Overview
- Group
- SmallGroup(960,1332)
- Rank
- 3
- Schläfli Type
- {20,12}
- Vertices, edges, …
- 40, 240, 24
- 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
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
Click an entry to reveal its facets and vertex figures.
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)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 51)( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)(101,116)(102,120)(103,119)(104,118)(105,117)(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)(151,226)(152,230)(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)(162,240)(163,239)(164,238)(165,237)(166,211)(167,215)(168,214)(169,213)(170,212)(171,216)(172,220)(173,219)(174,218)(175,217)(176,221)(177,225)(178,224)(179,223)(180,222);; 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)( 31,152)( 32,151)( 33,155)( 34,154)( 35,153)( 36,162)( 37,161)( 38,165)( 39,164)( 40,163)( 41,157)( 42,156)( 43,160)( 44,159)( 45,158)( 46,167)( 47,166)( 48,170)( 49,169)( 50,168)( 51,177)( 52,176)( 53,180)( 54,179)( 55,178)( 56,172)( 57,171)( 58,175)( 59,174)( 60,173)( 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)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,222)( 97,221)( 98,225)( 99,224)(100,223)(101,217)(102,216)(103,220)(104,219)(105,218)(106,227)(107,226)(108,230)(109,229)(110,228)(111,237)(112,236)(113,240)(114,239)(115,238)(116,232)(117,231)(118,235)(119,234)(120,233);; s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 81)( 62, 82)( 63, 83)( 64, 84)( 65, 85)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 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)(181,231)(182,232)(183,233)(184,234)(185,235)(186,226)(187,227)(188,228)(189,229)(190,230)(191,236)(192,237)(193,238)(194,239)(195,240)(196,216)(197,217)(198,218)(199,219)(200,220)(201,211)(202,212)(203,213)(204,214)(205,215)(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, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*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,
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)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 51)( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)(101,116)(102,120)(103,119)(104,118)(105,117)(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)(151,226)(152,230)(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)(162,240)(163,239)(164,238)(165,237)(166,211)(167,215)(168,214)(169,213)(170,212)(171,216)(172,220)(173,219)(174,218)(175,217)(176,221)(177,225)(178,224)(179,223)(180,222); 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)( 31,152)( 32,151)( 33,155)( 34,154)( 35,153)( 36,162)( 37,161)( 38,165)( 39,164)( 40,163)( 41,157)( 42,156)( 43,160)( 44,159)( 45,158)( 46,167)( 47,166)( 48,170)( 49,169)( 50,168)( 51,177)( 52,176)( 53,180)( 54,179)( 55,178)( 56,172)( 57,171)( 58,175)( 59,174)( 60,173)( 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)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,222)( 97,221)( 98,225)( 99,224)(100,223)(101,217)(102,216)(103,220)(104,219)(105,218)(106,227)(107,226)(108,230)(109,229)(110,228)(111,237)(112,236)(113,240)(114,239)(115,238)(116,232)(117,231)(118,235)(119,234)(120,233); s2 := Sym(240)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 81)( 62, 82)( 63, 83)( 64, 84)( 65, 85)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 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)(181,231)(182,232)(183,233)(184,234)(185,235)(186,226)(187,227)(188,228)(189,229)(190,230)(191,236)(192,237)(193,238)(194,239)(195,240)(196,216)(197,217)(198,218)(199,219)(200,220)(201,211)(202,212)(203,213)(204,214)(205,215)(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, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*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, 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.