Overview
- Group
- SmallGroup(1920,42362)
- Rank
- 3
- Schläfli Type
- {12,20}
- Vertices, edges, …
- 48, 480, 80
- 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
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
40 facets
- 40 of {12}*24
24 vertex figures
- 24 of {20}*40
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s2*s1)^2*s2> of order 2
40 facets
- 40 of {12}*24
24 vertex figures
- 24 of {20}*40
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s2*s1)^2*s2, s0*s1*s0*(s2*s1)^2*s0*(s2*s1)^3*s0> of order 4
20 facets
- 20 of {12}*24
15 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2> of order 4
20 facets
- 20 of {12}*24
12 vertex figures
- 12 of {20}*40
P/N, where N=<(s1*s0*s1*s2)^2, (s1*s0)^2*(s2*s1*s0)^3*s2*s1*s2> of order 4
20 facets
- 20 of {12}*24
12 vertex figures
- 12 of {20}*40
P/N, where N=<(s0*s1)^6, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
25 facets
12 vertex figures
- 12 of {20}*40
Representations
Permutation Representation (GAP)
s0 := ( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61,106)( 62,107)( 63,108)( 64,109)( 65,110)( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,111)( 72,112)( 73,113)( 74,114)( 75,115)( 76, 91)( 77, 92)( 78, 93)( 79, 94)( 80, 95)( 81,101)( 82,102)( 83,103)( 84,104)( 85,105)( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)(126,131)(127,132)(128,133)(129,134)(130,135)(141,146)(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)(159,164)(160,165)(171,176)(172,177)(173,178)(174,179)(175,180)(181,226)(182,227)(183,228)(184,229)(185,230)(186,236)(187,237)(188,238)(189,239)(190,240)(191,231)(192,232)(193,233)(194,234)(195,235)(196,211)(197,212)(198,213)(199,214)(200,215)(201,221)(202,222)(203,223)(204,224)(205,225)(206,216)(207,217)(208,218)(209,219)(210,220);; s1 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 12, 15)( 13, 14)( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 51)( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 72, 75)( 73, 74)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 87, 90)( 88, 89)( 91,111)( 92,115)( 93,114)( 94,113)( 95,112)( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)(103,119)(104,118)(105,117)(121,186)(122,190)(123,189)(124,188)(125,187)(126,181)(127,185)(128,184)(129,183)(130,182)(131,191)(132,195)(133,194)(134,193)(135,192)(136,201)(137,205)(138,204)(139,203)(140,202)(141,196)(142,200)(143,199)(144,198)(145,197)(146,206)(147,210)(148,209)(149,208)(150,207)(151,231)(152,235)(153,234)(154,233)(155,232)(156,226)(157,230)(158,229)(159,228)(160,227)(161,236)(162,240)(163,239)(164,238)(165,237)(166,216)(167,220)(168,219)(169,218)(170,217)(171,211)(172,215)(173,214)(174,213)(175,212)(176,221)(177,225)(178,224)(179,223)(180,222);; s2 := ( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)( 8,130)( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)( 64,184)( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)( 72,191)( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)( 88,210)( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,217)( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)(104,224)(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)(112,231)(113,235)(114,234)(115,233)(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*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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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,
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)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61,106)( 62,107)( 63,108)( 64,109)( 65,110)( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,111)( 72,112)( 73,113)( 74,114)( 75,115)( 76, 91)( 77, 92)( 78, 93)( 79, 94)( 80, 95)( 81,101)( 82,102)( 83,103)( 84,104)( 85,105)( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)(126,131)(127,132)(128,133)(129,134)(130,135)(141,146)(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)(159,164)(160,165)(171,176)(172,177)(173,178)(174,179)(175,180)(181,226)(182,227)(183,228)(184,229)(185,230)(186,236)(187,237)(188,238)(189,239)(190,240)(191,231)(192,232)(193,233)(194,234)(195,235)(196,211)(197,212)(198,213)(199,214)(200,215)(201,221)(202,222)(203,223)(204,224)(205,225)(206,216)(207,217)(208,218)(209,219)(210,220); s1 := Sym(240)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 12, 15)( 13, 14)( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 51)( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 72, 75)( 73, 74)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 87, 90)( 88, 89)( 91,111)( 92,115)( 93,114)( 94,113)( 95,112)( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)(103,119)(104,118)(105,117)(121,186)(122,190)(123,189)(124,188)(125,187)(126,181)(127,185)(128,184)(129,183)(130,182)(131,191)(132,195)(133,194)(134,193)(135,192)(136,201)(137,205)(138,204)(139,203)(140,202)(141,196)(142,200)(143,199)(144,198)(145,197)(146,206)(147,210)(148,209)(149,208)(150,207)(151,231)(152,235)(153,234)(154,233)(155,232)(156,226)(157,230)(158,229)(159,228)(160,227)(161,236)(162,240)(163,239)(164,238)(165,237)(166,216)(167,220)(168,219)(169,218)(170,217)(171,211)(172,215)(173,214)(174,213)(175,212)(176,221)(177,225)(178,224)(179,223)(180,222); s2 := Sym(240)!( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)( 8,130)( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)( 64,184)( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)( 72,191)( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)( 88,210)( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,217)( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)(104,224)(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)(112,231)(113,235)(114,234)(115,233)(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*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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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, 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.