Overview
- Group
- SmallGroup(1920,42337)
- Rank
- 3
- Schläfli Type
- {4,60}
- Vertices, edges, …
- 16, 480, 240
- 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=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 2
120 facets
- 120 of {4}*8
8 vertex figures
- 8 of {60}*120
P/N, where N=<s0*(s1*s0*s2)^2*s1*s0*(s2*s1)^13> of order 2
120 facets
- 120 of {4}*8
8 vertex figures
- 8 of {60}*120
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2> of order 4
60 facets
- 60 of {4}*8
4 vertex figures
- 4 of {60}*120
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 4
75 facets
4 vertex figures
- 4 of {60}*120
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*s2*s1*s0*(s2*s1)^14> of order 4
60 facets
- 60 of {4}*8
4 vertex figures
- 4 of {60}*120
Representations
Permutation Representation (GAP)
s0 := ( 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);; s1 := ( 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)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 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)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)(104,113)(105,112)(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)(151,226)(152,230)(153,229)(154,228)(155,227)(156,236)(157,240)(158,239)(159,238)(160,237)(161,231)(162,235)(163,234)(164,233)(165,232)(166,211)(167,215)(168,214)(169,213)(170,212)(171,221)(172,225)(173,224)(174,223)(175,222)(176,216)(177,220)(178,219)(179,218)(180,217);; s2 := ( 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)( 31,157)( 32,156)( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)( 40,153)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)( 48,175)( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 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)( 91,217)( 92,216)( 93,220)( 94,219)( 95,218)( 96,212)( 97,211)( 98,215)( 99,214)(100,213)(101,222)(102,221)(103,225)(104,224)(105,223)(106,232)(107,231)(108,235)(109,234)(110,233)(111,227)(112,226)(113,230)(114,229)(115,228)(116,237)(117,236)(118,240)(119,239)(120,238);; 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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*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(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); s1 := 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)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 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)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)(104,113)(105,112)(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)(151,226)(152,230)(153,229)(154,228)(155,227)(156,236)(157,240)(158,239)(159,238)(160,237)(161,231)(162,235)(163,234)(164,233)(165,232)(166,211)(167,215)(168,214)(169,213)(170,212)(171,221)(172,225)(173,224)(174,223)(175,222)(176,216)(177,220)(178,219)(179,218)(180,217); s2 := 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)( 31,157)( 32,156)( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)( 40,153)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)( 48,175)( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 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)( 91,217)( 92,216)( 93,220)( 94,219)( 95,218)( 96,212)( 97,211)( 98,215)( 99,214)(100,213)(101,222)(102,221)(103,225)(104,224)(105,223)(106,232)(107,231)(108,235)(109,234)(110,233)(111,227)(112,226)(113,230)(114,229)(115,228)(116,237)(117,236)(118,240)(119,239)(120,238); 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*s0*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*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*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.