Polytope of Type {6,40} with group SmallGroup(1920,238596)

Overview

Group: SmallGroup(1920,238596)
Rank: 3
Schläfli Type: {6,40}
Vertices, edges, …: 24, 480, 160
Order of s₀s₁s₂: 60
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

4-fold

{6,20}*480c

5-fold

{6,8}*384f

8-fold

10-fold

16-fold

{6,10}*120

20-fold

24-fold

{2,20}*80

40-fold

48-fold

{2,10}*40

80-fold

96-fold

{2,5}*20

120-fold

{2,4}*16

160-fold

{3,2}*12

240-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)^2> of order 3

80 facets

40 of {2}*4
40 of {6}*12

8 vertex figures

8 of {40}*80

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.