Overview
- Group
- SmallGroup(1920,240806)
- Rank
- 3
- Schläfli Type
- {12,12}
- Vertices, edges, …
- 80, 480, 80
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 20
- 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
8-fold
16-fold
120-fold
240-fold
Covers minimal covers in bold
None in this atlas.
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, 53)( 2, 54)( 3, 55)( 4, 56)( 5, 63)( 6, 64)( 7,103)( 8,104)( 9, 74)( 10, 73)( 11, 58)( 12, 57)( 13, 67)( 14, 68)( 15, 66)( 16, 65)( 17, 99)( 18,100)( 19, 89)( 20, 90)( 21, 61)( 22, 62)( 23, 97)( 24, 98)( 25,101)( 26,102)( 27, 81)( 28, 82)( 29, 80)( 30, 79)( 31, 86)( 32, 85)( 33, 83)( 34, 84)( 35, 93)( 36, 94)( 37, 72)( 38, 71)( 39, 95)( 40, 96)( 41, 88)( 42, 87)( 43, 92)( 44, 91)( 45, 76)( 46, 75)( 47, 70)( 48, 69)( 49, 78)( 50, 77)( 51, 60)( 52, 59);; s1 := ( 1, 55)( 2, 56)( 3, 53)( 4, 54)( 5, 69)( 6, 70)( 7, 64)( 8, 63)( 9, 84)( 10, 83)( 11, 59)( 12, 60)( 13,101)( 14,102)( 15, 97)( 16, 98)( 17, 58)( 18, 57)( 19, 73)( 20, 74)( 21, 72)( 22, 71)( 23, 89)( 24, 90)( 25, 86)( 26, 85)( 27, 92)( 28, 91)( 29, 88)( 30, 87)( 31, 61)( 32, 62)( 33, 77)( 34, 78)( 35, 81)( 36, 82)( 37, 76)( 38, 75)( 39, 79)( 40, 80)( 41, 99)( 42,100)( 43,103)( 44,104)( 45, 68)( 46, 67)( 47, 94)( 48, 93)( 49, 66)( 50, 65)( 51, 96)( 52, 95);; s2 := ( 3, 4)( 5, 13)( 6, 14)( 7, 8)( 9, 28)( 10, 27)( 11, 16)( 12, 15)( 17, 18)( 21, 30)( 22, 29)( 23, 45)( 24, 46)( 25, 49)( 26, 50)( 33, 34)( 35, 41)( 36, 42)( 37, 38)( 39, 43)( 40, 44)( 55, 56)( 57, 66)( 58, 65)( 61, 79)( 62, 80)( 63, 67)( 64, 68)( 71, 72)( 73, 81)( 74, 82)( 75, 98)( 76, 97)( 77,102)( 78,101)( 83, 84)( 87, 94)( 88, 93)( 91, 96)( 92, 95)( 99,100)(103,104);; 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*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(104)!( 1, 53)( 2, 54)( 3, 55)( 4, 56)( 5, 63)( 6, 64)( 7,103)( 8,104)( 9, 74)( 10, 73)( 11, 58)( 12, 57)( 13, 67)( 14, 68)( 15, 66)( 16, 65)( 17, 99)( 18,100)( 19, 89)( 20, 90)( 21, 61)( 22, 62)( 23, 97)( 24, 98)( 25,101)( 26,102)( 27, 81)( 28, 82)( 29, 80)( 30, 79)( 31, 86)( 32, 85)( 33, 83)( 34, 84)( 35, 93)( 36, 94)( 37, 72)( 38, 71)( 39, 95)( 40, 96)( 41, 88)( 42, 87)( 43, 92)( 44, 91)( 45, 76)( 46, 75)( 47, 70)( 48, 69)( 49, 78)( 50, 77)( 51, 60)( 52, 59); s1 := Sym(104)!( 1, 55)( 2, 56)( 3, 53)( 4, 54)( 5, 69)( 6, 70)( 7, 64)( 8, 63)( 9, 84)( 10, 83)( 11, 59)( 12, 60)( 13,101)( 14,102)( 15, 97)( 16, 98)( 17, 58)( 18, 57)( 19, 73)( 20, 74)( 21, 72)( 22, 71)( 23, 89)( 24, 90)( 25, 86)( 26, 85)( 27, 92)( 28, 91)( 29, 88)( 30, 87)( 31, 61)( 32, 62)( 33, 77)( 34, 78)( 35, 81)( 36, 82)( 37, 76)( 38, 75)( 39, 79)( 40, 80)( 41, 99)( 42,100)( 43,103)( 44,104)( 45, 68)( 46, 67)( 47, 94)( 48, 93)( 49, 66)( 50, 65)( 51, 96)( 52, 95); s2 := Sym(104)!( 3, 4)( 5, 13)( 6, 14)( 7, 8)( 9, 28)( 10, 27)( 11, 16)( 12, 15)( 17, 18)( 21, 30)( 22, 29)( 23, 45)( 24, 46)( 25, 49)( 26, 50)( 33, 34)( 35, 41)( 36, 42)( 37, 38)( 39, 43)( 40, 44)( 55, 56)( 57, 66)( 58, 65)( 61, 79)( 62, 80)( 63, 67)( 64, 68)( 71, 72)( 73, 81)( 74, 82)( 75, 98)( 76, 97)( 77,102)( 78,101)( 83, 84)( 87, 94)( 88, 93)( 91, 96)( 92, 95)( 99,100)(103,104); poly := sub<Sym(104)|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*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 >;
References
None.
to this polytope.