Polytope of Type {54,6} with group SmallGroup(1944,948)

Overview

Group: SmallGroup(1944,948)
Rank: 3
Schläfli Type: {54,6}
Vertices, edges, …: 162, 486, 18
Order of s₀s₁s₂: 54
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{54,6}*972a

3-fold

6-fold

{18,6}*324a

9-fold

18-fold

27-fold

54-fold

{9,2}*36

81-fold

162-fold

243-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^15*s0*s2*(s1*s0)^2*s2*s1> of order 3

6 facets

6 of {54}*108

54 vertex figures

54 of {6}*12

P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 3

6 facets

6 of {54}*108

90 vertex figures

36 of {6}*12
54 of {2}*4

Representations

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, 85)(  5, 87)(  6, 86)(  7, 88)(  8, 90)(  9, 89)( 10,102)( 11,101)( 12,100)( 13,105)( 14,104)( 15,103)( 16,108)( 17,107)( 18,106)( 19, 93)( 20, 92)( 21, 91)( 22, 96)( 23, 95)( 24, 94)( 25, 99)( 26, 98)( 27, 97)( 28,142)( 29,144)( 30,143)( 31,136)( 32,138)( 33,137)( 34,139)( 35,141)( 36,140)( 37,162)( 38,161)( 39,160)( 40,156)( 41,155)( 42,154)( 43,159)( 44,158)( 45,157)( 46,153)( 47,152)( 48,151)( 49,147)( 50,146)( 51,145)( 52,150)( 53,149)( 54,148)( 55,112)( 56,114)( 57,113)( 58,115)( 59,117)( 60,116)( 61,109)( 62,111)( 63,110)( 64,132)( 65,131)( 66,130)( 67,135)( 68,134)( 69,133)( 70,129)( 71,128)( 72,127)( 73,123)( 74,122)( 75,121)( 76,126)( 77,125)( 78,124)( 79,120)( 80,119)( 81,118)(163,183)(164,182)(165,181)(166,186)(167,185)(168,184)(169,189)(170,188)(171,187)(172,174)(175,177)(178,180)(190,243)(191,242)(192,241)(193,237)(194,236)(195,235)(196,240)(197,239)(198,238)(199,234)(200,233)(201,232)(202,228)(203,227)(204,226)(205,231)(206,230)(207,229)(208,225)(209,224)(210,223)(211,219)(212,218)(213,217)(214,222)(215,221)(216,220)(244,325)(245,327)(246,326)(247,328)(248,330)(249,329)(250,331)(251,333)(252,332)(253,345)(254,344)(255,343)(256,348)(257,347)(258,346)(259,351)(260,350)(261,349)(262,336)(263,335)(264,334)(265,339)(266,338)(267,337)(268,342)(269,341)(270,340)(271,385)(272,387)(273,386)(274,379)(275,381)(276,380)(277,382)(278,384)(279,383)(280,405)(281,404)(282,403)(283,399)(284,398)(285,397)(286,402)(287,401)(288,400)(289,396)(290,395)(291,394)(292,390)(293,389)(294,388)(295,393)(296,392)(297,391)(298,355)(299,357)(300,356)(301,358)(302,360)(303,359)(304,352)(305,354)(306,353)(307,375)(308,374)(309,373)(310,378)(311,377)(312,376)(313,372)(314,371)(315,370)(316,366)(317,365)(318,364)(319,369)(320,368)(321,367)(322,363)(323,362)(324,361)(406,426)(407,425)(408,424)(409,429)(410,428)(411,427)(412,432)(413,431)(414,430)(415,417)(418,420)(421,423)(433,486)(434,485)(435,484)(436,480)(437,479)(438,478)(439,483)(440,482)(441,481)(442,477)(443,476)(444,475)(445,471)(446,470)(447,469)(448,474)(449,473)(450,472)(451,468)(452,467)(453,466)(454,462)(455,461)(456,460)(457,465)(458,464)(459,463);;
s2 := (  1,271)(  2,272)(  3,273)(  4,277)(  5,278)(  6,279)(  7,274)(  8,275)(  9,276)( 10,280)( 11,281)( 12,282)( 13,286)( 14,287)( 15,288)( 16,283)( 17,284)( 18,285)( 19,289)( 20,290)( 21,291)( 22,295)( 23,296)( 24,297)( 25,292)( 26,293)( 27,294)( 28,244)( 29,245)( 30,246)( 31,250)( 32,251)( 33,252)( 34,247)( 35,248)( 36,249)( 37,253)( 38,254)( 39,255)( 40,259)( 41,260)( 42,261)( 43,256)( 44,257)( 45,258)( 46,262)( 47,263)( 48,264)( 49,268)( 50,269)( 51,270)( 52,265)( 53,266)( 54,267)( 55,298)( 56,299)( 57,300)( 58,304)( 59,305)( 60,306)( 61,301)( 62,302)( 63,303)( 64,307)( 65,308)( 66,309)( 67,313)( 68,314)( 69,315)( 70,310)( 71,311)( 72,312)( 73,316)( 74,317)( 75,318)( 76,322)( 77,323)( 78,324)( 79,319)( 80,320)( 81,321)( 82,352)( 83,353)( 84,354)( 85,358)( 86,359)( 87,360)( 88,355)( 89,356)( 90,357)( 91,361)( 92,362)( 93,363)( 94,367)( 95,368)( 96,369)( 97,364)( 98,365)( 99,366)(100,370)(101,371)(102,372)(103,376)(104,377)(105,378)(106,373)(107,374)(108,375)(109,325)(110,326)(111,327)(112,331)(113,332)(114,333)(115,328)(116,329)(117,330)(118,334)(119,335)(120,336)(121,340)(122,341)(123,342)(124,337)(125,338)(126,339)(127,343)(128,344)(129,345)(130,349)(131,350)(132,351)(133,346)(134,347)(135,348)(136,379)(137,380)(138,381)(139,385)(140,386)(141,387)(142,382)(143,383)(144,384)(145,388)(146,389)(147,390)(148,394)(149,395)(150,396)(151,391)(152,392)(153,393)(154,397)(155,398)(156,399)(157,403)(158,404)(159,405)(160,400)(161,401)(162,402)(163,433)(164,434)(165,435)(166,439)(167,440)(168,441)(169,436)(170,437)(171,438)(172,442)(173,443)(174,444)(175,448)(176,449)(177,450)(178,445)(179,446)(180,447)(181,451)(182,452)(183,453)(184,457)(185,458)(186,459)(187,454)(188,455)(189,456)(190,406)(191,407)(192,408)(193,412)(194,413)(195,414)(196,409)(197,410)(198,411)(199,415)(200,416)(201,417)(202,421)(203,422)(204,423)(205,418)(206,419)(207,420)(208,424)(209,425)(210,426)(211,430)(212,431)(213,432)(214,427)(215,428)(216,429)(217,460)(218,461)(219,462)(220,466)(221,467)(222,468)(223,463)(224,464)(225,465)(226,469)(227,470)(228,471)(229,475)(230,476)(231,477)(232,472)(233,473)(234,474)(235,478)(236,479)(237,480)(238,484)(239,485)(240,486)(241,481)(242,482)(243,483);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*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*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*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, 85)(  5, 87)(  6, 86)(  7, 88)(  8, 90)(  9, 89)( 10,102)( 11,101)( 12,100)( 13,105)( 14,104)( 15,103)( 16,108)( 17,107)( 18,106)( 19, 93)( 20, 92)( 21, 91)( 22, 96)( 23, 95)( 24, 94)( 25, 99)( 26, 98)( 27, 97)( 28,142)( 29,144)( 30,143)( 31,136)( 32,138)( 33,137)( 34,139)( 35,141)( 36,140)( 37,162)( 38,161)( 39,160)( 40,156)( 41,155)( 42,154)( 43,159)( 44,158)( 45,157)( 46,153)( 47,152)( 48,151)( 49,147)( 50,146)( 51,145)( 52,150)( 53,149)( 54,148)( 55,112)( 56,114)( 57,113)( 58,115)( 59,117)( 60,116)( 61,109)( 62,111)( 63,110)( 64,132)( 65,131)( 66,130)( 67,135)( 68,134)( 69,133)( 70,129)( 71,128)( 72,127)( 73,123)( 74,122)( 75,121)( 76,126)( 77,125)( 78,124)( 79,120)( 80,119)( 81,118)(163,183)(164,182)(165,181)(166,186)(167,185)(168,184)(169,189)(170,188)(171,187)(172,174)(175,177)(178,180)(190,243)(191,242)(192,241)(193,237)(194,236)(195,235)(196,240)(197,239)(198,238)(199,234)(200,233)(201,232)(202,228)(203,227)(204,226)(205,231)(206,230)(207,229)(208,225)(209,224)(210,223)(211,219)(212,218)(213,217)(214,222)(215,221)(216,220)(244,325)(245,327)(246,326)(247,328)(248,330)(249,329)(250,331)(251,333)(252,332)(253,345)(254,344)(255,343)(256,348)(257,347)(258,346)(259,351)(260,350)(261,349)(262,336)(263,335)(264,334)(265,339)(266,338)(267,337)(268,342)(269,341)(270,340)(271,385)(272,387)(273,386)(274,379)(275,381)(276,380)(277,382)(278,384)(279,383)(280,405)(281,404)(282,403)(283,399)(284,398)(285,397)(286,402)(287,401)(288,400)(289,396)(290,395)(291,394)(292,390)(293,389)(294,388)(295,393)(296,392)(297,391)(298,355)(299,357)(300,356)(301,358)(302,360)(303,359)(304,352)(305,354)(306,353)(307,375)(308,374)(309,373)(310,378)(311,377)(312,376)(313,372)(314,371)(315,370)(316,366)(317,365)(318,364)(319,369)(320,368)(321,367)(322,363)(323,362)(324,361)(406,426)(407,425)(408,424)(409,429)(410,428)(411,427)(412,432)(413,431)(414,430)(415,417)(418,420)(421,423)(433,486)(434,485)(435,484)(436,480)(437,479)(438,478)(439,483)(440,482)(441,481)(442,477)(443,476)(444,475)(445,471)(446,470)(447,469)(448,474)(449,473)(450,472)(451,468)(452,467)(453,466)(454,462)(455,461)(456,460)(457,465)(458,464)(459,463);
s2 := Sym(486)!(  1,271)(  2,272)(  3,273)(  4,277)(  5,278)(  6,279)(  7,274)(  8,275)(  9,276)( 10,280)( 11,281)( 12,282)( 13,286)( 14,287)( 15,288)( 16,283)( 17,284)( 18,285)( 19,289)( 20,290)( 21,291)( 22,295)( 23,296)( 24,297)( 25,292)( 26,293)( 27,294)( 28,244)( 29,245)( 30,246)( 31,250)( 32,251)( 33,252)( 34,247)( 35,248)( 36,249)( 37,253)( 38,254)( 39,255)( 40,259)( 41,260)( 42,261)( 43,256)( 44,257)( 45,258)( 46,262)( 47,263)( 48,264)( 49,268)( 50,269)( 51,270)( 52,265)( 53,266)( 54,267)( 55,298)( 56,299)( 57,300)( 58,304)( 59,305)( 60,306)( 61,301)( 62,302)( 63,303)( 64,307)( 65,308)( 66,309)( 67,313)( 68,314)( 69,315)( 70,310)( 71,311)( 72,312)( 73,316)( 74,317)( 75,318)( 76,322)( 77,323)( 78,324)( 79,319)( 80,320)( 81,321)( 82,352)( 83,353)( 84,354)( 85,358)( 86,359)( 87,360)( 88,355)( 89,356)( 90,357)( 91,361)( 92,362)( 93,363)( 94,367)( 95,368)( 96,369)( 97,364)( 98,365)( 99,366)(100,370)(101,371)(102,372)(103,376)(104,377)(105,378)(106,373)(107,374)(108,375)(109,325)(110,326)(111,327)(112,331)(113,332)(114,333)(115,328)(116,329)(117,330)(118,334)(119,335)(120,336)(121,340)(122,341)(123,342)(124,337)(125,338)(126,339)(127,343)(128,344)(129,345)(130,349)(131,350)(132,351)(133,346)(134,347)(135,348)(136,379)(137,380)(138,381)(139,385)(140,386)(141,387)(142,382)(143,383)(144,384)(145,388)(146,389)(147,390)(148,394)(149,395)(150,396)(151,391)(152,392)(153,393)(154,397)(155,398)(156,399)(157,403)(158,404)(159,405)(160,400)(161,401)(162,402)(163,433)(164,434)(165,435)(166,439)(167,440)(168,441)(169,436)(170,437)(171,438)(172,442)(173,443)(174,444)(175,448)(176,449)(177,450)(178,445)(179,446)(180,447)(181,451)(182,452)(183,453)(184,457)(185,458)(186,459)(187,454)(188,455)(189,456)(190,406)(191,407)(192,408)(193,412)(194,413)(195,414)(196,409)(197,410)(198,411)(199,415)(200,416)(201,417)(202,421)(203,422)(204,423)(205,418)(206,419)(207,420)(208,424)(209,425)(210,426)(211,430)(212,431)(213,432)(214,427)(215,428)(216,429)(217,460)(218,461)(219,462)(220,466)(221,467)(222,468)(223,463)(224,464)(225,465)(226,469)(227,470)(228,471)(229,475)(230,476)(231,477)(232,472)(233,473)(234,474)(235,478)(236,479)(237,480)(238,484)(239,485)(240,486)(241,481)(242,482)(243,483);
poly := sub<Sym(486)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*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*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*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.