Overview
- Group
- SmallGroup(960,2312)
- Rank
- 3
- Schläfli Type
- {20,24}
- Vertices, edges, …
- 20, 240, 24
- Order of s0s1s2
- 120
- Order of s0s1s2s1
- 2
- Also known as
- {20,24|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
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)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)(121,181)(122,185)(123,184)(124,183)(125,182)(126,186)(127,190)(128,189)(129,188)(130,187)(131,191)(132,195)(133,194)(134,193)(135,192)(136,196)(137,200)(138,199)(139,198)(140,197)(141,201)(142,205)(143,204)(144,203)(145,202)(146,206)(147,210)(148,209)(149,208)(150,207)(151,211)(152,215)(153,214)(154,213)(155,212)(156,216)(157,220)(158,219)(159,218)(160,217)(161,221)(162,225)(163,224)(164,223)(165,222)(166,226)(167,230)(168,229)(169,228)(170,227)(171,231)(172,235)(173,234)(174,233)(175,232)(176,236)(177,240)(178,239)(179,238)(180,237);; s1 := ( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,132)( 7,131)( 8,135)( 9,134)( 10,133)( 11,127)( 12,126)( 13,130)( 14,129)( 15,128)( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,147)( 22,146)( 23,150)( 24,149)( 25,148)( 26,142)( 27,141)( 28,145)( 29,144)( 30,143)( 31,167)( 32,166)( 33,170)( 34,169)( 35,168)( 36,177)( 37,176)( 38,180)( 39,179)( 40,178)( 41,172)( 42,171)( 43,175)( 44,174)( 45,173)( 46,152)( 47,151)( 48,155)( 49,154)( 50,153)( 51,162)( 52,161)( 53,165)( 54,164)( 55,163)( 56,157)( 57,156)( 58,160)( 59,159)( 60,158)( 61,182)( 62,181)( 63,185)( 64,184)( 65,183)( 66,192)( 67,191)( 68,195)( 69,194)( 70,193)( 71,187)( 72,186)( 73,190)( 74,189)( 75,188)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,202)( 87,201)( 88,205)( 89,204)( 90,203)( 91,227)( 92,226)( 93,230)( 94,229)( 95,228)( 96,237)( 97,236)( 98,240)( 99,239)(100,238)(101,232)(102,231)(103,235)(104,234)(105,233)(106,212)(107,211)(108,215)(109,214)(110,213)(111,222)(112,221)(113,225)(114,224)(115,223)(116,217)(117,216)(118,220)(119,219)(120,218);; s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)( 19, 24)( 20, 25)( 31, 51)( 32, 52)( 33, 53)( 34, 54)( 35, 55)( 36, 46)( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)(103,118)(104,119)(105,120)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)(135,165)(136,171)(137,172)(138,173)(139,174)(140,175)(141,166)(142,167)(143,168)(144,169)(145,170)(146,176)(147,177)(148,178)(149,179)(150,180)(181,216)(182,217)(183,218)(184,219)(185,220)(186,211)(187,212)(188,213)(189,214)(190,215)(191,221)(192,222)(193,223)(194,224)(195,225)(196,231)(197,232)(198,233)(199,234)(200,235)(201,226)(202,227)(203,228)(204,229)(205,230)(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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(240)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)(121,181)(122,185)(123,184)(124,183)(125,182)(126,186)(127,190)(128,189)(129,188)(130,187)(131,191)(132,195)(133,194)(134,193)(135,192)(136,196)(137,200)(138,199)(139,198)(140,197)(141,201)(142,205)(143,204)(144,203)(145,202)(146,206)(147,210)(148,209)(149,208)(150,207)(151,211)(152,215)(153,214)(154,213)(155,212)(156,216)(157,220)(158,219)(159,218)(160,217)(161,221)(162,225)(163,224)(164,223)(165,222)(166,226)(167,230)(168,229)(169,228)(170,227)(171,231)(172,235)(173,234)(174,233)(175,232)(176,236)(177,240)(178,239)(179,238)(180,237); s1 := Sym(240)!( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,132)( 7,131)( 8,135)( 9,134)( 10,133)( 11,127)( 12,126)( 13,130)( 14,129)( 15,128)( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,147)( 22,146)( 23,150)( 24,149)( 25,148)( 26,142)( 27,141)( 28,145)( 29,144)( 30,143)( 31,167)( 32,166)( 33,170)( 34,169)( 35,168)( 36,177)( 37,176)( 38,180)( 39,179)( 40,178)( 41,172)( 42,171)( 43,175)( 44,174)( 45,173)( 46,152)( 47,151)( 48,155)( 49,154)( 50,153)( 51,162)( 52,161)( 53,165)( 54,164)( 55,163)( 56,157)( 57,156)( 58,160)( 59,159)( 60,158)( 61,182)( 62,181)( 63,185)( 64,184)( 65,183)( 66,192)( 67,191)( 68,195)( 69,194)( 70,193)( 71,187)( 72,186)( 73,190)( 74,189)( 75,188)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,202)( 87,201)( 88,205)( 89,204)( 90,203)( 91,227)( 92,226)( 93,230)( 94,229)( 95,228)( 96,237)( 97,236)( 98,240)( 99,239)(100,238)(101,232)(102,231)(103,235)(104,234)(105,233)(106,212)(107,211)(108,215)(109,214)(110,213)(111,222)(112,221)(113,225)(114,224)(115,223)(116,217)(117,216)(118,220)(119,219)(120,218); s2 := Sym(240)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)( 19, 24)( 20, 25)( 31, 51)( 32, 52)( 33, 53)( 34, 54)( 35, 55)( 36, 46)( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)(103,118)(104,119)(105,120)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)(135,165)(136,171)(137,172)(138,173)(139,174)(140,175)(141,166)(142,167)(143,168)(144,169)(145,170)(146,176)(147,177)(148,178)(149,179)(150,180)(181,216)(182,217)(183,218)(184,219)(185,220)(186,211)(187,212)(188,213)(189,214)(190,215)(191,221)(192,222)(193,223)(194,224)(195,225)(196,231)(197,232)(198,233)(199,234)(200,235)(201,226)(202,227)(203,228)(204,229)(205,230)(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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.