Overview
- Group
- SmallGroup(480,552)
- Rank
- 3
- Schläfli Type
- {20,12}
- Vertices, edges, …
- 20, 120, 12
- Order of s0s1s2
- 60
- Order of s0s1s2s1
- 2
- Also known as
- {20,12|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 := ( 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)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66, 96)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71,101)( 72,105)( 73,104)( 74,103)( 75,102)( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)( 81,111)( 82,115)( 83,114)( 84,113)( 85,112)( 86,116)( 87,120)( 88,119)( 89,118)( 90,117);; s1 := ( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 72)( 7, 71)( 8, 75)( 9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 87)( 22, 86)( 23, 90)( 24, 89)( 25, 88)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31, 92)( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36,102)( 37,101)( 38,105)( 39,104)( 40,103)( 41, 97)( 42, 96)( 43,100)( 44, 99)( 45, 98)( 46,107)( 47,106)( 48,110)( 49,109)( 50,108)( 51,117)( 52,116)( 53,120)( 54,119)( 55,118)( 56,112)( 57,111)( 58,115)( 59,114)( 60,113);; 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);; 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*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(120)!( 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)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66, 96)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71,101)( 72,105)( 73,104)( 74,103)( 75,102)( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)( 81,111)( 82,115)( 83,114)( 84,113)( 85,112)( 86,116)( 87,120)( 88,119)( 89,118)( 90,117); s1 := Sym(120)!( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 72)( 7, 71)( 8, 75)( 9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 87)( 22, 86)( 23, 90)( 24, 89)( 25, 88)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31, 92)( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36,102)( 37,101)( 38,105)( 39,104)( 40,103)( 41, 97)( 42, 96)( 43,100)( 44, 99)( 45, 98)( 46,107)( 47,106)( 48,110)( 49,109)( 50,108)( 51,117)( 52,116)( 53,120)( 54,119)( 55,118)( 56,112)( 57,111)( 58,115)( 59,114)( 60,113); s2 := Sym(120)!( 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); 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*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.