Polytope of Type {3,6,54}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,54}*1944a
if this polytope has a name.
Group : SmallGroup(1944,948)
Rank : 4
Schlafli Type : {3,6,54}
Number of vertices, edges, etc : 3, 9, 162, 54
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 : {3,6,27}*972
3-fold quotients : {3,6,18}*648a, {3,2,54}*648
6-fold quotients : {3,6,9}*324, {3,2,27}*324
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.
Irregular Quotients (of which this is a minimal cover):
None.
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, 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);;
s2 := ( 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);;
s3 := ( 1,244)( 2,246)( 3,245)( 4,250)( 5,252)( 6,251)( 7,247)( 8,249)( 9,248)( 10,264)( 11,263)( 12,262)( 13,270)( 14,269)( 15,268)( 16,267)( 17,266)( 18,265)( 19,255)( 20,254)( 21,253)( 22,261)( 23,260)( 24,259)( 25,258)( 26,257)( 27,256)( 28,271)( 29,273)( 30,272)( 31,277)( 32,279)( 33,278)( 34,274)( 35,276)( 36,275)( 37,291)( 38,290)( 39,289)( 40,297)( 41,296)( 42,295)( 43,294)( 44,293)( 45,292)( 46,282)( 47,281)( 48,280)( 49,288)( 50,287)( 51,286)( 52,285)( 53,284)( 54,283)( 55,298)( 56,300)( 57,299)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)( 64,318)( 65,317)( 66,316)( 67,324)( 68,323)( 69,322)( 70,321)( 71,320)( 72,319)( 73,309)( 74,308)( 75,307)( 76,315)( 77,314)( 78,313)( 79,312)( 80,311)( 81,310)( 82,426)( 83,425)( 84,424)( 85,432)( 86,431)( 87,430)( 88,429)( 89,428)( 90,427)( 91,417)( 92,416)( 93,415)( 94,423)( 95,422)( 96,421)( 97,420)( 98,419)( 99,418)(100,408)(101,407)(102,406)(103,414)(104,413)(105,412)(106,411)(107,410)(108,409)(109,453)(110,452)(111,451)(112,459)(113,458)(114,457)(115,456)(116,455)(117,454)(118,444)(119,443)(120,442)(121,450)(122,449)(123,448)(124,447)(125,446)(126,445)(127,435)(128,434)(129,433)(130,441)(131,440)(132,439)(133,438)(134,437)(135,436)(136,480)(137,479)(138,478)(139,486)(140,485)(141,484)(142,483)(143,482)(144,481)(145,471)(146,470)(147,469)(148,477)(149,476)(150,475)(151,474)(152,473)(153,472)(154,462)(155,461)(156,460)(157,468)(158,467)(159,466)(160,465)(161,464)(162,463)(163,345)(164,344)(165,343)(166,351)(167,350)(168,349)(169,348)(170,347)(171,346)(172,336)(173,335)(174,334)(175,342)(176,341)(177,340)(178,339)(179,338)(180,337)(181,327)(182,326)(183,325)(184,333)(185,332)(186,331)(187,330)(188,329)(189,328)(190,372)(191,371)(192,370)(193,378)(194,377)(195,376)(196,375)(197,374)(198,373)(199,363)(200,362)(201,361)(202,369)(203,368)(204,367)(205,366)(206,365)(207,364)(208,354)(209,353)(210,352)(211,360)(212,359)(213,358)(214,357)(215,356)(216,355)(217,399)(218,398)(219,397)(220,405)(221,404)(222,403)(223,402)(224,401)(225,400)(226,390)(227,389)(228,388)(229,396)(230,395)(231,394)(232,393)(233,392)(234,391)(235,381)(236,380)(237,379)(238,387)(239,386)(240,385)(241,384)(242,383)(243,382);;
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*s1*s2*s1*s2*s3*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*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*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, 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);
s2 := 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);
s3 := Sym(486)!( 1,244)( 2,246)( 3,245)( 4,250)( 5,252)( 6,251)( 7,247)( 8,249)( 9,248)( 10,264)( 11,263)( 12,262)( 13,270)( 14,269)( 15,268)( 16,267)( 17,266)( 18,265)( 19,255)( 20,254)( 21,253)( 22,261)( 23,260)( 24,259)( 25,258)( 26,257)( 27,256)( 28,271)( 29,273)( 30,272)( 31,277)( 32,279)( 33,278)( 34,274)( 35,276)( 36,275)( 37,291)( 38,290)( 39,289)( 40,297)( 41,296)( 42,295)( 43,294)( 44,293)( 45,292)( 46,282)( 47,281)( 48,280)( 49,288)( 50,287)( 51,286)( 52,285)( 53,284)( 54,283)( 55,298)( 56,300)( 57,299)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)( 64,318)( 65,317)( 66,316)( 67,324)( 68,323)( 69,322)( 70,321)( 71,320)( 72,319)( 73,309)( 74,308)( 75,307)( 76,315)( 77,314)( 78,313)( 79,312)( 80,311)( 81,310)( 82,426)( 83,425)( 84,424)( 85,432)( 86,431)( 87,430)( 88,429)( 89,428)( 90,427)( 91,417)( 92,416)( 93,415)( 94,423)( 95,422)( 96,421)( 97,420)( 98,419)( 99,418)(100,408)(101,407)(102,406)(103,414)(104,413)(105,412)(106,411)(107,410)(108,409)(109,453)(110,452)(111,451)(112,459)(113,458)(114,457)(115,456)(116,455)(117,454)(118,444)(119,443)(120,442)(121,450)(122,449)(123,448)(124,447)(125,446)(126,445)(127,435)(128,434)(129,433)(130,441)(131,440)(132,439)(133,438)(134,437)(135,436)(136,480)(137,479)(138,478)(139,486)(140,485)(141,484)(142,483)(143,482)(144,481)(145,471)(146,470)(147,469)(148,477)(149,476)(150,475)(151,474)(152,473)(153,472)(154,462)(155,461)(156,460)(157,468)(158,467)(159,466)(160,465)(161,464)(162,463)(163,345)(164,344)(165,343)(166,351)(167,350)(168,349)(169,348)(170,347)(171,346)(172,336)(173,335)(174,334)(175,342)(176,341)(177,340)(178,339)(179,338)(180,337)(181,327)(182,326)(183,325)(184,333)(185,332)(186,331)(187,330)(188,329)(189,328)(190,372)(191,371)(192,370)(193,378)(194,377)(195,376)(196,375)(197,374)(198,373)(199,363)(200,362)(201,361)(202,369)(203,368)(204,367)(205,366)(206,365)(207,364)(208,354)(209,353)(210,352)(211,360)(212,359)(213,358)(214,357)(215,356)(216,355)(217,399)(218,398)(219,397)(220,405)(221,404)(222,403)(223,402)(224,401)(225,400)(226,390)(227,389)(228,388)(229,396)(230,395)(231,394)(232,393)(233,392)(234,391)(235,381)(236,380)(237,379)(238,387)(239,386)(240,385)(241,384)(242,383)(243,382);
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*s1*s2*s1*s2*s3*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*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*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