Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical group
|
| gptkbp:actsOn |
gptkb:Sphere
Euclidean plane Hyperbolic plane |
| gptkbp:application |
gptkb:geometry
gptkb:Group_theory Tessellations |
| gptkbp:category |
gptkb:algebra
|
| gptkbp:definedIn |
Three generators and three relations
|
| gptkbp:field |
gptkb:Mathematics
|
| gptkbp:finiteIf |
1/l + 1/m + 1/n > 1
|
| gptkbp:hasSpecialCase |
gptkb:Dihedral_group
gptkb:Modular_group gptkb:Symmetric_group |
| https://www.w3.org/2000/01/rdf-schema#label |
Triangle Group
|
| gptkbp:infiniteIf |
1/l + 1/m + 1/n ≤ 1
|
| gptkbp:namedAfter |
Triangle
|
| gptkbp:notation |
(l, m, n)
|
| gptkbp:presentedBy |
⟨x, y, z | x^l = y^m = z^n = xyz = 1⟩
|
| gptkbp:relatedTo |
gptkb:Weyl_group
Reflection group |
| gptkbp:studiedBy |
gptkb:Felix_Klein
gptkb:Henri_Poincaré |
| gptkbp:subclassOf |
modular group
Discrete group |
| gptkbp:bfsParent |
gptkb:Tire
|
| gptkbp:bfsLayer |
4
|