Overview
- Group
- SmallGroup(960,5069)
- Rank
- 3
- Schläfli Type
- {60,8}
- Vertices, edges, …
- 60, 240, 8
- Order of s0s1s2
- 120
- Order of s0s1s2s1
- 2
- Also known as
- {60,8|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
5-fold
6-fold
8-fold
10-fold
12-fold
15-fold
16-fold
20-fold
24-fold
30-fold
40-fold
48-fold
60-fold
80-fold
120-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117)(121,181)(122,185)(123,184)(124,183)(125,182)(126,191)(127,195)(128,194)(129,193)(130,192)(131,186)(132,190)(133,189)(134,188)(135,187)(136,196)(137,200)(138,199)(139,198)(140,197)(141,206)(142,210)(143,209)(144,208)(145,207)(146,201)(147,205)(148,204)(149,203)(150,202)(151,211)(152,215)(153,214)(154,213)(155,212)(156,221)(157,225)(158,224)(159,223)(160,222)(161,216)(162,220)(163,219)(164,218)(165,217)(166,226)(167,230)(168,229)(169,228)(170,227)(171,236)(172,240)(173,239)(174,238)(175,237)(176,231)(177,235)(178,234)(179,233)(180,232);; s1 := ( 1,127)( 2,126)( 3,130)( 4,129)( 5,128)( 6,122)( 7,121)( 8,125)( 9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,172)( 32,171)( 33,175)( 34,174)( 35,173)( 36,167)( 37,166)( 38,170)( 39,169)( 40,168)( 41,177)( 42,176)( 43,180)( 44,179)( 45,178)( 46,157)( 47,156)( 48,160)( 49,159)( 50,158)( 51,152)( 52,151)( 53,155)( 54,154)( 55,153)( 56,162)( 57,161)( 58,165)( 59,164)( 60,163)( 61,187)( 62,186)( 63,190)( 64,189)( 65,188)( 66,182)( 67,181)( 68,185)( 69,184)( 70,183)( 71,192)( 72,191)( 73,195)( 74,194)( 75,193)( 76,202)( 77,201)( 78,205)( 79,204)( 80,203)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,207)( 87,206)( 88,210)( 89,209)( 90,208)( 91,232)( 92,231)( 93,235)( 94,234)( 95,233)( 96,227)( 97,226)( 98,230)( 99,229)(100,228)(101,237)(102,236)(103,240)(104,239)(105,238)(106,217)(107,216)(108,220)(109,219)(110,218)(111,212)(112,211)(113,215)(114,214)(115,213)(116,222)(117,221)(118,225)(119,224)(120,223);; s2 := ( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(181,211)(182,212)(183,213)(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)(190,220)(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)(207,237)(208,238)(209,239)(210,240);; 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*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(240)!( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117)(121,181)(122,185)(123,184)(124,183)(125,182)(126,191)(127,195)(128,194)(129,193)(130,192)(131,186)(132,190)(133,189)(134,188)(135,187)(136,196)(137,200)(138,199)(139,198)(140,197)(141,206)(142,210)(143,209)(144,208)(145,207)(146,201)(147,205)(148,204)(149,203)(150,202)(151,211)(152,215)(153,214)(154,213)(155,212)(156,221)(157,225)(158,224)(159,223)(160,222)(161,216)(162,220)(163,219)(164,218)(165,217)(166,226)(167,230)(168,229)(169,228)(170,227)(171,236)(172,240)(173,239)(174,238)(175,237)(176,231)(177,235)(178,234)(179,233)(180,232); s1 := Sym(240)!( 1,127)( 2,126)( 3,130)( 4,129)( 5,128)( 6,122)( 7,121)( 8,125)( 9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,172)( 32,171)( 33,175)( 34,174)( 35,173)( 36,167)( 37,166)( 38,170)( 39,169)( 40,168)( 41,177)( 42,176)( 43,180)( 44,179)( 45,178)( 46,157)( 47,156)( 48,160)( 49,159)( 50,158)( 51,152)( 52,151)( 53,155)( 54,154)( 55,153)( 56,162)( 57,161)( 58,165)( 59,164)( 60,163)( 61,187)( 62,186)( 63,190)( 64,189)( 65,188)( 66,182)( 67,181)( 68,185)( 69,184)( 70,183)( 71,192)( 72,191)( 73,195)( 74,194)( 75,193)( 76,202)( 77,201)( 78,205)( 79,204)( 80,203)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,207)( 87,206)( 88,210)( 89,209)( 90,208)( 91,232)( 92,231)( 93,235)( 94,234)( 95,233)( 96,227)( 97,226)( 98,230)( 99,229)(100,228)(101,237)(102,236)(103,240)(104,239)(105,238)(106,217)(107,216)(108,220)(109,219)(110,218)(111,212)(112,211)(113,215)(114,214)(115,213)(116,222)(117,221)(118,225)(119,224)(120,223); s2 := Sym(240)!( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(181,211)(182,212)(183,213)(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)(190,220)(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)(207,237)(208,238)(209,239)(210,240); poly := sub<Sym(240)|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*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.