Overview
- Group
- SmallGroup(960,1009)
- Rank
- 3
- Schläfli Type
- {48,10}
- Vertices, edges, …
- 48, 240, 10
- Order of s0s1s2
- 240
- Order of s0s1s2s1
- 2
- Also known as
- {48,10|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 := ( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 56)( 37, 57)( 38, 58)( 39, 59)( 40, 60)( 41, 51)( 42, 52)( 43, 53)( 44, 54)( 45, 55)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66,101)( 67,102)( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)( 73, 98)( 74, 99)( 75,100)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)( 89,114)( 90,115)(121,181)(122,182)(123,183)(124,184)(125,185)(126,191)(127,192)(128,193)(129,194)(130,195)(131,186)(132,187)(133,188)(134,189)(135,190)(136,196)(137,197)(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)(144,209)(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,226)(152,227)(153,228)(154,229)(155,230)(156,236)(157,237)(158,238)(159,239)(160,240)(161,231)(162,232)(163,233)(164,234)(165,235)(166,211)(167,212)(168,213)(169,214)(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)(176,216)(177,217)(178,218)(179,219)(180,220);; s1 := ( 1,126)( 2,130)( 3,129)( 4,128)( 5,127)( 6,121)( 7,125)( 8,124)( 9,123)( 10,122)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)( 16,141)( 17,145)( 18,144)( 19,143)( 20,142)( 21,136)( 22,140)( 23,139)( 24,138)( 25,137)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,171)( 32,175)( 33,174)( 34,173)( 35,172)( 36,166)( 37,170)( 38,169)( 39,168)( 40,167)( 41,176)( 42,180)( 43,179)( 44,178)( 45,177)( 46,156)( 47,160)( 48,159)( 49,158)( 50,157)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,161)( 57,165)( 58,164)( 59,163)( 60,162)( 61,216)( 62,220)( 63,219)( 64,218)( 65,217)( 66,211)( 67,215)( 68,214)( 69,213)( 70,212)( 71,221)( 72,225)( 73,224)( 74,223)( 75,222)( 76,231)( 77,235)( 78,234)( 79,233)( 80,232)( 81,226)( 82,230)( 83,229)( 84,228)( 85,227)( 86,236)( 87,240)( 88,239)( 89,238)( 90,237)( 91,186)( 92,190)( 93,189)( 94,188)( 95,187)( 96,181)( 97,185)( 98,184)( 99,183)(100,182)(101,191)(102,195)(103,194)(104,193)(105,192)(106,201)(107,205)(108,204)(109,203)(110,202)(111,196)(112,200)(113,199)(114,198)(115,197)(116,206)(117,210)(118,209)(119,208)(120,207);; s2 := ( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120)(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)(181,182)(183,185)(186,187)(188,190)(191,192)(193,195)(196,197)(198,200)(201,202)(203,205)(206,207)(208,210)(211,212)(213,215)(216,217)(218,220)(221,222)(223,225)(226,227)(228,230)(231,232)(233,235)(236,237)(238,240);; 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,
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*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)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 56)( 37, 57)( 38, 58)( 39, 59)( 40, 60)( 41, 51)( 42, 52)( 43, 53)( 44, 54)( 45, 55)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66,101)( 67,102)( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)( 73, 98)( 74, 99)( 75,100)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)( 89,114)( 90,115)(121,181)(122,182)(123,183)(124,184)(125,185)(126,191)(127,192)(128,193)(129,194)(130,195)(131,186)(132,187)(133,188)(134,189)(135,190)(136,196)(137,197)(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)(144,209)(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,226)(152,227)(153,228)(154,229)(155,230)(156,236)(157,237)(158,238)(159,239)(160,240)(161,231)(162,232)(163,233)(164,234)(165,235)(166,211)(167,212)(168,213)(169,214)(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)(176,216)(177,217)(178,218)(179,219)(180,220); s1 := Sym(240)!( 1,126)( 2,130)( 3,129)( 4,128)( 5,127)( 6,121)( 7,125)( 8,124)( 9,123)( 10,122)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)( 16,141)( 17,145)( 18,144)( 19,143)( 20,142)( 21,136)( 22,140)( 23,139)( 24,138)( 25,137)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,171)( 32,175)( 33,174)( 34,173)( 35,172)( 36,166)( 37,170)( 38,169)( 39,168)( 40,167)( 41,176)( 42,180)( 43,179)( 44,178)( 45,177)( 46,156)( 47,160)( 48,159)( 49,158)( 50,157)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,161)( 57,165)( 58,164)( 59,163)( 60,162)( 61,216)( 62,220)( 63,219)( 64,218)( 65,217)( 66,211)( 67,215)( 68,214)( 69,213)( 70,212)( 71,221)( 72,225)( 73,224)( 74,223)( 75,222)( 76,231)( 77,235)( 78,234)( 79,233)( 80,232)( 81,226)( 82,230)( 83,229)( 84,228)( 85,227)( 86,236)( 87,240)( 88,239)( 89,238)( 90,237)( 91,186)( 92,190)( 93,189)( 94,188)( 95,187)( 96,181)( 97,185)( 98,184)( 99,183)(100,182)(101,191)(102,195)(103,194)(104,193)(105,192)(106,201)(107,205)(108,204)(109,203)(110,202)(111,196)(112,200)(113,199)(114,198)(115,197)(116,206)(117,210)(118,209)(119,208)(120,207); s2 := Sym(240)!( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120)(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)(181,182)(183,185)(186,187)(188,190)(191,192)(193,195)(196,197)(198,200)(201,202)(203,205)(206,207)(208,210)(211,212)(213,215)(216,217)(218,220)(221,222)(223,225)(226,227)(228,230)(231,232)(233,235)(236,237)(238,240); 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, 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*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.