Overview
- Group
- SmallGroup(480,1193)
- Rank
- 3
- Schläfli Type
- {20,6}
- Vertices, edges, …
- 40, 120, 12
- Order of s0s1s2
- 30
- 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
4-fold
5-fold
10-fold
12-fold
20-fold
24-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
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 4)( 5, 19)( 6, 20)( 7, 17)( 8, 18)( 9, 15)( 10, 16)( 11, 13)( 12, 14)( 21, 23)( 22, 24)( 25, 39)( 26, 40)( 27, 37)( 28, 38)( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 41, 43)( 42, 44)( 45, 59)( 46, 60)( 47, 57)( 48, 58)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 61, 63)( 62, 64)( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)( 72, 74)( 81, 83)( 82, 84)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89, 95)( 90, 96)( 91, 93)( 92, 94)(101,103)(102,104)(105,119)(106,120)(107,117)(108,118)(109,115)(110,116)(111,113)(112,114);; s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9, 17)( 10, 19)( 11, 18)( 12, 20)( 14, 15)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 41)( 26, 43)( 27, 42)( 28, 44)( 29, 57)( 30, 59)( 31, 58)( 32, 60)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 49)( 38, 51)( 39, 50)( 40, 52)( 61, 65)( 62, 67)( 63, 66)( 64, 68)( 69, 77)( 70, 79)( 71, 78)( 72, 80)( 74, 75)( 81,105)( 82,107)( 83,106)( 84,108)( 85,101)( 86,103)( 87,102)( 88,104)( 89,117)( 90,119)( 91,118)( 92,120)( 93,113)( 94,115)( 95,114)( 96,116)( 97,109)( 98,111)( 99,110)(100,112);; s2 := ( 1,101)( 2,104)( 3,103)( 4,102)( 5,105)( 6,108)( 7,107)( 8,106)( 9,109)( 10,112)( 11,111)( 12,110)( 13,113)( 14,116)( 15,115)( 16,114)( 17,117)( 18,120)( 19,119)( 20,118)( 21, 81)( 22, 84)( 23, 83)( 24, 82)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 89)( 30, 92)( 31, 91)( 32, 90)( 33, 93)( 34, 96)( 35, 95)( 36, 94)( 37, 97)( 38,100)( 39, 99)( 40, 98)( 41, 61)( 42, 64)( 43, 63)( 44, 62)( 45, 65)( 46, 68)( 47, 67)( 48, 66)( 49, 69)( 50, 72)( 51, 71)( 52, 70)( 53, 73)( 54, 76)( 55, 75)( 56, 74)( 57, 77)( 58, 80)( 59, 79)( 60, 78);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(120)!( 1, 3)( 2, 4)( 5, 19)( 6, 20)( 7, 17)( 8, 18)( 9, 15)( 10, 16)( 11, 13)( 12, 14)( 21, 23)( 22, 24)( 25, 39)( 26, 40)( 27, 37)( 28, 38)( 29, 35)( 30, 36)( 31, 33)( 32, 34)( 41, 43)( 42, 44)( 45, 59)( 46, 60)( 47, 57)( 48, 58)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 61, 63)( 62, 64)( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 75)( 70, 76)( 71, 73)( 72, 74)( 81, 83)( 82, 84)( 85, 99)( 86,100)( 87, 97)( 88, 98)( 89, 95)( 90, 96)( 91, 93)( 92, 94)(101,103)(102,104)(105,119)(106,120)(107,117)(108,118)(109,115)(110,116)(111,113)(112,114); s1 := Sym(120)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9, 17)( 10, 19)( 11, 18)( 12, 20)( 14, 15)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 41)( 26, 43)( 27, 42)( 28, 44)( 29, 57)( 30, 59)( 31, 58)( 32, 60)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 49)( 38, 51)( 39, 50)( 40, 52)( 61, 65)( 62, 67)( 63, 66)( 64, 68)( 69, 77)( 70, 79)( 71, 78)( 72, 80)( 74, 75)( 81,105)( 82,107)( 83,106)( 84,108)( 85,101)( 86,103)( 87,102)( 88,104)( 89,117)( 90,119)( 91,118)( 92,120)( 93,113)( 94,115)( 95,114)( 96,116)( 97,109)( 98,111)( 99,110)(100,112); s2 := Sym(120)!( 1,101)( 2,104)( 3,103)( 4,102)( 5,105)( 6,108)( 7,107)( 8,106)( 9,109)( 10,112)( 11,111)( 12,110)( 13,113)( 14,116)( 15,115)( 16,114)( 17,117)( 18,120)( 19,119)( 20,118)( 21, 81)( 22, 84)( 23, 83)( 24, 82)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 89)( 30, 92)( 31, 91)( 32, 90)( 33, 93)( 34, 96)( 35, 95)( 36, 94)( 37, 97)( 38,100)( 39, 99)( 40, 98)( 41, 61)( 42, 64)( 43, 63)( 44, 62)( 45, 65)( 46, 68)( 47, 67)( 48, 66)( 49, 69)( 50, 72)( 51, 71)( 52, 70)( 53, 73)( 54, 76)( 55, 75)( 56, 74)( 57, 77)( 58, 80)( 59, 79)( 60, 78); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0 >;
References
None.
to this polytope.