Overview
- Group
- SmallGroup(480,324)
- Rank
- 3
- Schläfli Type
- {24,10}
- Vertices, edges, …
- 24, 120, 10
- Order of s0s1s2
- 120
- Order of s0s1s2s1
- 2
- Also known as
- {24,10|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
10-fold
12-fold
15-fold
20-fold
24-fold
30-fold
40-fold
60-fold
Covers minimal covers in bold
2-fold
3-fold
4-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);; s1 := ( 1, 66)( 2, 70)( 3, 69)( 4, 68)( 5, 67)( 6, 61)( 7, 65)( 8, 64)( 9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 81)( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)( 24, 78)( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31,111)( 32,115)( 33,114)( 34,113)( 35,112)( 36,106)( 37,110)( 38,109)( 39,108)( 40,107)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46, 96)( 47,100)( 48, 99)( 49, 98)( 50, 97)( 51, 91)( 52, 95)( 53, 94)( 54, 93)( 55, 92)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102);; 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);; 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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(120)!( 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); s1 := Sym(120)!( 1, 66)( 2, 70)( 3, 69)( 4, 68)( 5, 67)( 6, 61)( 7, 65)( 8, 64)( 9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 81)( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)( 24, 78)( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31,111)( 32,115)( 33,114)( 34,113)( 35,112)( 36,106)( 37,110)( 38,109)( 39,108)( 40,107)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46, 96)( 47,100)( 48, 99)( 49, 98)( 50, 97)( 51, 91)( 52, 95)( 53, 94)( 54, 93)( 55, 92)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102); s2 := Sym(120)!( 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); poly := sub<Sym(120)|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 >;
References
None.
to this polytope.