Overview
- Group
- SmallGroup(1920,42340)
- Rank
- 3
- Schläfli Type
- {60,8}
- Vertices, edges, …
- 120, 480, 16
- Order of s0s1s2
- 60
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
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.
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)( 61,106)( 62,110)( 63,109)( 64,108)( 65,107)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 76, 91)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)(153,154)(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)(171,176)(172,180)(173,179)(174,178)(175,177)(181,226)(182,230)(183,229)(184,228)(185,227)(186,236)(187,240)(188,239)(189,238)(190,237)(191,231)(192,235)(193,234)(194,233)(195,232)(196,211)(197,215)(198,214)(199,213)(200,212)(201,221)(202,225)(203,224)(204,223)(205,222)(206,216)(207,220)(208,219)(209,218)(210,217);; 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 := ( 1,121)( 2,122)( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)( 9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,226)( 62,227)( 63,228)( 64,229)( 65,230)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,236)( 72,237)( 73,238)( 74,239)( 75,240)( 76,211)( 77,212)( 78,213)( 79,214)( 80,215)( 81,216)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)( 88,223)( 89,224)( 90,225)( 91,196)( 92,197)( 93,198)( 94,199)( 95,200)( 96,201)( 97,202)( 98,203)( 99,204)(100,205)(101,206)(102,207)(103,208)(104,209)(105,210)(106,181)(107,182)(108,183)(109,184)(110,185)(111,186)(112,187)(113,188)(114,189)(115,190)(116,191)(117,192)(118,193)(119,194)(120,195);; 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*s2*s0*s1*s2*s0*s1*s2*s1*s0*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)!( 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)( 61,106)( 62,110)( 63,109)( 64,108)( 65,107)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 76, 91)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)(153,154)(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)(171,176)(172,180)(173,179)(174,178)(175,177)(181,226)(182,230)(183,229)(184,228)(185,227)(186,236)(187,240)(188,239)(189,238)(190,237)(191,231)(192,235)(193,234)(194,233)(195,232)(196,211)(197,215)(198,214)(199,213)(200,212)(201,221)(202,225)(203,224)(204,223)(205,222)(206,216)(207,220)(208,219)(209,218)(210,217); 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)!( 1,121)( 2,122)( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)( 9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,226)( 62,227)( 63,228)( 64,229)( 65,230)( 66,231)( 67,232)( 68,233)( 69,234)( 70,235)( 71,236)( 72,237)( 73,238)( 74,239)( 75,240)( 76,211)( 77,212)( 78,213)( 79,214)( 80,215)( 81,216)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)( 88,223)( 89,224)( 90,225)( 91,196)( 92,197)( 93,198)( 94,199)( 95,200)( 96,201)( 97,202)( 98,203)( 99,204)(100,205)(101,206)(102,207)(103,208)(104,209)(105,210)(106,181)(107,182)(108,183)(109,184)(110,185)(111,186)(112,187)(113,188)(114,189)(115,190)(116,191)(117,192)(118,193)(119,194)(120,195); 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*s2*s0*s1*s2*s0*s1*s2*s1*s0*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.