Overview
- Group
- SmallGroup(1920,42337)
- Rank
- 3
- Schläfli Type
- {60,4}
- Vertices, edges, …
- 240, 480, 16
- Order of s0s1s2
- 120
- 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
8-fold
10-fold
12-fold
15-fold
16-fold
20-fold
24-fold
30-fold
32-fold
40-fold
48-fold
60-fold
80-fold
96-fold
120-fold
160-fold
240-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=<(s0*s1)^2*(s2*s1*s0)^2*s1*s2*s1> of order 2
8 facets
- 8 of {60}*120
120 vertex figures
- 120 of {4}*8
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 2
8 facets
- 8 of {60}*120
120 vertex figures
- 120 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2> of order 4
4 facets
- 4 of {60}*120
60 vertex figures
- 60 of {4}*8
P/N, where N=<(s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*s2> of order 4
4 facets
- 4 of {60}*120
75 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s2*s1*s2> of order 4
4 facets
- 4 of {60}*120
60 vertex figures
- 60 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 1,121)( 2,125)( 3,124)( 4,123)( 5,122)( 6,131)( 7,135)( 8,134)( 9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,146)( 22,150)( 23,149)( 24,148)( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)( 32,155)( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)( 40,162)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)( 48,169)( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,181)( 62,185)( 63,184)( 64,183)( 65,182)( 66,191)( 67,195)( 68,194)( 69,193)( 70,192)( 71,186)( 72,190)( 73,189)( 74,188)( 75,187)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)( 81,206)( 82,210)( 83,209)( 84,208)( 85,207)( 86,201)( 87,205)( 88,204)( 89,203)( 90,202)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,221)( 97,225)( 98,224)( 99,223)(100,222)(101,216)(102,220)(103,219)(104,218)(105,217)(106,226)(107,230)(108,229)(109,228)(110,227)(111,236)(112,240)(113,239)(114,238)(115,237)(116,231)(117,235)(118,234)(119,233)(120,232);; s1 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)( 32, 51)( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)( 86, 87)( 88, 90)( 91,112)( 92,111)( 93,115)( 94,114)( 95,113)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)(103,120)(104,119)(105,118)(121,187)(122,186)(123,190)(124,189)(125,188)(126,182)(127,181)(128,185)(129,184)(130,183)(131,192)(132,191)(133,195)(134,194)(135,193)(136,202)(137,201)(138,205)(139,204)(140,203)(141,197)(142,196)(143,200)(144,199)(145,198)(146,207)(147,206)(148,210)(149,209)(150,208)(151,232)(152,231)(153,235)(154,234)(155,233)(156,227)(157,226)(158,230)(159,229)(160,228)(161,237)(162,236)(163,240)(164,239)(165,238)(166,217)(167,216)(168,220)(169,219)(170,218)(171,212)(172,211)(173,215)(174,214)(175,213)(176,222)(177,221)(178,225)(179,224)(180,223);; s2 := ( 61,106)( 62,107)( 63,108)( 64,109)( 65,110)( 66,111)( 67,112)( 68,113)( 69,114)( 70,115)( 71,116)( 72,117)( 73,118)( 74,119)( 75,120)( 76, 91)( 77, 92)( 78, 93)( 79, 94)( 80, 95)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86,101)( 87,102)( 88,103)( 89,104)( 90,105)(181,226)(182,227)(183,228)(184,229)(185,230)(186,231)(187,232)(188,233)(189,234)(190,235)(191,236)(192,237)(193,238)(194,239)(195,240)(196,211)(197,212)(198,213)(199,214)(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)(208,223)(209,224)(210,225);; 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,
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,
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)!( 1,121)( 2,125)( 3,124)( 4,123)( 5,122)( 6,131)( 7,135)( 8,134)( 9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,146)( 22,150)( 23,149)( 24,148)( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)( 32,155)( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)( 40,162)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)( 48,169)( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,181)( 62,185)( 63,184)( 64,183)( 65,182)( 66,191)( 67,195)( 68,194)( 69,193)( 70,192)( 71,186)( 72,190)( 73,189)( 74,188)( 75,187)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)( 81,206)( 82,210)( 83,209)( 84,208)( 85,207)( 86,201)( 87,205)( 88,204)( 89,203)( 90,202)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,221)( 97,225)( 98,224)( 99,223)(100,222)(101,216)(102,220)(103,219)(104,218)(105,217)(106,226)(107,230)(108,229)(109,228)(110,227)(111,236)(112,240)(113,239)(114,238)(115,237)(116,231)(117,235)(118,234)(119,233)(120,232); s1 := Sym(240)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)( 32, 51)( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 67)( 62, 66)( 63, 70)( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)( 86, 87)( 88, 90)( 91,112)( 92,111)( 93,115)( 94,114)( 95,113)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)(103,120)(104,119)(105,118)(121,187)(122,186)(123,190)(124,189)(125,188)(126,182)(127,181)(128,185)(129,184)(130,183)(131,192)(132,191)(133,195)(134,194)(135,193)(136,202)(137,201)(138,205)(139,204)(140,203)(141,197)(142,196)(143,200)(144,199)(145,198)(146,207)(147,206)(148,210)(149,209)(150,208)(151,232)(152,231)(153,235)(154,234)(155,233)(156,227)(157,226)(158,230)(159,229)(160,228)(161,237)(162,236)(163,240)(164,239)(165,238)(166,217)(167,216)(168,220)(169,219)(170,218)(171,212)(172,211)(173,215)(174,214)(175,213)(176,222)(177,221)(178,225)(179,224)(180,223); s2 := Sym(240)!( 61,106)( 62,107)( 63,108)( 64,109)( 65,110)( 66,111)( 67,112)( 68,113)( 69,114)( 70,115)( 71,116)( 72,117)( 73,118)( 74,119)( 75,120)( 76, 91)( 77, 92)( 78, 93)( 79, 94)( 80, 95)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86,101)( 87,102)( 88,103)( 89,104)( 90,105)(181,226)(182,227)(183,228)(184,229)(185,230)(186,231)(187,232)(188,233)(189,234)(190,235)(191,236)(192,237)(193,238)(194,239)(195,240)(196,211)(197,212)(198,213)(199,214)(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)(208,223)(209,224)(210,225); 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, s1*s2*s1*s2*s1*s2*s1*s2, 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, 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.