(168,187)(169,186)
(170,185)(171,184)(172,174)(175,180)(176,179)(177,178)(190,213)(191,212)
(192,211)(193,210)(194,209)(195,208)(196,216)(197,215)(198,214)(199,204)
(200,203)(201,202)(205,207)(217,243)(218,242)(219,241)(220,240)(221,239)
(222,238)(223,237)(224,236)(225,235)(226,234)(227,233)(228,232)(229,231)
(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)(251,330)
(252,329)(253,345)(254,344)(255,343)(256,351)(257,350)(258,349)(259,348)
(260,347)(261,346)(262,336)(263,335)(264,334)(265,342)(266,341)(267,340)
(268,339)(269,338)(270,337)(271,355)(272,357)(273,356)(274,352)(275,354)
(276,353)(277,358)(278,360)(279,359)(280,375)(281,374)(282,373)(283,372)
(284,371)(285,370)(286,378)(287,377)(288,376)(289,366)(290,365)(291,364)
(292,363)(293,362)(294,361)(295,369)(296,368)(297,367)(298,385)(299,387)
(300,386)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)(307,405)
(308,404)(309,403)(310,402)(311,401)(312,400)(313,399)(314,398)(315,397)
(316,396)(317,395)(318,394)(319,393)(320,392)(321,391)(322,390)(323,389)
(324,388)(406,426)(407,425)(408,424)(409,432)(410,431)(411,430)(412,429)
(413,428)(414,427)(415,417)(418,423)(419,422)(420,421)(433,456)(434,455)
(435,454)(436,453)(437,452)(438,451)(439,459)(440,458)(441,457)(442,447)
(443,446)(444,445)(448,450)(460,486)(461,485)(462,484)(463,483)(464,482)
(465,481)(466,480)(467,479)(468,478)(469,477)(470,476)(471,475)(472,474);;
s2 := ( 1, 28)( 2, 29)( 3, 30)( 4, 34)( 5, 35)( 6, 36)( 7, 31)( 8, 32)
( 9, 33)( 10, 37)( 11, 38)( 12, 39)( 13, 43)( 14, 44)( 15, 45)( 16, 40)
( 17, 41)( 18, 42)( 19, 46)( 20, 47)( 21, 48)( 22, 52)( 23, 53)( 24, 54)
( 25, 49)( 26, 50)( 27, 51)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)
( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 82,109)( 83,110)( 84,111)( 85,115)
( 86,116)( 87,117)( 88,112)( 89,113)( 90,114)( 91,118)( 92,119)( 93,120)
( 94,124)( 95,125)( 96,126)( 97,121)( 98,122)( 99,123)(100,127)(101,128)
(102,129)(103,133)(104,134)(105,135)(106,130)(107,131)(108,132)(139,142)
(140,143)(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)(159,162)
(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)(170,194)
(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)
(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)(186,216)
(187,211)(188,212)(189,213)(220,223)(221,224)(222,225)(229,232)(230,233)
(231,234)(238,241)(239,242)(240,243)(244,271)(245,272)(246,273)(247,277)
(248,278)(249,279)(250,274)(251,275)(252,276)(253,280)(254,281)(255,282)
(256,286)(257,287)(258,288)(259,283)(260,284)(261,285)(262,289)(263,290)
(264,291)(265,295)(266,296)(267,297)(268,292)(269,293)(270,294)(301,304)
(302,305)(303,306)(310,313)(311,314)(312,315)(319,322)(320,323)(321,324)
(325,352)(326,353)(327,354)(328,358)(329,359)(330,360)(331,355)(332,356)
(333,357)(334,361)(335,362)(336,363)(337,367)(338,368)(339,369)(340,364)
(341,365)(342,366)(343,370)(344,371)(345,372)(346,376)(347,377)(348,378)
(349,373)(350,374)(351,375)(382,385)(383,386)(384,387)(391,394)(392,395)
(393,396)(400,403)(401,404)(402,405)(406,433)(407,434)(408,435)(409,439)
(410,440)(411,441)(412,436)(413,437)(414,438)(415,442)(416,443)(417,444)
(418,448)(419,449)(420,450)(421,445)(422,446)(423,447)(424,451)(425,452)
(426,453)(427,457)(428,458)(429,459)(430,454)(431,455)(432,456)(463,466)
(464,467)(465,468)(472,475)(473,476)(474,477)(481,484)(482,485)(483,486);;
s3 := ( 1,244)( 2,245)( 3,246)( 4,250)( 5,251)( 6,252)( 7,247)( 8,248)
( 9,249)( 10,253)( 11,254)( 12,255)( 13,259)( 14,260)( 15,261)( 16,256)
( 17,257)( 18,258)( 19,262)( 20,263)( 21,264)( 22,268)( 23,269)( 24,270)
( 25,265)( 26,266)( 27,267)( 28,298)( 29,299)( 30,300)( 31,304)( 32,305)
( 33,306)( 34,301)( 35,302)( 36,303)( 37,307)( 38,308)( 39,309)( 40,313)
( 41,314)( 42,315)( 43,310)( 44,311)( 45,312)( 46,316)( 47,317)( 48,318)
( 49,322)( 50,323)( 51,324)( 52,319)( 53,320)( 54,321)( 55,271)( 56,272)
( 57,273)( 58,277)( 59,278)( 60,279)( 61,274)( 62,275)( 63,276)( 64,280)
( 65,281)( 66,282)( 67,286)( 68,287)( 69,288)( 70,283)( 71,284)( 72,285)
( 73,289)( 74,290)( 75,291)( 76,295)( 77,296)( 78,297)( 79,292)( 80,293)
( 81,294)( 82,325)( 83,326)( 84,327)( 85,331)( 86,332)( 87,333)( 88,328)
( 89,329)( 90,330)( 91,334)( 92,335)( 93,336)( 94,340)( 95,341)( 96,342)
( 97,337)( 98,338)( 99,339)(100,343)(101,344)(102,345)(103,349)(104,350)
(105,351)(106,346)(107,347)(108,348)(109,379)(110,380)(111,381)(112,385)
(113,386)(114,387)(115,382)(116,383)(117,384)(118,388)(119,389)(120,390)
(121,394)(122,395)(123,396)(124,391)(125,392)(126,393)(127,397)(128,398)
(129,399)(130,403)(131,404)(132,405)(133,400)(134,401)(135,402)(136,352)
(137,353)(138,354)(139,358)(140,359)(141,360)(142,355)(143,356)(144,357)
(145,361)(146,362)(147,363)(148,367)(149,368)(150,369)(151,364)(152,365)
(153,366)(154,370)(155,371)(156,372)(157,376)(158,377)(159,378)(160,373)
(161,374)(162,375)(163,406)(164,407)(165,408)(166,412)(167,413)(168,414)
(169,409)(170,410)(171,411)(172,415)(173,416)(174,417)(175,421)(176,422)
(177,423)(178,418)(179,419)(180,420)(181,424)(182,425)(183,426)(184,430)
(185,431)(186,432)(187,427)(188,428)(189,429)(190,460)(191,461)(192,462)
(193,466)(194,467)(195,468)(196,463)(197,464)(198,465)(199,469)(200,470)
(201,471)(202,475)(203,476)(204,477)(205,472)(206,473)(207,474)(208,478)
(209,479)(210,480)(211,484)(212,485)(213,486)(214,481)(215,482)(216,483)
(217,433)(218,434)(219,435)(220,439)(221,440)(222,441)(223,436)(224,437)
(225,438)(226,442)(227,443)(228,444)(229,448)(230,449)(231,450)(232,445)
(233,446)(234,447)(235,451)(236,452)(237,453)(238,457)(239,458)(240,459)
(241,454)(242,455)(243,456);;
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,
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*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)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 21)( 11, 20)( 12, 19)
( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)
( 32, 36)( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)
( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)
( 65, 74)( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)
( 82,183)( 83,182)( 84,181)( 85,189)( 86,188)( 87,187)( 88,186)( 89,185)
( 90,184)( 91,174)( 92,173)( 93,172)( 94,180)( 95,179)( 96,178)( 97,177)
( 98,176)( 99,175)(100,165)(101,164)(102,163)(103,171)(104,170)(105,169)
(106,168)(107,167)(108,166)(109,210)(110,209)(111,208)(112,216)(113,215)
(114,214)(115,213)(116,212)(117,211)(118,201)(119,200)(120,199)(121,207)
(122,206)(123,205)(124,204)(125,203)(126,202)(127,192)(128,191)(129,190)
(130,198)(131,197)(132,196)(133,195)(134,194)(135,193)(136,237)(137,236)
(138,235)(139,243)(140,242)(141,241)(142,240)(143,239)(144,238)(145,228)
(146,227)(147,226)(148,234)(149,233)(150,232)(151,231)(152,230)(153,229)
(154,219)(155,218)(156,217)(157,225)(158,224)(159,223)(160,222)(161,221)
(162,220)(245,246)(247,250)(248,252)(249,251)(253,264)(254,263)(255,262)
(256,270)(257,269)(258,268)(259,267)(260,266)(261,265)(272,273)(274,277)
(275,279)(276,278)(280,291)(281,290)(282,289)(283,297)(284,296)(285,295)
(286,294)(287,293)(288,292)(299,300)(301,304)(302,306)(303,305)(307,318)
(308,317)(309,316)(310,324)(311,323)(312,322)(313,321)(314,320)(315,319)
(325,426)(326,425)(327,424)(328,432)(329,431)(330,430)(331,429)(332,428)
(333,427)(334,417)(335,416)(336,415)(337,423)(338,422)(339,421)(340,420)
(341,419)(342,418)(343,408)(344,407)(345,406)(346,414)(347,413)(348,412)
(349,411)(350,410)(351,409)(352,453)(353,452)(354,451)(355,459)(356,458)
(357,457)(358,456)(359,455)(360,454)(361,444)(362,443)(363,442)(364,450)
(365,449)(366,448)(367,447)(368,446)(369,445)(370,435)(371,434)(372,433)
(373,441)(374,440)(375,439)(376,438)(377,437)(378,436)(379,480)(380,479)
(381,478)(382,486)(383,485)(384,484)(385,483)(386,482)(387,481)(388,471)
(389,470)(390,469)(391,477)(392,476)(393,475)(394,474)(395,473)(396,472)
(397,462)(398,461)(399,460)(400,468)(401,467)(402,466)(403,465)(404,464)
(405,463);
s1 := Sym(486)!( 1, 82)( 2, 84)( 3, 83)( 4, 88)( 5, 90)( 6, 89)( 7, 85)
( 8, 87)( 9, 86)( 10,102)( 11,101)( 12,100)( 13,108)( 14,107)( 15,106)
( 16,105)( 17,104)( 18,103)( 19, 93)( 20, 92)( 21, 91)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28,112)( 29,114)( 30,113)( 31,109)
( 32,111)( 33,110)( 34,115)( 35,117)( 36,116)( 37,132)( 38,131)( 39,130)
( 40,129)( 41,128)( 42,127)( 43,135)( 44,134)( 45,133)( 46,123)( 47,122)
( 48,121)( 49,120)( 50,119)( 51,118)( 52,126)( 53,125)( 54,124)( 55,142)
( 56,144)( 57,143)( 58,139)( 59,141)( 60,140)( 61,136)( 62,138)( 63,137)
( 64,162)( 65,161)( 66,160)( 67,159)( 68,158)( 69,157)( 70,156)( 71,155)
( 72,154)( 73,153)( 74,152)( 75,151)( 76,150)( 77,149)( 78,148)( 79,147)
( 80,146)( 81,145)(163,183)(164,182)(165,181)(166,189)(167,188)(168,187)
(169,186)(170,185)(171,184)(172,174)(175,180)(176,179)(177,178)(190,213)
(191,212)(192,211)(193,210)(194,209)(195,208)(196,216)(197,215)(198,214)
(199,204)(200,203)(201,202)(205,207)(217,243)(218,242)(219,241)(220,240)
(221,239)(222,238)(223,237)(224,236)(225,235)(226,234)(227,233)(228,232)
(229,231)(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)
(251,330)(252,329)(253,345)(254,344)(255,343)(256,351)(257,350)(258,349)
(259,348)(260,347)(261,346)(262,336)(263,335)(264,334)(265,342)(266,341)
(267,340)(268,339)(269,338)(270,337)(271,355)(272,357)(273,356)(274,352)
(275,354)(276,353)(277,358)(278,360)(279,359)(280,375)(281,374)(282,373)
(283,372)(284,371)(285,370)(286,378)(287,377)(288,376)(289,366)(290,365)
(291,364)(292,363)(293,362)(294,361)(295,369)(296,368)(297,367)(298,385)
(299,387)(300,386)(301,382)(302,384)(303,383)(304,379)(305,381)(306,380)
(307,405)(308,404)(309,403)(310,402)(311,401)(312,400)(313,399)(314,398)
(315,397)(316,396)(317,395)(318,394)(319,393)(320,392)(321,391)(322,390)
(323,389)(324,388)(406,426)(407,425)(408,424)(409,432)(410,431)(411,430)
(412,429)(413,428)(414,427)(415,417)(418,423)(419,422)(420,421)(433,456)
(434,455)(435,454)(436,453)(437,452)(438,451)(439,459)(440,458)(441,457)
(442,447)(443,446)(444,445)(448,450)(460,486)(461,485)(462,484)(463,483)
(464,482)(465,481)(466,480)(467,479)(468,478)(469,477)(470,476)(471,475)
(472,474);
s2 := Sym(486)!( 1, 28)( 2, 29)( 3, 30)( 4, 34)( 5, 35)( 6, 36)( 7, 31)
( 8, 32)( 9, 33)( 10, 37)( 11, 38)( 12, 39)( 13, 43)( 14, 44)( 15, 45)
( 16, 40)( 17, 41)( 18, 42)( 19, 46)( 20, 47)( 21, 48)( 22, 52)( 23, 53)
( 24, 54)( 25, 49)( 26, 50)( 27, 51)( 58, 61)( 59, 62)( 60, 63)( 67, 70)
( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 82,109)( 83,110)( 84,111)
( 85,115)( 86,116)( 87,117)( 88,112)( 89,113)( 90,114)( 91,118)( 92,119)
( 93,120)( 94,124)( 95,125)( 96,126)( 97,121)( 98,122)( 99,123)(100,127)
(101,128)(102,129)(103,133)(104,134)(105,135)(106,130)(107,131)(108,132)
(139,142)(140,143)(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)
(159,162)(163,190)(164,191)(165,192)(166,196)(167,197)(168,198)(169,193)
(170,194)(171,195)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)
(178,202)(179,203)(180,204)(181,208)(182,209)(183,210)(184,214)(185,215)
(186,216)(187,211)(188,212)(189,213)(220,223)(221,224)(222,225)(229,232)
(230,233)(231,234)(238,241)(239,242)(240,243)(244,271)(245,272)(246,273)
(247,277)(248,278)(249,279)(250,274)(251,275)(252,276)(253,280)(254,281)
(255,282)(256,286)(257,287)(258,288)(259,283)(260,284)(261,285)(262,289)
(263,290)(264,291)(265,295)(266,296)(267,297)(268,292)(269,293)(270,294)
(301,304)(302,305)(303,306)(310,313)(311,314)(312,315)(319,322)(320,323)
(321,324)(325,352)(326,353)(327,354)(328,358)(329,359)(330,360)(331,355)
(332,356)(333,357)(334,361)(335,362)(336,363)(337,367)(338,368)(339,369)
(340,364)(341,365)(342,366)(343,370)(344,371)(345,372)(346,376)(347,377)
(348,378)(349,373)(350,374)(351,375)(382,385)(383,386)(384,387)(391,394)
(392,395)(393,396)(400,403)(401,404)(402,405)(406,433)(407,434)(408,435)
(409,439)(410,440)(411,441)(412,436)(413,437)(414,438)(415,442)(416,443)
(417,444)(418,448)(419,449)(420,450)(421,445)(422,446)(423,447)(424,451)
(425,452)(426,453)(427,457)(428,458)(429,459)(430,454)(431,455)(432,456)
(463,466)(464,467)(465,468)(472,475)(473,476)(474,477)(481,484)(482,485)
(483,486);
s3 := Sym(486)!( 1,244)( 2,245)( 3,246)( 4,250)( 5,251)( 6,252)( 7,247)
( 8,248)( 9,249)( 10,253)( 11,254)( 12,255)( 13,259)( 14,260)( 15,261)
( 16,256)( 17,257)( 18,258)( 19,262)( 20,263)( 21,264)( 22,268)( 23,269)
( 24,270)( 25,265)( 26,266)( 27,267)( 28,298)( 29,299)( 30,300)( 31,304)
( 32,305)( 33,306)( 34,301)( 35,302)( 36,303)( 37,307)( 38,308)( 39,309)
( 40,313)( 41,314)( 42,315)( 43,310)( 44,311)( 45,312)( 46,316)( 47,317)
( 48,318)( 49,322)( 50,323)( 51,324)( 52,319)( 53,320)( 54,321)( 55,271)
( 56,272)( 57,273)( 58,277)( 59,278)( 60,279)( 61,274)( 62,275)( 63,276)
( 64,280)( 65,281)( 66,282)( 67,286)( 68,287)( 69,288)( 70,283)( 71,284)
( 72,285)( 73,289)( 74,290)( 75,291)( 76,295)( 77,296)( 78,297)( 79,292)
( 80,293)( 81,294)( 82,325)( 83,326)( 84,327)( 85,331)( 86,332)( 87,333)
( 88,328)( 89,329)( 90,330)( 91,334)( 92,335)( 93,336)( 94,340)( 95,341)
( 96,342)( 97,337)( 98,338)( 99,339)(100,343)(101,344)(102,345)(103,349)
(104,350)(105,351)(106,346)(107,347)(108,348)(109,379)(110,380)(111,381)
(112,385)(113,386)(114,387)(115,382)(116,383)(117,384)(118,388)(119,389)
(120,390)(121,394)(122,395)(123,396)(124,391)(125,392)(126,393)(127,397)
(128,398)(129,399)(130,403)(131,404)(132,405)(133,400)(134,401)(135,402)
(136,352)(137,353)(138,354)(139,358)(140,359)(141,360)(142,355)(143,356)
(144,357)(145,361)(146,362)(147,363)(148,367)(149,368)(150,369)(151,364)
(152,365)(153,366)(154,370)(155,371)(156,372)(157,376)(158,377)(159,378)
(160,373)(161,374)(162,375)(163,406)(164,407)(165,408)(166,412)(167,413)
(168,414)(169,409)(170,410)(171,411)(172,415)(173,416)(174,417)(175,421)
(176,422)(177,423)(178,418)(179,419)(180,420)(181,424)(182,425)(183,426)
(184,430)(185,431)(186,432)(187,427)(188,428)(189,429)(190,460)(191,461)
(192,462)(193,466)(194,467)(195,468)(196,463)(197,464)(198,465)(199,469)
(200,470)(201,471)(202,475)(203,476)(204,477)(205,472)(206,473)(207,474)
(208,478)(209,479)(210,480)(211,484)(212,485)(213,486)(214,481)(215,482)
(216,483)(217,433)(218,434)(219,435)(220,439)(221,440)(222,441)(223,436)
(224,437)(225,438)(226,442)(227,443)(228,444)(229,448)(230,449)(231,450)
(232,445)(233,446)(234,447)(235,451)(236,452)(237,453)(238,457)(239,458)
(240,459)(241,454)(242,455)(243,456);
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,
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*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