Overview
- Group
- SmallGroup(1440,5900)
- Rank
- 3
- Schläfli Type
- {12,30}
- Vertices, edges, …
- 24, 360, 60
- Order of s0s1s2
- 30
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
5-fold
6-fold
10-fold
12-fold
15-fold
20-fold
24-fold
30-fold
36-fold
60-fold
72-fold
120-fold
180-fold
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.
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 43)( 22, 44)( 23, 41)( 24, 42)( 25, 47)( 26, 48)( 27, 45)( 28, 46)( 29, 51)( 30, 52)( 31, 49)( 32, 50)( 33, 55)( 34, 56)( 35, 53)( 36, 54)( 37, 59)( 38, 60)( 39, 57)( 40, 58)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81,103)( 82,104)( 83,101)( 84,102)( 85,107)( 86,108)( 87,105)( 88,106)( 89,111)( 90,112)( 91,109)( 92,110)( 93,115)( 94,116)( 95,113)( 96,114)( 97,119)( 98,120)( 99,117)(100,118)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,163)(142,164)(143,161)(144,162)(145,167)(146,168)(147,165)(148,166)(149,171)(150,172)(151,169)(152,170)(153,175)(154,176)(155,173)(156,174)(157,179)(158,180)(159,177)(160,178)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,223)(202,224)(203,221)(204,222)(205,227)(206,228)(207,225)(208,226)(209,231)(210,232)(211,229)(212,230)(213,235)(214,236)(215,233)(216,234)(217,239)(218,240)(219,237)(220,238)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,283)(262,284)(263,281)(264,282)(265,287)(266,288)(267,285)(268,286)(269,291)(270,292)(271,289)(272,290)(273,295)(274,296)(275,293)(276,294)(277,299)(278,300)(279,297)(280,298)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,343)(322,344)(323,341)(324,342)(325,347)(326,348)(327,345)(328,346)(329,351)(330,352)(331,349)(332,350)(333,355)(334,356)(335,353)(336,354)(337,359)(338,360)(339,357)(340,358);; s1 := ( 1, 21)( 2, 22)( 3, 24)( 4, 23)( 5, 37)( 6, 38)( 7, 40)( 8, 39)( 9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 29)( 14, 30)( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 43, 44)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 49, 53)( 50, 54)( 51, 56)( 52, 55)( 61,141)( 62,142)( 63,144)( 64,143)( 65,157)( 66,158)( 67,160)( 68,159)( 69,153)( 70,154)( 71,156)( 72,155)( 73,149)( 74,150)( 75,152)( 76,151)( 77,145)( 78,146)( 79,148)( 80,147)( 81,121)( 82,122)( 83,124)( 84,123)( 85,137)( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,129)( 94,130)( 95,132)( 96,131)( 97,125)( 98,126)( 99,128)(100,127)(101,161)(102,162)(103,164)(104,163)(105,177)(106,178)(107,180)(108,179)(109,173)(110,174)(111,176)(112,175)(113,169)(114,170)(115,172)(116,171)(117,165)(118,166)(119,168)(120,167)(181,201)(182,202)(183,204)(184,203)(185,217)(186,218)(187,220)(188,219)(189,213)(190,214)(191,216)(192,215)(193,209)(194,210)(195,212)(196,211)(197,205)(198,206)(199,208)(200,207)(223,224)(225,237)(226,238)(227,240)(228,239)(229,233)(230,234)(231,236)(232,235)(241,321)(242,322)(243,324)(244,323)(245,337)(246,338)(247,340)(248,339)(249,333)(250,334)(251,336)(252,335)(253,329)(254,330)(255,332)(256,331)(257,325)(258,326)(259,328)(260,327)(261,301)(262,302)(263,304)(264,303)(265,317)(266,318)(267,320)(268,319)(269,313)(270,314)(271,316)(272,315)(273,309)(274,310)(275,312)(276,311)(277,305)(278,306)(279,308)(280,307)(281,341)(282,342)(283,344)(284,343)(285,357)(286,358)(287,360)(288,359)(289,353)(290,354)(291,356)(292,355)(293,349)(294,350)(295,352)(296,351)(297,345)(298,346)(299,348)(300,347);; s2 := ( 1,245)( 2,248)( 3,247)( 4,246)( 5,241)( 6,244)( 7,243)( 8,242)( 9,257)( 10,260)( 11,259)( 12,258)( 13,253)( 14,256)( 15,255)( 16,254)( 17,249)( 18,252)( 19,251)( 20,250)( 21,265)( 22,268)( 23,267)( 24,266)( 25,261)( 26,264)( 27,263)( 28,262)( 29,277)( 30,280)( 31,279)( 32,278)( 33,273)( 34,276)( 35,275)( 36,274)( 37,269)( 38,272)( 39,271)( 40,270)( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)( 48,282)( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)( 56,294)( 57,289)( 58,292)( 59,291)( 60,290)( 61,185)( 62,188)( 63,187)( 64,186)( 65,181)( 66,184)( 67,183)( 68,182)( 69,197)( 70,200)( 71,199)( 72,198)( 73,193)( 74,196)( 75,195)( 76,194)( 77,189)( 78,192)( 79,191)( 80,190)( 81,205)( 82,208)( 83,207)( 84,206)( 85,201)( 86,204)( 87,203)( 88,202)( 89,217)( 90,220)( 91,219)( 92,218)( 93,213)( 94,216)( 95,215)( 96,214)( 97,209)( 98,212)( 99,211)(100,210)(101,225)(102,228)(103,227)(104,226)(105,221)(106,224)(107,223)(108,222)(109,237)(110,240)(111,239)(112,238)(113,233)(114,236)(115,235)(116,234)(117,229)(118,232)(119,231)(120,230)(121,305)(122,308)(123,307)(124,306)(125,301)(126,304)(127,303)(128,302)(129,317)(130,320)(131,319)(132,318)(133,313)(134,316)(135,315)(136,314)(137,309)(138,312)(139,311)(140,310)(141,325)(142,328)(143,327)(144,326)(145,321)(146,324)(147,323)(148,322)(149,337)(150,340)(151,339)(152,338)(153,333)(154,336)(155,335)(156,334)(157,329)(158,332)(159,331)(160,330)(161,345)(162,348)(163,347)(164,346)(165,341)(166,344)(167,343)(168,342)(169,357)(170,360)(171,359)(172,358)(173,353)(174,356)(175,355)(176,354)(177,349)(178,352)(179,351)(180,350);; 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*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(360)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 43)( 22, 44)( 23, 41)( 24, 42)( 25, 47)( 26, 48)( 27, 45)( 28, 46)( 29, 51)( 30, 52)( 31, 49)( 32, 50)( 33, 55)( 34, 56)( 35, 53)( 36, 54)( 37, 59)( 38, 60)( 39, 57)( 40, 58)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81,103)( 82,104)( 83,101)( 84,102)( 85,107)( 86,108)( 87,105)( 88,106)( 89,111)( 90,112)( 91,109)( 92,110)( 93,115)( 94,116)( 95,113)( 96,114)( 97,119)( 98,120)( 99,117)(100,118)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,163)(142,164)(143,161)(144,162)(145,167)(146,168)(147,165)(148,166)(149,171)(150,172)(151,169)(152,170)(153,175)(154,176)(155,173)(156,174)(157,179)(158,180)(159,177)(160,178)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,223)(202,224)(203,221)(204,222)(205,227)(206,228)(207,225)(208,226)(209,231)(210,232)(211,229)(212,230)(213,235)(214,236)(215,233)(216,234)(217,239)(218,240)(219,237)(220,238)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,283)(262,284)(263,281)(264,282)(265,287)(266,288)(267,285)(268,286)(269,291)(270,292)(271,289)(272,290)(273,295)(274,296)(275,293)(276,294)(277,299)(278,300)(279,297)(280,298)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,343)(322,344)(323,341)(324,342)(325,347)(326,348)(327,345)(328,346)(329,351)(330,352)(331,349)(332,350)(333,355)(334,356)(335,353)(336,354)(337,359)(338,360)(339,357)(340,358); s1 := Sym(360)!( 1, 21)( 2, 22)( 3, 24)( 4, 23)( 5, 37)( 6, 38)( 7, 40)( 8, 39)( 9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 29)( 14, 30)( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 43, 44)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 49, 53)( 50, 54)( 51, 56)( 52, 55)( 61,141)( 62,142)( 63,144)( 64,143)( 65,157)( 66,158)( 67,160)( 68,159)( 69,153)( 70,154)( 71,156)( 72,155)( 73,149)( 74,150)( 75,152)( 76,151)( 77,145)( 78,146)( 79,148)( 80,147)( 81,121)( 82,122)( 83,124)( 84,123)( 85,137)( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,129)( 94,130)( 95,132)( 96,131)( 97,125)( 98,126)( 99,128)(100,127)(101,161)(102,162)(103,164)(104,163)(105,177)(106,178)(107,180)(108,179)(109,173)(110,174)(111,176)(112,175)(113,169)(114,170)(115,172)(116,171)(117,165)(118,166)(119,168)(120,167)(181,201)(182,202)(183,204)(184,203)(185,217)(186,218)(187,220)(188,219)(189,213)(190,214)(191,216)(192,215)(193,209)(194,210)(195,212)(196,211)(197,205)(198,206)(199,208)(200,207)(223,224)(225,237)(226,238)(227,240)(228,239)(229,233)(230,234)(231,236)(232,235)(241,321)(242,322)(243,324)(244,323)(245,337)(246,338)(247,340)(248,339)(249,333)(250,334)(251,336)(252,335)(253,329)(254,330)(255,332)(256,331)(257,325)(258,326)(259,328)(260,327)(261,301)(262,302)(263,304)(264,303)(265,317)(266,318)(267,320)(268,319)(269,313)(270,314)(271,316)(272,315)(273,309)(274,310)(275,312)(276,311)(277,305)(278,306)(279,308)(280,307)(281,341)(282,342)(283,344)(284,343)(285,357)(286,358)(287,360)(288,359)(289,353)(290,354)(291,356)(292,355)(293,349)(294,350)(295,352)(296,351)(297,345)(298,346)(299,348)(300,347); s2 := Sym(360)!( 1,245)( 2,248)( 3,247)( 4,246)( 5,241)( 6,244)( 7,243)( 8,242)( 9,257)( 10,260)( 11,259)( 12,258)( 13,253)( 14,256)( 15,255)( 16,254)( 17,249)( 18,252)( 19,251)( 20,250)( 21,265)( 22,268)( 23,267)( 24,266)( 25,261)( 26,264)( 27,263)( 28,262)( 29,277)( 30,280)( 31,279)( 32,278)( 33,273)( 34,276)( 35,275)( 36,274)( 37,269)( 38,272)( 39,271)( 40,270)( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)( 48,282)( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)( 56,294)( 57,289)( 58,292)( 59,291)( 60,290)( 61,185)( 62,188)( 63,187)( 64,186)( 65,181)( 66,184)( 67,183)( 68,182)( 69,197)( 70,200)( 71,199)( 72,198)( 73,193)( 74,196)( 75,195)( 76,194)( 77,189)( 78,192)( 79,191)( 80,190)( 81,205)( 82,208)( 83,207)( 84,206)( 85,201)( 86,204)( 87,203)( 88,202)( 89,217)( 90,220)( 91,219)( 92,218)( 93,213)( 94,216)( 95,215)( 96,214)( 97,209)( 98,212)( 99,211)(100,210)(101,225)(102,228)(103,227)(104,226)(105,221)(106,224)(107,223)(108,222)(109,237)(110,240)(111,239)(112,238)(113,233)(114,236)(115,235)(116,234)(117,229)(118,232)(119,231)(120,230)(121,305)(122,308)(123,307)(124,306)(125,301)(126,304)(127,303)(128,302)(129,317)(130,320)(131,319)(132,318)(133,313)(134,316)(135,315)(136,314)(137,309)(138,312)(139,311)(140,310)(141,325)(142,328)(143,327)(144,326)(145,321)(146,324)(147,323)(148,322)(149,337)(150,340)(151,339)(152,338)(153,333)(154,336)(155,335)(156,334)(157,329)(158,332)(159,331)(160,330)(161,345)(162,348)(163,347)(164,346)(165,341)(166,344)(167,343)(168,342)(169,357)(170,360)(171,359)(172,358)(173,353)(174,356)(175,355)(176,354)(177,349)(178,352)(179,351)(180,350); poly := sub<Sym(360)|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*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.