Overview
- Group
- SmallGroup(1440,5901)
- Rank
- 3
- Schläfli Type
- {30,6}
- Vertices, edges, …
- 120, 360, 24
- Order of s0s1s2
- 60
- 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
3-fold
4-fold
5-fold
6-fold
8-fold
10-fold
12-fold
15-fold
20-fold
24-fold
30-fold
36-fold
40-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.
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 2
12 facets
- 12 of {30}*60
60 vertex figures
- 60 of {6}*12
P/N, where N=<(s0*s1)^11*s0*s2*(s1*s0)^2*s2*s1*s0*s2*s1*s2> of order 2
12 facets
- 12 of {30}*60
60 vertex figures
- 60 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2> of order 4
6 facets
- 6 of {30}*60
30 vertex figures
- 30 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 61,121)( 62,122)( 63,124)( 64,123)( 65,137)( 66,138)( 67,140)( 68,139)( 69,133)( 70,134)( 71,136)( 72,135)( 73,129)( 74,130)( 75,132)( 76,131)( 77,125)( 78,126)( 79,128)( 80,127)( 81,161)( 82,162)( 83,164)( 84,163)( 85,177)( 86,178)( 87,180)( 88,179)( 89,173)( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,165)( 98,166)( 99,168)(100,167)(101,141)(102,142)(103,144)(104,143)(105,157)(106,158)(107,160)(108,159)(109,153)(110,154)(111,156)(112,155)(113,149)(114,150)(115,152)(116,151)(117,145)(118,146)(119,148)(120,147)(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)(217,225)(218,226)(219,228)(220,227)(241,301)(242,302)(243,304)(244,303)(245,317)(246,318)(247,320)(248,319)(249,313)(250,314)(251,316)(252,315)(253,309)(254,310)(255,312)(256,311)(257,305)(258,306)(259,308)(260,307)(261,341)(262,342)(263,344)(264,343)(265,357)(266,358)(267,360)(268,359)(269,353)(270,354)(271,356)(272,355)(273,349)(274,350)(275,352)(276,351)(277,345)(278,346)(279,348)(280,347)(281,321)(282,322)(283,324)(284,323)(285,337)(286,338)(287,340)(288,339)(289,333)(290,334)(291,336)(292,335)(293,329)(294,330)(295,332)(296,331)(297,325)(298,326)(299,328)(300,327);; s1 := ( 1,265)( 2,268)( 3,267)( 4,266)( 5,261)( 6,264)( 7,263)( 8,262)( 9,277)( 10,280)( 11,279)( 12,278)( 13,273)( 14,276)( 15,275)( 16,274)( 17,269)( 18,272)( 19,271)( 20,270)( 21,245)( 22,248)( 23,247)( 24,246)( 25,241)( 26,244)( 27,243)( 28,242)( 29,257)( 30,260)( 31,259)( 32,258)( 33,253)( 34,256)( 35,255)( 36,254)( 37,249)( 38,252)( 39,251)( 40,250)( 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)( 61,205)( 62,208)( 63,207)( 64,206)( 65,201)( 66,204)( 67,203)( 68,202)( 69,217)( 70,220)( 71,219)( 72,218)( 73,213)( 74,216)( 75,215)( 76,214)( 77,209)( 78,212)( 79,211)( 80,210)( 81,185)( 82,188)( 83,187)( 84,186)( 85,181)( 86,184)( 87,183)( 88,182)( 89,197)( 90,200)( 91,199)( 92,198)( 93,193)( 94,196)( 95,195)( 96,194)( 97,189)( 98,192)( 99,191)(100,190)(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)(121,325)(122,328)(123,327)(124,326)(125,321)(126,324)(127,323)(128,322)(129,337)(130,340)(131,339)(132,338)(133,333)(134,336)(135,335)(136,334)(137,329)(138,332)(139,331)(140,330)(141,305)(142,308)(143,307)(144,306)(145,301)(146,304)(147,303)(148,302)(149,317)(150,320)(151,319)(152,318)(153,313)(154,316)(155,315)(156,314)(157,309)(158,312)(159,311)(160,310)(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);; s2 := ( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61,122)( 62,121)( 63,123)( 64,124)( 65,126)( 66,125)( 67,127)( 68,128)( 69,130)( 70,129)( 71,131)( 72,132)( 73,134)( 74,133)( 75,135)( 76,136)( 77,138)( 78,137)( 79,139)( 80,140)( 81,142)( 82,141)( 83,143)( 84,144)( 85,146)( 86,145)( 87,147)( 88,148)( 89,150)( 90,149)( 91,151)( 92,152)( 93,154)( 94,153)( 95,155)( 96,156)( 97,158)( 98,157)( 99,159)(100,160)(101,162)(102,161)(103,163)(104,164)(105,166)(106,165)(107,167)(108,168)(109,170)(110,169)(111,171)(112,172)(113,174)(114,173)(115,175)(116,176)(117,178)(118,177)(119,179)(120,180)(181,182)(185,186)(189,190)(193,194)(197,198)(201,202)(205,206)(209,210)(213,214)(217,218)(221,222)(225,226)(229,230)(233,234)(237,238)(241,302)(242,301)(243,303)(244,304)(245,306)(246,305)(247,307)(248,308)(249,310)(250,309)(251,311)(252,312)(253,314)(254,313)(255,315)(256,316)(257,318)(258,317)(259,319)(260,320)(261,322)(262,321)(263,323)(264,324)(265,326)(266,325)(267,327)(268,328)(269,330)(270,329)(271,331)(272,332)(273,334)(274,333)(275,335)(276,336)(277,338)(278,337)(279,339)(280,340)(281,342)(282,341)(283,343)(284,344)(285,346)(286,345)(287,347)(288,348)(289,350)(290,349)(291,351)(292,352)(293,354)(294,353)(295,355)(296,356)(297,358)(298,357)(299,359)(300,360);; 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*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(360)!( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 61,121)( 62,122)( 63,124)( 64,123)( 65,137)( 66,138)( 67,140)( 68,139)( 69,133)( 70,134)( 71,136)( 72,135)( 73,129)( 74,130)( 75,132)( 76,131)( 77,125)( 78,126)( 79,128)( 80,127)( 81,161)( 82,162)( 83,164)( 84,163)( 85,177)( 86,178)( 87,180)( 88,179)( 89,173)( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,165)( 98,166)( 99,168)(100,167)(101,141)(102,142)(103,144)(104,143)(105,157)(106,158)(107,160)(108,159)(109,153)(110,154)(111,156)(112,155)(113,149)(114,150)(115,152)(116,151)(117,145)(118,146)(119,148)(120,147)(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)(217,225)(218,226)(219,228)(220,227)(241,301)(242,302)(243,304)(244,303)(245,317)(246,318)(247,320)(248,319)(249,313)(250,314)(251,316)(252,315)(253,309)(254,310)(255,312)(256,311)(257,305)(258,306)(259,308)(260,307)(261,341)(262,342)(263,344)(264,343)(265,357)(266,358)(267,360)(268,359)(269,353)(270,354)(271,356)(272,355)(273,349)(274,350)(275,352)(276,351)(277,345)(278,346)(279,348)(280,347)(281,321)(282,322)(283,324)(284,323)(285,337)(286,338)(287,340)(288,339)(289,333)(290,334)(291,336)(292,335)(293,329)(294,330)(295,332)(296,331)(297,325)(298,326)(299,328)(300,327); s1 := Sym(360)!( 1,265)( 2,268)( 3,267)( 4,266)( 5,261)( 6,264)( 7,263)( 8,262)( 9,277)( 10,280)( 11,279)( 12,278)( 13,273)( 14,276)( 15,275)( 16,274)( 17,269)( 18,272)( 19,271)( 20,270)( 21,245)( 22,248)( 23,247)( 24,246)( 25,241)( 26,244)( 27,243)( 28,242)( 29,257)( 30,260)( 31,259)( 32,258)( 33,253)( 34,256)( 35,255)( 36,254)( 37,249)( 38,252)( 39,251)( 40,250)( 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)( 61,205)( 62,208)( 63,207)( 64,206)( 65,201)( 66,204)( 67,203)( 68,202)( 69,217)( 70,220)( 71,219)( 72,218)( 73,213)( 74,216)( 75,215)( 76,214)( 77,209)( 78,212)( 79,211)( 80,210)( 81,185)( 82,188)( 83,187)( 84,186)( 85,181)( 86,184)( 87,183)( 88,182)( 89,197)( 90,200)( 91,199)( 92,198)( 93,193)( 94,196)( 95,195)( 96,194)( 97,189)( 98,192)( 99,191)(100,190)(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)(121,325)(122,328)(123,327)(124,326)(125,321)(126,324)(127,323)(128,322)(129,337)(130,340)(131,339)(132,338)(133,333)(134,336)(135,335)(136,334)(137,329)(138,332)(139,331)(140,330)(141,305)(142,308)(143,307)(144,306)(145,301)(146,304)(147,303)(148,302)(149,317)(150,320)(151,319)(152,318)(153,313)(154,316)(155,315)(156,314)(157,309)(158,312)(159,311)(160,310)(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); s2 := Sym(360)!( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61,122)( 62,121)( 63,123)( 64,124)( 65,126)( 66,125)( 67,127)( 68,128)( 69,130)( 70,129)( 71,131)( 72,132)( 73,134)( 74,133)( 75,135)( 76,136)( 77,138)( 78,137)( 79,139)( 80,140)( 81,142)( 82,141)( 83,143)( 84,144)( 85,146)( 86,145)( 87,147)( 88,148)( 89,150)( 90,149)( 91,151)( 92,152)( 93,154)( 94,153)( 95,155)( 96,156)( 97,158)( 98,157)( 99,159)(100,160)(101,162)(102,161)(103,163)(104,164)(105,166)(106,165)(107,167)(108,168)(109,170)(110,169)(111,171)(112,172)(113,174)(114,173)(115,175)(116,176)(117,178)(118,177)(119,179)(120,180)(181,182)(185,186)(189,190)(193,194)(197,198)(201,202)(205,206)(209,210)(213,214)(217,218)(221,222)(225,226)(229,230)(233,234)(237,238)(241,302)(242,301)(243,303)(244,304)(245,306)(246,305)(247,307)(248,308)(249,310)(250,309)(251,311)(252,312)(253,314)(254,313)(255,315)(256,316)(257,318)(258,317)(259,319)(260,320)(261,322)(262,321)(263,323)(264,324)(265,326)(266,325)(267,327)(268,328)(269,330)(270,329)(271,331)(272,332)(273,334)(274,333)(275,335)(276,336)(277,338)(278,337)(279,339)(280,340)(281,342)(282,341)(283,343)(284,344)(285,346)(286,345)(287,347)(288,348)(289,350)(290,349)(291,351)(292,352)(293,354)(294,353)(295,355)(296,356)(297,358)(298,357)(299,359)(300,360); 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*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 >;
References
None.
to this polytope.